Why Rectified Power Unit Networks Fail and How to Improve It: An Effective Field Theory Perspective
School of Computational Sciences（计算科学学院）；Korea Institute for Advanced Study（韩国高级研究院）；Department of Mathematical Science（数学科学系）；Seoul National University（首尔国立大学）
The Rectified Power Unit (RePU) activation function, a differentiable generalization of the Rectified Linear Unit (ReLU), has shown promise in constructing neural networks due to its smoothness properties. However, deep RePU networks often suffer from critical issues such as vanishing or exploding values during training, rendering them unstable regardless of hyperparameter initialization. Leveraging the perspective of effective field theory, we identify the root causes of these failures and propose the Modified Rectified Power Unit (MRePU) activation function. MRePU addresses RePU's limitations while preserving its advantages, such as differentiability and universal approximation properties. Theoretical analysis demonstrates that MRePU satisfies criticality conditions necessary for stable training, placing it in a distinct universality class. Extensive experiments validate the effectiveness of MRePU, showing significant improvements in training stability and performance across various tasks, including polynomial regression, physics-informed neural networks (PINNs) and real-world vision tasks. Our findings highlight the potential of MRePU as a robust alternative for building deep neural networks.
Curse of Attention: A Kernel-Based Perspective for Why Transformers Fail to Generalize on Time Series Forecasting and Beyond
The University of Hong Kong（香港大学）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；The Simons Institute for the Theory of Computing（西蒙斯理论计算研究所）；UC Berkeley（加州大学伯克利分校）；Sun Yat-sen University（中山大学）
University of Amsterdam（阿姆斯特丹大学）；Ahold Delhaize（阿霍德德尔海兹）
In various business settings, there is an interest in using more complex machine learning techniques for sales forecasting. It is difficult to convince analysts, along with their superiors, to adopt these techniques since the models are considered to be "black boxes," even if they perform better than current models in use. We examine the impact of contrastive explanations about large errors on users' attitudes towards a "black-box'" model. We propose an algorithm, Monte Carlo Bounds for Reasonable Predictions. Given a large error, MC-BRP determines (1) feature values that would result in a rea…
University of Queensland（昆士兰大学）；International Computer Science Institute（国际计算机科学研究所）
An interesting approach to analyzing neural networks that has received renewed attention is to examine the equivalent kernel of the neural network. This is based on the fact that a fully connected feedforward network with one hidden layer, a certain weight distribution, an activation function, and an infinite number of neurons can be viewed as a mapping into a Hilbert space. We derive the equivalent kernels of MLPs with ReLU or Leaky ReLU activations for all rotationally-invariant weight distributions, generalizing a previous result that required Gaussian weight distributions. Additionally, th…
Why Low-Precision Transformer Training Fails: An Analysis on Flash Attention
Department of Electronic Engineering, Tsinghua University（清华大学电子工程系）；Beijing National Research Center for Information Science and Technology（北京信息科学与技术国家研究中心）；State Key laboratory of Space Network and Communications（空间网络与通信国家重点实验室）
Saliency Map, the gradient of the score function with respect to the input, is the most basic technique for interpreting deep neural network decisions. However, saliency maps are often visually noisy. Although several hypotheses were proposed to account for this phenomenon, there are few works that provide rigorous analyses of noisy saliency maps. In this paper, we firstly propose a new hypothesis that noise may occur in saliency maps when irrelevant features pass through ReLU activation functions. Then, we propose Rectified Gradient, a method that alleviates this problem through layer-wise th…
Catastrophic Compositional Generation: Why Vanilla Diffusion Models Fail to Extrapolate
Machine Learning Department, Carnegie Mellon University（卡内基梅隆大学机器学习系）；Valence Labs；Department of Computer Science, University of Manchester（曼彻斯特大学计算机科学系）
Recently, neural networks in machine learning use rectified linear units (ReLUs) in early processing layers for better performance. Training these structures sometimes results in "dying ReLU units" with near-zero outputs. We first explore this condition via simulation using the CIFAR-10 dataset and variants of two popular convolutive neural network architectures. Our explorations show that the output activation probability Pr[y>0] is generally less than 0.5 at system convergence for layers that do not employ skip connections, and this activation probability tends to decrease as one progresses …
University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Recently, methods such as Decision Transformer that reduce reinforcement learning to a prediction task and solve it via supervised learning (RvS) have become popular due to their simplicity, robustness to hyperparameters, and strong overall performance on offline RL tasks. However, simply conditioning a probabilistic model on a desired return and taking the predicted action can fail dramatically in stochastic environments since trajectories that result in a return may have only achieved that return due to luck. In this work, we describe the limitations of RvS approaches in stochastic environme…
Rectified Linear Units (ReLU) seem to have displaced traditional 'smooth' nonlinearities as activation-function-du-jour in many - but not all - deep neural network (DNN) applications. However, nobody seems to know why. In this article, we argue that ReLU are useful because they are ideal demodulators - this helps them perform fast abstract learning. However, this fast learning comes at the expense of serious nonlinear distortion products - decoy features. We show that Parallel Dither acts to suppress the decoy features, preventing overfitting and leaving the true features cleanly demodulated f…
Department of Electrical and Computer Engineering, National University of Singapore（新加坡国立大学电气与计算机工程系）；School of Computing, Department of Computer Science, National University of Singapore（新加坡国立大学计算机学院计算机科学系）；School of Computer Science and Engineering, University of Electronic Science and Technology of China（电子科技大学计算机科学与工程学院）；Department of Computer and Information Sciences, Faculty of Engineering and Environment, Northumbria University（诺森比亚大学工程与环境学院计算机与信息科学系）；Zhejiang Lab（浙江实验室）
Spiking Neural Networks (SNNs) use spatio-temporal spike patterns to represent and transmit information, which is not only biologically realistic but also suitable for ultra-low-power event-driven neuromorphic implementation. Motivated by the success of deep learning, the study of Deep Spiking Neural Networks (DeepSNNs) provides promising directions for artificial intelligence applications. However, training of DeepSNNs is not straightforward because the well-studied error back-propagation (BP) algorithm is not directly applicable. In this paper, we first establish an understanding as to why e…
A proper initialization of the weights in a neural network is critical to its convergence. Current insights into weight initialization come primarily from linear activation functions. In this paper, I develop a theory for weight initializations with non-linear activations. First, I derive a general weight initialization strategy for any neural network using activation functions differentiable at 0. Next, I derive the weight initialization strategy for the Rectified Linear Unit (RELU), and provide theoretical insights into why the Xavier initialization is a poor choice with RELU activations. My…
Detecting out-of-distribution (OOD) data is crucial for robust machine learning systems. Normalizing flows are flexible deep generative models that often surprisingly fail to distinguish between in- and out-of-distribution data: a flow trained on pictures of clothing assigns higher likelihood to handwritten digits. We investigate why normalizing flows perform poorly for OOD detection. We demonstrate that flows learn local pixel correlations and generic image-to-latent-space transformations which are not specific to the target image dataset. We show that by modifying the architecture of flow co…
While the authors of Batch Normalization (BN) identify and address an important problem involved in training deep networks-- \textit{Internal Covariate Shift}-- the current solution has certain drawbacks. For instance, BN depends on batch statistics for layerwise input normalization during training which makes the estimates of mean and standard deviation of input (distribution) to hidden layers inaccurate due to shifting parameter values (especially during initial training epochs). Another fundamental problem with BN is that it cannot be used with batch-size $ 1 $ during training. We address t…
School of Computer Science (National Pilot Software Engineering School)（计算机科学学院（国家示范性软件工程学院））；Beijing University of Posts and Telecommunications（北京邮电大学）
As student failure rates continue to increase in higher education, predicting student performance in the following semester has become a significant demand. Personalized student performance prediction helps educators gain a comprehensive view of student status and effectively intervene in advance. However, existing works scarcely consider the explainability of student performance prediction, which educators are most concerned about. In this paper, we propose a novel Explainable Student performance prediction method with Personalized Attention (ESPA) by utilizing relationships in student profil…
Northwestern Polytechnical University（西北工业大学）；University of Cagliari（卡利亚里大学）；University of Genoa（热那亚大学）
Adversarial reprogramming allows repurposing a machine-learning model to perform a different task. For example, a model trained to recognize animals can be reprogrammed to recognize digits by embedding an adversarial program in the digit images provided as input. Recent work has shown that adversarial reprogramming may not only be used to abuse machine-learning models provided as a service, but also beneficially, to improve transfer learning when training data is scarce. However, the factors affecting its success are still largely unexplained. In this work, we develop a first-order linear mode…
Why Reasoning Fails to Plan: A Planning-Centric Analysis of Long-Horizon Decision Making in LLM Agents
University of Notre Dame（诺丁汉大学）；Stanford University（斯坦福大学）；Purdue University（普渡大学）；University of Edinburgh（爱丁堡大学）；University of Oxford（牛津大学）；Yale University（耶鲁大学）
Physics-informed neural networks (PINNs) have lately received great attention thanks to their flexibility in tackling a wide range of forward and inverse problems involving partial differential equations. However, despite their noticeable empirical success, little is known about how such constrained neural networks behave during their training via gradient descent. More importantly, even less is known about why such models sometimes fail to train at all. In this work, we aim to investigate these questions through the lens of the Neural Tangent Kernel (NTK); a kernel that captures the behavior …
