Daily Papers

RNN-like language models are getting renewed attention from NLP researchers in recent years and several models have made significant progress, which demonstrates performance comparable to traditional transformers. However, due to the recurrent nature of RNNs, this kind of language model can only store information in a set of fixed-length state vectors. As a consequence, they still suffer from forgetfulness though after a lot of improvements and optimizations, when given complex instructions or prompts. As the prompted generation is the main and most concerned function of LMs, solving the problem of forgetting in the process of generation is no wonder of vital importance. In this paper, focusing on easing the prompt forgetting during generation, we proposed an architecture to teach the model memorizing prompt during generation by synthetic gradient. To force the model to memorize the prompt, we derive the states that encode the prompt, then transform it into model parameter modification using low-rank gradient approximation, which hard-codes the prompt into model parameters temporarily. We construct a dataset for experiments, and the results have demonstrated the effectiveness of our method in solving the problem of forgetfulness in the process of prompted generation. We will release all the code upon acceptance.

Fine-tuning large-scale pretrained models is prohibitively expensive in terms of computational and memory costs. LoRA, as one of the most popular Parameter-Efficient Fine-Tuning (PEFT) methods, offers a cost-effective alternative by fine-tuning an auxiliary low-rank model that has significantly fewer parameters. Although LoRA reduces the computational and memory requirements significantly at each iteration, extensive empirical evidence indicates that it converges at a considerably slower rate compared to full fine-tuning, ultimately leading to increased overall compute and often worse test performance. In our paper, we perform an in-depth investigation of the initialization method of LoRA and show that careful initialization (without any change of the architecture and the training algorithm) can significantly enhance both efficiency and performance. In particular, we introduce a novel initialization method, LoRA-GA (Low Rank Adaptation with Gradient Approximation), which aligns the gradients of low-rank matrix product with those of full fine-tuning at the first step. Our extensive experiments demonstrate that LoRA-GA achieves a convergence rate comparable to that of full fine-tuning (hence being significantly faster than vanilla LoRA as well as various recent improvements) while simultaneously attaining comparable or even better performance. For example, on the subset of the GLUE dataset with T5-Base, LoRA-GA outperforms LoRA by 5.69% on average. On larger models such as Llama 2-7B, LoRA-GA shows performance improvements of 0.34, 11.52%, and 5.05% on MT-bench, GSM8K, and Human-eval, respectively. Additionally, we observe up to 2-4 times convergence speed improvement compared to vanilla LoRA, validating its effectiveness in accelerating convergence and enhancing model performance. Code is available at https://github.com/Outsider565/LoRA-GA.

Low-rank adapters have become standard for efficiently fine-tuning large language models (LLMs), but they often fall short of achieving the performance of full fine-tuning. We propose a method, LoRA Silver Bullet or LoRA-SB, that approximates full fine-tuning within low-rank subspaces using a carefully designed initialization strategy. We theoretically demonstrate that the architecture of LoRA-XS, which inserts a learnable (r x r) matrix between B and A while keeping other matrices fixed, provides the precise conditions needed for this approximation. We leverage its constrained update space to achieve optimal scaling for high-rank gradient updates while removing the need for hyperparameter tuning. We prove that our initialization offers an optimal low-rank approximation of the initial gradient and preserves update directions throughout training. Extensive experiments across mathematical reasoning, commonsense reasoning, and language understanding tasks demonstrate that our approach exceeds the performance of standard LoRA while using 27-90 times fewer learnable parameters, and comprehensively outperforms LoRA-XS. Our findings establish that it is possible to simulate full fine-tuning in low-rank subspaces, and achieve significant efficiency gains without sacrificing performance. Our code is publicly available at https://github.com/RaghavSinghal10/lora-sb.

Training modern neural networks on large datasets is computationally and environmentally costly. We introduce GRAFT, a scalable in-training subset selection method that (i) extracts a low-rank feature representation for each batch, (ii) applies a Fast MaxVol sampler to select a small, diverse subset that spans the batch's dominant subspace, and (iii) dynamically adjusts the subset size using a gradient-approximation criterion. By operating in low-rank subspaces and training on carefully chosen examples instead of full batches, GRAFT preserves the training trajectory while reducing wall-clock time, energy consumption, and CO_2 emissions. Across multiple benchmarks, GRAFT matches or exceeds recent selection baselines in both accuracy and efficiency, providing a favorable trade-off between accuracy, efficiency, and emissions.

Large Language Models (LLMs) have shown remarkable performance across various tasks, but the escalating demands on computational resources pose significant challenges, particularly in the extensive utilization of full fine-tuning for downstream tasks. To address this, parameter-efficient fine-tuning (PEFT) methods have been developed, but they often underperform compared to full fine-tuning and struggle with memory efficiency. In this work, we introduce Gradient Weight-Normalized Low-Rank Projection (GradNormLoRP), a novel approach that enhances both parameter and memory efficiency while maintaining comparable performance to full fine-tuning. GradNormLoRP normalizes the weight matrix to improve gradient conditioning, facilitating better convergence during optimization. Additionally, it applies low-rank approximations to the weight and gradient matrices, significantly reducing memory usage during training. Extensive experiments demonstrate that our 8-bit GradNormLoRP reduces optimizer memory usage by up to 89.5% and enables the pre-training of large LLMs, such as LLaMA 7B, on consumer-level GPUs like the NVIDIA RTX 4090, without additional inference costs. Moreover, GradNormLoRP outperforms existing low-rank methods in fine-tuning tasks. For instance, when fine-tuning the RoBERTa model on all GLUE tasks with a rank of 8, GradNormLoRP achieves an average score of 80.65, surpassing LoRA's score of 79.23. These results underscore GradNormLoRP as a promising alternative for efficient LLM pre-training and fine-tuning. Source code: https://github.com/Jhhuangkay/Gradient-Weight-normalized-Low-rank-Projection-for-Efficient-LLM-Training

In this work, we re-formulate the model compression problem into the customized compensation problem: Given a compressed model, we aim to introduce residual low-rank paths to compensate for compression errors under customized requirements from users (e.g., tasks, compression ratios), resulting in greater flexibility in adjusting overall capacity without being constrained by specific compression formats. However, naively applying SVD to derive residual paths causes suboptimal utilization of the low-rank representation capacity. Instead, we propose Training-free Eigenspace Low-Rank Approximation (EoRA), a method that directly minimizes compression-induced errors without requiring gradient-based training, achieving fast optimization in minutes using a small amount of calibration data. EoRA projects compression errors into the eigenspace of input activations, leveraging eigenvalues to effectively prioritize the reconstruction of high-importance error components. Moreover, EoRA can be seamlessly integrated with fine-tuning and quantization to further improve effectiveness and efficiency. EoRA consistently outperforms previous methods in compensating errors for compressed LLaMA2/3 models on various tasks, such as language generation, commonsense reasoning, and math reasoning tasks (e.g., 31.31%/12.88% and 9.69% improvements on ARC-Easy/ARC-Challenge and MathQA when compensating LLaMA3-8B that is quantized to 4-bit and pruned to 2:4 sparsity). EoRA offers a scalable, training-free solution to compensate for compression errors, making it a powerful tool to deploy LLMs in various capacity and efficiency requirements.

Low-rank optimization has emerged as a promising approach to enabling memory-efficient training of large language models (LLMs). Existing low-rank optimization methods typically project gradients onto a low-rank subspace, reducing the memory cost of storing optimizer states. A key challenge in these methods is selecting suitable subspaces to ensure an effective optimization trajectory. Most existing approaches select the dominant subspace to preserve gradient information, as this intuitively provides the best approximation. However, we find that in practice, the dominant subspace stops changing during pretraining, thereby constraining weight updates to similar subspaces. In this paper, we propose importance sampling for low-rank optimization in LLM pretraining with a provable convergence guarantee, which the dominant subspace approach does not have. Empirically, we demonstrate that our method significantly outperforms previous methods in LLM pretraining tasks.

Data-parallel distributed training of deep neural networks (DNN) has gained very widespread adoption, but can still experience communication bottlenecks. To address this issue, entire families of compression mechanisms have been developed, including quantization, sparsification, and low-rank approximation, some of which are seeing significant practical adoption. Despite this progress, almost all known compression schemes apply compression uniformly across DNN layers, although layers are heterogeneous in terms of parameter count and their impact on model accuracy. In this work, we provide a general framework for adapting the degree of compression across the model's layers dynamically during training, improving the overall compression, while leading to substantial speedups, without sacrificing accuracy. Our framework, called L-GreCo, is based on an adaptive algorithm, which automatically picks the optimal compression parameters for model layers guaranteeing the best compression ratio while satisfying an error constraint. Extensive experiments over image classification and language modeling tasks shows that L-GreCo is effective across all existing families of compression methods, and achieves up to 2.5times training speedup and up to 5times compression improvement over efficient implementations of existing approaches, while recovering full accuracy. Moreover, L-GreCo is complementary to existing adaptive algorithms, improving their compression ratio by 50% and practical throughput by 66%.

Recent work has shown that orthonormal matrix updates speed up neural network optimization, improve training stability, and offer better hyperparameter transfer across model sizes. Applying these updates efficiently when model weights and optimizer states are sharded across a large-scale distributed LLM training system remains a major challenge. We introduce Dion (DIstributed OrthoNormalization), a scalable and communication-efficient orthonormalizing optimizer. Dion leverages low-rank approximation and decoupled momentum buffers, eliminating the need for full gradient synchronization while producing numerically equivalent results. It is compatible with simultaneous DDP, FSDP, and TP parallelism, and it computes an orthonormalized update without unsharding a full parameter matrix on any single device. We evaluate Dion on language models from 120M to 3B parameters and find that its benefits improve with increasing model size and batch size.

Low-rank optimization has emerged as a promising direction in training large language models (LLMs) to reduce the memory usage of adaptive optimizers by constraining learning to a lower-dimensional space. Prior work typically projects gradients of linear layers using approaches based on Singular Value Decomposition (SVD). However, applying SVD-based procedures individually to each layer in large models is computationally expensive and incurs additional memory costs due to storing the projection matrices. In this work, we propose a computationally efficient and conceptually simple two-step procedure to approximate SVD-based gradient projections into lower-dimensional spaces. First, we construct a complete orthogonal basis using predefined orthogonal matrices of the Discrete Cosine Transform (DCT). Second, we adaptively select basis columns based on their alignment with the gradient of each layer. Each projection matrix in our method is obtained via a single matrix multiplication followed by a lightweight sorting step to identify the most relevant basis vectors. Due to the predefined nature of the orthogonal bases, they are computed once at the start of training. During training, we store only the indices of the selected columns, avoiding the need to store full projection matrices for each layer. Our numerical experiments on both pre-training and fine-tuning tasks demonstrate the effectiveness of our dual strategy in approximating optimal low-rank projections, matching the performance of costly SVD-based methods while achieving faster runtime and reduced memory usage.

We study the computational limits of Low-Rank Adaptation (LoRA) update for finetuning transformer-based models using fine-grained complexity theory. Our key observation is that the existence of low-rank decompositions within the gradient computation of LoRA adaptation leads to possible algorithmic speedup. This allows us to (i) identify a phase transition behavior and (ii) prove the existence of nearly linear algorithms by controlling the LoRA update computation term by term, assuming the Strong Exponential Time Hypothesis (SETH). For the former, we identify a sharp transition in the efficiency of all possible rank-r LoRA update algorithms for transformers, based on specific norms resulting from the multiplications of the input sequence X, pretrained weights W^star, and adapter matrices alpha B A / r. Specifically, we derive a shared upper bound threshold for such norms and show that efficient (sub-quadratic) approximation algorithms of LoRA exist only below this threshold. For the latter, we prove the existence of nearly linear approximation algorithms for LoRA adaptation by utilizing the hierarchical low-rank structures of LoRA gradients and approximating the gradients with a series of chained low-rank approximations. To showcase our theory, we consider two practical scenarios: partial (e.g., only W_V and W_Q) and full adaptations (e.g., W_Q, W_V, and W_K) of weights in attention heads.

Large Language Models (LLMs) have achieved remarkable success in natural language processing, but their full fine-tuning remains resource-intensive. Parameter-Efficient Fine-Tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), have emerged as a practical solution by approximating parameter updates with low-rank matrices. However, LoRA often exhibits a "double descent" phenomenon during fine-tuning, where model performance degrades due to overfitting and limited expressiveness caused by low-rank constraints. To address this issue, we propose LoRA-GGPO (Gradient-Guided Perturbation Optimization), a novel method that leverages gradient and weight norms to generate targeted perturbations. By optimizing the sharpness of the loss landscape, LoRA-GGPO guides the model toward flatter minima, mitigating the double descent problem and improving generalization. Extensive experiments on natural language understanding (NLU) and generation (NLG) tasks demonstrate that LoRA-GGPO outperforms LoRA and its state-of-the-art variants. Furthermore, extended experiments specifically designed to analyze the double descent phenomenon confirm that LoRA-GGPO effectively alleviates this issue, producing more robust and generalizable models. Our work provides a robust and efficient solution for fine-tuning LLMs, with broad applicability in real-world scenarios. The code is available at https://github.com/llm172/LoRA-GGPO.

Quantizing the weights of a neural network has two steps: (1) Finding a good low bit-complexity representation for weights (which we call the quantization grid) and (2) Rounding the original weights to values in the quantization grid. In this paper, we study the problem of rounding optimally given any quantization grid. The simplest and most commonly used way to round is Round-to-Nearest (RTN). By rounding in a data-dependent way instead, one can improve the quality of the quantized model significantly. We study the rounding problem from the lens of discrepancy theory, which studies how well we can round a continuous solution to a discrete solution without affecting solution quality too much. We prove that given m=poly(1/ε) samples from the data distribution, we can round all but O(m) model weights such that the expected approximation error of the quantized model on the true data distribution is le ε as long as the space of gradients of the original model is approximately low rank (which we empirically validate). Our proof, which is algorithmic, inspired a simple and practical rounding algorithm called DiscQuant. In our experiments, we demonstrate that DiscQuant significantly improves over the prior state-of-the-art rounding method called GPTQ and the baseline RTN over a range of benchmarks on Phi3mini-3.8B and Llama3.1-8B. For example, rounding Phi3mini-3.8B to a fixed quantization grid with 3.25 bits per parameter using DiscQuant gets 64\% accuracy on the GSM8k dataset, whereas GPTQ achieves 54\% and RTN achieves 31\% (the original model achieves 84\%). We make our code available at https://github.com/jerry-chee/DiscQuant.