Neural network (NN) compression via techniques such as pruning, quantization requires setting compression hyperparameters (e.g., number of channels to be pruned, bitwidths for quantization) for each layer either manually or via neural architecture search (NAS) which can be computationally expensive. We address this problem by providing an end-to-end technique that optimizes for model's Floating Point Operations (FLOPs) or for on-device latency via a novel $\frac{\ell_1}{\ell_2}$ latency surrogate. Our algorithm is versatile and can be used with many popular compression methods including pruning, low-rank factorization, and quantization. Crucially, it is fast and runs in almost the same amount of time as single model training; which is a significant training speed-up over standard NAS methods. For BERT compression on GLUE fine-tuning tasks, we achieve $50\%$ reduction in FLOPs with only $1\%$ drop in performance. For compressing MobileNetV3 on ImageNet-1K, we achieve $15\%$ reduction in FLOPs, and $11\%$ reduction in on-device latency without drop in accuracy, while still requiring $3\times$ less training compute than SOTA compression techniques. Finally, for transfer learning on smaller datasets, our technique identifies $1.2\times$-$1.4\times$ cheaper architectures than standard MobileNetV3, EfficientNet suite of architectures at almost the same training cost and accuracy.
Pre-trained Transformer models like T5 and BART have advanced the state of the art on a wide range of text generation tasks. Compressing these models into smaller ones has become critically important for practical use. Common neural network compression techniques such as knowledge distillation or quantization are limited to static compression where the compression ratio is fixed. In this paper, we introduce Modular Transformers, a modularized encoder-decoder framework for flexible sequence-to-sequence model compression. Modular Transformers train modularized layers that have the same function of two or more consecutive layers in the original model via module replacing and knowledge distillation. After training, the modularized layers can be flexibly assembled into sequence-to-sequence models that meet different performance-efficiency trade-offs. Experimental results show that after a single training phase, by simply varying the assembling strategy, Modular Transformers can achieve flexible compression ratios from 1.1x to 6x with little to moderate relative performance drop.
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.
There is a lot of ongoing research effort into developing different techniques for neural networks compression. However, the community lacks standardised evaluation metrics, which are key to identifying the most suitable compression technique for different applications. This paper reviews existing neural network compression evaluation metrics and implements them into a standardisation framework called NetZIP. We introduce two novel metrics to cover existing gaps of evaluation in the literature: 1) Compression and Hardware Agnostic Theoretical Speed (CHATS) and 2) Overall Compression Success (OCS). We demonstrate the use of NetZIP using two case studies on two different hardware platforms (a PC and a Raspberry Pi 4) focusing on object classification and object detection.
Tensor decompositions have been successfully applied to compress neural networks. The compression algorithms using tensor decompositions commonly minimize the approximation error on the weights. Recent work assumes the approximation error on the weights is a proxy for the performance of the model to compress multiple layers and fine-tune the compressed model. Surprisingly, little research has systematically evaluated which approximation errors can be used to make choices regarding the layer, tensor decomposition method, and level of compression. To close this gap, we perform an experimental study to test if this assumption holds across different layers and types of decompositions, and what the effect of fine-tuning is. We include the approximation error on the features resulting from a compressed layer in our analysis to test if this provides a better proxy, as it explicitly takes the data into account. We find the approximation error on the weights has a positive correlation with the performance error, before as well as after fine-tuning. Basing the approximation error on the features does not improve the correlation significantly. While scaling the approximation error commonly is used to account for the different sizes of layers, the average correlation across layers is smaller than across all choices (i.e. layers, decompositions, and level of compression) before fine-tuning. When calculating the correlation across the different decompositions, the average rank correlation is larger than across all choices. This means multiple decompositions can be considered for compression and the approximation error can be used to choose between them.
Neural network model compression techniques can address the computation issue of deep neural networks on embedded devices in industrial systems. The guaranteed output error computation problem for neural network compression with quantization is addressed in this paper. A merged neural network is built from a feedforward neural network and its quantized version to produce the exact output difference between two neural networks. Then, optimization-based methods and reachability analysis methods are applied to the merged neural network to compute the guaranteed quantization error. Finally, a numerical example is proposed to validate the applicability and effectiveness of the proposed approach.
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.
Deep reinforcement learning has achieved great success in various fields with its super decision-making ability. However, the policy learning process requires a large amount of training time, causing energy consumption. Inspired by the redundancy of neural networks, we propose a lightweight parallel training framework based on neural network compression, AcceRL, to accelerate the policy learning while ensuring policy quality. Specifically, AcceRL speeds up the experience collection by flexibly combining various neural network compression methods. Overall, the AcceRL consists of five components, namely Actor, Learner, Compressor, Corrector, and Monitor. The Actor uses the Compressor to compress the Learner's policy network to interact with the environment. And the generated experiences are transformed by the Corrector with Off-Policy methods, such as V-trace, Retrace and so on. Then the corrected experiences are feed to the Learner for policy learning. We believe this is the first general reinforcement learning framework that incorporates multiple neural network compression techniques. Extensive experiments conducted in gym show that the AcceRL reduces the time cost of the actor by about 2.0 X to 4.13 X compared to the traditional methods. Furthermore, the AcceRL reduces the whole training time by about 29.8% to 40.3% compared to the traditional methods while keeps the same policy quality.
Binarization is a powerful compression technique for neural networks, significantly reducing FLOPs, but often results in a significant drop in model performance. To address this issue, partial binarization techniques have been developed, but a systematic approach to mixing binary and full-precision parameters in a single network is still lacking. In this paper, we propose a controlled approach to partial binarization, creating a budgeted binary neural network (B2NN) with our MixBin strategy. This method optimizes the mixing of binary and full-precision components, allowing for explicit selection of the fraction of the network to remain binary. Our experiments show that B2NNs created using MixBin outperform those from random or iterative searches and state-of-the-art layer selection methods by up to 3% on the ImageNet-1K dataset. We also show that B2NNs outperform the structured pruning baseline by approximately 23% at the extreme FLOP budget of 15%, and perform well in object tracking, with up to a 12.4% relative improvement over other baselines. Additionally, we demonstrate that B2NNs developed by MixBin can be transferred across datasets, with some cases showing improved performance over directly applying MixBin on the downstream data.
Compression of convolutional neural network models has recently been dominated by pruning approaches. A class of previous works focuses solely on pruning the unimportant filters to achieve network compression. Another important direction is the design of sparsity-inducing constraints which has also been explored in isolation. This paper presents a novel training scheme based on composite constraints that prune redundant filters and minimize their effect on overall network learning via sparsity promotion. Also, as opposed to prior works that employ pseudo-norm-based sparsity-inducing constraints, we propose a sparse scheme based on gradient counting in our framework. Our tests on several pixel-wise segmentation benchmarks show that the number of neurons and the memory footprint of networks in the test phase are significantly reduced without affecting performance. MobileNetV3 and UNet, two well-known architectures, are used to test the proposed scheme. Our network compression method not only results in reduced parameters but also achieves improved performance compared to MobileNetv3, which is an already optimized architecture.
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.
Quantization, knowledge distillation, and magnitude pruning are among the most popular methods for neural network compression in NLP. Independently, these methods reduce model size and can accelerate inference, but their relative benefit and combinatorial interactions have not been rigorously studied. For each of the eight possible subsets of these techniques, we compare accuracy vs. model size tradeoffs across six BERT architecture sizes and eight GLUE tasks. We find that quantization and distillation consistently provide greater benefit than pruning. Surprisingly, except for the pair of pruning and quantization, using multiple methods together rarely yields diminishing returns. Instead, we observe complementary and super-multiplicative reductions to model size. Our work quantitatively demonstrates that combining compression methods can synergistically reduce model size, and that practitioners should prioritize (1) quantization, (2) knowledge distillation, and (3) pruning to maximize accuracy vs. model size tradeoffs.
In this paper, we introduce a novel method of neural network weight compression. In our method, we store weight tensors as sparse, quantized matrix factors, whose product is computed on the fly during inference to generate the target model's weights. We use projected gradient descent methods to find quantized and sparse factorization of the weight tensors. We show that this approach can be seen as a unification of weight SVD, vector quantization, and sparse PCA. Combined with end-to-end fine-tuning our method exceeds or is on par with previous state-of-the-art methods in terms of the trade-off between accuracy and model size. Our method is applicable to both moderate compression regimes, unlike vector quantization, and extreme compression regimes.
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.
Model compression, such as pruning and quantization, has been widely applied to optimize neural networks on resource-limited classical devices. Recently, there are growing interest in variational quantum circuits (VQC), that is, a type of neural network on quantum computers (a.k.a., quantum neural networks). It is well known that the near-term quantum devices have high noise and limited resources (i.e., quantum bits, qubits); yet, how to compress quantum neural networks has not been thoroughly studied. One might think it is straightforward to apply the classical compression techniques to quantum scenarios. However, this paper reveals that there exist differences between the compression of quantum and classical neural networks. Based on our observations, we claim that the compilation/traspilation has to be involved in the compression process. On top of this, we propose the very first systematical framework, namely CompVQC, to compress quantum neural networks (QNNs).In CompVQC, the key component is a novel compression algorithm, which is based on the alternating direction method of multipliers (ADMM) approach. Experiments demonstrate the advantage of the CompVQC, reducing the circuit depth (almost over 2.5 %) with a negligible accuracy drop (<1%), which outperforms other competitors. Another promising truth is our CompVQC can indeed promote the robustness of the QNN on the near-term noisy quantum devices.
The goal of model compression is to reduce the size of a large neural network while retaining a comparable performance. As a result, computation and memory costs in resource-limited applications may be significantly reduced by dropping redundant weights, neurons, or layers. There have been many model compression algorithms proposed that provide impressive empirical success. However, a theoretical understanding of model compression is still limited. One problem is understanding if a network is more compressible than another of the same structure. Another problem is quantifying how much one can prune a network with theoretically guaranteed accuracy degradation. In this work, we propose to use the sparsity-sensitive $\ell_q$-norm ($0<q<1$) to characterize compressibility and provide a relationship between soft sparsity of the weights in the network and the degree of compression with a controlled accuracy degradation bound. We also develop adaptive algorithms for pruning each neuron in the network informed by our theory. Numerical studies demonstrate the promising performance of the proposed methods compared with standard pruning algorithms.
Network compression is crucial to making the deep networks to be more efficient, faster, and generalizable to low-end hardware. Current network compression methods have two open problems: first, there lacks a theoretical framework to estimate the maximum compression rate; second, some layers may get over-prunned, resulting in significant network performance drop. To solve these two problems, this study propose a gradient-matrix singularity analysis-based method to estimate the maximum network redundancy. Guided by that maximum rate, a novel and efficient hierarchical network pruning algorithm is developed to maximally condense the neuronal network structure without sacrificing network performance. Substantial experiments are performed to demonstrate the efficacy of the new method for pruning several advanced convolutional neural network (CNN) architectures. Compared to existing pruning methods, the proposed pruning algorithm achieved state-of-the-art performance. At the same or similar compression ratio, the new method provided the highest network prediction accuracy as compared to other methods.