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.
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.
The development of model compression is continuously motivated by the evolution of various neural network accelerators with ASIC or FPGA. On the algorithm side, the ultimate goal of quantization or pruning is accelerating the expensive DNN computations on low-power hardware. However, such a "design-and-deploy" workflow faces under-explored challenges in the current hardware-algorithm co-design community. First, although the state-of-the-art quantization algorithm can achieve low precision with negligible degradation of accuracy, the latest deep learning framework (e.g., PyTorch) can only support non-customizable 8-bit precision, data format, and parameter extraction. Secondly, the objective of quantization is to enable the computation with low-precision data. However, the current SoTA algorithm treats the quantized integer as an intermediate result, while the final output of the quantizer is the "discretized" floating-point values, ignoring the practical needs and adding additional workload to hardware designers for integer parameter extraction and layer fusion. Finally, the compression toolkits designed by the industry are constrained to their in-house product or a handful of algorithms. The limited degree of freedom in the current toolkit and the under-explored customization hinder the prototype ASIC or FPGA-based accelerator design. To resolve these challenges, we propose Torch2Chip, an open-sourced, fully customizable, and high-performance toolkit that supports user-designed compression followed by automatic model fusion and parameter extraction. Torch2Chip incorporates the hierarchical design workflow, and the user-customized compression algorithm will be directly packed into the deployment-ready format for prototype chip verification with either CNN or vision transformer (ViT). The code is available at https://github.com/SeoLabCornell/torch2chip.
Structural pruning of neural networks conventionally relies on identifying and discarding less important neurons, a practice often resulting in significant accuracy loss that necessitates subsequent fine-tuning efforts. This paper introduces a novel approach named Intra-Fusion, challenging this prevailing pruning paradigm. Unlike existing methods that focus on designing meaningful neuron importance metrics, Intra-Fusion redefines the overlying pruning procedure. Through utilizing the concepts of model fusion and Optimal Transport, we leverage an agnostically given importance metric to arrive at a more effective sparse model representation. Notably, our approach achieves substantial accuracy recovery without the need for resource-intensive fine-tuning, making it an efficient and promising tool for neural network compression. Additionally, we explore how fusion can be added to the pruning process to significantly decrease the training time while maintaining competitive performance. We benchmark our results for various networks on commonly used datasets such as CIFAR-10, CIFAR-100, and ImageNet. More broadly, we hope that the proposed Intra-Fusion approach invigorates exploration into a fresh alternative to the predominant compression approaches. Our code is available here: https://github.com/alexandertheus/Intra-Fusion.
Model quantization, which aims to compress deep neural networks and accelerate inference speed, has greatly facilitated the development of cumbersome models on mobile and edge devices. There is a common assumption in quantization methods from prior works that training data is available. In practice, however, this assumption cannot always be fulfilled due to reasons of privacy and security, rendering these methods inapplicable in real-life situations. Thus, data-free network quantization has recently received significant attention in neural network compression. Causal reasoning provides an intuitive way to model causal relationships to eliminate data-driven correlations, making causality an essential component of analyzing data-free problems. However, causal formulations of data-free quantization are inadequate in the literature. To bridge this gap, we construct a causal graph to model the data generation and discrepancy reduction between the pre-trained and quantized models. Inspired by the causal understanding, we propose the Causality-guided Data-free Network Quantization method, Causal-DFQ, to eliminate the reliance on data via approaching an equilibrium of causality-driven intervened distributions. Specifically, we design a content-style-decoupled generator, synthesizing images conditioned on the relevant and irrelevant factors; then we propose a discrepancy reduction loss to align the intervened distributions of the pre-trained and quantized models. It is worth noting that our work is the first attempt towards introducing causality to data-free quantization problem. Extensive experiments demonstrate the efficacy of Causal-DFQ. The code is available at https://github.com/42Shawn/Causal-DFQ.
Modern deep neural networks, particularly recent large language models, come with massive model sizes that require significant computational and storage resources. To enable the deployment of modern models on resource-constrained environments and accelerate inference time, researchers have increasingly explored pruning techniques as a popular research direction in neural network compression. However, there is a dearth of up-to-date comprehensive review papers on pruning. To address this issue, in this survey, we provide a comprehensive review of existing research works on deep neural network pruning in a taxonomy of 1) universal/specific speedup, 2) when to prune, 3) how to prune, and 4) fusion of pruning and other compression techniques. We then provide a thorough comparative analysis of eight pairs of contrast settings for pruning and explore emerging topics, including pruning for large language models, large multimodal models, post-training pruning, and different supervision levels for pruning to shed light on the commonalities and differences of existing methods and lay the foundation for further method development. To facilitate future research, we build a curated collection of datasets, networks, and evaluations on different applications. Finally, we provide valuable recommendations on selecting pruning methods and prospect several promising research directions. We build a repository at https://github.com/hrcheng1066/awesome-pruning.
Neural network compression has been an increasingly important subject, not only due to its practical relevance, but also due to its theoretical implications, as there is an explicit connection between compressibility and generalization error. Recent studies have shown that the choice of the hyperparameters of stochastic gradient descent (SGD) can have an effect on the compressibility of the learned parameter vector. These results, however, rely on unverifiable assumptions and the resulting theory does not provide a practical guideline due to its implicitness. In this study, we propose a simple modification for SGD, such that the outputs of the algorithm will be provably compressible without making any nontrivial assumptions. We consider a one-hidden-layer neural network trained with SGD, and show that if we inject additive heavy-tailed noise to the iterates at each iteration, for any compression rate, there exists a level of overparametrization such that the output of the algorithm will be compressible with high probability. To achieve this result, we make two main technical contributions: (i) we prove a 'propagation of chaos' result for a class of heavy-tailed stochastic differential equations, and (ii) we derive error estimates for their Euler discretization. Our experiments suggest that the proposed approach not only achieves increased compressibility with various models and datasets, but also leads to robust test performance under pruning, even in more realistic architectures that lie beyond our theoretical setting.
This paper introduces a novel theoretical framework for the analysis of vector-valued neural networks through the development of vector-valued variation spaces, a new class of reproducing kernel Banach spaces. These spaces emerge from studying the regularization effect of weight decay in training networks with activations like the rectified linear unit (ReLU). This framework offers a deeper understanding of multi-output networks and their function-space characteristics. A key contribution of this work is the development of a representer theorem for the vector-valued variation spaces. This representer theorem establishes that shallow vector-valued neural networks are the solutions to data-fitting problems over these infinite-dimensional spaces, where the network widths are bounded by the square of the number of training data. This observation reveals that the norm associated with these vector-valued variation spaces encourages the learning of features that are useful for multiple tasks, shedding new light on multi-task learning with neural networks. Finally, this paper develops a connection between weight-decay regularization and the multi-task lasso problem. This connection leads to novel bounds for layer widths in deep networks that depend on the intrinsic dimensions of the training data representations. This insight not only deepens the understanding of the deep network architectural requirements, but also yields a simple convex optimization method for deep neural network compression. The performance of this compression procedure is evaluated on various architectures.
Transformers' compute-intensive operations pose enormous challenges for their deployment in resource-constrained EdgeAI / tinyML devices. As an established neural network compression technique, quantization reduces the hardware computational and memory resources. In particular, fixed-point quantization is desirable to ease the computations using lightweight blocks, like adders and multipliers, of the underlying hardware. However, deploying fully-quantized Transformers on existing general-purpose hardware, generic AI accelerators, or specialized architectures for Transformers with floating-point units might be infeasible and/or inefficient. Towards this, we propose SwiftTron, an efficient specialized hardware accelerator designed for Quantized Transformers. SwiftTron supports the execution of different types of Transformers' operations (like Attention, Softmax, GELU, and Layer Normalization) and accounts for diverse scaling factors to perform correct computations. We synthesize the complete SwiftTron architecture in a $65$ nm CMOS technology with the ASIC design flow. Our Accelerator executes the RoBERTa-base model in 1.83 ns, while consuming 33.64 mW power, and occupying an area of 273 mm^2. To ease the reproducibility, the RTL of our SwiftTron architecture is released at https://github.com/albertomarchisio/SwiftTron.
Filter pruning has attracted increasing attention in recent years for its capacity in compressing and accelerating convolutional neural networks. Various data-independent criteria, including norm-based and relationship-based ones, were proposed to prune the most unimportant filters. However, these state-of-the-art criteria fail to fully consider the dissimilarity of filters, and thus might lead to performance degradation. In this paper, we first analyze the limitation of relationship-based criteria with examples, and then introduce a new data-independent criterion, Weighted Hybrid Criterion (WHC), to tackle the problems of both norm-based and relationship-based criteria. By taking the magnitude of each filter and the linear dependence between filters into consideration, WHC can robustly recognize the most redundant filters, which can be safely pruned without introducing severe performance degradation to networks. Extensive pruning experiments in a simple one-shot manner demonstrate the effectiveness of the proposed WHC. In particular, WHC can prune ResNet-50 on ImageNet with more than 42% of floating point operations reduced without any performance loss in top-5 accuracy.
Structural pruning enables model acceleration by removing structurally-grouped parameters from neural networks. However, the parameter-grouping patterns vary widely across different models, making architecture-specific pruners, which rely on manually-designed grouping schemes, non-generalizable to new architectures. In this work, we study a highly-challenging yet barely-explored task, any structural pruning, to tackle general structural pruning of arbitrary architecture like CNNs, RNNs, GNNs and Transformers. The most prominent obstacle towards this goal lies in the structural coupling, which not only forces different layers to be pruned simultaneously, but also expects all removed parameters to be consistently unimportant, thereby avoiding structural issues and significant performance degradation after pruning. To address this problem, we propose a general and {fully automatic} method, \emph{Dependency Graph} (DepGraph), to explicitly model the dependency between layers and comprehensively group coupled parameters for pruning. In this work, we extensively evaluate our method on several architectures and tasks, including ResNe(X)t, DenseNet, MobileNet and Vision transformer for images, GAT for graph, DGCNN for 3D point cloud, alongside LSTM for language, and demonstrate that, even with a simple norm-based criterion, the proposed method consistently yields gratifying performances.
Post-training quantization (PTQ) is a neural network compression technique that converts a full-precision model into a quantized model using lower-precision data types. Although it can help reduce the size and computational cost of deep neural networks, it can also introduce quantization noise and reduce prediction accuracy, especially in extremely low-bit settings. How to determine the appropriate quantization parameters (e.g., scaling factors and rounding of weights) is the main problem facing now. Existing methods attempt to determine these parameters by minimize the distance between features before and after quantization, but such an approach only considers local information and may not result in the most optimal quantization parameters. We analyze this issue and ropose PD-Quant, a method that addresses this limitation by considering global information. It determines the quantization parameters by using the information of differences between network prediction before and after quantization. In addition, PD-Quant can alleviate the overfitting problem in PTQ caused by the small number of calibration sets by adjusting the distribution of activations. Experiments show that PD-Quant leads to better quantization parameters and improves the prediction accuracy of quantized models, especially in low-bit settings. For example, PD-Quant pushes the accuracy of ResNet-18 up to 53.14% and RegNetX-600MF up to 40.67% in weight 2-bit activation 2-bit. The code is released at https://github.com/hustvl/PD-Quant.
We propose to minimize a generic differentiable objective with $L_1$ constraint using a simple reparametrization and straightforward stochastic gradient descent. Our proposal is the direct generalization of previous ideas that the $L_1$ penalty may be equivalent to a differentiable reparametrization with weight decay. We prove that the proposed method, \textit{spred}, is an exact differentiable solver of $L_1$ and that the reparametrization trick is completely ``benign" for a generic nonconvex function. Practically, we demonstrate the usefulness of the method in (1) training sparse neural networks to perform gene selection tasks, which involves finding relevant features in a very high dimensional space, and (2) neural network compression task, to which previous attempts at applying the $L_1$-penalty have been unsuccessful. Conceptually, our result bridges the gap between the sparsity in deep learning and conventional statistical learning.
Recent isotropic networks, such as ConvMixer and vision transformers, have found significant success across visual recognition tasks, matching or outperforming non-isotropic convolutional neural networks (CNNs). Isotropic architectures are particularly well-suited to cross-layer weight sharing, an effective neural network compression technique. In this paper, we perform an empirical evaluation on methods for sharing parameters in isotropic networks (SPIN). We present a framework to formalize major weight sharing design decisions and perform a comprehensive empirical evaluation of this design space. Guided by our experimental results, we propose a weight sharing strategy to generate a family of models with better overall efficiency, in terms of FLOPs and parameters versus accuracy, compared to traditional scaling methods alone, for example compressing ConvMixer by 1.9x while improving accuracy on ImageNet. Finally, we perform a qualitative study to further understand the behavior of weight sharing in isotropic architectures. The code is available at https://github.com/apple/ml-spin.
Convolutional Neural Networks (CNNs) are known for requiring extensive computational resources, and quantization is among the best and most common methods for compressing them. While aggressive quantization (i.e., less than 4-bits) performs well for classification, it may cause severe performance degradation in image-to-image tasks such as semantic segmentation and depth estimation. In this paper, we propose Wavelet Compressed Convolution (WCC) -- a novel approach for high-resolution activation maps compression integrated with point-wise convolutions, which are the main computational cost of modern architectures. To this end, we use an efficient and hardware-friendly Haar-wavelet transform, known for its effectiveness in image compression, and define the convolution on the compressed activation map. We experiment with various tasks that benefit from high-resolution input. By combining WCC with light quantization, we achieve compression rates equivalent to 1-4bit activation quantization with relatively small and much more graceful degradation in performance. Our code is available at https://github.com/BGUCompSci/WaveletCompressedConvolution.
Memory footprint is one of the main limiting factors for large neural network training. In backpropagation, one needs to store the input to each operation in the computational graph. Every modern neural network model has quite a few pointwise nonlinearities in its architecture, and such operation induces additional memory costs which -- as we show -- can be significantly reduced by quantization of the gradients. We propose a systematic approach to compute optimal quantization of the retained gradients of the pointwise nonlinear functions with only a few bits per each element. We show that such approximation can be achieved by computing optimal piecewise-constant approximation of the derivative of the activation function, which can be done by dynamic programming. The drop-in replacements are implemented for all popular nonlinearities and can be used in any existing pipeline. We confirm the memory reduction and the same convergence on several open benchmarks.
ACAS Xu is an air-to-air collision avoidance system designed for unmanned aircraft that issues horizontal turn advisories to avoid an intruder aircraft. Due the use of a large lookup table in the design, a neural network compression of the policy was proposed. Analysis of this system has spurred a significant body of research in the formal methods community on neural network verification. While many powerful methods have been developed, most work focuses on open-loop properties of the networks, rather than the main point of the system -- collision avoidance -- which requires closed-loop analysis. In this work, we develop a technique to verify a closed-loop approximation of the system using state quantization and backreachability. We use favorable assumptions for the analysis -- perfect sensor information, instant following of advisories, ideal aircraft maneuvers and an intruder that only flies straight. When the method fails to prove the system is safe, we refine the quantization parameters until generating counterexamples where the original (non-quantized) system also has collisions.
Filter pruning has been widely used for neural network compression because of its enabled practical acceleration. To date, most of the existing filter pruning works explore the importance of filters via using intra-channel information. In this paper, starting from an inter-channel perspective, we propose to perform efficient filter pruning using Channel Independence, a metric that measures the correlations among different feature maps. The less independent feature map is interpreted as containing less useful information$/$knowledge, and hence its corresponding filter can be pruned without affecting model capacity. We systematically investigate the quantification metric, measuring scheme and sensitiveness$/$reliability of channel independence in the context of filter pruning. Our evaluation results for different models on various datasets show the superior performance of our approach. Notably, on CIFAR-10 dataset our solution can bring $0.90\%$ and $0.94\%$ accuracy increase over baseline ResNet-56 and ResNet-110 models, respectively, and meanwhile the model size and FLOPs are reduced by $42.8\%$ and $47.4\%$ (for ResNet-56) and $48.3\%$ and $52.1\%$ (for ResNet-110), respectively. On ImageNet dataset, our approach can achieve $40.8\%$ and $44.8\%$ storage and computation reductions, respectively, with $0.15\%$ accuracy increase over the baseline ResNet-50 model. The code is available at https://github.com/Eclipsess/CHIP_NeurIPS2021.
We propose a novel neural representation for videos (NeRV) which encodes videos in neural networks. Unlike conventional representations that treat videos as frame sequences, we represent videos as neural networks taking frame index as input. Given a frame index, NeRV outputs the corresponding RGB image. Video encoding in NeRV is simply fitting a neural network to video frames and decoding process is a simple feedforward operation. As an image-wise implicit representation, NeRV output the whole image and shows great efficiency compared to pixel-wise implicit representation, improving the encoding speed by 25x to 70x, the decoding speed by 38x to 132x, while achieving better video quality. With such a representation, we can treat videos as neural networks, simplifying several video-related tasks. For example, conventional video compression methods are restricted by a long and complex pipeline, specifically designed for the task. In contrast, with NeRV, we can use any neural network compression method as a proxy for video compression, and achieve comparable performance to traditional frame-based video compression approaches (H.264, HEVC \etc). Besides compression, we demonstrate the generalization of NeRV for video denoising. The source code and pre-trained model can be found at https://github.com/haochen-rye/NeRV.git.
Knowledge Distillation is becoming one of the primary trends among neural network compression algorithms to improve the generalization performance of a smaller student model with guidance from a larger teacher model. This momentous rise in applications of knowledge distillation is accompanied by the introduction of numerous algorithms for distilling the knowledge such as soft targets and hint layers. Despite this advancement in different techniques for distilling the knowledge, the aggregation of different paths for distillation has not been studied comprehensively. This is of particular significance, not only because different paths have different importance, but also due to the fact that some paths might have negative effects on the generalization performance of the student model. Hence, we need to adaptively adjust the importance of each path to maximize the impact of distillation on the student model. In this paper, we explore different approaches for aggregating these different paths and introduce our proposed adaptive approach based on multitask learning methods. We empirically demonstrate the effectiveness of the proposed approach over other baselines on the applications of knowledge distillation in classification, semantic segmentation, and object detection tasks.