Daily Papers

The rapid progress of large language models (LLMs) is increasingly constrained by memory and deployment costs, motivating compression methods for practical deployment. Many state-of-the-art compression pipelines leverage the low-rank structure of trained weight matrices, a phenomenon often associated with the properties of popular optimizers such as Adam. In this context, Muon is a recently proposed optimizer that improves LLM pretraining via full-rank update steps, but its induced weight-space structure has not been characterized yet. In this work, we report a surprising empirical finding: despite imposing full-rank updates, Muon-trained models exhibit pronounced low-rank structure in their weight matrices and are readily compressible under standard pipelines. Motivated by this insight, we propose NuMuon, which augments Muon with a nuclear-norm constraint on the update direction, further constraining the learned weights toward low-rank structure. Across billion-parameter-scale models, we show that NuMuon increases weight compressibility and improves post-compression model quality under state-of-the-art LLM compression pipelines while retaining Muon's favorable convergence behavior.

Despite rapid advancements in the research and deployment of large language models (LLMs), the statistical distribution of model parameters, as well as their influence on initialization, training dynamics, and downstream efficiency, has received surprisingly little attention. A recent work introduced BackSlash, a training-time compression algorithm. It first demonstrated that pre-trained LLM parameters follow generalized Gaussian distributions (GGDs) better. By optimizing GG priors during training, BackSlash can reduce parameters by up to 90\% with minimal performance loss. Building on this foundational insight, we propose a unified, end-to-end framework for LLM optimization based on the GG model. Our contributions are threefold: (1) GG-based initialization scheme that aligns with the statistical structure of trained models, resulting in faster convergence and improved accuracy; (2) DeepShape, a post-training regularization method that reshapes weight distributions to match a GG profile, improving compressibility with minimized degradation in performance; and (3) RF8, a compact and hardware-efficient 8-bit floating-point format designed for GG-distributed-initialized BackSlash training, enabling low-cost inference without compromising accuracy. Experiments across diverse model architectures show that our framework consistently yields smaller and faster models that match or outperform standard training baselines. By grounding LLM development in principled statistical modeling, this work forges a new path toward efficient, scalable, and hardware-aware AI systems. The code is available on our project page: https://huggingface.co/spaces/shifeng3711/gg_prior.

Nonlinear elastic properties of polymers and polymeric composites are essential for accurate prediction of their response to dynamic loads, which is crucial in a wide range of applications. These properties can be affected by strain rate, temperature, and pressure. The temperature susceptibility of nonlinear elastic moduli of polymers remains poorly understood. We have recently observed a significant frequency dependence of the nonlinear elastic (Murnaghan) moduli of polystyrene. In this paper we expand this analysis by the temperature dependence. The measurement methodology was based on the acousto-elastic effect, and involved analysis of the dependencies of velocities of longitudinal and shear single-frequency ultrasonic waves in the sample on the applied static pressure. Measurements were performed at different temperatures in the range of 25-65 {\deg}C and at different frequencies in the range of 0.75-3 MHz. The temperature susceptibility of the nonlinear moduli l and m was found to be two orders of magnitude larger than that of linear moduli lambda and mu. At the same time, the observed variations of n modulus with temperature were low and within the measurement tolerance. The observed tendencies can be explained by different influence of pressure on relaxation processes in the material at different temperatures.

With the growth of model sizes and the scale of their deployment, their sheer size burdens the infrastructure requiring more network and more storage to accommodate these. While there is a vast model compression literature deleting parts of the model weights for faster inference, we investigate a more traditional type of compression - one that represents the model in a compact form and is coupled with a decompression algorithm that returns it to its original form and size - namely lossless compression. We present ZipNN a lossless compression tailored to neural networks. Somewhat surprisingly, we show that specific lossless compression can gain significant network and storage reduction on popular models, often saving 33% and at times reducing over 50% of the model size. We investigate the source of model compressibility and introduce specialized compression variants tailored for models that further increase the effectiveness of compression. On popular models (e.g. Llama 3) ZipNN shows space savings that are over 17% better than vanilla compression while also improving compression and decompression speeds by 62%. We estimate that these methods could save over an ExaByte per month of network traffic downloaded from a large model hub like Hugging Face.

Deep neural networks have delivered remarkable performance and have been widely used in various visual tasks. However, their huge size causes significant inconvenience for transmission and storage. Many previous studies have explored model size compression. However, these studies often approach various lossy and lossless compression methods in isolation, leading to challenges in achieving high compression ratios efficiently. This work proposes a post-training model size compression method that combines lossy and lossless compression in a unified way. We first propose a unified parametric weight transformation, which ensures different lossy compression methods can be performed jointly in a post-training manner. Then, a dedicated differentiable counter is introduced to guide the optimization of lossy compression to arrive at a more suitable point for later lossless compression. Additionally, our method can easily control a desired global compression ratio and allocate adaptive ratios for different layers. Finally, our method can achieve a stable 10times compression ratio without sacrificing accuracy and a 20times compression ratio with minor accuracy loss in a short time. Our code is available at https://github.com/ModelTC/L2_Compression .

Convolutional neural networks are now seeing widespread use in a variety of fields, including image classification, facial and object recognition, medical imaging analysis, and many more. In addition, there are applications such as physics-informed simulators in which accurate forecasts in real time with a minimal lag are required. The present neural network designs include millions of parameters, which makes it difficult to install such complex models on devices that have limited memory. Compression techniques might be able to resolve these issues by decreasing the size of CNN models that are created by reducing the number of parameters that contribute to the complexity of the models. We propose a compressed tensor format of convolutional layer, a priori, before the training of the neural network. 3-way kernels or 2-way kernels in convolutional layers are replaced by one-way fiters. The overfitting phenomena will be reduced also. The time needed to make predictions or time required for training using the original Convolutional Neural Networks model would be cut significantly if there were fewer parameters to deal with. In this paper we present a method of a priori compressing convolutional neural networks for finite element (FE) predictions of physical data. Afterwards we validate our a priori compressed models on physical data from a FE model solving a 2D wave equation. We show that the proposed convolutinal compression technique achieves equivalent performance as classical convolutional layers with fewer trainable parameters and lower memory footprint.

Scaling laws have shaped recent advances in machine learning by enabling predictable scaling of model performance based on model size, computation, and data volume. Concurrently, the rise in computational cost for AI has motivated model compression techniques, notably quantization and sparsification, which have emerged to mitigate the steep computational demands associated with large-scale training and inference. This paper investigates the interplay between scaling laws and compression formats, exploring whether a unified scaling framework can accurately predict model performance when training occurs over various compressed representations, such as sparse, scalar-quantized, sparse-quantized or even vector-quantized formats. Our key contributions include validating a general scaling law formulation and showing that it is applicable both individually but also composably across compression types. Based on this, our main finding is demonstrating both theoretically and empirically that there exists a simple "capacity" metric -- based on the representation's ability to fit random Gaussian data -- which can robustly predict parameter efficiency across multiple compressed representations. On the practical side, we extend our formulation to directly compare the accuracy potential of different compressed formats, and to derive better algorithms for training over sparse-quantized formats.

In recent years, deep network pruning has attracted significant attention in order to enable the rapid deployment of AI into small devices with computation and memory constraints. Pruning is often achieved by dropping redundant weights, neurons, or layers of a deep network while attempting to retain a comparable test performance. Many deep pruning algorithms have been proposed with impressive empirical success. However, existing approaches lack a quantifiable measure to estimate the compressibility of a sub-network during each pruning iteration and thus may under-prune or over-prune the model. In this work, we propose PQ Index (PQI) to measure the potential compressibility of deep neural networks and use this to develop a Sparsity-informed Adaptive Pruning (SAP) algorithm. Our extensive experiments corroborate the hypothesis that for a generic pruning procedure, PQI decreases first when a large model is being effectively regularized and then increases when its compressibility reaches a limit that appears to correspond to the beginning of underfitting. Subsequently, PQI decreases again when the model collapse and significant deterioration in the performance of the model start to occur. Additionally, our experiments demonstrate that the proposed adaptive pruning algorithm with proper choice of hyper-parameters is superior to the iterative pruning algorithms such as the lottery ticket-based pruning methods, in terms of both compression efficiency and robustness.

Regularization is a set of techniques that are used to improve the generalization ability of deep neural networks. In this paper, we introduce weight compander (WC), a novel effective method to improve generalization by reparameterizing each weight in deep neural networks using a nonlinear function. It is a general, intuitive, cheap and easy to implement method, which can be combined with various other regularization techniques. Large weights in deep neural networks are a sign of a more complex network that is overfitted to the training data. Moreover, regularized networks tend to have a greater range of weights around zero with fewer weights centered at zero. We introduce a weight reparameterization function which is applied to each weight and implicitly reduces overfitting by restricting the magnitude of the weights while forcing them away from zero at the same time. This leads to a more democratic decision-making in the network. Firstly, individual weights cannot have too much influence in the prediction process due to the restriction of their magnitude. Secondly, more weights are used in the prediction process, since they are forced away from zero during the training. This promotes the extraction of more features from the input data and increases the level of weight redundancy, which makes the network less sensitive to statistical differences between training and test data. We extend our method to learn the hyperparameters of the introduced weight reparameterization function. This avoids hyperparameter search and gives the network the opportunity to align the weight reparameterization with the training progress. We show experimentally that using weight compander in addition to standard regularization methods improves the performance of neural networks.

Sparse neural networks are a key factor in developing resource-efficient machine learning applications. We propose the novel and powerful sparse learning method Adaptive Regularized Training (ART) to compress dense into sparse networks. Instead of the commonly used binary mask during training to reduce the number of model weights, we inherently shrink weights close to zero in an iterative manner with increasing weight regularization. Our method compresses the pre-trained model knowledge into the weights of highest magnitude. Therefore, we introduce a novel regularization loss named HyperSparse that exploits the highest weights while conserving the ability of weight exploration. Extensive experiments on CIFAR and TinyImageNet show that our method leads to notable performance gains compared to other sparsification methods, especially in extremely high sparsity regimes up to 99.8 percent model sparsity. Additional investigations provide new insights into the patterns that are encoded in weights with high magnitudes.

Large deep learning models have achieved remarkable success but are resource-intensive, posing challenges such as memory usage. We introduce CURing, a novel model compression method based on CUR matrix decomposition, which approximates weight matrices as the product of selected columns (C) and rows (R), and a small linking matrix (U). We apply this decomposition to weights chosen based on the combined influence of their magnitudes and activations. By identifying and retaining informative rows and columns, CURing significantly reduces model size with minimal performance loss. For example, it reduces Llama3.1-8B's parameters to 7.32B (-9%) in just 129 seconds, over 20 times faster than prior compression methods.

In this paper, we revisit the joint low-Mach and low-Frode number limit for the compressible Navier-Stokes equations with degenerate, density-dependent viscosity. Employing the relative entropy framework based on the concept of κ-entropy, we rigorously justify the convergence of weak solutions toward the generalized anelastic system in a three-dimensional periodic domain for well-prepared initial data. For general ill-prepared initial data, we establish a similar convergence result in the whole space, relying essentially on dispersive estimates for acoustic waves. Compared with the work of Fanelli and Zatorska [Commun. Math. Phys., 400 (2023), pp. 1463-1506], our analysis is conducted for the standard isentropic pressure law, thereby eliminating the need for the cold pressure term that played a crucial role in the previous approach. To the best of our knowledge, this is the first rigorous singular limit result for the compressible Navier-Stokes equations with degenerate viscosity that requires no additional regularization of the system.

Large language models rely on kv-caches to avoid redundant computation during autoregressive decoding, but as context length grows, reading and writing the cache can quickly saturate GPU memory bandwidth. Recent work has explored KV-cache compression, yet most approaches neglect the data-dependent nature of kv-caches and their variation across layers. We introduce KV-CoRE KV-cache Compressibility by Rank Evaluation), an SVD-based method for quantifying the data-dependent low-rank compressibility of kv-caches. KV-CoRE computes the optimal low-rank approximation under the Frobenius norm and, being gradient-free and incremental, enables efficient dataset-level, layer-wise evaluation. Using this method, we analyze multiple models and datasets spanning five English domains and sixteen languages, uncovering systematic patterns that link compressibility to model architecture, training data, and language coverage. As part of this analysis, we employ the Normalized Effective Rank as a metric of compressibility and show that it correlates strongly with performance degradation under compression. Our study establishes a principled evaluation framework and the first large-scale benchmark of kv-cache compressibility in LLMs, offering insights for dynamic, data-aware compression and data-centric model development.

We present ROCKET, a training-free model compression method that achieves state-of-the-art performance in comparison with factorization, structured-sparsification and dynamic compression baselines. Operating under a global compression budget, ROCKET comprises two key innovations: First, it formulates layer-wise compression allocation as a multi-choice knapsack problem, selecting the optimal compression level for each layer to minimize total reconstruction error while adhering to a target model size. Second, it introduces a single-step sparse matrix factorization inspired by dictionary learning: using only a small calibration set, it sparsifies weight coefficients based on activation-weights sensitivity and then updates the dictionary in closed form via least squares bypassing iterative optimization, sparse coding, or backpropagation entirely. ROCKET consistently outperforms existing compression approaches across different model architectures at 20-50\% compression rates. Notably, it retains over 90\% of the original model's performance at 30\% compression without any fine-tuning. Moreover, when applying a light fine-tuning phase, recovery is substantially enhanced: for instance, compressing Qwen3-14B to an 8B-parameter model and healing it with just 30 million tokens yields performance nearly on par with the original Qwen3-8B. The code for ROCKET is at github.com/mts-ai/ROCKET/tree/main.

We present a novel approach to determine the constitutive properties of metals under large plastic strains and strain rates that otherwise are difficult to access using conventional materials testing methods. The approach exploits large-strain plastic flow past a sharp wedge, coupled with high-speed photography and image velocimetry to capture the underlying plastic flow dynamics. The inverse problem of estimating material parameters from the flow field is solved using an iterative optimization procedure that minimizes the gap between internal and external plastic work. A major advantage of the method is that it neither makes any assumptions about the flow nor requires computational simulations. To counter the problem of non-unique parameter estimates, we propose a parameterization scheme that takes advantage of the functional form of the constitutive model and reformulates the problem into a more tractable form to identify plasticity parameters uniquely. We present studies to illustrate the principle of the method with two materials with widely different plastic flow characteristics: copper (strain hardening) and a lead-free solder alloy (rate sensitive and deformation history dependent). The results demonstrate the efficacy of the method in reliably determining the material parameters under high strain/strain rate conditions of relevance to a range of practical engineering problems.