The large capacity of neural networks enables them to learn complex functions. To avoid overfitting, networks however require a lot of training data that can be expensive and time-consuming to collect. A common practical approach to attenuate overfitting is the use of network regularization techniques. We propose a novel regularization method that progressively penalizes the magnitude of activations during training. The combined activation signals produced by all neurons in a given layer form the representation of the input image in that feature space. We propose to regularize this representation in the last feature layer before classification layers. Our method's effect on generalization is analyzed with label randomization tests and cumulative ablations. Experimental results show the advantages of our approach in comparison with commonly-used regularizers on standard benchmark datasets.
In recent years novel activation functions have been proposed to improve the performance of neural networks, and they show superior performance compared to the ReLU counterpart. However, there are environments, where the availability of complex activations is limited, and usually only the ReLU is supported. In this paper we propose methods that can be used to improve the performance of ReLU networks by using these efficient novel activations during model training. More specifically, we propose ensemble activations that are composed of the ReLU and one of these novel activations. Furthermore, t…
Structured Progressive Knowledge Activation for LLM-Driven Neural Architecture Search
State Key Laboratory of Human-Machine Hybrid Augmented Intelligence, Institute of Artificial Intelligence and Robotics, Xi'an Jiaotong University.（人机混合增强智能国家重点实验室，人工智能与机器人研究院，西安交通大学）；MiLM Plus, Xiaomi Inc.（小米MiLM Plus）；North China University of Technology, Beijing.（华北电力大学（北京））；Zhongguancun Academy, Beijing, China（中关村学院，北京，中国）
Seoul National University（首尔国立大学）；Hanyang University（汉阳大学）；NAVER Corp（NAVER公司）
An activation boundary for a neuron refers to a separating hyperplane that determines whether the neuron is activated or deactivated. It has been long considered in neural networks that the activations of neurons, rather than their exact output values, play the most important role in forming classification friendly partitions of the hidden feature space. However, as far as we know, this aspect of neural networks has not been considered in the literature of knowledge transfer. In this paper, we propose a knowledge transfer method via distillation of activation boundaries formed by hidden neuron…
University of California San Diego（加州大学圣地亚哥分校）；Academia Sinica（中央研究院）；Taiwan AI Labs（台湾人工智能实验室）
Recent years have seen adversarial losses been applied to many fields. Their applications extend beyond the originally proposed generative modeling to conditional generative and discriminative settings. While prior work has proposed various output activation functions and regularization approaches, some open questions still remain unanswered. In this paper, we aim to study the following two research questions: 1) What types of output activation functions form a well-behaved adversarial loss? 2) How different combinations of output activation functions and regularization approaches perform empi…
The University of Sydney（悉尼大学）；University of Science and Technology of China（中国科学技术大学）
Understanding the loss surface of a neural network is fundamentally important to the understanding of deep learning. This paper presents how piecewise linear activation functions substantially shape the loss surfaces of neural networks. We first prove that {\it the loss surfaces of many neural networks have infinite spurious local minima} which are defined as the local minima with higher empirical risks than the global minima. Our result demonstrates that the networks with piecewise linear activations possess substantial differences to the well-studied linear neural networks. This result holds…
Regularization and normalization have become indispensable components in training deep neural networks, resulting in faster training and improved generalization performance. We propose the projected error function regularization loss (PER) that encourages activations to follow the standard normal distribution. PER randomly projects activations onto one-dimensional space and computes the regularization loss in the projected space. PER is similar to the Pseudo-Huber loss in the projected space, thus taking advantage of both $L^1$ and $L^2$ regularization losses. Besides, PER can capture the inte…
Depth factorization and quantization have emerged as two of the principal strategies for designing efficient deep convolutional neural network (CNN) architectures tailored for low-power inference on the edge. However, there is still little detailed understanding of how different depth factorization choices affect the final, trained distributions of each layer in a CNN, particularly in the situation of quantized weights and activations. In this study, we introduce a progressive depth factorization strategy for efficient CNN architecture exploration under quantization constraints. By algorithmic…
Tel Aviv University（特拉维夫大学）；Facebook AI Research（脸书人工智能研究院）
Normalization techniques play an important role in supporting efficient and often more effective training of deep neural networks. While conventional methods explicitly normalize the activations, we suggest to add a loss term instead. This new loss term encourages the variance of the activations to be stable and not vary from one random mini-batch to the next. As we prove, this encourages the activations to be distributed around a few distinct modes. We also show that if the inputs are from a mixture of two Gaussians, the new loss would either join the two together, or separate between them op…
University of California, Berkeley（加州大学伯克利分校）；Google（谷歌）
We establish conditions under which gradient descent applied to fixed-width deep networks drives the logistic loss to zero, and prove bounds on the rate of convergence. Our analysis applies for smoothed approximations to the ReLU, such as Swish and the Huberized ReLU, proposed in previous applied work. We provide two sufficient conditions for convergence. The first is simply a bound on the loss at initialization. The second is a data separation condition used in prior analyses.
Leipzig University（莱比锡大学）；Leipzig University Medical Centre（莱比锡大学医学中心）
The sigmoid activation is the standard output activation function in binary classification and segmentation with neural networks. Still, there exist a variety of other potential output activation functions, which may lead to improved results in medical image segmentation. In this work, we consider how the asymptotic behavior of different output activation and loss functions affects the prediction probabilities and the corresponding segmentation errors. For cross entropy, we show that a faster rate of change of the activation function correlates with better predictions, while a slower rate of c…
University of Science and Technology of China（中国科学技术大学）；Suzhou Institute for Advanced Research, University of Science and Technology of China（中国科学技术大学苏州高等研究院）
Deep convolutional neural networks often perform poorly when faced with datasets that suffer from quantity imbalances and classification difficulties. Despite advances in the field, existing two-stage approaches still exhibit dataset bias or domain shift. To counter this, a phased progressive learning schedule has been proposed that gradually shifts the emphasis from representation learning to training the upper classifier. This approach is particularly beneficial for datasets with larger imbalances or fewer samples. Another new method a coupling-regulation-imbalance loss function is proposed,…
The early layers of a deep neural net have the fewest parameters, but take up the most computation. In this extended abstract, we propose to only train the hidden layers for a set portion of the training run, freezing them out one-by-one and excluding them from the backward pass. Through experiments on CIFAR, we empirically demonstrate that FreezeOut yields savings of up to 20% wall-clock time during training with 3% loss in accuracy for DenseNets, a 20% speedup without loss of accuracy for ResNets, and no improvement for VGG networks. Our code is publicly available at https://github.com/ajbro…
Trainable at Depth, Solvable at Small Size: What the Loss Surface of a Polynomial Activation Dictates for Designing, Initializing and Training Networks
On progressive sharpening, flat minima and generalisation
Mathematical Institute for Data Science（数据科学数学研究所）；Johns Hopkins University（约翰斯·霍普金斯大学）；Australian Institute for Machine Learning（澳大利亚机器学习研究所）；University of Adelaide（阿德莱德大学）
In this work, we evaluate how neural networks with periodic activation functions can be leveraged to reliably compress large multidimensional medical image datasets, with proof-of-concept application to 4D diffusion-weighted MRI (dMRI). In the medical imaging landscape, multidimensional MRI is a key area of research for developing biomarkers that are both sensitive and specific to the underlying tissue microstructure. However, the high-dimensional nature of these data poses a challenge in terms of both storage and sharing capabilities and associated costs, requiring appropriate algorithms able…
Pattern recognition applications often suffer from skewed data distributions between classes, which may vary during operations w.r.t. the design data. Two-class classification systems designed using skewed data tend to recognize the majority class better than the minority class of interest. Several data-level techniques have been proposed to alleviate this issue by up-sampling minority samples or under-sampling majority samples. However, some informative samples may be neglected by random under-sampling and adding synthetic positive samples through up-sampling adds to training complexity. In t…
Shanghai Grandhonor Information Technology Co.Ltd（上海冠勇信息科技有限公司）；New York University（纽约大学）；New York University Abu Dhabi（纽约大学阿布扎比分校）
This paper studies the problem of Person Re-Identification (ReID)for large-scale applications. Recent research efforts have been devoted to building complicated part models, which introduce considerably high computational cost and memory consumption, inhibiting its practicability in large-scale applications. This paper aims to develop a novel learning strategy to find efficient feature embeddings while maintaining the balance of accuracy and model complexity. More specifically, we find by enhancing the classical triplet loss together with cross-entropy loss, our method can explore the hard exa…
Tel-Aviv University（特拉维夫大学）；Facebook AI Research（脸书人工智能研究院）
The problem of maximum likelihood decoding with a neural decoder for error-correcting code is considered. It is shown that the neural decoder can be improved with two novel loss terms on the node's activations. The first loss term imposes a sparse constraint on the node's activations. Whereas, the second loss term tried to mimic the node's activations from a teacher decoder which has better performance. The proposed method has the same run time complexity and model size as the neural Belief Propagation decoder, while improving the decoding performance by up to $1.1dB$ on BCH codes.
The choice of activation function can significantly influence the performance of neural networks. The lack of guiding principles for the selection of activation function is lamentable. We try to address this issue by introducing our variational neural networks, where the activation function is represented as a linear combination of possible candidate functions, and an optimal activation is obtained via minimization of a loss function using gradient descent method. The gradient formulae for the loss function with respect to these expansion coefficients are central for the implementation of grad…
Carnegie Mellon University（卡内基梅隆大学）；University of Southern California（南加州大学）
We provide new theoretical insights on why over-parametrization is effective in learning neural networks. For a $k$ hidden node shallow network with quadratic activation and $n$ training data points, we show as long as $ k \ge \sqrt{2n}$, over-parametrization enables local search algorithms to find a \emph{globally} optimal solution for general smooth and convex loss functions. Further, despite that the number of parameters may exceed the sample size, using theory of Rademacher complexity, we show with weight decay, the solution also generalizes well if the data is sampled from a regular distr…
The lack of a large amount of training data has always been the constraining factor in solving a lot of problems in machine learning, making One Shot Learning one of the most intriguing ideas in machine learning. It aims to learn information about object categories from one, or only a few training examples. This process of learning in deep learning is usually accomplished by proper objective function, i.e; loss function and embeddings extraction i.e; architecture. In this paper, we discussed about metrics based deep learning architectures for one shot learning such as Siamese neural networks a…
Spectral Lens: Activation and Gradient Spectra as Diagnostics of LLM Optimization
Department of Applied Physics, Yale University, New Haven, CT 06511, United States（耶鲁大学应用物理系）；Department of Mathematics and Statistics, McGill University（麦吉尔大学数学与统计学系）；Department of Applied Physics, Yale University, New Haven, Connecticut 06511, USA（耶鲁大学应用物理系）；Energy Sciences Institute, Yale University, West Haven, Connecticut 06516, USA（耶鲁大学能源科学研究所）
Université Paris-Saclay（巴黎-萨克雷大学）；CNRS（法国国家科学研究中心）；CEA（法国原子能和替代能源委员会）；Institut de physique théorique（理论物理研究所）；Courant Institute, New York University（纽约大学柯朗研究所）
We study the dynamics of optimization and the generalization properties of one-hidden layer neural networks with quadratic activation function in the over-parametrized regime where the layer width $m$ is larger than the input dimension $d$. We consider a teacher-student scenario where the teacher has the same structure as the student with a hidden layer of smaller width $m^*\le m$. We describe how the empirical loss landscape is affected by the number $n$ of data samples and the width $m^*$ of the teacher network. In particular we determine how the probability that there be no spurious minima …
Binary Neural Networks (BNNs) have been garnering interest thanks to their compute cost reduction and memory savings. However, BNNs suffer from performance degradation mainly due to the gradient mismatch caused by binarizing activations. Previous works tried to address the gradient mismatch problem by reducing the discrepancy between activation functions used at forward pass and its differentiable approximation used at backward pass, which is an indirect measure. In this work, we use the gradient of smoothed loss function to better estimate the gradient mismatch in quantized neural network. An…
IBM Research India（IBM印度研究院）；IBM Research USA（IBM美国研究院）
We develop a novel method, called PoWER-BERT, for improving the inference time of the popular BERT model, while maintaining the accuracy. It works by: a) exploiting redundancy pertaining to word-vectors (intermediate encoder outputs) and eliminating the redundant vectors. b) determining which word-vectors to eliminate by developing a strategy for measuring their significance, based on the self-attention mechanism. c) learning how many word-vectors to eliminate by augmenting the BERT model and the loss function. Experiments on the standard GLUE benchmark shows that PoWER-BERT achieves up to 4.5…
Gradient-only line searches (GOLS) adaptively determine step sizes along search directions for discontinuous loss functions resulting from dynamic mini-batch sub-sampling in neural network training. Step sizes in GOLS are determined by localizing Stochastic Non-Negative Associated Gradient Projection Points (SNN-GPPs) along descent directions. These are identified by a sign change in the directional derivative from negative to positive along a descent direction. Activation functions are a significant component of neural network architectures as they introduce non-linearities essential for comp…
Overfitting is one of the fundamental challenges when training convolutional neural networks and is usually identified by a diverging training and test loss. The underlying dynamics of how the flow of activations induce overfitting is however poorly understood. In this study we introduce a perplexity-based sparsity definition to derive and visualise layer-wise activation measures. These novel explainable AI strategies reveal a surprising relationship between activation sparsity and overfitting, namely an increase in sparsity in the feature extraction layers shortly before the test loss starts …
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；University of California, Irvine（加利福尼亚大学尔湾分校）；Qualcomm AI Research（高通人工智能研究院）
Training activation quantized neural networks involves minimizing a piecewise constant function whose gradient vanishes almost everywhere, which is undesirable for the standard back-propagation or chain rule. An empirical way around this issue is to use a straight-through estimator (STE) (Bengio et al., 2013) in the backward pass only, so that the "gradient" through the modified chain rule becomes non-trivial. Since this unusual "gradient" is certainly not the gradient of loss function, the following question arises: why searching in its negative direction minimizes the training loss? In this …
This paper studies probability distributions of penultimate activations of classification networks. We show that, when a classification network is trained with the cross-entropy loss, its final classification layer forms a Generative-Discriminative pair with a generative classifier based on a specific distribution of penultimate activations. More importantly, the distribution is parameterized by the weights of the final fully-connected layer, and can be considered as a generative model that synthesizes the penultimate activations without feeding input data. We empirically demonstrate that this…
Deep classifiers have achieved great success in visual recognition. However, real-world data is long-tailed by nature, leading to the mismatch between training and testing distributions. In this report, we introduce Balanced Activation (Balanced Softmax and Balanced Sigmoid), an elegant unbiased, and simple extension of Sigmoid and Softmax activation function, to accommodate the label distribution shift between training and testing in object detection. We derive the generalization bound for multiclass Softmax regression and show our loss minimizes the bound. In our experiments, we demonstrate …
Recurrent neural networks (RNN) are capable of learning to encode and exploit activation history over an arbitrary timescale. However, in practice, state of the art gradient descent based training methods are known to suffer from difficulties in learning long term dependencies. Here, we describe a novel training method that involves concurrent parallel cloned networks, each sharing the same weights, each trained at different stimulus phase and each maintaining independent activation histories. Training proceeds by recursively performing batch-updates over the parallel clones as activation hist…
School of Computing, Montclair State University（蒙特克莱尔州立大学计算机学院）；Department of Computer Science and Engineering, Southern University of Science and Technology（南方科技大学计算机科学与工程系）
