Overparameterized neural networks often contain many removable neurons, yet what makes a neuron redundant remains poorly understood. Existing pruning criteria commonly rely on local quantities such as weight magnitude, activation strength, or gradient sensitivity, but these measures provide limited insight into the structural role of a neuron in the transformation performed by a layer. Here we show that neuronal redundancy can be characterized by weak participation in the spectral structural distortion induced by layer-wise representation transformations. For each hidden layer of a trained network, we record pre-activation and post-activation hidden states, model neurons as graph nodes, and construct input-side and output-side graphs that describe neuron-level relational structure before and after the layer transformation. We then define a spectral structural importance score that measures the contribution of each neuron to the dominant graph-spectral distortion between these two relational structures. Low-participation neurons are treated as structurally redundant and removed through an iterative pruning process in which scores are recomputed after each structural change. No parameter updates are performed during intermediate pruning rounds; after the target parameter reduction is reached, a single recovery fine-tuning stage is applied to the compact model. Direct ablation analysis and experiments across conventional neural networks, encoder-only Transformers, and decoder-only language models show that this graph-spectral criterion identifies removable neurons and Transformer units while preserving task performance after compression. These results suggest that neural redundancy is not merely a consequence of small weights or weak activations, but can be understood through weak participation in the spectral distortion of layer-wise relational structure.
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Horizon Robotics（地平线机器人）；Center for Excellence in Brain Science and Intelligence Technology, CAS（中国科学院脑科学与智能技术卓越创新中心）
Deep supervised hashing has become an active topic in information retrieval. It generates hashing bits by the output neurons of a deep hashing network. During binary discretization, there often exists much redundancy between hashing bits that degenerates retrieval performance in terms of both storage and accuracy. This paper proposes a simple yet effective Neurons Merging Layer (NMLayer) for deep supervised hashing. A graph is constructed to represent the redundancy relationship between hashing bits that is used to guide the learning of a hashing network. Specifically, it is dynamically learne…
Nowadays, the number of layers and of neurons in each layer of a deep network are typically set manually. While very deep and wide networks have proven effective in general, they come at a high memory and computation cost, thus making them impractical for constrained platforms. These networks, however, are known to have many redundant parameters, and could thus, in principle, be replaced by more compact architectures. In this paper, we introduce an approach to automatically determining the number of neurons in each layer of a deep network during learning. To this end, we propose to make use of…
State-of-the-art neural networks are getting deeper and wider. While their performance increases with the increasing number of layers and neurons, it is crucial to design an efficient deep architecture in order to reduce computational and memory costs. Designing an efficient neural network, however, is labor intensive requiring many experiments, and fine-tunings. In this paper, we introduce network trimming which iteratively optimizes the network by pruning unimportant neurons based on analysis of their outputs on a large dataset. Our algorithm is inspired by an observation that the outputs of…
We introduce Divnet, a flexible technique for learning networks with diverse neurons. Divnet models neuronal diversity by placing a Determinantal Point Process (DPP) over neurons in a given layer. It uses this DPP to select a subset of diverse neurons and subsequently fuses the redundant neurons into the selected ones. Compared with previous approaches, Divnet offers a more principled, flexible technique for capturing neuronal diversity and thus implicitly enforcing regularization. This enables effective auto-tuning of network architecture and leads to smaller network sizes without hurting per…
Quantifying which neurons are important with respect to the classification decision of a trained neural network is essential for understanding their inner workings. Previous work primarily attributed importance to individual neurons. In this work, we study which groups of neurons contain synergistic or redundant information using a multivariate mutual information method called the O-information. We observe the first layer is dominated by redundancy suggesting general shared features (i.e. detecting edges) while the last layer is dominated by synergy indicating local class-specific features (i.…
Event-based cameras have recently shown great potential for high-speed motion estimation owing to their ability to capture temporally rich information asynchronously. Spiking Neural Networks (SNNs), with their neuro-inspired event-driven processing can efficiently handle such asynchronous data, while neuron models such as the leaky-integrate and fire (LIF) can keep track of the quintessential timing information contained in the inputs. SNNs achieve this by maintaining a dynamic state in the neuron memory, retaining important information while forgetting redundant data over time. Thus, we posit…
Compressing Deep Reinforcement Learning Networks with a Dynamic Structured Pruning Method for Autonomous Driving
School of Automation, Guangdong University of Technology（广东工业大学自动化学院）；School of Computer Science and Engineering, Nanyang Technological University（南洋理工大学计算机科学与工程学院）
What should a neuron aim for? Designing local objective functions based on information theory
Faculty of Physics, Institute for the Dynamics of Complex Systems, University of Göttingen（物理学院、复杂系统动力学研究所、哥廷根大学）；Max Planck Institute for Dynamics and Self-Organization, Göttingen（动态与自我组织马克斯·普朗克研究所，哥廷根）；Göttingen Campus Institute for Dynamics of Biological Networks, University of Göttingen（哥廷根校区生物网络动力学研究所、哥廷根大学）；Institute of Computer Science and Campus Institute Data Science, University of Göttingen（计算机科学研究所和校园数据科学研究所、哥廷根大学）
University of Reading（雷丁大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）；University of Catania（卡塔尼亚大学）；University of Cambridge（剑桥大学）
We identify fragile and robust neurons of deep learning architectures using nodal dropouts of the first convolutional layer. Using an adversarial targeting algorithm, we correlate these neurons with the distribution of adversarial attacks on the network. Adversarial robustness of neural networks has gained significant attention in recent times and highlights intrinsic weaknesses of deep learning networks against carefully constructed distortion applied to input images. In this paper, we evaluate the robustness of state-of-the-art image classification models trained on the MNIST and CIFAR10 dat…
University of Sheffield（谢菲尔德大学）；The University of Sheffield（谢菲尔德大学）
"Sparse" neural networks, in which relatively few neurons or connections are active, are common in both machine learning and neuroscience. Whereas in machine learning, "sparsity" is related to a penalty term that leads to some connecting weights becoming small or zero, in biological brains, sparsity is often created when high spiking thresholds prevent neuronal activity. Here we introduce sparsity into a reservoir computing network via neuron-specific learnable thresholds of activity, allowing neurons with low thresholds to contribute to decision-making but suppressing information from neurons…
Biological neurons have adaptive nature and perform complex computations involving the filtering of redundant information. However, most common neural cell models, including biologically plausible, such as Hodgkin-Huxley or Izhikevich, do not possess predictive dynamics on a single-cell level. Moreover, the modern rules of synaptic plasticity or interconnections weights adaptation also do not provide grounding for the ability of neurons to adapt to the ever-changing input signal intensity. While natural neuron synaptic growth is precisely controlled and restricted by protein supply and recycli…
Peking University（北京大学）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；Peng Cheng Laboratory（鹏城实验室）；The University of Sydney（悉尼大学）
Deep neural networks often consist of a great number of trainable parameters for extracting powerful features from given datasets. On one hand, massive trainable parameters significantly enhance the performance of these deep networks. On the other hand, they bring the problem of over-fitting. To this end, dropout based methods disable some elements in the output feature maps during the training phase for reducing the co-adaptation of neurons. Although the generalization ability of the resulting models can be enhanced by these approaches, the conventional binary dropout is not the optimal solut…
In a deep neural network (DNN), the number of the parameters is usually huge to get high learning performances. For that reason, it costs a lot of memory and substantial computational resources, and also causes overfitting. It is known that some parameters are redundant and can be removed from the network without decreasing performance. Many sparse regularization criteria have been proposed to solve this problem. In a convolutional neural network (CNN), group sparse regularizations are often used to remove unnecessary subsets of the weights, such as filters or channels. When we apply a group s…
University of Texas at Austin（德克萨斯大学奥斯汀分校）；Carnegie Mellon University（卡内基梅隆大学）；University of California, Santa Barbara（加州大学圣巴巴拉分校）；Michigan State University（密歇根州立大学）；MIT-IBM Watson AI Lab（MIT-IBM沃森人工智能实验室）；IBM Research（IBM研究院）
Certifiable robustness is a highly desirable property for adopting deep neural networks (DNNs) in safety-critical scenarios, but often demands tedious computations to establish. The main hurdle lies in the massive amount of non-linearity in large DNNs. To trade off the DNN expressiveness (which calls for more non-linearity) and robustness certification scalability (which prefers more linearity), we propose a novel solution to strategically manipulate neurons, by "grafting" appropriate levels of linearity. The core of our proposal is to first linearize insignificant ReLU neurons, to eliminate t…
Massachusetts Institute of Technology（麻省理工学院）；UC Davis（加州大学戴维斯分校）；Harvard University（哈佛大学）；UT Austin（德克萨斯大学奥斯汀分校）
Verifying the robustness property of a general Rectified Linear Unit (ReLU) network is an NP-complete problem [Katz, Barrett, Dill, Julian and Kochenderfer CAV17]. Although finding the exact minimum adversarial distortion is hard, giving a certified lower bound of the minimum distortion is possible. Current available methods of computing such a bound are either time-consuming or delivering low quality bounds that are too loose to be useful. In this paper, we exploit the special structure of ReLU networks and provide two computationally efficient algorithms Fast-Lin and Fast-Lip that are able t…
the University of Texas, Austin（得克萨斯大学奥斯汀分校）；the University of Chicago（芝加哥大学）；Google Research（谷歌研究院）
Recent empirical works show that large deep neural networks are often highly redundant and one can find much smaller subnetworks without a significant drop of accuracy. However, most existing methods of network pruning are empirical and heuristic, leaving it open whether good subnetworks provably exist, how to find them efficiently, and if network pruning can be provably better than direct training using gradient descent. We answer these problems positively by proposing a simple greedy selection approach for finding good subnetworks, which starts from an empty network and greedily adds importa…
Extreme learning machine (ELM) is a new single hidden layer feedback neural network. The weights of the input layer and the biases of neurons in hidden layer are randomly generated, the weights of the output layer can be analytically determined. ELM has been achieved good results for a large number of classification tasks. In this paper, a new extreme learning machine called rough extreme learning machine (RELM) was proposed. RELM uses rough set to divide data into upper approximation set and lower approximation set, and the two approximation sets are utilized to train upper approximation neur…
Deploying deep learning models, comprising of non-linear combination of millions, even billions, of parameters is challenging given the memory, power and compute constraints of the real world. This situation has led to research into model compression techniques most of which rely on suboptimal heuristics and do not consider the parameter redundancies due to linear dependence between neuron activations in overparametrized networks. In this paper, we propose a novel model compression approach based on exploitation of linear dependence, that compresses networks by elimination of entire neurons an…
Most of today's popular deep architectures are hand-engineered to be generalists. However, this design procedure usually leads to massive redundant, useless, or even harmful features for specific tasks. Unnecessarily high complexities render deep nets impractical for many real-world applications, especially those without powerful GPU support. In this paper, we attempt to derive task-dependent compact models from a deep discriminant analysis perspective. We propose an iterative and proactive approach for classification tasks which alternates between (1) a pushing step, with an objective to simu…
With the general trend of increasing Convolutional Neural Network (CNN) model sizes, model compression and acceleration techniques have become critical for the deployment of these models on edge devices. In this paper, we provide a comprehensive survey on Pruning, a major compression strategy that removes non-critical or redundant neurons from a CNN model. The survey covers the overarching motivation for pruning, different strategies and criteria, their advantages and drawbacks, along with a compilation of major pruning techniques. We conclude the survey with a discussion on alternatives to pr…
Technische Universität Wien (TU Wien)（维也纳工业大学（TU Wien））；New York University Abu Dhabi (NYUAD)（纽约大学阿布扎比分校（NYUAD））
Specialized hardware accelerators have been designed and employed to maximize the performance efficiency of Spiking Neural Networks (SNNs). However, such accelerators are vulnerable to transient faults (i.e., soft errors), which occur due to high-energy particle strikes, and manifest as bit flips at the hardware layer. These errors can change the weight values and neuron operations in the compute engine of SNN accelerators, thereby leading to incorrect outputs and accuracy degradation. However, the impact of soft errors in the compute engine and the respective mitigation techniques have not be…
Pruning Deep Neural Networks (DNNs) is a prominent field of study in the goal of inference runtime acceleration. In this paper, we introduce a novel data-free pruning protocol RED++. Only requiring a trained neural network, and not specific to DNN architecture, we exploit an adaptive data-free scalar hashing which exhibits redundancies among neuron weight values. We study the theoretical and empirical guarantees on the preservation of the accuracy from the hashing as well as the expected pruning ratio resulting from the exploitation of said redundancies. We propose a novel data-free pruning te…
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 …
Samsung Advanced Institute of Technology (SAIT)（三星先进技术研究院（SAIT））
In this paper, we propose self-reorganizing and rejuvenating convolutional neural networks; a biologically inspired method for improving the computational resource utilization of neural networks. The proposed method utilizes the channel activations of a convolution layer in order to reorganize that layers parameters. The reorganized parameters are clustered to avoid parameter redundancies. As such, redundant neurons with similar activations are merged leaving room for the remaining parameters to rejuvenate. The rejuvenated parameters learn different features to supplement those learned by the …
This work proposes a comprehensively progressive Bayesian neural network for robust continual learning of a sequence of tasks. A Bayesian neural network is progressively pruned and grown such that there are sufficient network resources to represent a sequence of tasks, while the network does not explode. It starts with the contention that similar tasks should have the same number of total network resources, to ensure fair representation of all tasks in a continual learning scenario. Thus, as the data for new task streams in, sufficient neurons are added to the network such that the total numbe…
Deep Neural Networks (DNNs) on hardware is facing excessive computation cost due to the massive number of parameters. A typical training pipeline to mitigate over-parameterization is to pre-define a DNN structure first with redundant learning units (filters and neurons) under the goal of high accuracy, then to prune redundant learning units after training with the purpose of efficient inference. We argue that it is sub-optimal to introduce redundancy into training for the purpose of reducing redundancy later in inference. Moreover, the fixed network structure further results in poor adaption t…
With the rapid development of deep learning, the sizes of neural networks become larger and larger so that the training and inference often overwhelm the hardware resources. Given the fact that neural networks are often over-parameterized, one effective way to reduce such computational overhead is neural network pruning, by removing redundant parameters from trained neural networks. It has been recently observed that pruning can not only reduce computational overhead but also can improve empirical robustness of deep neural networks (NNs), potentially owing to removing spurious correlations whi…
We show that finite-width deep ReLU neural networks yield rate-distortion optimal approximation (Bölcskei et al., 2018) of polynomials, windowed sinusoidal functions, one-dimensional oscillatory textures, and the Weierstrass function, a fractal function which is continuous but nowhere differentiable. Together with their recently established universal approximation property of affine function systems (Bölcskei et al., 2018), this shows that deep neural networks approximate vastly different signal structures generated by the affine group, the Weyl-Heisenberg group, or through warping, and even c…
Redundancy Maximization as a Principle of Associative Memory Learning in Hopfield Networks
Complex Systems Theory, Max Planck Institute for Dynamics and Self-Organization（复杂系统理论，马克斯·普朗克动态与自组织研究所）；Faculty of Physics, Institute for the Dynamics of Complex Systems, University of Göttingen（物理系，复杂系统动力学研究所，哥廷根大学）；Göttingen Campus Institute for Dynamics of Biological Networks, University of Göttingen（哥廷根校区生物网络动力学研究所，哥廷根大学）；Champalimaud Centre for the Unknown, Lisbon, Portugal（查帕利马德未知中心，里斯本，葡萄牙）；Max Planck Institute for Dynamics and Self-Organization（马克斯·普朗克动态与自组织研究所）
Pruning-induced phases in fully-connected neural networks: the eumentia, the dementia, and the amentia
Department of Physics and Astronomy, Center for Materials Theory, Rutgers University（物理与天文学系，材料理论中心，罗格斯大学）；Center for Computational Quantum Physics, Flatiron Institute（计算量子物理中心，Flatiron研究所）
