Multi-task learning (MTL) is a common paradigm that seeks to improve the generalization performance of task learning by training related tasks simultaneously. However, it is still a challenging problem to search the flexible and accurate architecture that can be shared among multiple tasks. In this paper, we propose a novel deep learning model called Task Adaptive Activation Network (TAAN) that can automatically learn the optimal network architecture for MTL. The main principle of TAAN is to derive flexible activation functions for different tasks from the data with other parameters of the network fully shared. We further propose two functional regularization methods that improve the MTL performance of TAAN. The improved performance of both TAAN and the regularization methods is demonstrated by comprehensive experiments.
Purdue University（普渡大学）；The University of Chicago（芝加哥大学）；National University of Singapore（新加坡国立大学）
Overfitting frequently occurs in deep learning. In this paper, we propose a novel regularization method called Drop-Activation to reduce overfitting and improve generalization. The key idea is to drop nonlinear activation functions by setting them to be identity functions randomly during training time. During testing, we use a deterministic network with a new activation function to encode the average effect of dropping activations randomly. Our theoretical analyses support the regularization effect of Drop-Activation as implicit parameter reduction and verify its capability to be used together…
University of Waterloo（滑铁卢大学）；Ruhr-University Bochum（波鸿鲁尔大学）
Deep learning requires several design choices, such as the nodes' activation functions and the widths, types, and arrangements of the layers. One consideration when making these choices is the vanishing-gradient problem, which is the phenomenon of algorithms getting stuck at suboptimal points due to small gradients. In this paper, we revisit the vanishing-gradient problem in the context of sigmoid-type activation. We use mathematical arguments to highlight two different sources of the phenomenon, namely large individual parameters and effects across layers, and to illustrate two simple remedie…
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…
TU Darmstadt（达姆施塔特工业大学）；Centre for Cognitive Science, TU Darmstadt（达姆施塔特工业大学认知科学中心）
The performance of deep network learning strongly depends on the choice of the non-linear activation function associated with each neuron. However, deciding on the best activation is non-trivial, and the choice depends on the architecture, hyper-parameters, and even on the dataset. Typically these activations are fixed by hand before training. Here, we demonstrate how to eliminate the reliance on first picking fixed activation functions by using flexible parametric rational functions instead. The resulting Padé Activation Units (PAUs) can both approximate common activation functions and also l…
Stanford University（斯坦福大学）；Purdue University（普渡大学）；Institute for Advanced Study（高等研究院）
We consider networks, trained via stochastic gradient descent to minimize $\ell_2$ loss, with the training labels perturbed by independent noise at each iteration. We characterize the behavior of the training dynamics near any parameter vector that achieves zero training error, in terms of an implicit regularization term corresponding to the sum over the data points, of the squared $\ell_2$ norm of the gradient of the model with respect to the parameter vector, evaluated at each data point. This holds for networks of any connectivity, width, depth, and choice of activation function. We interpr…
Sapienza University of Rome（罗马第一大学）；University of Cantabria（坎塔布里亚大学）
Gated recurrent neural networks have achieved remarkable results in the analysis of sequential data. Inside these networks, gates are used to control the flow of information, allowing to model even very long-term dependencies in the data. In this paper, we investigate whether the original gate equation (a linear projection followed by an element-wise sigmoid) can be improved. In particular, we design a more flexible architecture, with a small number of adaptable parameters, which is able to model a wider range of gating functions than the classical one. To this end, we replace the sigmoid func…
Simon Fraser University（西蒙弗雷泽大学）；Microsoft Research（微软研究院）
It is fundamental to measure model complexity of deep neural networks. The existing literature on model complexity mainly focuses on neural networks with piecewise linear activation functions. Model complexity of neural networks with general curve activation functions remains an open problem. To tackle the challenge, in this paper, we first propose the linear approximation neural network (LANN for short), a piecewise linear framework to approximate a given deep model with curve activation function. LANN constructs individual piecewise linear approximation for the activation function of each ne…
Astro: Activation-guided Structured Regularization for Outlier-Robust LLM Post-Training Quantization
Beijing Institute of Technology（北京理工大学）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；Hebei Province Key Laboratory of Big Data Science and Intelligent Technology（河北省大数据科学与智能技术重点实验室）
Cranfield University（克兰菲尔德大学）；University of Warwick（华威大学）；Alan Turing Institute（艾伦·图灵研究所）
Achieving transparency in black-box deep learning algorithms is still an open challenge. High dimensional features and decisions given by deep neural networks (NN) require new algorithms and methods to expose its mechanisms. Current state-of-the-art NN interpretation methods (e.g. Saliency maps, DeepLIFT, LIME, etc.) focus more on the direct relationship between NN outputs and inputs rather than the NN structure and operations itself. In current deep NN operations, there is uncertainty over the exact role played by neurons with fixed activation functions. In this paper, we achieve partially ex…
École polytechnique fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
Training certifiable neural networks enables one to obtain models with robustness guarantees against adversarial attacks. In this work, we introduce a framework to bound the adversary-free region in the neighborhood of the input data by a polyhedral envelope, which yields finer-grained certified robustness. We further introduce polyhedral envelope regularization (PER) to encourage larger polyhedral envelopes and thus improve the provable robustness of the models. We demonstrate the flexibility and effectiveness of our framework on standard benchmarks; it applies to networks of different archit…
A wide variety of activation functions have been proposed for neural networks. The Rectified Linear Unit (ReLU) is especially popular today. There are many practical reasons that motivate the use of the ReLU. This paper provides new theoretical characterizations that support the use of the ReLU, its variants such as the leaky ReLU, as well as other activation functions in the case of univariate, single-hidden layer feedforward neural networks. Our results also explain the importance of commonly used strategies in the design and training of neural networks such as "weight decay" and "path-norm"…
The asymptotic mean squared test error and sensitivity of the Random Features Regression model (RFR) have been recently studied. We build on this work and identify in closed-form the family of Activation Functions (AFs) that minimize a combination of the test error and sensitivity of the RFR under different notions of functional parsimony. We find scenarios under which the optimal AFs are linear, saturated linear functions, or expressible in terms of Hermite polynomials. Finally, we show how using optimal AFs impacts well-established properties of the RFR model, such as its double descent curv…
University of Manchester（曼彻斯特大学）；The Alan Turing Institute（艾伦·图灵研究所）
Standard neural network architectures are non-linear only by virtue of a simple element-wise activation function, making them both brittle and excessively large. In this paper, we consider methods for making the feed-forward layer more flexible while preserving its basic structure. We develop simple drop-in replacements that learn to adapt their parameterization conditional on the input, thereby increasing statistical efficiency significantly. We present an adaptive LSTM that advances the state of the art for the Penn Treebank and WikiText-2 word-modeling tasks while using fewer parameters and…
CRAN；Université de Lorraine（洛林大学）；CNRS（法国国家科学研究中心）
Activation functions (AFs) are an important part of the design of neural networks (NNs), and their choice plays a predominant role in the performance of a NN. In this work, we are particularly interested in the estimation of flexible activation functions using tensor-based solutions, where the AFs are expressed as a weighted sum of predefined basis functions. To do so, we propose a new learning algorithm which solves a constrained coupled matrix-tensor factorization (CMTF) problem. This technique fuses the first and zeroth order information of the NN, where the first-order information is conta…
Information Sciences Institute（信息科学研究所）；University of Southern California（南加州大学）
In this paper, we introduce a novel non-linear activation function that spontaneously induces class-compactness and regularization in the embedding space of neural networks. The function is dubbed DOME for Difference Of Mirrored Exponential terms. The basic form of the function can replace the sigmoid or the hyperbolic tangent functions as an output activation function for binary classification problems. The function can also be extended to the case of multi-class classification, and used as an alternative to the standard softmax function. It can also be further generalized to take more flexib…
Duke University（杜克大学）；Black Sesame Technologies（黑芝麻科技）
With the rapid scaling up of deep neural networks (DNNs), extensive research studies on network model compression such as weight pruning have been performed for improving deployment efficiency. This work aims to advance the compression beyond the weights to neuron activations. We propose the joint regularization technique which simultaneously regulates the distribution of weights and activations. By distinguishing and leveraging the significance difference among neuron responses and connections during learning, the jointly pruned network, namely \textit{JPnet}, optimizes the sparsity of activa…
École polytechnique fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
The minimization of a data-fidelity term and an additive regularization functional gives rise to a powerful framework for supervised learning. In this paper, we present a unifying regularization functional that depends on an operator and on a generic Radon-domain norm. We establish the existence of a minimizer and give the parametric form of the solution(s) under very mild assumptions. When the norm is Hilbertian, the proposed formulation yields a solution that involves radial-basis functions and is compatible with the classical methods of machine learning. By contrast, for the total-variation…
Most neural network designs for FPGAs are inflexible. In this paper, we propose a flexible VHDL structure that would allow any neural network to be implemented on multiple FPGAs. Moreover, the VHDL structure allows for testing as well as training multiple neural networks. The VHDL design consists of multiple processor groups. There are two types of processor groups: Mini Vector Machine Processor Group and Activation Processor Group. Each processor group consists of individual Mini Vector Machines and Activation Processor. The Mini Vector Machines apply vector operations to the data, while the …
Predictive Modeling of Flexible EHD Pumps using Kolmogorov-Arnold Networks
College of Mechanical Engineering, Chongqing University of Technology（重庆理工大学机械工程学院）；Nagoya University（名古屋大学）；Faculty of Engineering, Yamaguchi University（山口大学工程学院）
Texas State University（德克萨斯州立大学）；Yale University（耶鲁大学）
Neural networks have attracted a lot of attention due to its success in applications such as natural language processing and computer vision. For large scale data, due to the tremendous number of parameters in neural networks, overfitting is an issue in training neural networks. To avoid overfitting, one common approach is to penalize the parameters especially the weights in neural networks. Although neural networks has demonstrated its advantages in many applications, the theoretical foundation of penalized neural networks has not been well-established. Our goal of this paper is to propose th…
Sapienza University of Rome（罗马大学）；University of Cantabria（坎塔布里亚大学）
Neural networks are generally built by interleaving (adaptable) linear layers with (fixed) nonlinear activation functions. To increase their flexibility, several authors have proposed methods for adapting the activation functions themselves, endowing them with varying degrees of flexibility. None of these approaches, however, have gained wide acceptance in practice, and research in this topic remains open. In this paper, we introduce a novel family of flexible activation functions that are based on an inexpensive kernel expansion at every neuron. Leveraging over several properties of kernel-ba…
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…
Deep Neural Networks (DNNs) have obtained impressive performance across tasks, however they still remain as black boxes, e.g., hard to theoretically analyze. At the same time, Polynomial Networks (PNs) have emerged as an alternative method with a promising performance and improved interpretability but have yet to reach the performance of the powerful DNN baselines. In this work, we aim to close this performance gap. We introduce a class of PNs, which are able to reach the performance of ResNet across a range of six benchmarks. We demonstrate that strong regularization is critical and conduct a…
We present a method for training a deep neural network containing sinusoidal activation functions to fit to time-series data. Weights are initialized using a fast Fourier transform, then trained with regularization to improve generalization. A simple dynamic parameter tuning method is employed to adjust both the learning rate and regularization term, such that stability and efficient training are both achieved. We show how deeper layers can be utilized to model the observed sequence using a sparser set of sinusoid units, and how non-uniform regularization can improve generalization by promotin…
George Mason University（乔治梅森大学）；Argonne National Laboratory（阿贡国家实验室）
In this work we consider a generalized bilevel optimization framework for solving inverse problems. We introduce fractional Laplacian as a regularizer to improve the reconstruction quality, and compare it with the total variation regularization. We emphasize that the key advantage of using fractional Laplacian as a regularizer is that it leads to a linear operator, as opposed to the total variation regularization which results in a nonlinear degenerate operator. Inspired by residual neural networks, to learn the optimal strength of regularization and the exponent of fractional Laplacian, we de…
University of Toronto（多伦多大学）；Stony Brook University（纽约州立大学石溪分校）
Activation functions play a pivotal role in determining the training dynamics and neural network performance. The widely adopted activation function ReLU despite being simple and effective has few disadvantages including the Dying ReLU problem. In order to tackle such problems, we propose a novel activation function called Serf which is self-regularized and nonmonotonic in nature. Like Mish, Serf also belongs to the Swish family of functions. Based on several experiments on computer vision (image classification and object detection) and natural language processing (machine translation, sentime…
Stable and Steerable Sparse Autoencoders with Weight Regularization
Department of Biology, University of Oxford, Oxford, UK（牛津大学生物学系）；Kavli Institute for Nanoscience Discovery, University of Oxford, Oxford, UK（牛津大学纳科学发现研究所）；Department of Chemistry, University of Oxford, Oxford, UK（牛津大学化学系）
Princeton University（普林斯顿大学）；Facebook AI Research（脸书人工智能研究院）；Stanford University（斯坦福大学）
We show that the gradient descent algorithm provides an implicit regularization effect in the learning of over-parameterized matrix factorization models and one-hidden-layer neural networks with quadratic activations. Concretely, we show that given $\tilde{O}(dr^{2})$ random linear measurements of a rank $r$ positive semidefinite matrix $X^{\star}$, we can recover $X^{\star}$ by parameterizing it by $UU^\top$ with $U\in \mathbb R^{d\times d}$ and minimizing the squared loss, even if $r \ll d$. We prove that starting from a small initialization, gradient descent recovers $X^{\star}$ in $\tilde{…
The large amount of memory bandwidth between local buffer and external DRAM has become the speedup bottleneck of CNN hardware accelerators, especially for activation maps. To reduce memory bandwidth, we propose to learn pruning unimportant blocks dynamically with zero block regularization of activation maps (Zebra). This strategy has low computational overhead and could easily integrate with other pruning methods for better performance. The experimental results show that the proposed method can reduce 70\% of memory bandwidth for Resnet-18 on Tiny-Imagenet within 1\% accuracy drops and 2\% acc…
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…
Overfitting is one of the most common problems when training deep neural networks on comparatively small datasets. Here, we demonstrate that neural network activation sparsity is a reliable indicator for overfitting which we utilize to propose novel targeted sparsity visualization and regularization strategies. Based on these strategies we are able to understand and counteract overfitting caused by activation sparsity and filter correlation in a targeted layer-by-layer manner. Our results demonstrate that targeted sparsity regularization can efficiently be used to regularize well-known dataset…
Yale Department of Computer Science（耶鲁大学计算机科学系）；Yale Department of Genetics（耶鲁大学遗传学系）；Université de Montréal, Dept. of Math. & Stat.（蒙特利尔大学数学与统计系）；Mila（米拉研究院）
While neural networks are powerful approximators used to classify or embed data into lower dimensional spaces, they are often regarded as black boxes with uninterpretable features. Here we propose Graph Spectral Regularization for making hidden layers more interpretable without significantly impacting performance on the primary task. Taking inspiration from spatial organization and localization of neuron activations in biological networks, we use a graph Laplacian penalty to structure the activations within a layer. This penalty encourages activations to be smooth either on a predetermined gra…
University of Waterloo（滑铁卢大学）；Layer 6 AI（Layer 6人工智能公司）
Given a pair of models with similar training set performance, it is natural to assume that the model that possesses simpler internal representations would exhibit better generalization. In this work, we provide empirical evidence for this intuition through an analysis of the intrinsic dimension (ID) of model activations, which can be thought of as the minimal number of factors of variation in the model's representation of the data. First, we show that common regularization techniques uniformly decrease the last-layer ID (LLID) of validation set activations for image classification models and s…
State-of-the-art deep neural networks (DNNs) are highly effective at tackling many real-world tasks. However, their wide adoption in mission-critical contexts is hampered by two major weaknesses - their susceptibility to adversarial attacks and their opaqueness. The former raises concerns about the security and generalization of DNNs in real-world conditions, whereas the latter impedes users' trust in their output. In this research, we (1) examine the effect of adversarial robustness on interpretability and (2) present a novel approach for improving the interpretability of DNNs that is based o…
Batch normalization is widely used in deep learning to normalize intermediate activations. Deep networks suffer from notoriously increased training complexity, mandating careful initialization of weights, requiring lower learning rates, etc. These issues have been addressed by Batch Normalization (\textbf{BN}), by normalizing the inputs of activations to zero mean and unit standard deviation. Making this batch normalization part of the training process dramatically accelerates the training process of very deep networks. A new field of research has been going on to examine the exact theoretical…
Ping An Technology (Shenzhen) Co., Ltd.（平安科技（深圳）有限公司）
Knowledge distillation refers to a technique of transferring the knowledge from a large learned model or an ensemble of learned models to a small model. This method relies on access to the original training set, which might not always be available. A possible solution is a data-free adversarial distillation framework, which deploys a generative network to transfer the teacher model's knowledge to the student model. However, the data generation efficiency is low in the data-free adversarial distillation. We add an activation regularizer and a virtual interpolation method to improve the data gen…
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 representat…
Mitigating the Impact of Outlier Channels for Language Model Quantization with Activation Regularization
Massachusetts Institute of Technology（麻省理工学院）；MIT-IBM Watson AI Lab（MIT-IBM沃森人工智能实验室）；IBM Research（IBM研究院）；IST Austria（奥地利科学技术研究所）；Neural Magic, Inc.（Neural Magic公司）
ETH Z\"urich, D-Math, R\"amistrasse 101, CH-8092 Z\"urich, Switzerland
Randomized neural networks (randomized NNs), where only the terminal layer's weights are optimized constitute a powerful model class to reduce computational time in training the neural network model. At the same time, these models generalize surprisingly well in various regression and classification tasks. In this paper, we give an exact macroscopic characterization (i.e., a characterization in function space) of the generalization behavior of randomized, shallow NNs with ReLU activation (RSNs). We show that RSNs correspond to a generalized additive model (GAM)-typed regression in which infini…
Konica Minolta Laboratory Europe（柯尼卡美能达欧洲实验室）；Technical University of Munich（慕尼黑工业大学）
Variational methods for revealing visual concepts learned by convolutional neural networks have gained significant attention during the last years. Being based on noisy gradients obtained via back-propagation such methods require the application of regularization strategies. We present a mathematical framework unifying previously employed regularization methods. Within this framework, we propose a novel technique based on Sobolev gradients which can be implemented via convolutions and does not require specialized numerical treatment, such as total variation regularization. The experiments perf…
Recent works have shown that the input domain of any machine learning classifier is bound to contain adversarial examples. Thus we can no longer hope to immune classifiers against adversarial examples and instead can only aim to achieve the following two defense goals: 1) making adversarial examples harder to find, or 2) weakening their adversarial nature by pushing them further away from correctly classified data points. Most if not all the previously suggested defense mechanisms attend to just one of those two goals, and as such, could be bypassed by adaptive attacks that take the defense me…
Many previous proposals for adversarial training of deep neural nets have included di- rectly modifying the gradient, training on a mix of original and adversarial examples, using contractive penalties, and approximately optimizing constrained adversarial ob- jective functions. In this paper, we show these proposals are actually all instances of optimizing a general, regularized objective we call DataGrad. Our proposed DataGrad framework, which can be viewed as a deep extension of the layerwise contractive au- toencoder penalty, cleanly simplifies prior work and easily allows extensions such a…
Motivating Next-Gen Accelerators with Flexible (N:M) Activation Sparsity via Benchmarking Lightweight Post-Training Sparsification Approaches
Applied AI（应用人工智能）；Artificial Intelligence Research Institute（人工智能研究所）；HSE University（俄罗斯高等经济大学）；Sb AI Lab（Sb人工智能实验室）；MWS AI（MWS人工智能）；Yandex；Independent Researcher（独立研究者）
