Improving Graph Convolutional Networks with Non-Parametric Activation Functions
Dept. Information Eng., Electronics and Telecomm., Sapienza University of Rome（罗马一大信息工程、电子与电信系）；Dept. Communications Eng., University of Cantabria（坎塔布里亚大学通信工程系）
Simone Scardapane, Steven Van Vaerenbergh, Danilo Comminiello, Aurelio Uncini
Graph neural networks (GNNs) are a class of neural networks that allow to efficiently perform inference on data that is associated to a graph structure, such as, e.g., citation networks or knowledge graphs. While several variants of GNNs have been proposed, they only consider simple nonlinear activation functions in their layers, such as rectifiers or squashing functions. In this paper, we investigate the use of graph convolutional networks (GCNs) when combined with more complex activation functions, able to adapt from the training data. More specifically, we extend the recently proposed kernel activation function, a non-parametric model which can be implemented easily, can be regularized with standard $\ell_p$-norms techniques, and is smooth over its entire domain. Our experimental evaluation shows that the proposed architecture can significantly improve over its baseline, while similar improvements cannot be obtained by simply increasing the depth or size of the original GCN.
University of Oxford（牛津大学）；The Alan Turing Institute（阿兰·图灵研究所）
Deep Convolutional Sparse Coding (D-CSC) is a framework reminiscent of deep convolutional neural networks (DCNNs), but by omitting the learning of the dictionaries one can more transparently analyse the role of the activation function and its ability to recover activation paths through the layers. Papyan, Romano, and Elad conducted an analysis of such an architecture, demonstrated the relationship with DCNNs and proved conditions under which the D-CSC is guaranteed to recover specific activation paths. A technical innovation of their work highlights that one can view the efficacy of the ReLU n…
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Cognizant AI Labs（高知特人工智能实验室）
Recent studies have shown that the choice of activation function can significantly affect the performance of deep learning networks. However, the benefits of novel activation functions have been inconsistent and task dependent, and therefore the rectified linear unit (ReLU) is still the most commonly used. This paper proposes a technique for customizing activation functions automatically, resulting in reliable improvements in performance. Evolutionary search is used to discover the general form of the function, and gradient descent to optimize its parameters for different parts of the network …
National Digital Switching System Engineering and Technological R&D Center（国家数字交换系统工程技术研究中心）
Activation functions play a key role in providing remarkable performance in deep neural networks, and the rectified linear unit (ReLU) is one of the most widely used activation functions. Various new activation functions and improvements on ReLU have been proposed, but each carry performance drawbacks. In this paper, we propose an improved activation function, which we name the natural-logarithm-rectified linear unit (NLReLU). This activation function uses the parametric natural logarithmic transform to improve ReLU and is simply defined as. NLReLU not only retains the sparse activation charac…
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…
University of Alberta（阿尔伯塔大学）；Hong Kong University of Science and Technology（香港科技大学）；University of Washington（华盛顿大学）；Carnegie Mellon University（卡内基梅隆大学）
In this paper we investigate the performance of different types of rectified activation functions in convolutional neural network: standard rectified linear unit (ReLU), leaky rectified linear unit (Leaky ReLU), parametric rectified linear unit (PReLU) and a new randomized leaky rectified linear units (RReLU). We evaluate these activation function on standard image classification task. Our experiments suggest that incorporating a non-zero slope for negative part in rectified activation units could consistently improve the results. Thus our findings are negative on the common belief that sparsi…
Activation function is a key component in deep learning that performs non-linear mappings between the inputs and outputs. Rectified Linear Unit (ReLU) has been the most popular activation function across the deep learning community. However, ReLU contains several shortcomings that can result in inefficient training of the deep neural networks, these are: 1) the negative cancellation property of ReLU tends to treat negative inputs as unimportant information for the learning, resulting in a performance degradation; 2) the inherent predefined nature of ReLU is unlikely to promote additional flexi…
Deep Neural Networks (DNNs) and Convolutional Neural Networks (CNNs) are useful for many practical tasks in machine learning. Synaptic weights, as well as neuron activation functions within the deep network are typically stored with high-precision formats, e.g. 32 bit floating point. However, since storage capacity is limited and each memory access consumes power, both storage capacity and memory access are two crucial factors in these networks. Here we present a method and present the ADaPTION toolbox to extend the popular deep learning library Caffe to support training of deep CNNs with redu…
Aalen University（阿伦大学）；Óbuda University（奥布达大学）；SupplyPike（SupplyPike公司）；University of Texas at El Paso（得克萨斯大学埃尔帕索分校）；University of Stuttgart（斯图加特大学）
We present a deep learning model for finding human-understandable connections between input features. Our approach uses a parameterized, differentiable activation function, based on the theoretical background of nilpotent fuzzy logic and multi-criteria decision-making (MCDM). The learnable parameter has a semantic meaning indicating the level of compensation between input features. The neural network determines the parameters using gradient descent to find human-understandable relationships between input features. We demonstrate the utility and effectiveness of the model by successfully applyi…
Adaptive Parametric Activation: Unifying and Generalising Activation Functions Across Tasks
Huawei Noah’s Ark Lab（华为诺亚实验室）；Department of Computing, Imperial College London（帝国理工学院计算机系）；Department of Computer Science, University of Liverpool（利物浦大学计算机科学系）；Department of Engineering, King’s College London（伦敦国王学院工程系）
We propose a simple extension to the ReLU-family of activation functions that allows them to shift the mean activation across a layer towards zero. Combined with proper weight initialization, this alleviates the need for normalization layers. We explore the training of deep vanilla recurrent neural networks (RNNs) with up to 144 layers, and show that bipolar activation functions help learning in this setting. On the Penn Treebank and Text8 language modeling tasks we obtain competitive results, improving on the best reported results for non-gated networks. In experiments with convolutional neur…
Mila - Quebec Artificial Intelligence Institute（米拉——魁北克人工智能研究所）；Université de Montréal（蒙特利尔大学）
Dynamic adaptation in single-neuron response plays a fundamental role in neural coding in biological neural networks. Yet, most neural activation functions used in artificial networks are fixed and mostly considered as an inconsequential architecture choice. In this paper, we investigate nonlinear activation function adaptation over the large time scale of learning, and outline its impact on sequential processing in recurrent neural networks. We introduce a novel parametric family of nonlinear activation functions, inspired by input-frequency response curves of biological neurons, which allows…
Recent work has shown that the activation function of the convolutional neural network can meet the Lipschitz condition, then the corresponding convolutional neural network structure can be constructed according to the scale of the data set, and the data set can be trained more deeply, more accurately and more effectively. In this article, we have accepted the experimental results and introduced the core block N-Gauss, N-Gauss, and Swish (Conv1, Conv2, FC1) neural network structure design to train MNIST, CIFAR10, and CIFAR100 respectively. Experiments show that N-Gauss gives full play to the m…
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…
The success of deep convolutional architectures is often attributed in part to their ability to learn multiscale and invariant representations of natural signals. However, a precise study of these properties and how they affect learning guarantees is still missing. In this paper, we consider deep convolutional representations of signals; we study their invariance to translations and to more general groups of transformations, their stability to the action of diffeomorphisms, and their ability to preserve signal information. This analysis is carried by introducing a multilayer kernel based on co…
CISPA Helmholtz Center for Information Security（CISPA亥姆霍兹信息安全中心）
The Lottery Ticket Hypothesis continues to have a profound practical impact on the quest for small scale deep neural networks that solve modern deep learning tasks at competitive performance. These lottery tickets are identified by pruning large randomly initialized neural networks with architectures that are as diverse as their applications. Yet, theoretical insights that attest their existence have been mostly focused on deep fully-connected feed forward networks with ReLU activation functions. We prove that also modern architectures consisting of convolutional and residual layers that can b…
Many activation functions have been proposed in the past, but selecting an adequate one requires trial and error. We propose a new methodology of designing activation functions within a neural network at each layer. We call this technique an "activation ensemble" because it allows the use of multiple activation functions at each layer. This is done by introducing additional variables, $α$, at each activation layer of a network to allow for multiple activation functions to be active at each neuron. By design, activations with larger $α$ values at a neuron is equivalent to having the largest mag…
In neural networks, non-linearity is introduced by activation functions. One commonly used activation function is Rectified Linear Unit (ReLU). ReLU has been a popular choice as an activation but has flaws. State-of-the-art functions like Swish and Mish are now gaining attention as a better choice as they combat many flaws presented by other activation functions. CoLU is an activation function similar to Swish and Mish in properties. It is defined as f(x)=x/(1-xe^-(x+e^x)). It is smooth, continuously differentiable, unbounded above, bounded below, non-saturating, and non-monotonic. Based on ex…
We propose convex relaxations for convolutional neural nets with one hidden layer where the output weights are fixed. For convex activation functions such as rectified linear units, the relaxations are convex second order cone programs which can be solved very efficiently. We prove that the relaxation recovers the global minimum under a planted model assumption, given sufficiently many training samples from a Gaussian distribution. We also identify a phase transition phenomenon in recovering the global minimum for the relaxation.
Massachusetts Institute of Technology（麻省理工学院）；MIT-IBM Watson AI Lab, IBM Research（IBM研究院MIT-IBM沃森人工智能实验室）
Verifying robustness of neural network classifiers has attracted great interests and attention due to the success of deep neural networks and their unexpected vulnerability to adversarial perturbations. Although finding minimum adversarial distortion of neural networks (with ReLU activations) has been shown to be an NP-complete problem, obtaining a non-trivial lower bound of minimum distortion as a provable robustness guarantee is possible. However, most previous works only focused on simple fully-connected layers (multilayer perceptrons) and were limited to ReLU activations. This motivates us…
The Rectified Linear Unit is currently a state-of-the-art activation function in deep convolutional neural networks. To combat ReLU's dying neuron problem, we propose the Parametric Variational Linear Unit (PVLU), which adds a sinusoidal function with trainable coefficients to ReLU. Along with introducing nonlinearity and non-zero gradients across the entire real domain, PVLU acts as a mechanism of fine-tuning when implemented in the context of transfer learning. On a simple, non-transfer sequential CNN, PVLU substitution allowed for relative error decreases of 16.3% and 11.3% (without and wit…
In this paper, we propose a winner-take-all method for learning hierarchical sparse representations in an unsupervised fashion. We first introduce fully-connected winner-take-all autoencoders which use mini-batch statistics to directly enforce a lifetime sparsity in the activations of the hidden units. We then propose the convolutional winner-take-all autoencoder which combines the benefits of convolutional architectures and autoencoders for learning shift-invariant sparse representations. We describe a way to train convolutional autoencoders layer by layer, where in addition to lifetime spars…
The predictive power of neural networks often costs model interpretability. Several techniques have been developed for explaining model outputs in terms of input features; however, it is difficult to translate such interpretations into actionable insight. Here, we propose a framework to analyze predictions in terms of the model's internal features by inspecting information flow through the network. Given a trained network and a test image, we select neurons by two metrics, both measured over a set of images created by perturbations to the input image: (1) magnitude of the correlation between t…
We investigate the potential of stochastic neural networks for learning effective waveform-based acoustic models. The waveform-based setting, inherent to fully end-to-end speech recognition systems, is motivated by several comparative studies of automatic and human speech recognition that associate standard non-adaptive feature extraction techniques with information loss which can adversely affect robustness. Stochastic neural networks, on the other hand, are a class of models capable of incorporating rich regularization mechanisms into the learning process. We consider a deep convolutional ne…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Deep neural networks can suffer from the exploding and vanishing activation problem, in which the networks fail to train properly because the neural signals either amplify or attenuate across the layers and become saturated. While other normalization methods aim to fix the stated problem, most of them have inference speed penalties in those applications that require running averages of the neural activations. Here we extend the unitary framework based on Lie algebra to neural networks of any dimensionalities, overcoming the major constraints of the prior arts that limit synaptic weights to be …
In this paper we introduce activation functions that move the entire computation of Convolutional Networks into the frequency domain, where they are actually Hadamard Networks. To achieve this result we employ the properties of Discrete Fourier Transform. We present some implementation details and experimental results, as well as some insights into why convolutional networks perform well in learning use cases.
We propose a new type of neural networks, Kronecker neural networks (KNNs), that form a general framework for neural networks with adaptive activation functions. KNNs employ the Kronecker product, which provides an efficient way of constructing a very wide network while keeping the number of parameters low. Our theoretical analysis reveals that under suitable conditions, KNNs induce a faster decay of the loss than that by the feed-forward networks. This is also empirically verified through a set of computational examples. Furthermore, under certain technical assumptions, we establish global co…
University of Waterloo（滑铁卢大学）；Waterloo Artificial Intelligence Institute（滑铁卢人工智能研究所）；DarwinAI Corp.（达尔文人工智能公司）
From fully connected neural networks to convolutional neural networks, the learned parameters within a neural network have been primarily relegated to the linear parameters (e.g., convolutional filters). The non-linear functions (e.g., activation functions) have largely remained, with few exceptions in recent years, parameter-less, static throughout training, and seen limited variation in design. Largely ignored by the deep learning community, radial basis function (RBF) networks provide an interesting mechanism for learning more complex non-linear activation functions in addition to the linea…
Georgetown University Medical Center（乔治城大学医学中心）；Virginia Tech（弗吉尼亚理工大学）
Transformationally invariant processors constructed by transformed input vectors or operators have been suggested and applied to many applications. In this study, transformationally identical processing based on combining results of all sub-processes with corresponding transformations at one of the processing steps or at the beginning step were found to be equivalent for a given condition. This property can be applied to most convolutional neural network (CNN) systems. Specifically, a transformationally identical CNN can be constructed by arranging internally symmetric operations in parallel w…
Charles Sturt University（查尔斯特大学）；Asia Pacific International College（亚太国际学院）；Worcester State University（伍斯特州立大学）；University of Kurdistan Hewler（库尔德斯坦埃尔比勒大学）
Background and Aim: Each stage of sleep can affect human health, and not getting enough sleep at any stage may lead to sleep disorder like parasomnia, apnea, insomnia, etc. Sleep-related diseases could be diagnosed using Convolutional Neural Network Classifier. However, this classifier has not been successfully implemented into sleep stage classification systems due to high complexity and low accuracy of classification. The aim of this research is to increase the accuracy and reduce the learning time of Convolutional Neural Network Classifier. Methodology: The proposed system used a modified O…
Deep neural networks are known to be vulnerable to adversarially perturbed inputs. A commonly used defense is adversarial training, whose performance is influenced by model capacity. While previous works have studied the impact of varying model width and depth on robustness, the impact of increasing capacity by using learnable parametric activation functions (PAFs) has not been studied. We study how using learnable PAFs can improve robustness in conjunction with adversarial training. We first ask the question: how should we incorporate parameters into activation functions to improve robustness…
Fuzhou University（福州大学）；University of Vienna（维也纳大学）
In practical applications, multi-view data depicting objectives from assorted perspectives can facilitate the accuracy increase of learning algorithms. However, given multi-view data, there is limited work for learning discriminative node relationships and graph information simultaneously via graph convolutional network that has drawn the attention from considerable researchers in recent years. Most of existing methods only consider the weighted sum of adjacency matrices, yet a joint neural network of both feature and graph fusion is still under-explored. To cope with these issues, this paper …
MINES Paris（巴黎矿业学院）；PSL University（巴黎文理研究大学）；Centre for mathematical morphology (CMM)（数学形态学中心（CMM））
This paper analyses both nonlinear activation functions and spatial max-pooling for Deep Convolutional Neural Networks (DCNNs) by means of the algebraic basis of mathematical morphology. Additionally, a general family of activation functions is proposed by considering both max-pooling and nonlinear operators in the context of morphological representations. Experimental section validates the goodness of our approach on classical benchmarks for supervised learning by DCNN.
Computerized detection of colonic polyps remains an unsolved issue because of the wide variation in the appearance, texture, color, size, and presence of the multiple polyp-like imitators during colonoscopy. In this paper, we propose a deep convolutional neural network based model for the computerized detection of polyps within colonoscopy images. The proposed model comprises 16 convolutional layers with 2 fully connected layers, and a Softmax layer, where we implement a unique approach using different convolutional kernels within the same hidden layer for deeper feature extraction. We applied…
National Digital Switching System Engineering and Technological R&D Center（国家数字交换系统工程技术研究中心）；Eindhoven University of Technology（埃因霍温理工大学）
The classification of sentences is very challenging, since sentences contain the limited contextual information. In this paper, we proposed an Attention-Gated Convolutional Neural Network (AGCNN) for sentence classification, which generates attention weights from the feature's context windows of different sizes by using specialized convolution encoders. It makes full use of limited contextual information to extract and enhance the influence of important features in predicting the sentence's category. Experimental results demonstrated that our model can achieve up to 3.1% higher accuracy than s…
Université Savoie Mont Blanc（萨瓦大学）；TLECOM Bretagne（布列塔尼电信学院）
The paper proposes representation functionals in a dual paradigm where learning jointly concerns both linear convolutional weights and parametric forms of nonlinear activation functions. The nonlinear forms proposed for performing the functional representation are associated with a new class of parametric neural transfer functions called rectified power sigmoid units. This class is constructed to integrate both advantages of sigmoid and rectified linear unit functions, in addition with rejecting the drawbacks of these functions. Moreover, the analytic form of this new neural class involves sca…
Image space formalism of convolutional neural networks for k-space interpolation
University of Würzburg（维尔茨堡大学）；University Hospital Erlangen（埃尔朗根大学医院）；Fraunhofer Institute for Integrated Circuits IIS（弗劳恩霍夫集成电路研究所）；University Hospital Würzburg（维尔茨堡大学医院）
本文提出 RAKI 的图像空间形式化方法，通过激活掩码与雅可比矩阵解析分析 k 空间非线性激活对噪声传播和重建伪影的影响，实现 g 因子图的解析量化与噪声鲁棒性调控。
In this paper we present a class of convolutional neural networks (CNNs) called non-overlapping CNNs in the study of approximation capabilities of CNNs. We prove that such networks with sigmoidal activation function are capable of approximating arbitrary continuous function defined on compact input sets with any desired degree of accuracy. This result extends existing results where only multilayer feedforward networks are a class of approximators. Evaluations elucidate the accuracy and efficiency of our result and indicate that the proposed non-overlapping CNNs are less sensitive to noise.
Complex-valued neural networks (CVNNs) are a powerful modeling tool for domains where data can be naturally interpreted in terms of complex numbers. However, several analytical properties of the complex domain (e.g., holomorphicity) make the design of CVNNs a more challenging task than their real counterpart. In this paper, we consider the problem of flexible activation functions (AFs) in the complex domain, i.e., AFs endowed with sufficient degrees of freedom to adapt their shape given the training data. While this problem has received considerable attention in the real case, a very limited l…
We propose DoReFa-Net, a method to train convolutional neural networks that have low bitwidth weights and activations using low bitwidth parameter gradients. In particular, during backward pass, parameter gradients are stochastically quantized to low bitwidth numbers before being propagated to convolutional layers. As convolutions during forward/backward passes can now operate on low bitwidth weights and activations/gradients respectively, DoReFa-Net can use bit convolution kernels to accelerate both training and inference. Moreover, as bit convolutions can be efficiently implemented on CPU, F…
Object recognition is an important task for improving the ability of visual systems to perform complex scene understanding. Recently, the Exponential Linear Unit (ELU) has been proposed as a key component for managing bias shift in Convolutional Neural Networks (CNNs), but defines a parameter that must be set by hand. In this paper, we propose learning a parameterization of ELU in order to learn the proper activation shape at each layer in the CNNs. Our results on the MNIST, CIFAR-10/100 and ImageNet datasets using the NiN, Overfeat, All-CNN and ResNet networks indicate that our proposed Param…
We show that, during inference with Convolutional Neural Networks (CNNs), more than 2x to $8x ineffectual work can be exposed if instead of targeting those weights and activations that are zero, we target different combinations of value stream properties. We demonstrate a practical application with Bit-Tactical (TCL), a hardware accelerator which exploits weight sparsity, per layer precision variability and dynamic fine-grain precision reduction for activations, and optionally the naturally occurring sparse effectual bit content of activations to improve performance and energy efficiency. TCL …
A new, radical CNN design approach is presented in this paper, considering the reduction of the total computational load during inference. This is achieved by a new holistic intervention on both the CNN architecture and the training procedure, which targets to the parsimonious inference by learning to exploit or remove the redundant capacity of a CNN architecture. This is accomplished, by the introduction of a new structural element that can be inserted as an add-on to any contemporary CNN architecture, whilst preserving or even improving its recognition accuracy. Our approach formulates a sys…
We introduce a simple and effective method for regularizing large convolutional neural networks. We replace the conventional deterministic pooling operations with a stochastic procedure, randomly picking the activation within each pooling region according to a multinomial distribution, given by the activities within the pooling region. The approach is hyper-parameter free and can be combined with other regularization approaches, such as dropout and data augmentation. We achieve state-of-the-art performance on four image datasets, relative to other approaches that do not utilize data augmentati…
CSEM SA（瑞士电子与微技术中心）；Swiss Federal Institute of Technology, ETH Zurich（苏黎世联邦理工学院）；University of Bologna（博洛尼亚大学）
While the accuracy of convolutional neural networks has achieved vast improvements by introducing larger and deeper network architectures, also the memory footprint for storing their parameters and activations has increased. This trend especially challenges power- and resource-limited accelerator designs, which are often restricted to store all network data in on-chip memory to avoid interfacing energy-hungry external memories. Maximizing the network size that fits on a given accelerator thus requires to maximize its memory utilization. While the traditionally used ping-pong buffering techniqu…
NVIDIA（英伟达）；Massachusetts Institute of Technology（麻省理工学院）；UC-Berkeley（加州大学伯克利分校）；Stanford University（斯坦福大学）
Convolutional Neural Networks (CNNs) have emerged as a fundamental technology for machine learning. High performance and extreme energy efficiency are critical for deployments of CNNs in a wide range of situations, especially mobile platforms such as autonomous vehicles, cameras, and electronic personal assistants. This paper introduces the Sparse CNN (SCNN) accelerator architecture, which improves performance and energy efficiency by exploiting the zero-valued weights that stem from network pruning during training and zero-valued activations that arise from the common ReLU operator applied du…
Imperial College London（帝国理工学院）；Cortexica Vision Systems Limited（Cortexica视觉系统有限公司）
In recent work, it was shown that combining multi-kernel based support vector machines (SVMs) can lead to near state-of-the-art performance on an action recognition dataset (HMDB-51 dataset). This was 0.4\% lower than frameworks that used hand-crafted features in addition to the deep convolutional feature extractors. In the present work, we show that combining distributed Gaussian Processes with multi-stream deep convolutional neural networks (CNN) alleviate the need to augment a neural network with hand-crafted features. In contrast to prior work, we treat each deep neural convolutional netwo…
