In neural network compression, most current methods reduce unnecessary parameters by measuring importance and redundancy. To augment already highly optimized existing solutions, we propose linearity-based compression as a novel way to reduce weights in a neural network. It is based on the intuition that with ReLU-like activation functions, neurons that are almost always activated behave linearly, allowing for merging of subsequent layers. We introduce the theory underlying this compression and evaluate our approach experimentally. Our novel method achieves a lossless compression down to 1/4 of the original model size in over the majority of tested models. Applying our method on already importance-based pruned models shows very little interference between different types of compression, demonstrating the option of successful combination of techniques. Overall, our work lays the foundation for a new type of compression method that enables smaller and ultimately more efficient neural network models.
The rapid development of deep learning has led to challenges in deploying neural networks on edge devices, mainly due to their high memory and runtime complexity. Network compression techniques, such as quantization and pruning, aim to reduce this complexity while maintaining accuracy. However, existing incremental verification methods often focus only on quantization and struggle with structural changes. This paper presents MUC-G4 (Minimal Unsat Core-Guided Incremental Verification), a novel framework for incremental verification of compressed deep neural networks. It encodes both the original and compressed networks into SMT formulas, classifies changes, and use \emph{Minimal Unsat Cores (MUCs)} from the original network to guide efficient verification for the compressed network. Experimental results show its effectiveness in handling quantization and pruning, with high proof reuse rates and significant speedup in verification time compared to traditional methods. MUC-G4 hence offers a promising solution for ensuring the safety and reliability of compressed neural networks in practical applications.
Quantum optimization is the most mature quantum computing technology to date, providing a promising approach towards efficiently solving complex combinatorial problems. Methods such as adiabatic quantum computing (AQC) have been employed in recent years on important optimization problems across various domains. In deep learning, deep neural networks (DNN) have reached immense sizes to support new predictive capabilities. Optimization of large-scale models is critical for sustainable deployment, but becomes increasingly challenging with ever-growing model sizes and complexity. While quantum optimization is suitable for solving complex problems, its application to DNN optimization is not straightforward, requiring thorough reformulation for compatibility with commercially available quantum devices. In this work, we explore the potential of adopting AQC for fine-grained pruning-quantization of convolutional neural networks. We rework established heuristics to formulate model compression as a quadratic unconstrained binary optimization (QUBO) problem, and assess the solution space offered by commercial quantum annealing devices. Through our exploratory efforts of reformulation, we demonstrate that AQC can achieve effective compression of practical DNN models. Experiments demonstrate that adiabatic quantum computing (AQC) not only outperforms classical algorithms like genetic algorithms and reinforcement learning in terms of time efficiency but also excels at identifying global optima.
Neural networks hold great potential to act as approximate models of nonlinear dynamical systems, with the resulting neural approximations enabling verification and control of such systems. However, in safety-critical contexts, the use of neural approximations requires formal bounds on their closeness to the underlying system. To address this fundamental challenge, we propose a novel, adaptive, and parallelizable verification method based on certified first-order models. Our approach provides formal error bounds on the neural approximations of dynamical systems, allowing them to be safely employed as surrogates by interpreting the error bound as bounded disturbances acting on the approximated dynamics. We demonstrate the effectiveness and scalability of our method on a range of established benchmarks from the literature, showing that it outperforms the state-of-the-art. Furthermore, we highlight the flexibility of our framework by applying it to two novel scenarios not previously explored in this context: neural network compression and an autoencoder-based deep learning architecture for learning Koopman operators, both yielding compelling results.
Deep Neural Networks (DNNs) have encountered an emerging deployment challenge due to large and expensive memory and computation requirements. In this paper, we present a new Adaptive-Rank Singular Value Decomposition (ARSVD) method that approximates the optimal rank for compressing weight matrices in neural networks using spectral entropy. Unlike conventional SVD-based methods that apply a fixed-rank truncation across all layers, ARSVD uses an adaptive selection of the rank per layer through the entropy distribution of its singular values. This approach ensures that each layer will retain a certain amount of its informational content, thereby reducing redundancy. Our method enables efficient, layer-wise compression, yielding improved performance with reduced space and time complexity compared to static-rank reduction techniques.
Zero-shot quantization (ZSQ) enables neural network compression without original training data, making it a promising solution for restricted data access scenarios. To compensate for the lack of data, recent ZSQ methods typically rely on synthetic inputs generated from the full-precision model. However, these synthetic inputs often lead to activation distortion, especially under low-bit settings. As a result, existing methods struggle to mitigate this issue due to coarse activation scaling. To address this issue, we propose GranQ, a novel activation quantization framework that efficiently applies per-channel scaling through vectorized computation. In contrast to conventional channel-wise methods, which apply vectorization only to the quantization step, GranQ improves efficiency by vectorizing the scaling operation. This design allows GranQ to maintain fine-grained quantization granularity with minimal computational overhead, even in low-bit environments. Extensive experiments under quantization-aware training (QAT) settings demonstrate that GranQ consistently outperforms state-of-the-art ZSQ methods across CIFAR and ImageNet. In particular, our method achieves up to 5.45% higher accuracy in the 3-bit setting on CIFAR-100 and even surpasses the full-precision baseline on CIFAR-10. Furthermore, GranQ achieves significant speedup in quantization latency over conventional per-channel methods, demonstrating improved efficiency. With these findings, we anticipate that GranQ will inspire future research beyond conventional ZSQ approaches centered on data generation and model fine-tuning.
Quantization-Aware Training (QAT) is one of the prevailing neural network compression solutions. However, its stability has been challenged for yielding deteriorating performances as the quantization error is inevitable. We find that the sharp landscape of loss, which leads to a dramatic performance drop, is an essential factor that causes instability. Theoretically, we have discovered that the perturbations in the feature would bring a flat local minima. However, simply adding perturbations into either weight or feature empirically deteriorates the performance of the Full Precision (FP) model. In this paper, we propose Feature-Perturbed Quantization (FPQ) to stochastically perturb the feature and employ the feature distillation method to the quantized model. Our method generalizes well to different network architectures and various QAT methods. Furthermore, we mathematically show that FPQ implicitly regularizes the Hessian norm, which calibrates the smoothness of a loss landscape. Extensive experiments demonstrate that our approach significantly outperforms the current State-Of-The-Art (SOTA) QAT methods and even the FP counterparts.
The deployment of deep learning (DL) models for precoding in massive multiple-input multiple-output (mMIMO) systems is often constrained by high computational demands and energy consumption. In this paper, we investigate the compute energy efficiency of mMIMO precoders using DL-based approaches, comparing them to conventional methods such as zero forcing and weighted minimum mean square error (WMMSE). Our energy consumption model accounts for both memory access and calculation energy within DL accelerators. We propose a framework that incorporates mixed-precision quantization-aware training and neural architecture search to reduce energy usage without compromising accuracy. Using a ray-tracing dataset covering various base station sites, we analyze how site-specific conditions affect the energy efficiency of compressed models. Our results show that deep neural network compression generates precoders with up to 35 times higher energy efficiency than WMMSE at equal performance, depending on the scenario and the desired rate. These results establish a foundation and a benchmark for the development of energy-efficient DL-based mMIMO precoders.
Deep neural networks suffer from storing millions and billions of weights in memory post-training, making challenging memory-intensive models to deploy on embedded devices. The weight-sharing technique is one of the popular compression approaches that use fewer weight values and share across specific connections in the network. In this paper, we propose a multi-objective evolutionary algorithm (MOEA) based compression framework independent of neural network architecture, dimension, task, and dataset. We use uniformly sized bins to quantize network weights into a single codebook (lookup table) for efficient weight representation. Using MOEA, we search for Pareto optimal $k$ bins by optimizing two objectives. Then, we apply the iterative merge technique to non-dominated Pareto frontier solutions by combining neighboring bins without degrading performance to decrease the number of bins and increase the compression ratio. Our approach is model- and layer-independent, meaning the weights are mixed in the clusters from any layer, and the uniform quantization method used in this work has $O(N)$ complexity instead of non-uniform quantization methods such as k-means with $O(Nkt)$ complexity. In addition, we use the center of clusters as the shared weight values instead of retraining shared weights, which is computationally expensive. The advantage of using evolutionary multi-objective optimization is that it can obtain non-dominated Pareto frontier solutions with respect to performance and shared weights. The experimental results show that we can reduce the neural network memory by $13.72 \sim14.98 \times$ on CIFAR-10, $11.61 \sim 12.99\times$ on CIFAR-100, and $7.44 \sim 8.58\times$ on ImageNet showcasing the effectiveness of the proposed deep neural network compression framework.
Knowledge Distillation is a commonly used Deep Neural Network (DNN) compression method, which often maintains overall generalization performance. However, we show that even for balanced image classification datasets, such as CIFAR-100, Tiny ImageNet and ImageNet, as many as 41% of the classes are statistically significantly affected by distillation when comparing class-wise accuracy (i.e. class bias) between a teacher/distilled student or distilled student/non-distilled student model. Changes in class bias are not necessarily an undesirable outcome when considered outside of the context of a model's usage. Using two common fairness metrics, Demographic Parity Difference (DPD) and Equalized Odds Difference (EOD) on models trained with the CelebA, Trifeature, and HateXplain datasets, our results suggest that increasing the distillation temperature improves the distilled student model's fairness, and the distilled student fairness can even surpass the fairness of the teacher model at high temperatures. Additionally, we examine individual fairness, ensuring similar instances receive similar predictions. Our results confirm that higher temperatures also improve the distilled student model's individual fairness. This study highlights the uneven effects of distillation on certain classes and its potentially significant role in fairness, emphasizing that caution is warranted when using distilled models for sensitive application domains.
Knowledge Distillation (KD) has emerged as a pivotal technique for neural network compression and performance enhancement. Most KD methods aim to transfer dark knowledge from a cumbersome teacher model to a lightweight student model based on Kullback-Leibler (KL) divergence loss. However, the student performance improvements achieved through KD exhibit diminishing marginal returns, where a stronger teacher model does not necessarily lead to a proportionally stronger student model. To address this issue, we empirically find that the KL-based KD method may implicitly change the inter-class relationships learned by the student model, resulting in a more complex and ambiguous decision boundary, which in turn reduces the model's accuracy and generalization ability. Therefore, this study argues that the student model should learn not only the probability values from the teacher's output but also the relative ranking of classes, and proposes a novel Correlation Matching Knowledge Distillation (CMKD) method that combines the Pearson and Spearman correlation coefficients-based KD loss to achieve more efficient and robust distillation from a stronger teacher model. Moreover, considering that samples vary in difficulty, CMKD dynamically adjusts the weights of the Pearson-based loss and Spearman-based loss. CMKD is simple yet practical, and extensive experiments demonstrate that it can consistently achieve state-of-the-art performance on CIRAR-100 and ImageNet, and adapts well to various teacher architectures, sizes, and other KD methods.
Despite the widespread use of statistical prior models in various fields, such models for neural network gradients have long been overlooked. The inherent challenge stems from their high-dimensional structures and complex interdependencies, which complicate effective modeling. In this work, we demonstrate the potential of large language models (LLMs) to act as gradient priors in a zero-shot setting. We examine the property by considering lossless gradient compression -- a critical application in distributed learning -- that depends heavily on precise probability modeling. To achieve this, we introduce LM-GC, a novel method that integrates LLMs with arithmetic coding. Our technique converts plain gradients into text-like formats, enhancing token efficiency by up to 38 times compared to their plain representations. We ensure that this data conversion maintains a close alignment with the structure of plain gradients and the symbols commonly recognized by LLMs. Our experiments indicate that LM-GC surpasses existing state-of-the-art lossless compression methods, improving compression rates by 10% up to 17.2% across various datasets and architectures. Additionally, our approach shows promising compatibility with lossy compression techniques such as quantization and sparsification. These findings highlight the significant potential of LLMs as a model for effectively handling gradients. Code is available at https://github.com/hui-po-wang/LM-GC.
This paper introduces a dynamic, error-bounded hierarchical matrix (H-matrix) compression method tailored for Physics-Informed Neural Networks (PINNs). The proposed approach reduces the computational complexity and memory demands of large-scale physics-based models while preserving the essential properties of the Neural Tangent Kernel (NTK). By adaptively refining hierarchical matrix approximations based on local error estimates, our method ensures efficient training and robust model performance. Empirical results demonstrate that this technique outperforms traditional compression methods, such as Singular Value Decomposition (SVD), pruning, and quantization, by maintaining high accuracy and improving generalization capabilities. Additionally, the dynamic H-matrix method enhances inference speed, making it suitable for real-time applications. This approach offers a scalable and efficient solution for deploying PINNs in complex scientific and engineering domains, bridging the gap between computational feasibility and real-world applicability.
We present TropNNC, a framework for compressing neural networks with linear and convolutional layers and ReLU activations. TropNNC is a structured compression framework based on a geometrical approach to machine/deep learning, using tropical geometry and extending the work of Misiakos et al. (2022). We use the Hausdorff distance of zonotopes in its standard continuous form to achieve a tighter approximation bound for tropical polynomials compared to previous work. This enhancement leads to the development of an effective compression algorithm that achieves superior functional approximations of neural networks. Our method is significantly easier to implement compared to other frameworks, and does not depend on the availability of training data samples. We validate our framework through extensive empirical evaluations on the MNIST, CIFAR, and ImageNet datasets. Our results demonstrate that TropNNC achieves performance on par with state-of-the-art methods like ThiNet (even surpassing it in compressing linear layers) and CUP. To the best of our knowledge, it is the first method that achieves this using tropical geometry.
Despite their high accuracy, complex neural networks demand significant computational resources, posing challenges for deployment on resource-constrained devices such as mobile phones and embedded systems. Compression algorithms have been developed to address these challenges by reducing model size and computational demands while maintaining accuracy. Among these approaches, factorization methods based on tensor decomposition are theoretically sound and effective. However, they face difficulties in selecting the appropriate rank for decomposition. This paper tackles this issue by presenting a unified framework that simultaneously applies decomposition and optimal rank selection, employing a composite compression loss within defined rank constraints. Our approach includes an automatic rank search in a continuous space, efficiently identifying optimal rank configurations without the use of training data, making it computationally efficient. Combined with a subsequent fine-tuning step, our approach maintains the performance of highly compressed models on par with their original counterparts. Using various benchmark datasets, we demonstrate the efficacy of our method through a comprehensive analysis.
Deep neural networks typically impose significant computational loads and memory consumption. Moreover, the large parameters pose constraints on deploying the model on edge devices such as embedded systems. Tensor decomposition offers a clear advantage in compressing large-scale weight tensors. Nevertheless, direct utilization of low-rank decomposition typically leads to significant accuracy loss. This paper proposes a model compression method that integrates Variational Bayesian Matrix Factorization (VBMF) with orthogonal regularization. Initially, the model undergoes over-parameterization and training, with orthogonal regularization applied to enhance its likelihood of achieving the accuracy of the original model. Secondly, VBMF is employed to estimate the rank of the weight tensor at each layer. Our framework is sufficiently general to apply to other convolutional neural networks and easily adaptable to incorporate other tensor decomposition methods. Experimental results show that for both high and low compression ratios, our compression model exhibits advanced performance.
Knowledge distillation (KD) is a key element in neural network compression that allows knowledge transfer from a pre-trained teacher model to a more compact student model. KD relies on access to the training dataset, which may not always be fully available due to privacy concerns or logistical issues related to the size of the data. To address this, "data-free" KD methods use synthetic data, generated through model inversion, to mimic the target data distribution. However, conventional model inversion methods are not designed to utilize supplementary information from the target dataset, and thus, cannot leverage it to improve performance, even when it is available. In this paper, we consider condensed samples, as a form of supplementary information, and introduce a method for using them to better approximate the target data distribution, thereby enhancing the KD performance. Our approach is versatile, evidenced by improvements of up to 11.4% in KD accuracy across various datasets and model inversion-based methods. Importantly, it remains effective even when using as few as one condensed sample per class, and can also enhance performance in few-shot scenarios where only limited real data samples are available.
The fast development of object detection techniques has attracted attention to developing efficient Deep Neural Networks (DNNs). However, the current state-of-the-art DNN models can not provide a balanced solution among accuracy, speed, and model size. This paper proposes an efficient real-time object detection framework on resource-constrained hardware devices through hardware and software co-design. The Tensor Train (TT) decomposition is proposed for compressing the YOLOv5 model. By unitizing the unique characteristics given by the TT decomposition, we develop an efficient hardware accelerator based on FPGA devices. Experimental results show that the proposed method can significantly reduce the model size and improve the execution time.
Large neural networks have aroused impressive progress in various real world applications. However, the expensive storage and computational resources requirement for running deep networks make them problematic to be deployed on mobile devices. Recently, matrix and tensor decompositions have been employed for compressing neural networks. In this paper, we develop a simultaneous tensor decomposition technique for network optimization. The shared network structure is first discussed. Sometimes, not only the structure but also the parameters are shared to form a compressed model at the expense of degraded performance. This indicates that the weight tensors between layers within one network contain both identical components and independent components. To utilize this characteristic, two new coupled tensor train decompositions are developed for fully and partly structure sharing cases, and an alternating optimization approach is proposed for low rank tensor computation. Finally, we restore the performance of the neural network model by fine-tuning. The compression ratio of the devised approach can then be calculated. Experimental results are also included to demonstrate the benefits of our algorithm for both applications of image reconstruction and classification, using the well known datasets such as Cifar-10/Cifar-100 and ImageNet and widely used networks such as ResNet. Comparing to the state-of-the-art independent matrix and tensor decomposition based methods, our model can obtain a better network performance under the same compression ratio.
Binary Neural Networks (BNNs) enable efficient deep learning by saving on storage and computational costs. However, as the size of neural networks continues to grow, meeting computational requirements remains a challenge. In this work, we propose a new form of quantization to tile neural network layers with sequences of bits to achieve sub-bit compression of binary-weighted neural networks. The method learns binary vectors (i.e. tiles) to populate each layer of a model via aggregation and reshaping operations. During inference, the method reuses a single tile per layer to represent the full tensor. We employ the approach to both fully-connected and convolutional layers, which make up the breadth of space in most neural architectures. Empirically, the approach achieves near fullprecision performance on a diverse range of architectures (CNNs, Transformers, MLPs) and tasks (classification, segmentation, and time series forecasting) with up to an 8x reduction in size compared to binary-weighted models. We provide two implementations for Tiled Bit Networks: 1) we deploy the model to a microcontroller to assess its feasibility in resource-constrained environments, and 2) a GPU-compatible inference kernel to facilitate the reuse of a single tile per layer in memory.