Daily Papers

Large Language Models generate text autoregressively, but open-ended generation is prone to verbatim looping, in which models repeat spans already present in context. Standard defenses such as repetition, presence, and frequency penalties and n-gram blocking act on token recurrence rather than the sequential structure of a loop, and often suppress looping only at strengths that also degrade formatting or fluency. We propose Don't Repeat Yourself (DRY), a sampling-time logit adjustment that penalizes a candidate token only when generating it would extend the current suffix into an exact continuation of a span seen earlier in the context. Sequence breakers protect chat templates and formatting tokens. Across models from 1.5B to 120B parameters, nine prompt families, and a 600-pair human study, DRY reduces suffix-extension rate by 47% while improving lexical diversity. An intervention-matched placebo produces no comparable reduction, identifying suffix matching as the operative mechanism. On AWQ-quantized 70B and 120B models, DRY reduces loop rate by roughly half while preserving MT-Bench, MMLU, and GSM8K performance, whereas standard alternatives lose measurable ground. DRY has been adopted by popular open-source LLM inference frameworks including llama.cpp, ExLlamaV2, and text-generation-webui, highlighting its practical impact on text generation.

Large Language Models (LLMs) are powerful but often too slow and costly for real-world use during inference. Looped transformers save on parameters by reusing the same weights for multiple computational steps, or "loops." However, this approach has a major flaw: the loops run one after another, causing inference latency and memory requirements to increase with each added loop. This makes them impractical for fast applications. To solve this problem, we introduce the Parallel Loop Transformer (PLT). PLT is a new architecture that delivers the performance benefits of a deep, looped model but with the low latency of a standard, non-looped model. PLT works using two key techniques. First, Cross-Loop Parallelism (CLP) breaks the sequential dependency by computing different loops for different tokens at the same time, all within a single pass. Second, to prevent memory costs from growing, we use an Efficient Representation Enhancement strategy. This method shares the memory (KV cache) from the first loop with all other loops. It then uses a Gated Sliding-Window Attention (G-SWA) to combine this shared global information with local information, maintaining high accuracy. Our experiments show that PLT achieves the high accuracy of a traditional looped model but with almost no extra latency or memory cost compared to a standard transformer.

Looped language models (LoopLMs) improve parameter efficiency by recursively reusing Transformer blocks, enabling deeper computation under a fixed model size. However, this reuse makes LoopLMs more fragile under post-training quantization (PTQ). We present the first systematic study of quantization in LoopLMs and identify three challenges: distribution shift across roles, state reuse across loop transitions, and recursive error accumulation. To address these challenges, we propose LoopQ, a loop-aware PTQ framework that preserves a shared quantized backbone while introducing lightweight adaptations. LoopQ combines activation scaling, selective transformation, cross-loop state alignment, and trajectory-aware optimization to reduce distributional mismatch within loops and error accumulation across loops. Experiments across seven benchmarks show that, under W4A4 quantization, LoopQ improves average downstream accuracy by 68.8% and reduces average perplexity by 87.7% compared with the strongest static PTQ baseline.

Augmenting Large Language Models (LLMs) with external tools enables them to execute complex, multi-step tasks. However, tool learning is hampered by the static synthetic data pipelines where data generation and model training are executed as two separate, non-interactive processes. This approach fails to adaptively focus on a model's specific weaknesses and allows noisy labels to persist, degrading training efficiency. We introduce LoopTool, a fully automated, model-aware data evolution framework that closes this loop by tightly integrating data synthesis and model training. LoopTool iteratively refines both the data and the model through three synergistic modules: (1) Greedy Capability Probing (GCP) diagnoses the model's mastered and failed capabilities; (2) Judgement-Guided Label Verification (JGLV) uses an open-source judge model to find and correct annotation errors, progressively purifying the dataset; and (3) Error-Driven Data Expansion (EDDE) generates new, challenging samples based on identified failures. This closed-loop process operates within a cost-effective, open-source ecosystem, eliminating dependence on expensive closed-source APIs. Experiments show that our 8B model trained with LoopTool significantly surpasses its 32B data generator and achieves new state-of-the-art results on the BFCL-v3 and ACEBench benchmarks for its scale. Our work demonstrates that closed-loop, self-refining data pipelines can dramatically enhance the tool-use capabilities of LLMs.

Looped computation shows promise in improving the reasoning-oriented performance of LLMs by scaling test-time compute. However, existing approaches typically require either training recurrent models from scratch or applying disruptive retrofits, which involve substantial computational costs and may compromise pretrained capabilities. To address these limitations, we introduce Looped Depth Up-Scaling (LoopUS), a post-training framework that converts a standard pretrained LLM into a looped architecture. As a key technical contribution, LoopUS recasts the pretrained LLM into an encoder, a looped reasoning block, and a decoder. It operationalizes this latent-refinement architecture through four core components: (1) block decomposition, guided by staged representation dynamics; (2) an input-dependent selective gate to mitigate hidden-state drift; (3) random deep supervision for memory-efficient learning over long recursive horizons; and (4) a confidence head for adaptive early exiting. Collectively, these mechanisms transform a standard non-looped model into a looped form while stabilizing it against both computational bottlenecks and representation collapse. Through stable latent looping, LoopUS improves reasoning-oriented performance without extending the generated traces or requiring recurrent training from scratch. For more details, see https://thrillcrazyer.github.io/LoopUS

Looped language models repeat a set of transformer layers through depth, reducing memory costs and providing natural early-exit points at loop boundaries. However, looped models do not scale as favorably as standard transformers with unique layers. We compare standard and Mixture-of-Experts (MoE) transformers, with and without looping, and find two main results. First, we find Looped-MoE models scale better than the standard baseline while dense looped models do not. We trace this to routing divergence between loops: in Looped-MoE models, different experts are activated on each pass through the same shared layers, recovering expressivity without additional parameters. Our second finding is that looped models have better compute-quality trade-offs with early exits than standard models. Because each loop ends with the same layers that produce the final output, loop boundaries are superior exit points, as confirmed by earlier output convergence at these points. In sum, we provide a clear direction for scaling looped models: a Looped-MoE model with early exits can not only beat standard transformers at scale, but also enable significant memory and inference savings with minimal degradation in quality.

Recently, large language models (LLMs) have demonstrated excellent performance in understanding human instructions and generating code, which has inspired researchers to explore the feasibility of generating RTL code with LLMs. However, the existing approaches to fine-tune LLMs on RTL codes typically are conducted on fixed datasets, which do not fully stimulate the capability of LLMs and require large amounts of reference data. To mitigate these issues , we introduce a simple yet effective iterative training paradigm named ITERTL. During each iteration, samples are drawn from the model trained in the previous cycle. Then these new samples are employed for training in this loop. Through this iterative approach, the distribution mismatch between the model and the training samples is reduced. Additionally, the model is thus enabled to explore a broader generative space and receive more comprehensive feedback. Theoretical analyses are conducted to investigate the mechanism of the effectiveness. Experimental results show the model trained through our proposed approach can compete with and even outperform the state-of-the-art (SOTA) open-source model with nearly 37\% reference samples, achieving remarkable 42.9\% and 62.2\% pass@1 rate on two VerilogEval evaluation datasets respectively. While using the same amount of reference samples, our method can achieved a relative improvement of 16.9\% and 12.5\% in pass@1 compared to the non-iterative method. This study facilitates the application of LLMs for generating RTL code in practical scenarios with limited data.

Large Language Models (LLMs) frequently memorize long sequences verbatim, often with serious legal and privacy implications. Much prior work has studied such verbatim memorization using observational data. To complement such work, we develop a framework to study verbatim memorization in a controlled setting by continuing pre-training from Pythia checkpoints with injected sequences. We find that (1) non-trivial amounts of repetition are necessary for verbatim memorization to happen; (2) later (and presumably better) checkpoints are more likely to verbatim memorize sequences, even for out-of-distribution sequences; (3) the generation of memorized sequences is triggered by distributed model states that encode high-level features and makes important use of general language modeling capabilities. Guided by these insights, we develop stress tests to evaluate unlearning methods and find they often fail to remove the verbatim memorized information, while also degrading the LM. Overall, these findings challenge the hypothesis that verbatim memorization stems from specific model weights or mechanisms. Rather, verbatim memorization is intertwined with the LM's general capabilities and thus will be very difficult to isolate and suppress without degrading model quality.

We measure how much one extra recurrence is worth to a looped (depth-recurrent) language model, in equivalent unique parameters. From an iso-depth sweep of 116 pretraining runs across recurrence counts r in {1, 2, 4, 8} spanning {sim}50times in training compute, we fit a joint scaling law L = E + A,(N_once + r^φ N_rec)^{-α} + B,D^{-β} and recover a new recurrence-equivalence exponent φ= 0.46. Intuitively, φ tells us whether looping a block r times is equivalent in validation loss to r unique blocks of a non-looped model (full equivalence, φ{=}1) or to a single block run repeatedly with no capacity gain (φ{=}0). Our φ= 0.46 sits in between, so each additional recurrence predictably increases validation loss at matched training compute. For example, at r{=}4 a 410M looped model performs on par with a 580M non-looped model, but incurs the training cost of a 1B non-looped one. We demonstrate the utility of φ as a measurement tool on two probes. Truncated backpropagation lowers φ to 0.38, indicating that the loop mechanism is poorly trained under truncation, even though validation loss decreases. Conversely, hyperconnections raise φ to 0.65, a genuine capacity gain. Our method applies to any looped LM and separates true loop improvements from token-budget gains.

Scaling Transformer-based click-through rate (CTR) models by stacking more parameters brings growing computational and storage overhead, creating a widening gap between scaling ambitions and the stringent industrial deployment constraints. We propose LoopCTR, which introduces a loop scaling paradigm that increases training-time computation through recursive reuse of shared model layers, decoupling computation from parameter growth. LoopCTR adopts a sandwich architecture enhanced with Hyper-Connected Residuals and Mixture-of-Experts, and employs process supervision at every loop depth to encode multi-loop benefits into the shared parameters. This enables a train-multi-loop, infer-zero-loop strategy where a single forward pass without any loop already outperforms all baselines. Experiments on three public benchmarks and one industrial dataset demonstrate state-of-the-art performance. Oracle analysis further reveals 0.02--0.04 AUC of untapped headroom, with models trained with fewer loops exhibiting higher oracle ceilings, pointing to a promising frontier for adaptive inference.

Synthesizing inductive loop invariants is fundamental to automating program verification. In this work, we observe that Large Language Models (such as gpt-3.5 or gpt-4) are capable of synthesizing loop invariants for a class of programs in a 0-shot setting, yet require several samples to generate the correct invariants. This can lead to a large number of calls to a program verifier to establish an invariant. To address this issue, we propose a {\it re-ranking} approach for the generated results of LLMs. We have designed a ranker that can distinguish between correct inductive invariants and incorrect attempts based on the problem definition. The ranker is optimized as a contrastive ranker. Experimental results demonstrate that this re-ranking mechanism significantly improves the ranking of correct invariants among the generated candidates, leading to a notable reduction in the number of calls to a verifier.

Large language models have shown remarkable reasoning abilities and scaling laws suggest that large parameter count, especially along the depth axis, is the primary driver. In this work, we make a stronger claim -- many reasoning problems require a large depth but not necessarily many parameters. This unlocks a novel application of looped models for reasoning. Firstly, we show that for many synthetic reasoning problems like addition, p-hop induction, and math problems, a k-layer transformer looped L times nearly matches the performance of a kL-layer non-looped model, and is significantly better than a k-layer model. This is further corroborated by theoretical results showing that many such reasoning problems can be solved via iterative algorithms, and thus, can be solved effectively using looped models with nearly optimal depth. Perhaps surprisingly, these benefits also translate to practical settings of language modeling -- on many downstream reasoning tasks, a language model with k-layers looped L times can be competitive to, if not better than, a kL-layer language model. In fact, our empirical analysis reveals an intriguing phenomenon: looped and non-looped models exhibit scaling behavior that depends on their effective depth, akin to the inference-time scaling of chain-of-thought (CoT) reasoning. We further elucidate the connection to CoT reasoning by proving that looped models implicitly generate latent thoughts and can simulate T steps of CoT with T loops. Inspired by these findings, we also present an interesting dichotomy between reasoning and memorization, and design a looping-based regularization that is effective on both fronts.

We introduce training-free looped transformers, in which a lightweight inference-time wrapper loops a contiguous mid-stack block of layers of a frozen checkpoint without additional fine-tuning, continued training, or architectural changes. Unlike prior looped transformer methods that train with the looped structure end-to-end, we retrofit recurrence onto pretrained models at test time. We show that naive block reapplication usually degrades performance, highlighting the importance of the loop application strategy. Motivated by viewing a pre-norm transformer block as a forward Euler step on an ODE, we instead treat looping as a refinement of the same approximation, replacing one large update with smaller damped sub-steps. Across seven dense, sparse MoE, and MLA+MoE model families, our method improves Qwen3-4B-Instruct by +2.64 pp on MMLU-Pro, Qwen3-30B-A3B-Instruct by +1.14 pp on CommonsenseQA, and Moonlight-16B-A3B-Instruct by +1.20 pp on OpenBookQA.

Recently, Carlini et al. demonstrated the widely used model Stable Diffusion can regurgitate real training samples, which is troublesome from a copyright perspective. In this work, we provide an efficient extraction attack on par with the recent attack, with several order of magnitudes less network evaluations. In the process, we expose a new phenomena, which we dub template verbatims, wherein a diffusion model will regurgitate a training sample largely in tact. Template verbatims are harder to detect as they require retrieval and masking to correctly label. Furthermore, they are still generated by newer systems, even those which de-duplicate their training set, and we give insight into why they still appear during generation. We extract training images from several state of the art systems, including Stable Diffusion 2.0, Deep Image Floyd, and finally Midjourney v4. We release code to verify our extraction attack, perform the attack, as well as all extracted prompts at https://github.com/ryanwebster90/onestep-extraction.

Masked diffusion models (MDMs) have emerged as a promising alternative to autoregressive models for language modeling, yet the effective design of transformer architectures for MDMs remains underexplored. In this paper, we show that selectively looping the early-middle transformer layers significantly improves both training efficiency and model performance in MDMs. We call this approach LoopMDM(Looped Masked Diffusion Model), which brings two key benefits: looping layers at training-time yields a depth-scaling effect without adding parameters, while varying the number of loops at inference-time enables flexible compute scaling. Despite the simplicity, the results are striking: across multiple pre-training corpora, LoopMDM matches the performance of same-size MDMs with up to 3.3 fewer training FLOPs, while its final performance outperforms them on various reasoning benchmarks, including up to 8.5 points on GSM8K. It even surpasses deeper non-looped MDMs trained with comparable per-step compute, indicating that selective looping is more effective than naive depth scaling. Furthermore, LoopMDM can scale inference-time compute by increasing the number of loops. Adaptively adjusting the number of loops throughout the sampling process further yields additional gains in compute efficiency while maintaining performance. Lastly, with attention analysis, we provide evidence that looping is effective in MDMs by promoting interactions among masked positions. Our code and weights will be publicly released.

Modern LLMs are trained to "think" primarily via explicit text generation, such as chain-of-thought (CoT), which defers reasoning to post-training and under-leverages pre-training data. We present and open-source Ouro, named after the recursive Ouroboros, a family of pre-trained Looped Language Models (LoopLM) that instead build reasoning into the pre-training phase through (i) iterative computation in latent space, (ii) an entropy-regularized objective for learned depth allocation, and (iii) scaling to 7.7T tokens. Ouro 1.4B and 2.6B models enjoy superior performance that match the results of up to 12B SOTA LLMs across a wide range of benchmarks. Through controlled experiments, we show this advantage stems not from increased knowledge capacity, but from superior knowledge manipulation capabilities. We also show that LoopLM yields reasoning traces more aligned with final outputs than explicit CoT. We hope our results show the potential of LoopLM as a novel scaling direction in the reasoning era. Our model could be found in: http://ouro-llm.github.io.

Looped Transformers scale sequential computation by applying a compact stack of physical blocks for multiple rounds, increasing unrolled depth without increasing stored parameters. This reuse changes the residual-scaling problem: in an untied Transformer, each residual branch receives and applies its own parameter update, whereas in a looped Transformer one shared update aggregates gradients from repeated visits and is read back by those same visits in the next linearized forward pass. We formalize this tied-depth effect through a first-order perturbation bound controlled by a visit-alignment coefficient κ_R. The bound recovers the DeepNorm exponent when visits decorrelate, but in the conservative aligned regime it requires the exponent to increase from 1/4 to 1/2 as loop count grows at fixed physical depth. The resulting method, DeepLoop, keeps the Post-LN DeepNorm architecture and sets α=(2N)^{1/2} and β=(8N)^{-1/2} for unrolled depth N. On GPT-style looped language models at GPT-2 small and GPT-2 medium scale, DeepLoop is neutral when no physical block is revisited and improves validation loss and downstream accuracy once recurrent depth is activated. These results show that stable recurrent depth requires residual scaling rules that account for parameter visits, not only nominal layer count.

Looped Transformers scale latent computation by repeatedly applying shared blocks, but sequential looping increases latency and KV-cache memory with the loop count. Parallel loop Transformers (PLT) alleviate this cost through cross-loop position offsets (CLP) and shared-KV gated sliding-window attention, making loop count a practical design choice. We therefore study PLT loop-count selection through a gain--cost view: an extra loop may refine representations, but CLP also introduces a positional mismatch at each loop boundary. We instantiate this study by training LoopCoder-v2, a family of 7B PLT coders with different loop counts, from scratch on 18T tokens, followed by matched instruction tuning and evaluation. Empirically, the two-loop variant delivers broad gains over the non-looped baseline across code generation, code reasoning, agentic software engineering, and tool-use benchmarks, improving SWE-bench Verified from 43.0 to 64.4 points and Multi-SWE from 14.0 to 31.0 points. In contrast, variants with three or more loops regress, revealing a strongly non-monotonic loop-count effect. Our diagnostics show that loop 2 provides the main productive refinement, while later loops yield diminishing, oscillatory updates and reduced representational diversity. Because the CLP-induced mismatch remains roughly fixed as refinement gains shrink, the offset cost increasingly dominates. This gain--cost trade-off explains PLT's saturation at two loops and provides diagnostics for loop-count selection.

Looping, reusing a block of layers across depth, and depth growing, training shallow-to-deep models by duplicating middle layers, have both been linked to stronger reasoning, but their relationship remains unclear. We provide a mechanistic unification: looped and depth-grown models exhibit convergent depth-wise signatures, including increased reliance on late layers and recurring patterns aligned with the looped or grown block. These shared signatures support the view that their gains stem from a common form of iterative computation. Building on this connection, we show that the two techniques are adaptable and composable: applying inference-time looping to the middle blocks of a depth-grown model improves accuracy on some reasoning primitives by up to 2times, despite the model never being trained to loop. Both approaches also adapt better than the baseline when given more in-context examples or additional supervised fine-tuning data. Additionally, depth-grown models achieve the largest reasoning gains when using higher-quality, math-heavy cooldown mixtures, which can be further boosted by adapting a middle block to loop. Overall, our results position depth growth and looping as complementary, practical methods for inducing and scaling iterative computation to improve reasoning.

Chain-of-thought (CoT) prompting enables reasoning in language models but requires explicit verbalization of intermediate steps. Looped transformers offer an alternative by iteratively refining representations within hidden states. This parameter efficiency comes at a cost, as looped models lack the storage capacity of deeper models which use unique weights per layer. In this work, we investigate transformer models that feature both adaptive per-layer looping, where each transformer block learns to iterate its hidden state via a learned halting mechanism, and gated memory banks, that provide additional learned storage. We find that looping primarily benefits mathematical reasoning, while memory banks help recover performance on commonsense tasks compared to parameter and FLOP matched models. Combining both mechanisms yields a model that outperforms an iso-FLOP baseline, with three times the number of layers, across math benchmarks. Analysis of model internals reveals layer specialization: early layers learn to loop minimally and access memory sparingly, while later layers do both more heavily.

Looped language models have shown promising results on reasoning benchmarks, yet their potential for agentic tool use remains largely unexplored. We study this question in compositional tool-calling settings, where models must coordinate multiple API calls, maintain intermediate state, and preserve dependencies across tool interactions. We evaluate native and retrofitted looped language models on API-Bank, BFCL, and NESTful, comparing looped and non-looped models trained under matched supervised fine-tuning recipes and varying recurrent depth at inference time. In controlled experiments, recurrent computation generally benefits compositional and dependency-aware tool use, while providing smaller and more model-dependent gains on isolated API invocation. Accuracy on multi-step tool use generally increases with recurrent depth; adaptive inference, however, achieves a more favorable compute-performance trade-off by allocating additional computation only when needed. Our results suggest that looped language models are a promising architecture for agentic systems that require reliable planning, coordination, and execution of compositional tool use workflows.

Large Multimodal Models (LMMs) have achieved remarkable success in vision-language tasks, yet their vast parameter counts are often underutilized during both training and inference. In this work, we embrace the idea of looping back to move forward: reusing model parameters through recursive refinement to extract stronger multimodal representations without increasing model size. We propose RecursiveVLM, a recursive Transformer architecture tailored for LMMs. Two key innovations enable effective looping: (i) a Recursive Connector that aligns features across recursion steps by fusing intermediate-layer hidden states and applying modality-specific projections, respecting the distinct statistical structures of vision and language tokens; (ii) a Monotonic Recursion Loss that supervises every step and guarantees performance improves monotonically with recursion depth. This design transforms recursion into an on-demand refinement mechanism: delivering strong results with few loops on resource-constrained devices and progressively improving outputs when more computation resources are available. Experiments show consistent gains of +3% over standard Transformers and +7% over vanilla recursive baselines, demonstrating that strategic looping is a powerful path toward efficient, deployment-adaptive LMMs.

Looped, weight-tied Transformers reduce parameters by reusing a single block, but decoding still stores a separate K/V cache for every recurrence step. We show that this loop-indexed cache is highly structured. For a fixed token, layer and head, K/V vectors trace a short low-rank trajectory across loops, while the head and layer axes remain much flatter. We introduce Looped Latent Attention (), a post-training cache codec that stores compact K and V latents and reconstructs loop-specific K/V vectors only when attention reads them. The default per-head codec compresses recurrence, while -2D also folds heads into one latent for the extreme-compression regime. The codec is initialized from the SVD of teacher activations and refined with logit and attention-output distillation. At matched cache budget, per-head outperforms head-axis MLA, cross-layer sharing, KV quantization and final-loop reuse, showing that the recurrent cache is low-rank but not safely collapsible to a single state. The same axis advantage holds on Ouro-2.6B-Thinking and transfers to Huginn-3.5B, where an SVD codec remains near-lossless to 32times compression in decoder-independent evaluation. The cache reduction is exact. On one H200, the latent-store path increases measured Ouro-1.4B batch capacity at 4k context from 32 to 768 sequences at 21.3times compression. Lastly, for long reasoning rollouts such as in MATH-500, on-policy refinement on student-generated prefixes raises accuracy at 4times compression from 0.43 to 0.66 and reduces no-answer generations when compared to token-level off-policy distillation.

Looped Language Models (LoopLMs) enable efficient latent reasoning through depth recurrence, yet exhibit unreliable test-time scaling behavior: performance often peaks at a certain iteration depth and then collapses with further recurrence. Through latent dynamics analysis, we find an inherent trade-off between stability and effectiveness in existing architectures and strategies. By conceptualizing reasoning as uncertainty reduction, we propose that convergence toward stable fixed points while preserving effectiveness represents a promising way. To this end, we propose STARS (STAbility-driven Recurrent Scaling), a training framework that constrains latent states to approach asymptotically stable fixed points. This is realized via efficient Jacobian Spectral Radius Regularization with random loop sampling, enabling STARS to maximize effectiveness while ensuring rigorous stability. Experiments on arithmetic tasks show that STARS achieves reliable test-time scaling, and on complex mathematical reasoning it substantially mitigates performance degradation as recurrence depth increases while also improving peak performance.

Loop invariants are fundamental to reasoning about programs with loops. They establish properties about a given loop's behavior. When they additionally are inductive, they become useful for the task of formal verification that seeks to establish strong mathematical guarantees about program's runtime behavior. The inductiveness ensures that the invariants can be checked locally without consulting the entire program, thus are indispensable artifacts in a formal proof of correctness. Finding inductive loop invariants is an undecidable problem, and despite a long history of research towards practical solutions, it remains far from a solved problem. This paper investigates the capabilities of the Large Language Models (LLMs) in offering a new solution towards this old, yet important problem. To that end, we first curate a dataset of verification problems on programs with loops. Next, we design a prompt for exploiting LLMs, obtaining inductive loop invariants, that are checked for correctness using sound symbolic tools. Finally, we explore the effectiveness of using an efficient combination of a symbolic tool and an LLM on our dataset and compare it against a purely symbolic baseline. Our results demonstrate that LLMs can help improve the state-of-the-art in automated program verification.

The success of large-scale language models like GPT can be attributed to their ability to efficiently predict the next token in a sequence. However, these models rely on constant computational effort regardless of the complexity of the token they are predicting, lacking the capacity for iterative refinement. In this paper, we introduce a novel Loop-Residual Neural Network, which achieves better performance by utilizing longer computational time without increasing the model size. Our approach revisits the input multiple times, refining the prediction by iteratively looping over a subset of the model with residual connections. We demonstrate the effectiveness of this method through experiments comparing versions of GPT-2 with our Loop-Residual models, showing improved performance in language modeling tasks while maintaining similar parameter counts. Importantly, these improvements are achieved without the need for extra training data.

We study auto research as a closed empirical loop driven by external measurement. Each submitted trial carries a hypothesis, an executable code edit, an evaluator-owned outcome, and feedback that shapes the next proposal. The output is not a generated paper or a single model checkpoint, but an auditable trajectory of proposals, code diffs, experiments, scores, and failure labels. We instantiate this loop with specialist agents that partition recipe surfaces and share measured lineage across trials. The central empirical finding is that lineage feedback lets agents turn evaluator outcomes, including crashes, budget overruns, size failures, and accuracy-gate misses, into later program-level recipe edits rather than one-shot suggestions. Across 1,197 headline-run trials plus 600 Parameter Golf control trials after one-time setup and launch, humans did not choose proposals, edit recipes, override scores, or repair failed trials during the search. In the three headline runs, the same submitted-trial loop reduces Parameter Golf validation bpb by 0.81%, raises NanoChat-D12 CORE by 38.7%, and reduces CIFAR-10 Airbench96 wallclock by 4.59%, with each task measured by its own external evaluator and legality checks. The trace includes a strict architecture-domain audit of 157 headline-run submissions and program rewrites such as a NanoChat attention-kernel path change. Within this scope the loop autonomously writes code, submits experiments, absorbs feedback, applies and combines known techniques inside each environment, and improves public starting recipes.

A dense, pretrained language model can be retrofitted with recurrent depth and learn an iterative latent transition that persists after outcome-only annealing. Qwen2.5-0.5B-Instruct is split into a Prelude, a weight-tied Recurrent Block, and a Coda, with an identity-preserving one-loop path and a re-entry bridge on later loops. At loop 1 the retrofit remains non-inferior to its base on a preregistered ARC battery. Three findings. First, the mechanism is a reusable procedure rather than terminal-answer lookup, and installs at two budgets: 6M trained parameters over frozen base weights and 180M full-block. With intermediate-step supervision, the model computes one task step per loop and persists when only final answers are graded. The adapter matched the full block overall (83.8% versus 84.0%), led through depth 11, and trailed beyond. Verbal fine-tuning reached 79-86% on controlled verbal renderings (zero-shot transfer was minimal), and adapter verbal training begun from the installed mechanism outpaced matched fresh training by 18.6 points, including on a held-out test set. Second, the operation extrapolates to roughly 1.5 times its supervised depth, holding 70% accuracy through depth 18. Third, a same-size scratchpad-trained model matched the recurrent model within its learned horizon but collapsed beyond it. The recurrent model won overall, 84% versus 72%, retained 53% versus 2.5% beyond depth 10, and answered 7.6 times faster. An iterative transformer can therefore perform deeper reasoning in latent space faster than comparable or larger models fine-tuned on the same task, in a system-level comparison. A second task, running the rule in reverse, exposed the limits: the inverse was learnable in isolation, but no continuation acquired it while preserving the installed mechanism and general capability, a catastrophic-interference boundary. Learned depth selection remains open.

Looped language models (LoopLMs) perform iterative latent computation to refine internal representations, offering a promising alternative to explicit chain-of-thought (CoT) reasoning. However, existing reinforcement learning (RL) paradigms primarily target output tokens, creating a structural mismatch with looped architectures whose reasoning unfolds implicitly. In this work, we propose LoopRPT, a reinforcement pre-training framework tailored for LoopLMs. By reframing next-token prediction as a next-token reasoning task, LoopRPT assigns reinforcement signals directly to latent steps using an EMA teacher reference and noisy latent rollouts. This formulation enables RL to directly shape intermediate representations, compressing effective reasoning into fewer iterations. We instantiate LoopRPT on the Ouro architecture across multiple model scales. Results demonstrate that LoopRPT consistently improves per-step representation quality, achieving Pareto dominance in accuracy-computation trade-offs. Notably, significant gains on hard tokens indicate that LoopRPT enhances early-stage reasoning rather than merely encouraging premature exits. Our findings highlight reinforcement pre-training as a principled paradigm for learning efficient latent reasoning in LoopLMs.

As Large Language Models (LLMs) become increasingly widespread, understanding how specific training data shapes their outputs is crucial for transparency, accountability, privacy, and fairness. To explore how LLMs leverage and replicate their training data, we introduce a systematic approach centered on analyzing low-perplexity sequences - high-probability text spans generated by the model. Our pipeline reliably extracts such long sequences across diverse topics while avoiding degeneration, then traces them back to their sources in the training data. Surprisingly, we find that a substantial portion of these low-perplexity spans cannot be mapped to the corpus. For those that do match, we quantify the distribution of occurrences across source documents, highlighting the scope and nature of verbatim recall and paving a way toward better understanding of how LLMs training data impacts their behavior.

Intermediate reasoning or acting steps have successfully improved large language models (LLMs) for handling various downstream natural language processing (NLP) tasks. When applying LLMs for code generation, recent works mainly focus on directing the models to articulate intermediate natural-language reasoning steps, as in chain-of-thought (CoT) prompting, and then output code with the natural language or other structured intermediate steps. However, such output is not suitable for code translation or generation tasks since the standard CoT has different logical structures and forms of expression with the code. In this work, we introduce the universal code (UniCode) as the intermediate representation. It is a description of algorithm steps using a mix of conventions of programming languages, such as assignment operator, conditional operator, and loop. Hence, we collect an instruction dataset UniCoder-Instruct to train our model UniCoder on multi-task learning objectives. UniCoder-Instruct comprises natural-language questions, code solutions, and the corresponding universal code. The alignment between the intermediate universal code representation and the final code solution significantly improves the quality of the generated code. The experimental results demonstrate that UniCoder with the universal code significantly outperforms the previous prompting methods by a large margin, showcasing the effectiveness of the structural clues in pseudo-code.

Multi-turn dialogues are essential in many real-world applications of large language models, such as chatbots and virtual assistants. As conversation histories become longer, existing large language models face increasing computational and memory challenges, which hinder their ability to provide efficient and responsive interactions. Most current acceleration methods either compress the context or optimize key value caching, but they often rely on fixed or position-based heuristics that do not adapt well to the dynamic and unpredictable patterns found in actual multi-turn conversations. In this paper, we present LoopServe, an adaptive dual-phase inference acceleration framework for large language models in multi-turn dialogues. LoopServe introduces two main innovations. First, it performs online sparsification during the prefilling phase by dynamically selecting the most important parts of the attention matrix for each new input. Second, it uses progressive key value compression during decoding by adaptively maintaining a relevant and efficient cache based on the most recently generated output tokens. We also propose a https://huggingface.co/datasets/TreeAILab/Multi-turn_Long-context_Benchmark_for_LLMs{new benchmark} with eleven multi-turn datasets that reflect realistic query positions and conversational dependencies. Extensive experiments demonstrate that LoopServe consistently achieves superior effectiveness compared to existing baselines and significantly accelerates LLM inference across a wide range of long-context dialogue tasks.

Looped Transformers increase effective depth by iterating a shared block of layers, but most evaluations compare at fixed model size, conflating architectural advantage with extra FLOPs. We study looping on Mixture-of-Experts Transformers while closely matching per-token FLOPs, total non-embedding parameters, and KV cache. Through a series of ablations, we arrive at a recipe we call SMELT (Sparse MoE Transformer, middle layers Loop Twice), which loops the middle half of layers twice while matching the unlooped Baseline on all three budgets. We scale SMELT across four sizes up to 54B non-embedding parameters and fit a separate Chinchilla-style scaling law for each architecture. SMELT's loss drops faster with compute, saving 6.8--18.0\% of training FLOPs on the compute-optimal frontier. The advantage transfers to downstream benchmarks beyond what validation loss predicts, is largest on Code, and grows with sample length and the number of in-context examples. Mechanistic analysis shows that the second visit reduces the attention sink and redirects mass toward content-relevant tokens, an inductive bias that may underlie the observed performance gains. These results show that looping can improve Transformers even under budget matching, offering a practical recipe that turns depth reuse into measurable gains.

The performance of large language models (LLMs) in program synthesis and mathematical reasoning is fundamentally limited by the quality of their pre-training corpora. We introduce two openly licensed datasets, released under the Llama 3.3 Community License, that significantly enhance LLM performance by systematically rewriting public data. SwallowCode (approximately 16.1 billion tokens) refines Python snippets from The-Stack-v2 through a novel four-stage pipeline: syntax validation, pylint-based style filtering, and a two-stage LLM rewriting process that enforces style conformity and transforms snippets into self-contained, algorithmically efficient examples. Unlike prior methods that rely on exclusionary filtering or limited transformations, our transform-and-retain approach upgrades low-quality code, maximizing data utility. SwallowMath (approximately 2.3 billion tokens) enhances Finemath-4+ by removing boilerplate, restoring context, and reformatting solutions into concise, step-by-step explanations. Within a fixed 50 billion token training budget, continual pre-training of Llama-3.1-8B with SwallowCode boosts pass@1 by +17.0 on HumanEval and +17.7 on HumanEval+ compared to Stack-Edu, surpassing the baseline model's code generation capabilities. Similarly, substituting SwallowMath yields +12.4 accuracy on GSM8K and +7.6 on MATH. Ablation studies confirm that each pipeline stage contributes incrementally, with rewriting delivering the largest gains. All datasets, prompts, and checkpoints are publicly available, enabling reproducible research and advancing LLM pre-training for specialized domains.

When LLMs perform zero-shot inference, they typically use a prompt with a task specification, and generate a completion. However, there is no work to explore the possibility of the reverse - going from completion to task specification. In this paper, we employ both directions to perform cycle-supervised learning entirely in-context. Our goal is to create a forward map f : X -> Y (e.g. image -> generated caption), coupled with a backward map g : Y -> X (e.g. caption -> generated image) to construct a cycle-consistency "loss" (formulated as an update to the prompt) to enforce g(f(X)) ~= X. The technique, called CyclePrompt, uses cycle-consistency as a free supervisory signal to iteratively craft the prompt. Importantly, CyclePrompt reinforces model performance without expensive fine-tuning, without training data, and without the complexity of external environments (e.g. compilers, APIs). We demonstrate CyclePrompt in two domains: code generation and image captioning. Our results on the HumanEval coding benchmark put us in first place on the leaderboard among models that do not rely on extra training data or usage of external environments, and third overall. Compared to the GPT4 baseline, we improve accuracy from 80.5% to 87.2%. In the vision-language space, we generate detailed image captions which outperform baseline zero-shot GPT4V captions, when tested against natural (VQAv2) and diagrammatic (FigureQA) visual question-answering benchmarks. To the best of our knowledge, this is the first use of self-supervised learning for prompting.

Looped Transformers have emerged as an efficient and powerful class of models for reasoning in the language domain. Recent studies show that these models achieve strong performance on algorithmic and reasoning tasks, suggesting that looped architectures possess an inductive bias toward latent reasoning. However, prior approaches fix the number of loop iterations during training and inference, leaving open the question of whether these models can flexibly adapt their computational depth under variable compute budgets. We introduce LoopFormer, a looped Transformer trained on variable-length trajectories to enable budget-conditioned reasoning. Our core contribution is a shortcut-consistency training scheme that aligns trajectories of different lengths, ensuring that shorter loops yield informative representations while longer loops continue to refine them. LoopFormer conditions each loop on the current time and step size, enabling representations to evolve consistently across trajectories of varying length rather than drifting or stagnating. Empirically, LoopFormer demonstrates robust performance on language modeling and reasoning benchmarks even under aggressive compute constraints, while scaling gracefully with additional budget. These results show that looped Transformers are inherently suited for adaptive language modeling, opening a path toward controllable and budget-aware large language models.

Large Language Models (LLMs) often exhibit a gap between their internal knowledge and their explicit linguistic outputs. In this report, we empirically investigate whether Looped Transformers (LTs)--architectures that increase computational depth by iterating shared layers--can bridge this gap by utilizing their iterative nature as a form of introspection. Our experiments reveal that while increasing loop iterations narrows the gap, it is partly driven by a degradation of their internal knowledge carried by representations. Moreover, another empirical analysis suggests that current LTs' ability to perceive representations does not improve across loops; it is only present in the final loop. These results suggest that while LTs offer a promising direction for scaling computational depth, they have yet to achieve the introspection required to truly link representation space and natural language.

In-context learning has been recognized as a key factor in the success of Large Language Models (LLMs). It refers to the model's ability to learn patterns on the fly from provided in-context examples in the prompt during inference. Previous studies have demonstrated that the Transformer architecture used in LLMs can implement a single-step gradient descent update by processing in-context examples in a single forward pass. Recent work has further shown that, during in-context learning, a looped Transformer can implement multi-step gradient descent updates in forward passes. However, their theoretical results require an exponential number of in-context examples, n = exp(Ω(T)), where T is the number of loops or passes, to achieve a reasonably low error. In this paper, we study linear looped Transformers in-context learning on linear vector generation tasks. We show that linear looped Transformers can implement multi-step gradient descent efficiently for in-context learning. Our results demonstrate that as long as the input data has a constant condition number, e.g., n = O(d), the linear looped Transformers can achieve a small error by multi-step gradient descent during in-context learning. Furthermore, our preliminary experiments validate our theoretical analysis. Our findings reveal that the Transformer architecture possesses a stronger in-context learning capability than previously understood, offering new insights into the mechanisms behind LLMs and potentially guiding the better design of efficient inference algorithms for LLMs.

Large language models achieve strong performance on many reasoning tasks when allowed to externalize intermediate steps as Chain-of-Thought (CoT). However, many questions require the model to internalize the multi-step reasoning within a single forward pass before generating the answer. We study this challenge through two-hop reasoning, a representative task where the model must compose multiple pieces of parametric knowledge within a single forward pass. Standard non-recurrent Transformers suffer from a depth-local storage problem: facts learned in earlier layers are unavailable where second-hop retrieval happens. We found that Looped Transformers mitigate this issue by reusing the same memory, but still generalize imperfectly. We show that the remaining bottleneck is representational. In the two-hop reasoning task, the first loop often makes the correct bridge entity nearly perfectly decodable, yet the corresponding hidden state remains poorly aligned with the bridge token embedding. Surprisingly, an easy training-free realignment intervention nearly closes the generalization gap. Building upon this insight, we propose DiscoLoop, a looping architecture whose recurrence carries both a discrete embedding channel and a continuous hidden-state channel. DiscoLoop achieves near-perfect accuracy with substantially fewer training steps across symbolic and synthetic-language multi-hop reasoning tasks. When applied to real-world pretraining, DiscoLoop attains lower training loss and stronger benchmark performance than looped-transformer baselines, suggesting that the mixed-channel design transfers to practical language modeling.

Studying data memorization in neural language models helps us understand the risks (e.g., to privacy or copyright) associated with models regurgitating training data and aids in the development of countermeasures. Many prior works -- and some recently deployed defenses -- focus on "verbatim memorization", defined as a model generation that exactly matches a substring from the training set. We argue that verbatim memorization definitions are too restrictive and fail to capture more subtle forms of memorization. Specifically, we design and implement an efficient defense that perfectly prevents all verbatim memorization. And yet, we demonstrate that this "perfect" filter does not prevent the leakage of training data. Indeed, it is easily circumvented by plausible and minimally modified "style-transfer" prompts -- and in some cases even the non-modified original prompts -- to extract memorized information. We conclude by discussing potential alternative definitions and why defining memorization is a difficult yet crucial open question for neural language models.

Yes. Can it cure doom loops? Probably not. The Gemma 4 instruction-tuned models share a reproducible failure: on long factual enumeration prompts, such as listing every episode of a TV series, the 88 IAU constellations, or the 151 original Pokemon, they collapse into repetition, either a tight verbatim loop or a list whose entries decay onto a single answer. These loops occur at rates as high as 95% and survive prompt rewording, inference-engine changes, and most sampling adjustments. In this paper we explore whether this behavior is localized enough to remove by weight edits. To localize the cause, we use per-layer ablation and per-neuron attribution, then confirm the strongest candidates with full-generation sweeps. The loops trace to a small set of MLP neurons (or, in the 26B-A4B Mixture-of-Experts model, a few routed experts) which we suppress with static weight edits. These "surgeries" can be as small as a single sign-inverted neuron (in the E2B model). The size of the effective edits grows with model scale, but in all cases, the loop patterns can be addressed at normal generation budgets while preserving general-purpose benchmark scores. However, the edits do not solve everything: we also study longer thinking budgets, where the two larger models most visibly enter doom looping, i.e. a non-convergent regime in which the model self-corrects in circles over a fact it cannot recall, exhausting the budget without committing to a final answer. We show this residual failure is reduced but not eliminated by the same edits, and argue it is fundamentally a knowledge-precision problem rather than a removable circuit; weight surgery can delete a loop, but it cannot supply a missing fact. Our results are both a feasibility demonstration, that is, evidence that a concrete generation pathology can be localized to a few parameters and edited out, and a delineation of where that approach stops.

Looped Language Models (LoopLMs) perform multi-step latent reasoning prior to token generation and outperform conventional LLMs on reasoning benchmarks at smaller parameter budgets. However, attempts to further improve LoopLM reasoning with reinforcement learning have failed - standard objectives such as Group Relative Policy Optimization (GRPO) only assign credit to the final latent state, creating a fundamental mismatch with the model's internal computation. To resolve this, we introduce RLTT (Reward Latent Thought Trajectories), a reinforcement learning framework which distributes reward across the full latent reasoning trajectory. RLTT provides dense, trajectory-level credit assignment without relying on external verifiers and can directly replace GRPO with negligible overhead. Across extensive experiments with Ouro-2.6B-Thinking under identical training and inference conditions, RLTT yields substantial improvements over GRPO on challenging mathematical reasoning benchmarks, improving accuracy by +14.4% on MATH-500, +16.6% on AIME24, and +10.0% on BeyondAIME. Despite being trained exclusively on mathematics, RLTT also transfers effectively to non-mathematical reasoning benchmarks, demonstrating the effectiveness of trajectory-level credit assignment for reinforcement learning in LoopLMs.

Language models typically reason via explicit chain-of-thought (CoT), generating intermediate steps token-by-token. Latent CoT offers an alternative: it performs multi-step reasoning in the model's hidden states, replacing decoded tokens with continuous representations for greater efficiency. However, existing latent CoT methods underperform explicit CoT beyond 1B parameters, and the gap widens with scale. Looped, or recurrent-depth, Transformers, which reuse their weights to increase computation depth without adding parameters, are a natural fit for latent reasoning. We therefore ask whether looped Transformers can bridge this gap. We answer affirmatively with a simple recipe: a looped padded Transformer that processes K latent blocks in parallel for R iterations, with a cross-entropy loss on each latent position's gold CoT-step token, similar to explicit CoT supervision. We instantiate it as LOTUS (Looped Transformers with parallel supervision on latents). LOTUS is, to our knowledge, the first latent-CoT method to bridge the gap to explicit CoT at the 3B scale, while cutting thought-phase latency by 2.5x-6.9x from compact math expressions to natural language. Projecting LOTUS's post-loop latents through the base LM head recovers the gold reasoning steps and even surfaces alternative valid intermediate steps, evidence that its latent space is interpretable and CoT-aligned. Ablations confirm that both the looped backbone and the parallel supervision on gold CoT tokens are essential.

Iterative repair loops have become a core design pattern in LLM-based software engineering systems. These workflows repeatedly generate, validate, and repair artifacts using feedback such as compiler errors or test failures. Despite their widespread use, the impact of repair-loop iteration limits remains poorly understood, as most prior work adopts fixed, often arbitrary, repair budgets. We study repair-loop effectiveness across multiple software engineering tasks, including code generation, test generation, and code translation. Across several representative workflows, datasets, and contemporary low-cost LLMs, we observe a consistent pattern of diminishing returns: the first three to four repair iterations account for most achievable gains, while later iterations contribute only marginal improvements. We further find that repair behavior is influenced more strongly by workflow orchestration and feedback design than by the underlying model itself. These results suggest that repair budgets should be treated as an explicit experimental variable, as they directly affect evaluation outcomes, computational cost, runtime, and reproducibility in LLM-based software engineering research.

Autonomous improvement loops are hard to trust because the improvement process is usually external scaffolding bolted onto the agent: failures go unlogged, diagnoses cannot be replayed, and promote-or-discard decisions land in a side database rather than the agent's own history. We show that an event-sourced agent runtime removes that friction and turns controlled improvement into a first-class workflow. When the agent's state is a deterministic projection of an append-only event log, failures are recorded, a run replays exactly from its log, candidate patches scope to typed pipeline seams, gates are auditable, and every promotion or discard is itself an event. We demonstrate this with Regimes, a loop on the ActiveGraph runtime that diagnoses failed evaluations, proposes a repair at a pipeline point, and promotes it only after static checks, sandbox execution, in-sample evaluation, and held-out validation. The loop is target-agnostic: the same control flow runs against different tasks through a common interface. On LongMemEval-S the dominant failure is not retrieval but reconciliation: the evidence is already in the assembled context, yet the reader answers incorrectly. Across five seeded held-out splits, Regimes discovers reader-prompt repairs that improve final held-out accuracy by +0.05 to +0.10 in four splits and +0.01 in one over-promotion split; two splits are individually significant (seed 5 unadjusted for its sequential promotion structure), and the pooled count is descriptive only, since the splits share one 500-question pool. The durable contributions are ActiveGraph as an auditable substrate that makes controlled improvement loops tractable, the held-out-gated loop it supports, the failure-regime taxonomy routing each failure to a pipeline location (whose marginal value over an unrouted baseline is the primary open question), and the prompt-as-discovery-probe hypothesis.

As the ever-increasing token limits of large language models (LLMs) have enabled long context as input, prompting with single data samples might no longer an efficient way. A straightforward strategy improving efficiency is to batch data within the token limit (e.g., 8k for gpt-3.5-turbo; 32k for GPT-4), which we call BatchPrompt. We have two initial observations for prompting with batched data. First, we find that prompting with batched data in longer contexts will inevitably lead to worse performance, compared to single-data prompting. Second, the performance of the language model is significantly correlated with the positions and order of the batched data, due to the corresponding change in decoder context. To retain efficiency and overcome performance loss, we propose Batch Permutation and Ensembling (BPE), and a novel Self-reflection-guided EArly Stopping (SEAS) technique. Our comprehensive experimental evaluation demonstrates that BPE can boost the performance of BatchPrompt with a striking margin on a range of popular NLP tasks, including question answering (Boolq), textual entailment (RTE), and duplicate questions identification (QQP). These performances are even competitive with/higher than single-data prompting(SinglePrompt), while BatchPrompt requires much fewer LLM calls and input tokens (For SinglePrompt v.s. BatchPrompt with batch size 32, using just 9%-16% the number of LLM calls, Boolq accuracy 90.6% to 90.9% with 27.4% tokens, QQP accuracy 87.2% to 88.4% with 18.6% tokens, RTE accuracy 91.5% to 91.1% with 30.8% tokens). To the best of our knowledge, this is the first work to technically improve prompting efficiency of large language models. We hope our simple yet effective approach will shed light on the future research of large language models. The code will be released.

Reasoning has become a central capability in large language models. Recent research has shown that reasoning performance can be improved by looping an LLM's layers in the latent dimension, resulting in looped reasoning language models. Despite promising results, few works have investigated how their internal dynamics differ from those of standard feedforward models. In this paper, we conduct a mechanistic analysis of the latent states in looped language models, focusing in particular on how the stages of inference observed in feedforward models compare to those observed in looped ones. To this end, we analyze cyclic recurrence and show that for many of the studied models each layer in the cycle converges to a distinct fixed point; consequently, the recurrent block follows a consistent cyclic trajectory in the latent space. We provide evidence that as these fixed points are reached, attention-head behavior stabilizes, leading to constant behavior across recurrences. Empirically, we discover that recurrent blocks learn stages of inference that closely mirror those of feedforward models, repeating these stages in depth with each iteration. We study how recurrent block size, input injection, and normalization influence the emergence and stability of these cyclic fixed points. We believe these findings help translate mechanistic insights into practical guidance for architectural design.

With the advent of large language models (LLMs) like GPT-3, a natural question is the extent to which these models can be utilized for source code optimization. This paper presents methodologically stringent case studies applied to well-known open source python libraries pillow and numpy. We find that contemporary LLM ChatGPT-4 (state September and October 2023) is surprisingly adept at optimizing energy and compute efficiency. However, this is only the case in interactive use, with a human expert in the loop. Aware of experimenter bias, we document our qualitative approach in detail, and provide transcript and source code. We start by providing a detailed description of our approach in conversing with the LLM to optimize the _getextrema function in the pillow library, and a quantitative evaluation of the performance improvement. To demonstrate qualitative replicability, we report further attempts on another locus in the pillow library, and one code locus in the numpy library, to demonstrate generalization within and beyond a library. In all attempts, the performance improvement is significant (factor up to 38). We have also not omitted reporting of failed attempts (there were none). We conclude that LLMs are a promising tool for code optimization in open source libraries, but that the human expert in the loop is essential for success. Nonetheless, we were surprised by how few iterations were required to achieve substantial performance improvements that were not obvious to the expert in the loop. We would like bring attention to the qualitative nature of this study, more robust quantitative studies would need to introduce a layer of selecting experts in a representative sample -- we invite the community to collaborate.

Loop Engineering is emerging as a practice for organizing development work around coding agents. Instead of writing each prompt by hand, practitioners design loops that monitor progress, assign work, run checks, and decide what the agent should do next. Even with a capable coding agent, a loop may trust a stale progress note, skip needed verification, spend its budget in the wrong direction, or stop before the task is safe to submit. Yet the final outcome of one end-to-end run cannot tell whether success or failure reflects the loop's guidance or the coding agent's ability to carry out the task. We introduce LoopArena, a benchmark for evaluating how well one model can guide a separate coding agent through a long-running task. The model under evaluation is the Controller: after each coding round, it receives a structured summary of the run and instructs a separate, fixed coding agent, the Worker, on what to do or verify next, or decides whether to stop. LoopArena evaluates this ability in three complementary settings that differ in execution scope and cost. Type I scores next-step Loop Contract selection through execution-validated questions without running the Worker at evaluation time. Type II executes repeated control over a selected slice of a full task, while Type III evaluates the paired full task from its original state. On full tasks, the best observed Strict Success Rate is 24.69\%, leaving substantial room for improvement in long-horizon loop control. Across Controllers, the paired reduction in estimated inference cost averages 64.4\%, and Type II produces a similar ordering under the main Core criterion (Spearman's \(ρ=0.9747\)). We release the benchmark data and evaluation code at https://github.com/AMAP-ML/LoopArena .

The Abstraction and Reasoning Corpus (ARC) tests whether a model can infer an unseen transformation from a few input-output examples and apply it to a new grid. Looped visual reasoners refine predictions over multiple iterations, but conventional training constrains only the final output, leaving intermediate refinements unconstrained. We propose that these refinements should instead follow the transformation step by step. We introduce TraceViT, a looped visual reasoner trained with semantically monotonic transformation chains. We obtain these chains by rewriting and verifying programmatic task implementations, decomposing each solution into intermediate grid states. Each iteration is grounded by a task reference derived from the few-shot demonstrations and an object workspace representing the current grid state. Because these chains may differ in length from the loop, soft trace alignment enforces only their ordering, letting the model allocate iterations freely. TraceViT achieves 67.8% pass@2 on ARC-AGI-1 and 24.3% on ARC-AGI-2. Controlled ablations on ARC-AGI-1 show that trace supervision becomes beneficial only when paired with grounding. Code and data will be available at https://github.com/LiuBinnan/TraceViT.

Modern language models (LMs) tend to memorize portions of their training data and emit verbatim spans. When the underlying sources are sensitive or copyright-protected, such reproduction raises issues of consent and compensation for creators and compliance risks for developers. We propose Anchored Decoding, a plug-and-play inference-time method for suppressing verbatim copying: it enables decoding from any risky LM trained on mixed-license data by keeping generation in bounded proximity to a permissively trained safe LM. Anchored Decoding adaptively allocates a user-chosen information budget over the generation trajectory and enforces per-step constraints that yield a sequence-level guarantee, enabling a tunable risk-utility trade-off. To make Anchored Decoding practically useful, we introduce a new permissively trained safe model (TinyComma 1.8B), as well as Anchored_{Byte} Decoding, a byte-level variant of our method that enables cross-vocabulary fusion via the ByteSampler framework (Hayase et al., 2025). We evaluate our methods across six model pairs on long-form evaluations of copyright risk and utility. Anchored and Anchored_{Byte} Decoding define a new Pareto frontier, preserving near-original fluency and factuality while eliminating up to 75% of the measurable copying gap (averaged over six copying metrics) between the risky baseline and a safe reference, at a modest inference overhead.

Large language models (LLMs) can suggest missing elements from items listed in a prompt, which can be used for list completion or recommendations based on users' history. However, their performance degrades when presented with too many items, as they start to suggest items already included in the input list. This occurs at around 100 items for mid-2024 flagship LLMs. We evaluate this phenomenon on both synthetic problems (e.g., finding missing numbers in a given range of shuffled integers) and realistic movie recommendation scenarios. We refer to this issue as attention overflow, as preventing repetition requires attending to all items simultaneously. Although iterative loops can mitigate this problem, their costs increase with the repetition rate, affecting the language models' ability to derive novelty from lengthy inputs.

Current multimodal language models (MLMs) evaluation and training approaches overlook the influence of instruction format, presenting an elephant-in-the-room problem. Previous research deals with this problem by manually crafting instructions, failing to yield significant insights due to limitations in diversity and scalability. In this work, we propose a programmatic instruction template generator capable of producing over 39B unique template combinations by filling randomly sampled positional synonyms into weighted sampled meta templates, enabling us to comprehensively examine the MLM's performance across diverse instruction templates. Our experiments across eight common MLMs on five benchmark datasets reveal that MLMs have high template sensitivities with at most 29% performance gaps between different templates. We further augment the instruction tuning dataset of LLaVA-1.5 with our template generator and perform instruction tuning on LLaVA-1.5-7B and LLaVA-1.5-13B. Models tuned on our augmented dataset achieve the best overall performance when compared with the same scale MLMs tuned on at most 75 times the scale of our augmented dataset, highlighting the importance of instruction templates in MLM training. The code is available at https://github.com/shijian2001/TemplateMatters .

Despite the success of test-time scaling, Large Reasoning Models (LRMs) frequently encounter repetitive loops that lead to computational waste and inference failure. In this paper, we identify a distinct failure mode termed Circular Reasoning. Unlike traditional model degeneration, this phenomenon manifests as a self-reinforcing trap where generated content acts as a logical premise for its own recurrence, compelling the reiteration of preceding text. To systematically analyze this phenomenon, we introduce LoopBench, a dataset designed to capture two distinct loop typologies: numerical loops and statement loops. Mechanistically, we characterize circular reasoning as a state collapse exhibiting distinct boundaries, where semantic repetition precedes textual repetition. We reveal that reasoning impasses trigger the loop onset, which subsequently persists as an inescapable cycle driven by a self-reinforcing V-shaped attention mechanism. Guided by these findings, we employ the Cumulative Sum (CUSUM) algorithm to capture these precursors for early loop prediction. Experiments across diverse LRMs validate its accuracy and elucidate the stability of long-chain reasoning.

Coding agent infrastructure is shifting from harness engineering toward loop engineering as coding agents are deployed for sustained long-horizon software development. Existing benchmarks often center on localized tasks or end-state outcomes, offering limited insight into sustained execution. We introduce LOOPSBENCH, a long-horizon benchmark for loop engineering in coding agent evaluation. Each task is a dependency DAG over separately testable development units with source-evidenced prerequisite edges. LOOPSBENCH comprises 112 tasks from authentic sources spanning 8 programming languages and 9 domains. Its flow-aware runtime releases tests along the ready frontier and retains completed nodes as regression obligations. We evaluate frontier coding agents paired with widely used loop implementations. The strongest configuration, Opus-4.7 with Claude Code and outer continuation, resolves 25.00% of tasks. Recorded plans recover only part of the source-recovered prerequisite DAG, and regression events remain visible across the evaluated loop profiles. We open source the benchmark data and code, including all tasks, more than 5,300 development units, and executable tests, at microsoft/Loopsbench.

Looped Transformers (LT) have emerged as a powerful architecture by iterating their layers multiple times before decoding the final token. However, pairing them with full attention retains quadratic complexity, making them computationally expensive and slow. We introduce LT2 (Linear-Time Looped Transformers), a family of looped architectures that replace quadratic softmax attention with subquadratic, linear-time attention. We study two variants: LT2-linear with linear attention and LT2-sparse with sparse attention. We find that looping uniquely synergizes with these variants: it enables iterative memory refinement in linear attention and progressively expands the effective receptive field in sparse attention. We formalize these benefits theoretically and demonstrate consistent empirical gains across controlled recall, state-tracking, and language modeling tasks. We then explore LT2-hybrid, which combines different attention variants in a looped setting. Two variants are especially promising: LT2-hybrid (GDN+DSA), which interleaves linear and sparse attention to maximize efficiency and matches the standard looped transformer's quality at fully linear-time cost; and LT2-hybrid (Full+GDN), which interleaves GDN with a small fraction of full attention layers to maximize quality, surpassing the standard looped transformer in both performance and efficiency. We also show how to convert a pre-trained LT into an LT2-hybrid model. With about 1B tokens of training, our converted model, Ouro-hybrid-1.4B, outperforms industry-level 1B models and is competitive with industry-level 4B models while retaining the speed benefits of linear-time attention. Together, these results show a clear path toward making looped transformers more scalable and advancing efficient, capable small language models.

Traditional fixed-depth architectures scale quality by increasing training FLOPs, typically through increased parameterization, at the expense of a higher memory footprint, or data. A potential alternative is looped architectures, which instead increase FLOPs by sending activations through a block of layers in a loop. While promising, existing recipes for training looped architectures can be unstable, suffering from residual explosion and loss spikes. We address these challenges by recasting looping as a nonlinear time-variant dynamical system over the residual stream. Via a linear approximation to this system, we find that instability occurs in existing looped architectures as a result of large spectral norms in their injection parameters. To address these instability issues, we propose Parcae, a novel stable, looped architecture that constrains the spectral norm of the injection parameters via discretization of a negative diagonal parameterization. As a result, Parcae achieves up to 6.3% lower validation perplexity over prior large-scale looped models. Using our stable looped architecture, we investigate the scaling properties of looping as a medium to improve quality by increasing FLOPs in training and test-time. For training, we derive predictable power laws to scale FLOPs while keeping parameter count fixed. Our initial scaling laws suggest that looping and data should be increased in tandem, given a fixed FLOP budget. At test-time, we find that Parcae can use looping to scale compute, following a predictable, saturating exponential decay. When scaled up to 1.3B parameters, we find that Parcae improves CORE and Core-Extended quality by 2.99 and 1.18 points when compared to strong Transformer baselines under a fixed parameter and data budget, achieving a relative quality of up to 87.5% a Transformer twice the size.

Large language models (LLMs) are leading significant progress in code generation. Beyond one-pass code generation, recent works further integrate unit tests and program verifiers into LLMs to iteratively refine the generated programs. However, these works consider the generated programs as an indivisible entity, which falls short for LLMs in debugging the programs, especially when the programs contain complex logic flows and data operations. In contrast, when human developers debug programs, they typically set breakpoints and selectively examine runtime execution information. The execution flow and the intermediate variables play a crucial role in the debugging process, yet they are underutilized in the existing literature on code generation. In this study, we introduce Large Language Model Debugger (LDB), a novel debugging framework that enables LLMs to refine their generated programs with the runtime execution information. Specifically, LDB segments the programs into basic blocks and tracks the values of intermediate variables after each block throughout the runtime execution. This allows LLMs to concentrate on simpler code units within the overall execution flow, verify their correctness against the task description block by block, and efficiently pinpoint any potential errors. Experiments demonstrate that LDB consistently enhances the baseline performance by up to 9.8% across the HumanEval, MBPP, and TransCoder benchmarks, archiving new state-of-the-art performance in code debugging for various LLM selections.

In mid-2026 a slogan reorganized how practitioners talk about coding agents: stop prompting your agent, start designing the loop that prompts it. We take this claim seriously and give it a careful treatment. We call the object of the new practice the loop specification: a bounded, reusable artifact, made of a trigger, a goal, a verification step, a stopping rule and a memory, that a human hands to an agent harness (such as Claude Code or Codex) so the agent pursues a goal on its own, in place of step-by-step prompting. We distinguish this external loop specification from two things it is often confused with: an ordinary programming loop, and the internal perceive-act-observe cycle that the harness already provides as plumbing. We position loop engineering as a new layer in the progression from prompt to context to harness to loop, and we argue, against the stronger headlines, that it does not retire prompt engineering; loop and prompt are distinct tools with distinct uses. We offer four contributions: a definition and scope for the discipline; an anatomy and taxonomy of loop specifications organized around trigger, goal type, a five-level verification ladder, architecture, and named terminal states; a descriptive analysis of the Loop Library, a public corpus of fifty real loops that we code by hand; and a set of design principles and anti-patterns grounded in the scientific literature on self-correction, reward hacking and model-as-judge fragility. The corpus shows that practice has matured most where the discipline says it matters: seventy percent of loops verify in the autonomous zone of the ladder and seventy-four percent name their terminal states, while automated triggering and durable memory remain comparatively underdeveloped. We close with the limits the practice must respect, including the verification burden, comprehension debt and the risk of cognitive surrender.

End-to-end ASR systems typically use fixed-depth acoustic encoders at inference, making it difficult to trade additional test-time computation for improved recognition without training a larger model. A natural approach is to reuse a shared Transformer block recurrently, but we find that naive looping does not fully exploit additional recurrent compute. We introduce LARM, a depth-conditioned looped Transformer that turns recurrent encoder depth into a controllable test-time compute axis. LARM combines sparse CTC checkpoints, supervision-clock embeddings, FiLM depth conditioning, and delayed soft-posterior feedback. These components structure the loop into recognition checkpoints separated by latent refinement phases and allow shared weights to specialize across recurrent steps. On LibriSpeech, LARM improves WER as the number of inference loops increases and achieves performance competitive with deeper unshared-parameter baselines. Our results show that test-time compute scaling can extend beyond autoregressive language-model reasoning to continuous non-autoregressive speech recognition.

Autoformalization, which translates natural language mathematics into machine-verifiable formal statements, is critical for using formal mathematical reasoning to solve math problems stated in natural language. While Large Language Models can generate syntactically correct formal statements, they often fail to preserve the original problem's semantic intent. This limitation arises from the LLM approaches' treating autoformalization as a simplistic translation task which lacks mechanisms for self-reflection and iterative refinement that human experts naturally employ. To address these issues, we propose ReForm, a Reflective Autoformalization method that tightly integrates semantic consistency evaluation into the autoformalization process. This enables the model to iteratively generate formal statements, assess its semantic fidelity, and self-correct identified errors through progressive refinement. To effectively train this reflective model, we introduce Prospective Bounded Sequence Optimization (PBSO), which employs different rewards at different sequence positions to ensure that the model develops both accurate autoformalization and correct semantic validations, preventing superficial critiques that would undermine the purpose of reflection. Extensive experiments across four autoformalization benchmarks demonstrate that ReForm achieves an average improvement of 17.2 percentage points over the strongest baselines. To further ensure evaluation reliability, we introduce ConsistencyCheck, a benchmark of 859 expert-annotated items that not only validates LLMs as judges but also reveals that autoformalization is inherently difficult: even human experts produce semantic errors in up to 38.5% of cases.

Following natural instructions is crucial for the effective application of Retrieval-Augmented Generation (RAG) systems. Despite recent advancements in Large Language Models (LLMs), research on assessing and improving instruction-following (IF) alignment within the RAG domain remains limited. To address this issue, we propose VIF-RAG, the first automated, scalable, and verifiable synthetic pipeline for instruction-following alignment in RAG systems. We start by manually crafting a minimal set of atomic instructions (<100) and developing combination rules to synthesize and verify complex instructions for a seed set. We then use supervised models for instruction rewriting while simultaneously generating code to automate the verification of instruction quality via a Python executor. Finally, we integrate these instructions with extensive RAG and general data samples, scaling up to a high-quality VIF-RAG-QA dataset (>100k) through automated processes. To further bridge the gap in instruction-following auto-evaluation for RAG systems, we introduce FollowRAG Benchmark, which includes approximately 3K test samples, covering 22 categories of general instruction constraints and four knowledge-intensive QA datasets. Due to its robust pipeline design, FollowRAG can seamlessly integrate with different RAG benchmarks. Using FollowRAG and eight widely-used IF and foundational abilities benchmarks for LLMs, we demonstrate that VIF-RAG markedly enhances LLM performance across a broad range of general instruction constraints while effectively leveraging its capabilities in RAG scenarios. Further analysis offers practical insights for achieving IF alignment in RAG systems. Our code and datasets are released at https://FollowRAG.github.io.

Looped Transformers provide advantages in parameter efficiency, computational capabilities, and generalization for reasoning tasks. However, their expressive power regarding function approximation remains underexplored. In this paper, we establish the approximation rate of Looped Transformers by defining the modulus of continuity for sequence-to-sequence functions. This reveals a limitation specific to the looped architecture. That is, the analysis prompts the incorporation of scaling parameters for each loop, conditioned on timestep encoding. Experiments validate the theoretical results, showing that increasing the number of loops enhances performance, with further gains achieved through the timestep encoding.

Deep Learning architectures, and in particular Transformers, are conventionally viewed as a composition of layers. These layers are actually often obtained as the sum of two contributions: a residual path that copies the input and the output of a Transformer block. As a consequence, the inner representations (i.e. the input of these blocks) can be interpreted as iterative refinement of a propagated latent representation. Under this lens, many works suggest that the inner space is shared across layers, meaning that tokens can be decoded at early stages. Mechanistic interpretability even goes further by conjecturing that some layers act as refinement layers. Following this path, we propose inference-time inner looping, which prolongs refinement in pretrained off-the-shelf language models by repeatedly re-applying a selected block range. Across multiple benchmarks, inner looping yields modest but consistent accuracy improvements. Analyses of the resulting latent trajectories suggest more stable state evolution and continued semantic refinement. Overall, our results suggest that additional refinement can be obtained through simple test-time looping, extending computation in frozen pretrained models.

Prior work has shown that finetuning large language models (LLMs) using machine-generated instruction-following data enables such models to achieve remarkable zero-shot capabilities on new tasks, and no human-written instructions are needed. In this paper, we present the first attempt to use GPT-4 to generate instruction-following data for LLM finetuning. Our early experiments on instruction-tuned LLaMA models show that the 52K English and Chinese instruction-following data generated by GPT-4 leads to superior zero-shot performance on new tasks to the instruction-following data generated by previous state-of-the-art models. We also collect feedback and comparison data from GPT-4 to enable a comprehensive evaluation and reward model training. We make our data generated using GPT-4 as well as our codebase publicly available.

Recent work on looped language models suggests that many reasoning problems benefit from greater computational depth rather than from additional independent parameters. Existing studies, however, focus almost exclusively on Transformer backbones, leaving open whether this principle also applies to state-space language models. We investigate Looped Mamba and Looped Hybrid Mamba-Transformer architectures, which repeatedly apply a shared Mamba (or hybrid) block to introduce explicit finite-depth recurrent computation. On two controlled reasoning tasks-Mano (modular-arithmetic manipulation) and p-hop induction-Looped Mamba consistently outperforms parameter-matched non-looped baselines and, in several settings, matches or exceeds non-looped models of equal effective depth. We then extend the study to language model pre-training under matched iso-parameter and iso-FLOPs protocols, which jointly disentangle the effects of parameter sharing and effective depth: looped models remain competitive on downstream benchmarks with substantially fewer distinct parameters, although deeper non-looped models retain an advantage in validation perplexity under strict iso-FLOPs comparisons. Finally, we adapt Ouro's two-stage exit gate to Looped Mamba for threshold-controlled selection among recurrent-step outputs. Since all recurrent steps are still executed, the selected exit step represents prediction depth rather than reduced wall-clock computation. At the scales studied, adaptive exit-state selection improves downstream performance at intermediate depths, while actual inference-time savings require additional state-handling mechanisms.

In large language model training, input documents are typically concatenated together and then split into sequences of equal length to avoid padding tokens. Despite its efficiency, the concatenation approach compromises data integrity -- it inevitably breaks many documents into incomplete pieces, leading to excessive truncations that hinder the model from learning to compose logically coherent and factually consistent content that is grounded on the complete context. To address the issue, we propose Best-fit Packing, a scalable and efficient method that packs documents into training sequences through length-aware combinatorial optimization. Our method completely eliminates unnecessary truncations while retaining the same training efficiency as concatenation. Empirical results from both text and code pre-training show that our method achieves superior performance (e.g., relatively +4.7% on reading comprehension; +16.8% in context following; and +9.2% on program synthesis), and reduces closed-domain hallucination effectively by up to 58.3%.

Multistep instructions, such as recipes and how-to guides, greatly benefit from visual aids, such as a series of images that accompany the instruction steps. While Large Language Models (LLMs) have become adept at generating coherent textual steps, Large Vision/Language Models (LVLMs) are less capable of generating accompanying image sequences. The most challenging aspect is that each generated image needs to adhere to the relevant textual step instruction, as well as be visually consistent with earlier images in the sequence. To address this problem, we propose an approach for generating consistent image sequences, which integrates a Latent Diffusion Model (LDM) with an LLM to transform the sequence into a caption to maintain the semantic coherence of the sequence. In addition, to maintain the visual coherence of the image sequence, we introduce a copy mechanism to initialise reverse diffusion processes with a latent vector iteration from a previously generated image from a relevant step. Both strategies will condition the reverse diffusion process on the sequence of instruction steps and tie the contents of the current image to previous instruction steps and corresponding images. Experiments show that the proposed approach is preferred by humans in 46.6% of the cases against 26.6% for the second best method. In addition, automatic metrics showed that the proposed method maintains semantic coherence and visual consistency across steps in both domains.

For a complicated algorithm, its implementation by a human programmer usually starts with outlining a rough control flow followed by iterative enrichments, eventually yielding carefully generated syntactic structures and variables in a hierarchy. However, state-of-the-art large language models generate codes in a single pass, without intermediate warm-ups to reflect the structured thought process of "outline-then-detail". Inspired by the recent success of chain-of-thought prompting, we propose ChainCoder, a program synthesis language model that generates Python code progressively, i.e. from coarse to fine in multiple passes. We first decompose source code into layout frame components and accessory components via abstract syntax tree parsing to construct a hierarchical representation. We then reform our prediction target into a multi-pass objective, each pass generates a subsequence, which is concatenated in the hierarchy. Finally, a tailored transformer architecture is leveraged to jointly encode the natural language descriptions and syntactically aligned I/O data samples. Extensive evaluations show that ChainCoder outperforms state-of-the-arts, demonstrating that our progressive generation eases the reasoning procedure and guides the language model to generate higher-quality solutions. Our codes are available at: https://github.com/VITA-Group/ChainCoder.

Mixture-of-Experts (MoE) and looped architectures scale models along two orthogonal axes, namely parameter capacity and effective depth. However, mainstream looped architectures rely on dense backbones that couple parameter count with per-token FLOPs, which makes it impossible to isolate the effect of iterative computation under matched budgets. To this end, we present LoopMoE, a looped MoE language model that integrates sparse routing with iterative weight-shared computation through two designs. The first is IterAdaLN, which resolves weight-sharing symmetry via a modulation signal jointly conditioned on the iteration index and the per-token hidden state. The second is a capacity-balancing strategy that recovers the attention-to-FFN active parameter ratio of well-tuned non-looped references. Together, these designs enable the first strictly controlled, head-to-head evaluation of a looped MoE against a Vanilla MoE under identical total parameters, per-token FLOPs, and active sublayer ratios. At the 3B scale, LoopMoE outperforms the Vanilla MoE on 8 of 9 downstream benchmarks with an average improvement exceeding 1 point. At the 9B scale, LoopMoE continues to outperform the matched Vanilla MoE, indicating that the architectural gain persists at larger scale. Our work establishes a controlled synthesis of sparsity and recurrence, and suggests a promising direction for looped language models.

Best-of-N decoding methods instruct large language models (LLMs) to generate multiple solutions, score each using a scoring function, and select the highest scored as the final answer to mathematical reasoning problems. However, this repeated independent process often leads to the same mistakes, making the selected solution still incorrect. We propose a novel prompting method named Stepwise Correction (StepCo) that helps LLMs identify and revise incorrect steps in their generated reasoning paths. It iterates verification and revision phases that employ a process-supervised verifier. The verify-then-revise process not only improves answer correctness but also reduces token consumption with fewer paths needed to generate. With StepCo, a series of LLMs demonstrate exceptional performance. Notably, using GPT-4o as the backend LLM, StepCo achieves an average accuracy of 94.1 across eight datasets, significantly outperforming the state-of-the-art Best-of-N method by +2.4, while reducing token consumption by 77.8%.

High-quality pretraining data is the fossil fuel of large language models (LLMs), yet its reserves are running low for frontier models. In this paper, we introduce RePro, a novel web recycling method that trains a relatively small LM with reinforcement learning to generate effective and faithful rephrasings of pretraining data. Specifically, we design one quality reward and three faithfulness rewards, optimizing the LM rephraser to convert organic data into high-quality rephrasings while maintaining its core semantics and structure. In our experiment, we train a 4B rephraser to recycle 72B tokens sampled from DCLM-RefinedWeb. Pretraining results on 400M and 1.4B models demonstrate that RePro delivers 4.7%-14.0% relative accuracy gains over organic-only baseline on 22 downstream tasks. RePro also outperforms ReWire, the state-of-the-art web recycling method that prompts a 70B rephraser, as well as the organic baseline with a 4x larger data pool. Experiments with different amounts of recycled data highlight that RePro improves organic data efficiency by 2-3x. Individual and distributional analyses validate that RePro preserves more critical information and faithfully reflects the characteristics of organic data compared to prompting-based methods. Together, these results show that RePro provides an efficient and controllable path to effectively harness the fossil fuel of LLM pretraining. We open-source our code, rephraser, and recycled data at https://github.com/cxcscmu/RePro.

Transformers have demonstrated effectiveness in in-context solving data-fitting problems from various (latent) models, as reported by Garg et al. However, the absence of an inherent iterative structure in the transformer architecture presents a challenge in emulating the iterative algorithms, which are commonly employed in traditional machine learning methods. To address this, we propose the utilization of looped transformer architecture and its associated training methodology, with the aim of incorporating iterative characteristics into the transformer architectures. Experimental results suggest that the looped transformer achieves performance comparable to the standard transformer in solving various data-fitting problems, while utilizing less than 10\% of the parameter count.

In this work, we investigate a typical scenario in code generation where a developer edits existing code in real time and requests a code assistant, e.g., a large language model, to re-predict the next token or next line on the fly. Naively, the LLM needs to re-encode the entire KV cache to provide an accurate prediction. However, this process is computationally expensive, especially when the sequence length is long. Simply encoding the edited subsequence and integrating it to the original KV cache meets the temporal confusion problem, leading to significantly worse performance. We address this efficiency and accuracy trade-off by introducing \textbf{Positional \textbf{Integrity Encoding} (PIE). Building upon the rotary positional encoding, PIE first removes the rotary matrices in the Key cache that introduce temporal confusion and then reapplies the correct rotary matrices. This process ensures that positional relationships between tokens are correct and requires only a single round of matrix multiplication. We validate the effectiveness of PIE through extensive experiments on the RepoBench-C-8k dataset, utilizing DeepSeek-Coder models with 1.3B, 6.7B, and 33B parameters. Our evaluation includes three real-world coding tasks: code insertion, code deletion, and multi-place code editing. Results demonstrate that PIE reduces computational overhead by over 85% compared to the standard full recomputation approach across all model sizes and tasks while well approximating the model performance.

Despite the power of Large Language Models (LLMs) like GPT-4, they still struggle with tasks that require generating complex, structured outputs. In this study, we assess the capability of Current LLMs in generating complex structured data and propose a structure-aware fine-tuning approach as a solution to improve this ability. To perform a comprehensive evaluation, we propose Struc-Bench, include five representative LLMs (i.e., GPT-NeoX 20B, GPT-3.5, GPT-4, and Vicuna) and evaluate them on our carefully constructed datasets spanning raw text, HTML, and LaTeX tables. Based on our analysis of current model performance, we identify specific common formatting errors and areas of potential improvement. To address complex formatting requirements, we utilize FormatCoT (Chain-of-Thought) to generate format instructions from target outputs. Our experiments show that our structure-aware fine-tuning method, when applied to LLaMA-7B, significantly improves adherence to natural language constraints, outperforming other evaluated LLMs. Based on these results, we present an ability map of model capabilities from six dimensions (i.e., coverage, formatting, reasoning, comprehension, pragmatics, and hallucination). This map highlights the weaknesses of LLMs in handling complex structured outputs and suggests promising directions for future work. Our code and models can be found at https://github.com/gersteinlab/Struc-Bench.

When unsure about an answer, humans often respond with more words than necessary, hoping that part of the response will be correct. We observe a similar behavior in large language models (LLMs), which we term "Verbosity Compensation" (VC). VC is harmful because it confuses the user understanding, leading to low efficiency, and influences the LLM services by increasing the latency and cost of generating useless tokens. In this paper, we present the first work that defines and analyzes Verbosity Compensation, explores its causes, and proposes a simple mitigating approach. We define Verbosity Compensation as the behavior of generating responses that can be compressed without information loss when prompted to write concisely. Our experiments, conducted on five datasets of knowledge and reasoning-based QA tasks with 14 newly developed LLMs, reveal three conclusions. 1) We reveal a pervasive presence of verbosity compensation across all models and all datasets. Notably, GPT-4 exhibits a VC frequency of 50.40%. 2) We reveal the large performance gap between verbose and concise responses, with a notable difference of 27.61% on the Qasper dataset. We also demonstrate that this difference does not naturally diminish as LLM capability increases. Both 1) and 2) highlight the urgent need to mitigate the frequency of VC behavior and disentangle verbosity with veracity. We propose a simple yet effective cascade algorithm that replaces the verbose responses with the other model-generated responses. The results show that our approach effectively alleviates the VC of the Mistral model from 63.81% to 16.16% on the Qasper dataset. 3) We also find that verbose responses exhibit higher uncertainty across all five datasets, suggesting a strong connection between verbosity and model uncertainty. Our dataset and code are available at https://github.com/psunlpgroup/VerbosityLLM.

Code generation with Large Language Models (LLMs) has helped to increase software developer productivity in coding tasks, but has yet to have significant impact on the tasks of software developers that surround this code. In particular, the challenge of infrastructure management remains an open question. We investigate the ability of an LLM agent to construct infrastructure using the Infrastructure as Code (IaC) paradigm. We particularly investigate the use of a feedback loop that returns errors and warnings on the generated IaC to allow the LLM agent to improve the code. We find that, for each iteration of the loop, its effectiveness decreases exponentially until it plateaus at a certain point and becomes ineffective.

Recently, it was shown that small, looped architectures, such as Tiny Recursive Models (TRMs), can outperform Large Language Models (LLMs) on complex reasoning tasks, including the Abstraction and Reasoning Corpus (ARC). In this work, we investigate a core question: how can we further improve the efficiency of these methods with minimal changes? To address this, we frame the latent reasoning of TRMs as a form of classifier-free guidance and implicit policy improvement algorithm. Building on these insights, we propose a novel training scheme that provides a target for each loop during training. We demonstrate that our approach significantly enhances training efficiency. Our method reduces the total number of forward passes by 18x and eliminates halting mechanisms, while maintaining quality comparable to standard TRMs. Notably, we achieve 24% accuracy on ARC-1 with only 0.8M parameters, outperforming most LLMs.

Natural language to code generation is an important application area of LLMs and has received wide attention from the community. The majority of relevant studies have exclusively concentrated on increasing the quantity and functional correctness of training sets while disregarding other stylistic elements of programs. More recently, data quality has garnered a lot of interest and multiple works have showcased its importance for improving performance. In this work, we investigate data quality for code and find that making the code more structured and readable leads to improved code generation performance of the system. We build a novel data-cleaning pipeline that uses these principles to transform existing programs by 1.) renaming variables, 2.) modularizing and decomposing complex code into smaller helper sub-functions, and 3.) inserting natural-language based plans via LLM based transformations. We evaluate our approach on two challenging algorithmic code generation benchmarks and find that fine-tuning CodeLLaMa-7B on our transformed modularized programs improves the performance by up to 30% compared to fine-tuning on the original dataset. Additionally, we demonstrate improved performance from using a smaller amount of higher-quality data, finding that a model fine-tuned on the entire original dataset is outperformed by a model trained on 15% of our cleaned dataset. Even in comparison to closed-source models, our models outperform the much larger AlphaCoder models.

Software engineers mainly write code by editing existing programs. In contrast, large language models (LLMs) autoregressively synthesize programs in a single pass. One explanation for this is the scarcity of open-sourced edit data. While high-quality instruction data for code synthesis is already scarce, high-quality edit data is even scarcer. To fill this gap, we develop a synthetic data generation algorithm called LintSeq. This algorithm refactors existing code into a sequence of code edits by using a linter to procedurally sample across the error-free insertions that can be used to sequentially write programs. It outputs edit sequences as text strings consisting of consecutive program diffs. To test LintSeq, we use it to refactor a dataset of instruction + program pairs into instruction + program-diff-sequence tuples. Then, we instruction finetune a series of smaller LLMs ranging from 2.6B to 14B parameters on both the re-factored and original versions of this dataset, comparing zero-shot performance on code synthesis benchmarks. We show that during repeated sampling, edit sequence finetuned models produce more diverse programs than baselines. This results in better inference-time scaling for benchmark coverage as a function of samples, i.e. the fraction of problems "pass@k" solved by any attempt given "k" tries. For example, on HumanEval pass@50, small LLMs finetuned on synthetic edit sequences are competitive with GPT-4 and outperform models finetuned on the baseline dataset by +20% (+/-3%) in absolute score. Finally, we also pretrain our own tiny LMs for code understanding. We show that finetuning tiny models on synthetic code edits results in state-of-the-art code synthesis for the on-device model class. Our 150M parameter edit sequence LM matches or outperforms code models with twice as many parameters, both with and without repeated sampling, including Codex and AlphaCode.

Finetuning large language models with a variety of instruction-response pairs has enhanced their capability to understand and follow instructions. Current instruction tuning primarily relies on teacher models or human intervention to generate and refine the instructions and responses, which are costly, non-sustainable, and may lack diversity. In this paper, we introduce Mosaic Instruction Tuning (Mosaic-IT), a human/model-free method that can efficiently create rich and diverse augmentations from existing instruction tuning data to enhance the finetuned LLM.Mosaic-IT randomly concatenates multiple instruction data into one and trains the model to produce the corresponding responses with predefined higher-level meta-instructions to strengthen its multi-step instruction-following and format-following skills. Our extensive evaluations demonstrate a superior performance and training efficiency of Mosaic-IT, which achieves consistent performance improvements over various benchmarks and an 80% reduction in training costs compared with original instruction tuning. Our codes and data are available at https://github.com/tianyi-lab/Mosaic-IT.

We present a series of long-context LLMs that support effective context windows of up to 32,768 tokens. Our model series are built through continual pretraining from Llama 2 with longer training sequences and on a dataset where long texts are upsampled. We perform extensive evaluation on language modeling, synthetic context probing tasks, and a wide range of research benchmarks. On research benchmarks, our models achieve consistent improvements on most regular tasks and significant improvements on long-context tasks over Llama 2. Notably, with a cost-effective instruction tuning procedure that does not require human-annotated long instruction data, the 70B variant can already surpass gpt-3.5-turbo-16k's overall performance on a suite of long-context tasks. Alongside these results, we provide an in-depth analysis on the individual components of our method. We delve into Llama's position encodings and discuss its limitation in modeling long dependencies. We also examine the impact of various design choices in the pretraining process, including the data mix and the training curriculum of sequence lengths -- our ablation experiments suggest that having abundant long texts in the pretrain dataset is not the key to achieving strong performance, and we empirically verify that long context continual pretraining is more efficient and similarly effective compared to pretraining from scratch with long sequences.

In this paper, we study how to improve the zero-shot reasoning ability of large language models~(LLMs) over structured data in a unified way. Inspired by the study on tool augmentation for LLMs, we develop an Iterative Reading-then-Reasoning~(IRR) approach for solving question answering tasks based on structured data, called StructGPT. In our approach, we construct the specialized function to collect relevant evidence from structured data (\ie reading), and let LLMs concentrate the reasoning task based on the collected information (\ie reasoning). Specially, we propose an invoking-linearization-generation procedure to support LLMs in reasoning on the structured data with the help of the external interfaces. By iterating this procedures with provided interfaces, our approach can gradually approach the target answer to a given query. Extensive experiments conducted on three types of structured data demonstrate the effectiveness of our approach, which can significantly boost the performance of ChatGPT and achieve comparable performance against the full-data supervised-tuning baselines. Our codes and data are publicly available at~https://github.com/RUCAIBox/StructGPT.

Recurrent LLM architectures have emerged as a promising approach for improving reasoning, as they enable multi-step computation in the embedding space without generating intermediate tokens. Models such as Ouro perform reasoning by iteratively updating internal representations while retaining a standard Key-Value (KV) cache across iterations, causing memory consumption to grow linearly with reasoning depth. Consequently, increasing the number of reasoning iterations can lead to prohibitive memory usage, limiting the practical scalability of such architectures. In this work, we propose Memory-Efficient Looped Transformer (MELT), a novel architecture that decouples reasoning depth from memory consumption. Instead of using a standard KV cache per layer and loop, MELT maintains a single KV cache per layer that is shared across reasoning loops. This cache is updated over time via a learnable gating mechanism. To enable stable and efficient training under this architecture, we propose to train MELT using chunk-wise training in a two phase procedure: interpolated transition, followed by attention-aligned distillation, both from the LoopLM starting model to MELT. Empirically, we show that MELT models fine-tuned from pretrained Ouro parameters outperform standard LLMs of comparable size, while maintaining a memory footprint comparable to those models and dramatically smaller than Ouro's. Overall, MELT achieves constant-memory iterative reasoning without sacrificing LoopLM performance, using only a lightweight post-training procedure.

Language models are increasingly used in scientific discovery to generate hypotheses, propose candidate solutions, implement systems, and iteratively refine them. At the core of these trial-and-error loops lies evaluation: the process of obtaining feedback on candidate solutions via verifiers, simulators, or task-specific scoring functions. While prior work has highlighted the importance of evaluation, it has not explicitly formulated the problem of how evaluation-driven discovery loops can be scaled up in a principled and effective manner to push the boundaries of scientific discovery, a problem this paper seeks to address. We introduce Simple Test-time Evaluation-driven Scaling (SimpleTES), a general framework that strategically combines parallel exploration, feedback-driven refinement, and local selection, revealing substantial gains unlocked by scaling evaluation-driven discovery loops along the right dimensions. Across 21 scientific problems spanning six domains, SimpleTES discovers state-of-the-art solutions using gpt-oss models, consistently outperforming both frontier-model baselines and sophisticated optimization pipelines. Particularly, we sped up the widely used LASSO algorithm by over 2x, designed quantum circuit routing policies that reduce gate overhead by 24.5%, and discovered new Erdos minimum overlap constructions that surpass the best-known results. Beyond novel discoveries, SimpleTES produces trajectory-level histories that naturally supervise feedback-driven learning. When post-trained on successful trajectories, models not only improve efficiency on seen problems but also generalize to unseen problems, discovering solutions that base models fail to uncover. Together, our results establish effective evaluation-driven loop scaling as a central axis for advancing LLM-driven scientific discovery, and provide a simple yet practical framework for realizing these gains.

Recent Long-Context Language Models (LCLMs) can process hundreds of thousands of tokens in a single prompt, enabling new opportunities for knowledge-intensive multi-hop reasoning by integrating large sets of retrieved documents or, in some cases, directly all necessary information. However, simply feeding more documents into the context window fails to capture how evidence should be connected. We address this gap with thought templates, which recast reasoning as reusable thought caches, derived from prior problem solving traces, structuring how evidence is combined and guiding multi-hop inference with factual documents. To keep these templates effective, we propose an update strategy that iteratively refines templates derived from training data through natural-language feedback. Across diverse benchmarks and LCLM families, our approach delivers consistent gains over strong baselines in both retrieval-based and retrieval-free settings. Furthermore, we show that optimized templates can be distilled into smaller open-source models, demonstrating its broad applicability and transparent reasoning reuse. We refer to our framework as Thought Template Augmented LCLMs (ToTAL).

Latent-reasoning looped language models (LoopLMs) offer a different scaling path for machine translation (MT): instead of increasing parameter count or emitting explicit chain-of-thought tokens, they spend additional recurrent computation inside hidden states. We introduce LatentMT, the first systematic study of latent-reasoning LoopLMs for machine translation. LatentMT adapts a small 2.6B-parameter backbone model with lightweight training. Across 32 translation directions spanning high-, mid-, and low-resource languages, LatentMT achieves performance comparable to models three to five times larger. It is competitive in a high-resource language and achieves state-of-the-art performance on both mid-resource and low-resource languages. Studying the behavior of scaling the number of recurrent reasoning steps, we find that recurrent computation consistently improves translation quality in early steps, then saturates quickly afterwards. Our mechanistic analysis shows that hidden-representation differences shrink along the recurrent reasoning-step axis, supporting the observed saturation in performance. Finally, our efficiency analysis shows that LatentMT requires lower training and inference compute than much larger non-latent-reasoning models with similar performance, making latent recurrent computation a promising path toward compact, efficient, and strong machine translation.

Large pre-trained language models perform remarkably well on tasks that can be done "in one pass", such as generating realistic text or synthesizing computer programs. However, they struggle with tasks that require unbounded multi-step computation, such as adding integers or executing programs. Surprisingly, we find that these same models are able to perform complex multi-step computations -- even in the few-shot regime -- when asked to perform the operation "step by step", showing the results of intermediate computations. In particular, we train transformers to perform multi-step computations by asking them to emit intermediate computation steps into a "scratchpad". On a series of increasingly complex tasks ranging from long addition to the execution of arbitrary programs, we show that scratchpads dramatically improve the ability of language models to perform multi-step computations.

This work introduces a general code generation framework that incorporates infilling operations into auto-regressive decoding. Our approach capitalizes on the observation that recent code language models with infilling capabilities can perform self-infilling: whereas infilling operations aim to fill in the middle based on a predefined prefix and suffix, self-infilling sequentially generates both such surrounding context and the infilled content. We utilize this feature to develop an infilling-augmented decoding process that facilitates non-monotonic generation. This approach allows for postponing the generation of uncertain code snippets until a definitive suffix is established, leading to improved control over the generation sequence. In addition, it facilitates a looping mechanism, which can iteratively update and synchronize each piece of generation in a cyclic manner. Extensive experiments are conducted to demonstrate that our proposed decoding process is effective in enhancing regularity and quality across several code generation benchmarks.

Scaling model performance typically requires increasing model size. Looped Transformer offers a compelling alternative by iteratively reusing the same Transformer blocks, trading additional computation for improved performance without increasing parameter count or context length. Because the number of loop iterations can be adjusted at inference, it also provides a natural mechanism for balancing performance and test-time compute. However, Looped Transformer still suffers from training instability when the number of loop iterations increases. Our analysis reveals that this instability stems from two sources: gradient oscillation and residual explosion. To address these two problems, we propose the Fully Looped Transformer, which introduces two parameter-free modifications: (1) Fully Looped Architecture, which distributes inter-loop signals across all layers to mitigate residual explosion; (2) Attention Injection, which reuses the existing attention block to suppress gradient oscillation. These modifications stabilize training dynamics, enabling the Fully Looped Transformer to be trained stably up to 12 loop iterations, whereas other baseline looped models collapse in this regime. In milder settings where Looped Transformer does not collapse, Fully Looped Transformer still improves average downstream-task performance by up to 13.2\%. Overall, our experiments demonstrate that Fully Looped Transformer improves training stability, enhances downstream performance, and provides preliminary adaptability under different test-time compute budgets by varying loop iterations at inference.

Producing outputs that satisfy both semantic intent and format constraints is essential for deploying large language models in user-facing and system-integrated workflows. In this work, we focus on Markdown formatting, which is ubiquitous in assistants, documentation, and tool-augmented pipelines but still prone to subtle, hard-to-detect errors (e.g., broken lists, malformed tables, inconsistent headings, and invalid code blocks) that can significantly degrade downstream usability. We present FMBench, a benchmark for adaptive Markdown output formatting that evaluates models under a wide range of instruction-following scenarios with diverse structural requirements. FMBench emphasizes real-world formatting behaviors such as multi-level organization, mixed content (natural language interleaved with lists/tables/code), and strict adherence to user-specified layout constraints. To improve Markdown compliance without relying on hard decoding constraints, we propose a lightweight alignment pipeline that combines supervised fine-tuning (SFT) with reinforcement learning fine-tuning. Starting from a base model, we first perform SFT on instruction-response pairs, and then optimize a composite objective that balances semantic fidelity with structural correctness. Experiments on two model families (OpenPangu and Qwen) show that SFT consistently improves semantic alignment, while reinforcement learning provides additional gains in robustness to challenging Markdown instructions when initialized from a strong SFT policy. Our results also reveal an inherent trade-off between semantic and structural objectives, highlighting the importance of carefully designed rewards for reliable formatted generation. Code is available at: https://github.com/FudanCVL/FMBench.

If we cannot inspect the training data of a large language model (LLM), how can we ever know what it has seen? We believe the most compelling evidence arises when the model itself freely reproduces the target content. As such, we propose RECAP, an agentic pipeline designed to elicit and verify memorized training data from LLM outputs. At the heart of RECAP is a feedback-driven loop, where an initial extraction attempt is evaluated by a secondary language model, which compares the output against a reference passage and identifies discrepancies. These are then translated into minimal correction hints, which are fed back into the target model to guide subsequent generations. In addition, to address alignment-induced refusals, RECAP includes a jailbreaking module that detects and overcomes such barriers. We evaluate RECAP on EchoTrace, a new benchmark spanning over 30 full books, and the results show that RECAP leads to substantial gains over single-iteration approaches. For instance, with GPT-4.1, the average ROUGE-L score for the copyrighted text extraction improved from 0.38 to 0.47 - a nearly 24% increase.

Large language models (LLMs) are commonly trained on datasets consisting of fixed-length token sequences. These datasets are created by randomly concatenating documents of various lengths and then chunking them into sequences of a predetermined target length. However, this method of concatenation can lead to cross-document attention within a sequence, which is neither a desirable learning signal nor computationally efficient. Additionally, training on long sequences becomes computationally prohibitive due to the quadratic cost of attention. In this study, we introduce dataset decomposition, a novel variable sequence length training technique, to tackle these challenges. We decompose a dataset into a union of buckets, each containing sequences of the same size extracted from a unique document. During training, we use variable sequence length and batch size, sampling simultaneously from all buckets with a curriculum. In contrast to the concat-and-chunk baseline, which incurs a fixed attention cost at every step of training, our proposed method incurs a penalty proportional to the actual document lengths at each step, resulting in significant savings in training time. We train an 8k context-length 1B model at the same cost as a 2k context-length model trained with the baseline approach. Experiments on a web-scale corpus demonstrate that our approach significantly enhances performance on standard language evaluations and long-context benchmarks, reaching target accuracy 3x faster compared to the baseline. Our method not only enables efficient pretraining on long sequences but also scales effectively with dataset size. Lastly, we shed light on a critical yet less studied aspect of training large language models: the distribution and curriculum of sequence lengths, which results in a non-negligible difference in performance.

Existing benchmarks for evaluating long-context language models (LCLMs) primarily focus on long-context recall, requiring models to produce short responses based on a few critical snippets while processing thousands of irrelevant tokens. We introduce LongProc (Long Procedural Generation), a new benchmark that requires both the integration of highly dispersed information and long-form generation. LongProc consists of six diverse procedural generation tasks, such as extracting structured information from HTML pages into a TSV format and executing complex search procedures to create travel plans. These tasks challenge LCLMs by testing their ability to follow detailed procedural instructions, synthesize and reason over dispersed information, and generate structured, long-form outputs (up to 8K tokens). Furthermore, as these tasks adhere to deterministic procedures and yield structured outputs, they enable reliable rule-based evaluation. We evaluate 17 LCLMs on LongProc across three difficulty levels, with maximum numbers of output tokens set at 500, 2K, and 8K. Notably, while all tested models claim a context window size above 32K tokens, open-weight models typically falter on 2K-token tasks, and closed-source models like GPT-4o show significant degradation on 8K-token tasks. Further analysis reveals that LCLMs struggle to maintain long-range coherence in long-form generations. These findings highlight critical limitations in current LCLMs and suggest substantial room for improvement. Data and code available at: https://princeton-pli.github.io/LongProc

Looped architectures provide an inductive bias toward learning step-by-step procedures for tasks that require compositional reasoning. The number of effective layers reached by looping determines the quality of the solution these models find. Like deep architectures, looped architectures are prone to a signal propagation problem induced by depth as the halting decision is postponed. In this paper, we address this signal propagation issue using pre-norm layers and residual scaling. Building on these architectural modifications, we propose FPRM, a Transformer-based Fixed-Point Reasoning Model that uses fixed-point convergence as an end-to-end halting mechanism in a looped architecture. We show that fixed-point halting allows FPRM to adapt its compute to task difficulty. FPRM is effective on common reasoning benchmarks, namely Sudoku, Maze, state-tracking, and ARC-AGI.

Recently, multimodal large language models (MLLMs) have attracted increasing research attention due to their powerful visual understanding capabilities. While they have achieved impressive results on various vision tasks, their performance on chart-to-code generation remains suboptimal. This task requires MLLMs to generate executable code that can reproduce a given chart, demanding not only precise visual understanding but also accurate translation of visual elements into structured code. Directly prompting MLLMs to perform this complex task often yields unsatisfactory results. To address this challenge, we propose {ChartIR}, an iterative refinement method based on structured instruction. First, we distinguish two tasks: visual understanding and code translation. To accomplish the visual understanding component, we design two types of structured instructions: description and difference. The description instruction captures the visual elements of the reference chart, while the difference instruction characterizes the discrepancies between the reference chart and the generated chart. These instructions effectively transform visual features into language representations, thereby facilitating the subsequent code translation process. Second, we decompose the overall chart generation pipeline into two stages: initial code generation and iterative refinement, enabling progressive enhancement of the final output. Experimental results show that, compared to other method, our method achieves superior performance on both the open-source model Qwen2-VL and the closed-source model GPT-4o.

This paper introduces corpus-guided top-down synthesis as a mechanism for synthesizing library functions that capture common functionality from a corpus of programs in a domain specific language (DSL). The algorithm builds abstractions directly from initial DSL primitives, using syntactic pattern matching of intermediate abstractions to intelligently prune the search space and guide the algorithm towards abstractions that maximally capture shared structures in the corpus. We present an implementation of the approach in a tool called Stitch and evaluate it against the state-of-the-art deductive library learning algorithm from DreamCoder. Our evaluation shows that Stitch is 3-4 orders of magnitude faster and uses 2 orders of magnitude less memory while maintaining comparable or better library quality (as measured by compressivity). We also demonstrate Stitch's scalability on corpora containing hundreds of complex programs that are intractable with prior deductive approaches and show empirically that it is robust to terminating the search procedure early -- further allowing it to scale to challenging datasets by means of early stopping.

The integration of retrieved passages and large language models (LLMs), such as ChatGPTs, has significantly contributed to improving open-domain question answering. However, there is still a lack of exploration regarding the optimal approach for incorporating retrieved passages into the answer generation process. This paper aims to fill this gap by investigating different methods of combining retrieved passages with LLMs to enhance answer generation. We begin by examining the limitations of a commonly-used concatenation approach. Surprisingly, this approach often results in generating "unknown" outputs, even when the correct document is among the top-k retrieved passages. To address this issue, we explore four alternative strategies for integrating the retrieved passages with the LLMs. These strategies include two single-round methods that utilize chain-of-thought reasoning and two multi-round strategies that incorporate feedback loops. Through comprehensive analyses and experiments, we provide insightful observations on how to effectively leverage retrieved passages to enhance the answer generation capability of LLMs.

Turning a frontier vision-language model into a robot policy usually means fine-tuning it to emit an action representation it never saw in pretraining, which throws away much of the reasoning that made the model worth reaching for. We go the other way and keep the VLM frozen. It writes the policy as a short Python control function, with no demonstrations and no fine-tuning. Writing that code once is open-loop, though. Existing closed-loop methods react at the wrong level: they retry a fixed policy or pick a different subtask, but never rewrite the code that failed. VLCP closes the loop where the failure actually lives, on the control code, within a single episode. Every K steps the VLM re-observes the scene from multi-view RGB, proprioceptive state, and a state delta, then rewrites the control function from what it just saw, so a failure is caught before it compounds. We evaluate on a 57-task MuJoCo/RoboVerse sweep. This training-free policy reaches 35.1% pooled success, against 3.5% for the identical system queried once per episode. That tenfold gap holds with non-overlapping confidence intervals in every scene family. The gain traces to a 27.3% within-episode recovery rate on failed grasps: a miss an open-loop controller would carry to the end of the episode gets re-observed and fixed at the next replan. And the loop stays cheap. A median 84% of input tokens hit cache, an episode needs only about 10 compact queries, and control blocks written during any replan persist to a cross-episode skill library reused in later prompts.

Recently, given the docstring for the target problem and the target function signature, large language models (LLMs) have been used not only to generate source code, but also to generate test cases, consisting of test inputs and assertions (e.g., in the form of checking an actual output against the expected output). However, as shown by our empirical study on assertions generated by four LLMs for the HumanEval benchmark, over 62% of the generated assertions are incorrect (i.e., failed on the ground-truth problem solution). To detect incorrect assertions (given the docstring and the target function signature along with a sample of example inputs and outputs), in this paper, we propose a new approach named DeCon to effectively detect incorrect assertions via LLM-generated postconditions for the target problem (a postcondition is a predicate that must always be true just after the execution of the ground-truth problem solution). Our approach requires a small set of I/O examples (i.e., a sample of example inputs and outputs) for the target problem (e.g., the I/O examples included in the docstring for a target problem in HumanEval). We use the given I/O examples to filter out those LLM-generated postconditions that are violated by at least one given I/O example. We then use the remaining postconditions to detect incorrect assertions as those assertions that violate at least one remaining postcondition. Experimental results show that DeCon can detect averagely more than 64% (63% and 65.5% detected by GPT-3.5 and GPT-4, respectively) incorrect assertions generated by four state-of-the-art LLMs, and DeCon can also improve the effectiveness of these LLMs in code generation by 4% in terms of Pass@1. In addition, although DeCon might filter out correct assertions, the fault-finding ability of the remaining correct assertions decreases only slightly.

Multimodal Large Language Models (MLLMs) have shown significant promise in various applications, leading to broad interest from researchers and practitioners alike. However, a comprehensive evaluation of their long-context capabilities remains underexplored. To address these gaps, we introduce the MultiModal Needle-in-a-haystack (MMNeedle) benchmark, specifically designed to assess the long-context capabilities of MLLMs. Besides multi-image input, we employ image stitching to further increase the input context length, and develop a protocol to automatically generate labels for sub-image level retrieval. Essentially, MMNeedle evaluates MLLMs by stress-testing their capability to locate a target sub-image (needle) within a set of images (haystack) based on textual instructions and descriptions of image contents. This setup necessitates an advanced understanding of extensive visual contexts and effective information retrieval within long-context image inputs. With this benchmark, we evaluate state-of-the-art MLLMs, encompassing both API-based and open-source models. The findings reveal that GPT-4o consistently surpasses other models in long-context scenarios, but suffers from hallucination problems in negative samples, i.e., when needles are not in the haystacks. Our comprehensive long-context evaluation of MLLMs also sheds lights on the considerable performance gap between API-based and open-source models. All the code, data, and instructions required to reproduce the main results are available at https://github.com/Wang-ML-Lab/multimodal-needle-in-a-haystack.

Code provides a general syntactic structure to build complex programs and perform precise computations when paired with a code interpreter - we hypothesize that language models (LMs) can leverage code-writing to improve Chain of Thought reasoning not only for logic and arithmetic tasks, but also for semantic ones (and in particular, those that are a mix of both). For example, consider prompting an LM to write code that counts the number of times it detects sarcasm in an essay: the LM may struggle to write an implementation for "detect_sarcasm(string)" that can be executed by the interpreter (handling the edge cases would be insurmountable). However, LMs may still produce a valid solution if they not only write code, but also selectively "emulate" the interpreter by generating the expected output of "detect_sarcasm(string)". In this work, we propose Chain of Code (CoC), a simple yet surprisingly effective extension that improves LM code-driven reasoning. The key idea is to encourage LMs to format semantic sub-tasks in a program as flexible pseudocode that the interpreter can explicitly catch undefined behaviors and hand off to simulate with an LM (as an "LMulator"). Experiments demonstrate that Chain of Code outperforms Chain of Thought and other baselines across a variety of benchmarks; on BIG-Bench Hard, Chain of Code achieves 84%, a gain of 12% over Chain of Thought. In a nutshell, CoC broadens the scope of reasoning questions that LMs can answer by "thinking in code".

Recent advances in visual reasoning have leveraged vision transformers to tackle the ARC-AGI benchmark. However, we argue that the feed-forward architecture, where computational depth is strictly bound to parameter size, falls short of capturing the iterative, algorithmic nature of human induction. In this work, we propose a recursive architecture called Loop-ViT, which decouples reasoning depth from model capacity through weight-tied recurrence. Loop-ViT iterates a weight-tied Hybrid Block, combining local convolutions and global attention, to form a latent chain of thought. Crucially, we introduce a parameter-free Dynamic Exit mechanism based on predictive entropy: the model halts inference when its internal state ``crystallizes" into a low-uncertainty attractor. Empirical results on the ARC-AGI-1 benchmark validate this perspective: our 18M model achieves 65.8% accuracy, outperforming massive 73M-parameter ensembles. These findings demonstrate that adaptive iterative computation offers a far more efficient scaling axis for visual reasoning than simply increasing network width. The code is available at https://github.com/WenjieShu/LoopViT.

Effectively handling instructions with extremely long context remains a challenge for Large Language Models (LLMs), typically necessitating high-quality long data and substantial computational resources. This paper introduces Step-Skipping Alignment (SkipAlign), a new technique designed to enhance the long-context capabilities of LLMs in the phase of alignment without the need for additional efforts beyond training with original data length. SkipAlign is developed on the premise that long-range dependencies are fundamental to enhancing an LLM's capacity of long context. Departing from merely expanding the length of input samples, SkipAlign synthesizes long-range dependencies from the aspect of positions indices. This is achieved by the strategic insertion of skipped positions within instruction-following samples, which utilizes the semantic structure of the data to effectively expand the context. Through extensive experiments on base models with a variety of context window sizes, SkipAlign demonstrates its effectiveness across a spectrum of long-context tasks. Particularly noteworthy is that with a careful selection of the base model and alignment datasets, SkipAlign with only 6B parameters achieves it's best performance and comparable with strong baselines like GPT-3.5-Turbo-16K on LongBench.

In this work, we show that it is possible to extract significant amounts of alignment training data from a post-trained model -- useful to steer the model to improve certain capabilities such as long-context reasoning, safety, instruction following, and maths. While the majority of related work on memorisation has focused on measuring success of training data extraction through string matching, we argue that embedding models are better suited for our specific goals. Distances measured through a high quality embedding model can identify semantic similarities between strings that a different metric such as edit distance will struggle to capture. In fact, in our investigation, approximate string matching would have severely undercounted (by a conservative estimate of 10times) the amount of data that can be extracted due to trivial artifacts that deflate the metric. Interestingly, we find that models readily regurgitate training data that was used in post-training phases such as SFT or RL. We show that this data can be then used to train a base model, recovering a meaningful amount of the original performance. We believe our work exposes a possibly overlooked risk towards extracting alignment data. Finally, our work opens up an interesting discussion on the downstream effects of distillation practices: since models seem to be regurgitating aspects of their training set, distillation can therefore be thought of as indirectly training on the model's original dataset.

Although large language models (LLMs) have demonstrated impressive potential on simple tasks, their breadth of scope, lack of transparency, and insufficient controllability can make them less effective when assisting humans on more complex tasks. In response, we introduce the concept of Chaining LLM steps together, where the output of one step becomes the input for the next, thus aggregating the gains per step. We first define a set of LLM primitive operations useful for Chain construction, then present an interactive system where users can modify these Chains, along with their intermediate results, in a modular way. In a 20-person user study, we found that Chaining not only improved the quality of task outcomes, but also significantly enhanced system transparency, controllability, and sense of collaboration. Additionally, we saw that users developed new ways of interacting with LLMs through Chains: they leveraged sub-tasks to calibrate model expectations, compared and contrasted alternative strategies by observing parallel downstream effects, and debugged unexpected model outputs by "unit-testing" sub-components of a Chain. In two case studies, we further explore how LLM Chains may be used in future applications

Pretraining data processing is critical to the downstream performance of Large Language Models (LLMs). However, many existing approaches define a fixed processing strategy at the corpus or domain level and apply it uniformly to many examples, without adapting to the needs of each example. We propose DataOrchestra, a framework that unifies different processing operations and orchestrates an example-specific pipeline for each example. Given a chunk of pretraining data, an orchestrator decides whether to drop, untouch, or clean it. For a chunk to be cleaned, it selects one or more downstream operations, ranging from programmatic editing to different forms of LLM-based rewriting. For each rewriting step, it further generates a concrete instruction, which is executed by the corresponding downstream tool model. We pretrain models from 0.5B to 7B from scratch on web data processed by DataOrchestra and observe stable average gains over individual data-processing methods across 11 benchmarks. DataOrchestra is also effective for math continued pretraining and outperforms stronger processing baselines, while reducing processing compute by skipping unnecessary downstream operations.

Language models may memorize more than just facts, including entire chunks of texts seen during training. Fair use exemptions to copyright laws typically allow for limited use of copyrighted material without permission from the copyright holder, but typically for extraction of information from copyrighted materials, rather than {\em verbatim} reproduction. This work explores the issue of copyright violations and large language models through the lens of verbatim memorization, focusing on possible redistribution of copyrighted text. We present experiments with a range of language models over a collection of popular books and coding problems, providing a conservative characterization of the extent to which language models can redistribute these materials. Overall, this research highlights the need for further examination and the potential impact on future developments in natural language processing to ensure adherence to copyright regulations. Code is at https://github.com/coastalcph/CopyrightLLMs.

Training large language models is a computationally intensive process that often requires substantial resources to achieve state-of-the-art results. Incremental layer-wise training has been proposed as a potential strategy to optimize the training process by progressively introducing layers, with the expectation that this approach would lead to faster convergence and more efficient use of computational resources. In this paper, we investigate the effectiveness of incremental training for LLMs, dividing the training process into multiple stages where layers are added progressively. Our experimental results indicate that while the incremental approach initially demonstrates some computational efficiency, it ultimately requires greater overall computational costs to reach comparable performance to traditional full-scale training. Although the incremental training process can eventually close the performance gap with the baseline, it does so only after significantly extended continual training. These findings suggest that incremental layer-wise training may not be a viable alternative for training large language models, highlighting its limitations and providing valuable insights into the inefficiencies of this approach.

Instruction tuning is vital for aligning large language models (LLMs) with human intent, but current methods typically rely on costly human-annotated seed data or powerful external teacher models. While instruction back-translation techniques reduce this dependency, they remain fundamentally tethered to an initial seed set, which limits full automation, introduces biases, and can lead to inefficient use of unlabeled corpora. In this paper, we propose Cycle-Instruct, a novel framework that achieves fully seed-free instruction tuning. Inspired by cycle consistency, Cycle-Instruct employs a dual self-training loop where two models-an answer generator and a question generator-are bootstrapped solely from raw, unlabeled text. These models mutually supervise each other by reconstructing original text segments from their counterpart's generated pseudo-labels, effectively learning from the intrinsic structure of the data without any human-provided seeds. We demonstrate Cycle-Instruct's efficacy across four diverse data tracks, including general instruction-following, domain-specific tasks, dialogue logs, and plain text. Our extensive experiments show that Cycle-Instruct not only outperforms seed-driven back-translation baselines but also achieves performance comparable to strongly supervised methods.

When language models are trained on textual data, they acquire both knowledge about the structure of language as well as knowledge of facts about the world. At inference time, their knowledge of facts can be leveraged to solve interesting problems and perform useful knowledge work for users. It is well known that language models can verbatim memorize long sequences from their training data. However, it is much less well understood how language models memorize facts seen during training. In this work, we propose a new dataset to specifically empower researchers to study the dual processes of fact memorization and verbatim sequence memorization. The dataset consists of synthetically-generated, webtext-like documents about fictional events, as well as question-answer pairs about the events. We conduct training experiments showing how synthetic data about fictional events can be effective in teasing apart different forms of memorization. We also document the challenges in effectively building realistic, fictional synthetic data.

Autoregressive models, such as the GPT family, use a fixed order, usually left-to-right, to generate sequences. However, this is not a necessity. In this paper, we challenge this assumption and show that by simply adding a positional encoding for the output, this order can be modulated on-the-fly per-sample which offers key advantageous properties. It allows for the sampling of and conditioning on arbitrary subsets of tokens, and it also allows sampling in one shot multiple tokens dynamically according to a rejection strategy, leading to a sub-linear number of model evaluations. We evaluate our method across various domains, including language modeling, path-solving, and aircraft vertical rate prediction, decreasing the number of steps required for generation by an order of magnitude.

Training language models on long sequence data is a demanding requirement for enhancing the model's capability on complex tasks, e.g., long-chain reasoning. However, as the sequence length scales up, the memory cost for storing activation values becomes huge during the Backpropagation (BP) process, even with the application of gradient checkpointing technique. To tackle this challenge, we propose a memory-efficient and exact BP method called StreamBP, which performs a linear decomposition of the chain rule along the sequence dimension in a layer-wise manner, significantly reducing the memory cost of activation values and logits. The proposed method is applicable to common objectives such as SFT, GRPO, and DPO. From an implementation perspective, StreamBP achieves less computational FLOPs and faster BP speed by leveraging the causal structure of the language model. Compared to gradient checkpointing, StreamBP scales up the maximum sequence length of BP by 2.8-5.5 times larger, while using comparable or even less BP time. Note that StreamBP's sequence length scaling ability can be directly transferred to batch size scaling for accelerating training. We further develop a communication-efficient distributed StreamBP to effectively support multi-GPU training and broaden its applicability. Our code can be easily integrated into the training pipeline of any transformer models and is available at https://github.com/Ledzy/StreamBP.

This is a brief description of a project that has already autoformalized a large portion of the general topology from the Munkres textbook (which has in total 241 pages in 7 chapters and 39 sections). The project has been running since November 21, 2025 and has as of January 4, 2026, produced 160k lines of formalized topology. Most of it (about 130k lines) have been done in two weeks,from December 22 to January 4, for an LLM subscription cost of about \$100. This includes a 3k-line proof of Urysohn's lemma, a 2k-line proof of Urysohn's Metrization theorem, over 10k-line proof of the Tietze extension theorem, and many more (in total over 1.5k lemmas/theorems). The approach is quite simple and cheap: build a long-running feedback loop between an LLM and a reasonably fast proof checker equipped with a core foundational library. The LLM is now instantiated as ChatGPT (mostly 5.2) or Claude Sonnet (4.5) run through the respective Codex or Claude Code command line interfaces. The proof checker is Chad Brown's higher-order set theory system Megalodon, and the core library is Brown's formalization of basic set theory and surreal numbers (including reals, etc). The rest is some prompt engineering and technical choices which we describe here. Based on the fast progress, low cost, virtually unknown ITP/library, and the simple setup available to everyone, we believe that (auto)formalization may become quite easy and ubiquitous in 2026, regardless of which proof assistant is used.

Widespread LLM adoption has introduced characteristic repetitive phraseology, termed "slop," which degrades output quality and makes AI-generated text immediately recognizable. We present Antislop, a comprehensive framework providing tools to both detect and eliminate these overused patterns. Our approach combines three innovations: (1) The Antislop Sampler, which uses backtracking to suppress unwanted strings at inference time without destroying vocabulary; (2) An automated pipeline that profiles model-specific slop against human baselines and generates training data; (3) Final Token Preference Optimization (FTPO), a novel fine-tuning method that operates on individual tokens, surgically adjusting logits wherever a banned pattern has appeared in an inference trace. We demonstrate that some slop patterns appear over 1,000x more frequently in LLM output than human text. The Antislop Sampler successfully suppresses 8,000+ patterns while maintaining quality, whereas token banning becomes unusable at just 2,000. Most importantly, FTPO achieves 90% slop reduction while maintaining or improving performance in cross-domain evals including GSM8K, MMLU, and creative writing tasks. In contrast, DPO suffers significant degradation in writing quality and lexical diversity despite achieving weaker suppression. We release all code and results under MIT license: https://github.com/sam-paech/auto-antislop.

The proliferation of Large Language Models (LLMs) highlights the critical importance of conducting thorough evaluations to discern their comparative advantages, limitations, and optimal use cases. Particularly important is assessing their capacity to accurately retrieve information included in a given prompt. A model's ability to do this significantly influences how effectively it can utilize contextual details, thus impacting its practical efficacy and dependability in real-world applications. Our research analyzes the in-context recall performance of various LLMs using the needle-in-a-haystack method. In this approach, a factoid (the "needle") is embedded within a block of filler text (the "haystack"), which the model is asked to retrieve. We assess the recall performance of each model across various haystack lengths and with varying needle placements to identify performance patterns. This study demonstrates that an LLM's recall capability is not only contingent upon the prompt's content but also may be compromised by biases in its training data. Conversely, adjustments to model architecture, training strategy, or fine-tuning can improve performance. Our analysis provides insight into LLM behavior, offering direction for the development of more effective applications of LLMs.

As model finetuning is central to the modern NLP, we set to maximize its efficiency. Motivated by redundancy in training examples and the sheer sizes of pretrained models, we exploit a key opportunity: training only on important data. To this end, we set to filter training examples in a streaming fashion, in tandem with training the target model. Our key techniques are two: (1) automatically determine a training loss threshold for skipping backward training passes; (2) run a meta predictor for further skipping forward training passes. We integrate the above techniques in a holistic, three-stage training process. On a diverse set of benchmarks, our method reduces the required training examples by up to 5.3times and training time by up to 6.8times, while only seeing minor accuracy degradation. Our method is effective even when training one epoch, where each training example is encountered only once. It is simple to implement and is compatible with the existing finetuning techniques. Code is available at: https://github.com/xo28/efficient- NLP-multistage-training

Process or step-wise supervision has played a crucial role in advancing complex multi-step reasoning capabilities of Large Language Models (LLMs). However, efficient, high-quality automated process annotation remains a significant challenge. To address this, we introduce Single-Pass Annotation with Reference-Guided Evaluation (SPARE), a novel structured framework that enables single-pass, per-step annotation by aligning each solution step to one or multiple steps in a reference solution, accompanied by explicit reasoning for evaluation. We show that reference-guided step-level evaluation effectively facilitates process supervision on four datasets spanning three domains: mathematical reasoning, multi-hop compositional question answering, and spatial reasoning. We demonstrate that SPARE, when compared to baselines, improves reasoning performance when used for: (1) fine-tuning models in an offline RL setup for inference-time greedy-decoding, and (2) training reward models for ranking/aggregating multiple LLM-generated outputs. Additionally, SPARE achieves competitive performance on challenging mathematical datasets while offering 2.6 times greater efficiency, requiring only 38% of the runtime, compared to tree search-based automatic annotation. The codebase, along with a trained SPARE-PRM model, is publicly released to facilitate further research and reproducibility.

Recently, large language models (LLMs) have shown remarkable capabilities including understanding context, engaging in logical reasoning, and generating responses. However, this is achieved at the expense of stringent computational and memory requirements, hindering their ability to effectively support long input sequences. This survey provides an inclusive review of the recent techniques and methods devised to extend the sequence length in LLMs, thereby enhancing their capacity for long-context understanding. In particular, we review and categorize a wide range of techniques including architectural modifications, such as modified positional encoding and altered attention mechanisms, which are designed to enhance the processing of longer sequences while avoiding a proportional increase in computational requirements. The diverse methodologies investigated in this study can be leveraged across different phases of LLMs, i.e., training, fine-tuning and inference. This enables LLMs to efficiently process extended sequences. The limitations of the current methodologies is discussed in the last section along with the suggestions for future research directions, underscoring the importance of sequence length in the continued advancement of LLMs.

We propose a one-step constrained (OSC) beam search to accelerate recurrent neural network (RNN) transducer (RNN-T) inference. The original RNN-T beam search has a while-loop leading to speed down of the decoding process. The OSC beam search eliminates this while-loop by vectorizing multiple hypotheses. This vectorization is nontrivial as the expansion of the hypotheses within the original RNN-T beam search can be different from each other. However, we found that the hypotheses expanded only once at each decoding step in most cases; thus, we constrained the maximum expansion number to one, thereby allowing vectorization of the hypotheses. For further acceleration, we assign constraints to the prefixes of the hypotheses to prune the redundant search space. In addition, OSC beam search has duplication check among hypotheses during the decoding process as duplication can undesirably shrink the search space. We achieved significant speedup compared with other RNN-T beam search methods with lower phoneme and word error rate.