Accepted by ICML 2026. This version incorporates content from the preprint arXiv:2305.18506. The contributors of the relevant content have consented to its inclusion and have been listed as authors
Scaling factors in residual branches have emerged as a prevalent method for boosting neural network performance, especially in normalization-free architectures. While prior work has primarily examined scaling effects from an optimization perspective, this paper investigates their role in residual architectures through the lens of generalization theory. Specifically, we establish that wide residual networks (ResNets) with constant scaling factors become asymptotically unlearnable as depth increases. In contrast, when the scaling factor exhibits rapid depth-wise decay combined with early stopping, over-parameterized ResNets achieve minimax-optimal generalization rates. To establish this, we demonstrate that the generalization capability of wide ResNets can be approximated by kernel regression associated with the Neural Tangent Kernel (NTK). Our theoretical findings are validated through experiments on synthetic data and real-world classification tasks, including MNIST and CIFAR-100.
Recent works show that overparameterized networks contain small subnetworks that exhibit comparable accuracy to the full model when trained in isolation. These results highlight the potential to reduce training costs of deep neural networks without sacrificing generalization performance. However, existing approaches for finding these small networks rely on expensive multi-round train-and-prune procedures and are non-practical for large data sets and models. In this paper, we show how to find small networks that exhibit the same performance as their overparameterized counterparts after only a f…
Of theories for why large-scale machine learning models generalize despite being vastly overparameterized, which of their assumptions are needed to capture the qualitative phenomena of generalization in the real world? On one hand, we find that most theoretical analyses fall short of capturing these qualitative phenomena even for kernel regression, when applied to kernels derived from large-scale neural networks (e.g., ResNet-50) and real data (e.g., CIFAR-100). On the other hand, we find that the classical GCV estimator (Craven and Wahba, 1978) accurately predicts generalization risk even in …
A recent work from Bello shows that training and scaling strategies may be more significant than model architectures for visual recognition. This short note studies effective training and scaling strategies for video recognition models. We propose a simple scaling strategy for 3D ResNets, in combination with improved training strategies and minor architectural changes. The resulting models, termed 3D ResNet-RS, attain competitive performance of 81.0 on Kinetics-400 and 83.8 on Kinetics-600 without pre-training. When pre-trained on a large Web Video Text dataset, our best model achieves 83.5 an…
Neural networks (NNs) have been successfully deployed in many applications. However, architectural design of these models is still a challenging problem. Moreover, neural networks are known to have a lot of redundancy. This increases the computational cost of inference and poses an obstacle to deployment on Internet-of-Thing sensors and edge devices. To address these challenges, we propose the STEERAGE synthesis methodology. It consists of two complementary approaches: efficient architecture search, and grow-and-prune NN synthesis. The first step, covered in a global search module, uses an acc…
Yang (2020a) recently showed that the Neural Tangent Kernel (NTK) at initialization has an infinite-width limit for a large class of architectures including modern staples such as ResNet and Transformers. However, their analysis does not apply to training. Here, we show the same neural networks (in the so-called NTK parametrization) during training follow a kernel gradient descent dynamics in function space, where the kernel is the infinite-width NTK. This completes the proof of the *architectural universality* of NTK behavior. To achieve this result, we apply the Tensor Programs technique: Wr…
Cyber Physical Systems Technische Universität Wien（维也纳技术大学网络物理系统（Cyber Physical Systems））
This paper shows that ResNets, NeuralODEs, and CT-RNNs, are particular neural regulatory networks (NRNs), a biophysical model for the nonspiking neurons encountered in small species, such as the C.elegans nematode, and in the retina of large species. Compared to ResNets, NeuralODEs and CT-RNNs, NRNs have an additional multiplicative term in their synaptic computation, allowing them to adapt to each particular input. This additional flexibility makes NRNs $M$ times more succinct than NeuralODEs and CT-RNNs, where $M$ is proportional to the size of the training set. Moreover, as NeuralODEs and C…
Tsinghua University（清华大学）；Shanghai Jiao Tong University（上海交通大学）；PCL Research Center of Networks and Communications, Peng Cheng Laboratory（鹏城实验室网络通信PCL研究中心）；The University of Melbourne（墨尔本大学）
Skip connections are an essential component of current state-of-the-art deep neural networks (DNNs) such as ResNet, WideResNet, DenseNet, and ResNeXt. Despite their huge success in building deeper and more powerful DNNs, we identify a surprising security weakness of skip connections in this paper. Use of skip connections allows easier generation of highly transferable adversarial examples. Specifically, in ResNet-like (with skip connections) neural networks, gradients can backpropagate through either skip connections or residual modules. We find that using more gradients from the skip connecti…
Faculty of Engineering and Information Technology（工程与信息技术学院）；University of Technology Sydney（悉尼科技大学）；Suncorp Group Limited（Suncorp集团有限公司）
We show that Residual Networks (ResNet) is equivalent to boosting feature representation, without any modification to the underlying ResNet training algorithm. A regret bound based on Online Gradient Boosting theory is proved and suggests that ResNet could achieve Online Gradient Boosting regret bounds through neural network architectural changes with the addition of a shrinkage parameter in the identity skip-connections and using residual modules with max-norm bounds. Through this relation between ResNet and Online Boosting, novel feature representation boosting algorithms can be constructed …
Université Paris-Est（巴黎东部大学）；École des Ponts ParisTech（巴黎高科桥路学校）；Inria（法国国家信息与自动化研究所）
We propose to impose symmetry in neural network parameters to improve parameter usage and make use of dedicated convolution and matrix multiplication routines. Due to significant reduction in the number of parameters as a result of the symmetry constraints, one would expect a dramatic drop in accuracy. Surprisingly, we show that this is not the case, and, depending on network size, symmetry can have little or no negative effect on network accuracy, especially in deep overparameterized networks. We propose several ways to impose local symmetry in recurrent and convolutional neural networks, and…
Learning Faster without Deeper Networks: A*-Inspired Batch Selection for Efficient CNN Training
AI Laboratory, University Metropolitan Tirana（地拉那都市大学人工智能实验室）；Laboratory of Images Signals and Intelligent Systems, ESIEE Paris（巴黎高等电子与电工工程师学校图像信号与智能系统实验室）
Models recently used in the literature proving residual networks (ResNets) are better than linear predictors are actually different from standard ResNets that have been widely used in computer vision. In addition to the assumptions such as scalar-valued output or single residual block, these models have no nonlinearities at the final residual representation that feeds into the final affine layer. To codify such a difference in nonlinearities and reveal a linear estimation property, we define ResNEsts, i.e., Residual Nonlinear Estimators, by simply dropping nonlinearities at the last residual r…
TTI-Chicago（芝加哥丰田技术研究院）；University of Alberta（阿尔伯塔大学）；University of Chicago（芝加哥大学）
The search for efficient, sparse deep neural network models is most prominently performed by pruning: training a dense, overparameterized network and removing parameters, usually via following a manually-crafted heuristic. Additionally, the recent Lottery Ticket Hypothesis conjectures that, for a typically-sized neural network, it is possible to find small sub-networks which, when trained from scratch on a comparable budget, match the performance of the original dense counterpart. We revisit fundamental aspects of pruning algorithms, pointing out missing ingredients in previous approaches, and…
Google Research（谷歌研究院）；University of California, Berkeley（加州大学伯克利分校）；Princeton University（普林斯顿大学）
We study the interplay between memorization and generalization of overparameterized networks in the extreme case of a single training example and an identity-mapping task. We examine fully-connected and convolutional networks (FCN and CNN), both linear and nonlinear, initialized randomly and then trained to minimize the reconstruction error. The trained networks stereotypically take one of two forms: the constant function (memorization) and the identity function (generalization). We formally characterize generalization in single-layer FCNs and CNNs. We show empirically that different architect…
Deep equilibrium networks (DEQs) are a new class of models that eschews traditional depth in favor of finding the fixed point of a single nonlinear layer. These models have been shown to achieve performance competitive with the state-of-the-art deep networks while using significantly less memory. Yet they are also slower, brittle to architectural choices, and introduce potential instability to the model. In this paper, we propose a regularization scheme for DEQ models that explicitly regularizes the Jacobian of the fixed-point update equations to stabilize the learning of equilibrium models. W…
One of the most pressing challenges prevalent in the steel manufacturing industry is the identification of surface defects. Early identification of casting defects can help boost performance, including streamlining production processes. Though, deep learning models have helped bridge this gap and automate most of these processes, there is a dire need to come up with lightweight models that can be deployed easily with faster inference times. This research proposes a lightweight architecture that is efficient in terms of accuracy and inference time compared with sophisticated pre-trained CNN arc…
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of Michigan（密歇根大学）
We propose a scalable framework for the learning of high-dimensional parametric maps via adaptively constructed residual network (ResNet) maps between reduced bases of the inputs and outputs. When just few training data are available, it is beneficial to have a compact parametrization in order to ameliorate the ill-posedness of the neural network training problem. By linearly restricting high-dimensional maps to informed reduced bases of the inputs, one can compress high-dimensional maps in a constructive way that can be used to detect appropriate basis ranks, equipped with rigorous error esti…
Using an extended and formalized version of the Q/C map analysis of Poole et al. (2016), along with Neural Tangent Kernel theory, we identify the main pathologies present in deep networks that prevent them from training fast and generalizing to unseen data, and show how these can be avoided by carefully controlling the "shape" of the network's initialization-time kernel function. We then develop a method called Deep Kernel Shaping (DKS), which accomplishes this using a combination of precise parameter initialization, activation function transformations, and small architectural tweaks, all of w…
The rectified linear unit (ReLU) is a highly successful activation function in neural networks as it allows networks to easily obtain sparse representations, which reduces overfitting in overparameterized networks. However, in network pruning, we find that the sparsity introduced by ReLU, which we quantify by a term called dynamic dead neuron rate (DNR), is not beneficial for the pruned network. Interestingly, the more the network is pruned, the smaller the dynamic DNR becomes during optimization. This motivates us to propose a method to explicitly reduce the dynamic DNR for the pruned network…
Indian Institute of Technology Dharwad（印度理工学院达瓦德分校）；Durham University（杜伦大学）
In this work we explore different Convolutional Neural Network (CNN) architectures and their variants for non-temporal binary fire detection and localization in video or still imagery. We consider the performance of experimentally defined, reduced complexity deep CNN architectures for this task and evaluate the effects of different optimization and normalization techniques applied to different CNN architectures (spanning the Inception, ResNet and EfficientNet architectural concepts). Contrary to contemporary trends in the field, our work illustrates a maximum overall accuracy of 0.96 for full …
Institute for Infocomm Research, Agency for Science, Technology and Research（新加坡科技研究局资讯通信研究院）；College of Computer Science, Sichuan University（四川大学计算机学院）；Nanyang Technological University（南洋理工大学）
As Deep Neural Networks (DNNs) usually are overparameterized and have millions of weight parameters, it is challenging to deploy these large DNN models on resource-constrained hardware platforms, e.g., smartphones. Numerous network compression methods such as pruning and quantization are proposed to reduce the model size significantly, of which the key is to find suitable compression allocation (e.g., pruning sparsity and quantization codebook) of each layer. Existing solutions obtain the compression allocation in an iterative/manual fashion while finetuning the compressed model, thus sufferin…
Convolutional Neural Networks (CNNs) such as ResNet-50, DenseNet-40 and ResNeXt-56 are severely over-parameterized, necessitating a consequent increase in the computational resources required for model training which scales exponentially for increments in model depth. In this paper, we propose an Entropy-Based Convolutional Layer Estimation (EBCLE) heuristic which is robust and simple, yet effective in resolving the problem of over-parameterization with regards to network depth of CNN model. The EBCLE heuristic employs a priori knowledge of the entropic data distribution of input datasets to d…
Backbone architectures of most binary networks are well-known floating point architectures such as the ResNet family. Questioning that the architectures designed for floating point networks would not be the best for binary networks, we propose to search architectures for binary networks (BNAS) by defining a new search space for binary architectures and a novel search objective. Specifically, based on the cell based search method, we define the new search space of binary layer types, design a new cell template, and rediscover the utility of and propose to use the Zeroise layer instead of using …
Google Research, Brain Team（谷歌研究院，大脑团队）；Mila, Université de Montréal（蒙特利尔大学Mila研究所）；Mila, McGill University（麦吉尔大学Mila研究所）
We investigate the impact of aliasing on generalization in Deep Convolutional Networks and show that data augmentation schemes alone are unable to prevent it due to structural limitations in widely used architectures. Drawing insights from frequency analysis theory, we take a closer look at ResNet and EfficientNet architectures and review the trade-off between aliasing and information loss in each of their major components. We show how to mitigate aliasing by inserting non-trainable low-pass filters at key locations, particularly where networks lack the capacity to learn them. These simple arc…
Understand the Effectiveness of Shortcuts through the Lens of DCA
Yau Mathematical Sciences Center (YMSC), Tsinghua University（清华大学丘成桐数学科学中心）；Beijing Institute of Mathematical Sciences and Applications (BIMSA)（北京数学科学与应用研究院）
Microsoft Autonomous Systems and Robotics Research（微软自主系统与机器人研究部）；Microsoft Research AI4Science（微软研究院AI4Science）
Partial differential equations (PDEs) are central to describing complex physical system simulations. Their expensive solution techniques have led to an increased interest in deep neural network based surrogates. However, the practical utility of training such surrogates is contingent on their ability to model complex multi-scale spatio-temporal phenomena. Various neural network architectures have been proposed to target such phenomena, most notably Fourier Neural Operators (FNOs), which give a natural handle over local & global spatial information via parameterization of different Fourier mode…
University of Electronic Science and Technology of China（电子科技大学）
The channel redundancy in feature maps of convolutional neural networks (CNNs) results in the large consumption of memories and computational resources. In this work, we design a novel Slim Convolution (SlimConv) module to boost the performance of CNNs by reducing channel redundancies. Our SlimConv consists of three main steps: Reconstruct, Transform and Fuse, through which the features are splitted and reorganized in a more efficient way, such that the learned weights can be compressed effectively. In particular, the core of our model is a weight flipping operation which can largely improve t…
Backbone architectures of most binary networks are well-known floating point (FP) architectures such as the ResNet family. Questioning that the architectures designed for FP networks might not be the best for binary networks, we propose to search architectures for binary networks (BNAS) by defining a new search space for binary architectures and a novel search objective. Specifically, based on the cell based search method, we define the new search space of binary layer types, design a new cell template, and rediscover the utility of and propose to use the Zeroise layer instead of using it as a…
University of Oxford（牛津大学）；Arm ML Research Lab（安谋机器学习研究实验室）
Lightweight architectural designs of Convolutional Neural Networks (CNNs) together with quantization have paved the way for the deployment of demanding computer vision applications on mobile devices. Parallel to this, alternative formulations to the convolution operation such as FFT, Strassen and Winograd, have been adapted for use in CNNs offering further speedups. Winograd convolutions are the fastest known algorithm for spatially small convolutions, but exploiting their full potential comes with the burden of numerical error, rendering them unusable in quantized contexts. In this work we pr…
Sandia National Laboratories（桑迪亚国家实验室）；Infineon Technologies（英飞凌科技）；Arizona State University（亚利桑那州立大学）
Specialized accelerators have recently garnered attention as a method to reduce the power consumption of neural network inference. A promising category of accelerators utilizes nonvolatile memory arrays to both store weights and perform $\textit{in situ}$ analog computation inside the array. While prior work has explored the design space of analog accelerators to optimize performance and energy efficiency, there is seldom a rigorous evaluation of the accuracy of these accelerators. This work shows how architectural design decisions, particularly in mapping neural network parameters to analog m…
