Many applications, especially in physics and other sciences, call for easily interpretable and robust machine learning techniques. We propose a fully gradient-based technique for training radial basis function networks with an efficient and scalable open-source implementation. We derive novel closed-form optimization criteria for pruning the models for continuous as well as binary data which arise in a challenging real-world material physics problem. The pruned models are optimized to provide compact and interpretable versions of larger models based on informed assumptions about the data distribution. Visualizations of the pruned models provide insight into the atomic configurations that determine atom-level migration processes in solid matter; these results may inform future research on designing more suitable descriptors for use with machine learning algorithms.
University of Toronto（多伦多大学）；Vector Institute（向量研究所）；NVIDIA（英伟达）
Reducing the test time resource requirements of a neural network while preserving test accuracy is crucial for running inference on resource-constrained devices. To achieve this goal, we introduce a novel network reparameterization based on the Kronecker-factored eigenbasis (KFE), and then apply Hessian-based structured pruning methods in this basis. As opposed to existing Hessian-based pruning algorithms which do pruning in parameter coordinates, our method works in the KFE where different weights are approximately independent, enabling accurate pruning and fast computation. We demonstrate em…
US Naval Surface Warfare Center（美国海军水面作战中心）；University of Florida（佛罗里达大学）
Radial-basis-function networks are traditionally defined for sets of vector-based observations. In this short paper, we reformulate such networks so that they can be applied to adjacency-matrix representations of weighted, directed graphs that represent the relationships between object pairs. We re-state the sum-of-squares objective function so that it is purely dependent on entries from the adjacency matrix. From this objective function, we derive a gradient descent update for the network weights. We also derive a gradient update that simulates the repositioning of the radial basis prototypes…
Many neural network pruning algorithms proceed in three steps: train the network to completion, remove unwanted structure to compress the network, and retrain the remaining structure to recover lost accuracy. The standard retraining technique, fine-tuning, trains the unpruned weights from their final trained values using a small fixed learning rate. In this paper, we compare fine-tuning to alternative retraining techniques. Weight rewinding (as proposed by Frankle et al., (2019)), rewinds unpruned weights to their values from earlier in training and retrains them from there using the original …
While Bayesian neural networks have many appealing characteristics, current priors do not easily allow users to specify basic properties such as expected lengthscale or amplitude variance. In this work, we introduce Poisson Process Radial Basis Function Networks, a novel prior that is able to encode amplitude stationarity and input-dependent lengthscale. We prove that our novel formulation allows for a decoupled specification of these properties, and that the estimated regression function is consistent as the number of observations tends to infinity. We demonstrate its behavior on synthetic an…
One of the most effective methods of channel pruning is to trim on the basis of the importance of each neuron. However, measuring the importance of each neuron is an NP-hard problem. Previous works have proposed to trim by considering the statistics of a single layer or a plurality of successive layers of neurons. These works cannot eliminate the influence of different data on the model in the reconstruction error, and currently, there is no work to prove that the absolute values of the parameters can be directly used as the basis for judging the importance of the weights. A more reasonable ap…
Robert Bosch GmbH（罗伯特·博世有限公司）；University of Lübeck（吕贝克大学）
Unstructured pruning is well suited to reduce the memory footprint of convolutional neural networks (CNNs), both at training and inference time. CNNs contain parameters arranged in $K \times K$ filters. Standard unstructured pruning (SP) reduces the memory footprint of CNNs by setting filter elements to zero, thereby specifying a fixed subspace that constrains the filter. Especially if pruning is applied before or during training, this induces a strong bias. To overcome this, we introduce interspace pruning (IP), a general tool to improve existing pruning methods. It uses filters represented i…
Amazon Web Services（亚马逊云服务）；Brown University（布朗大学）；Duke University（杜克大学）
A core operation in reinforcement learning (RL) is finding an action that is optimal with respect to a learned value function. This operation is often challenging when the learned value function takes continuous actions as input. We introduce deep radial-basis value functions (RBVFs): value functions learned using a deep network with a radial-basis function (RBF) output layer. We show that the maximum action-value with respect to a deep RBVF can be approximated easily and accurately. Moreover, deep RBVFs can represent any true value function owing to their support for universal function approx…
Deep neural networks have evolved to become power demanding and consequently difficult to apply to small-size mobile platforms. Network parameter reduction methods have been introduced to systematically deal with the computational and memory complexity of deep networks. We propose to examine the ability of attentive connection pruning to deal with redundancy reduction in neural networks as a contribution to the reduction of computational demand. In this work, we describe a Top-Down attention mechanism that is added to a Bottom-Up feedforward network to select important connections and subseque…
University of Ballarat（巴拉瑞特大学）；Australian National University（澳大利亚国立大学）
Radial Basis Functions Neural Networks (RBFNNs) are tools widely used in regression problems. One of their principal drawbacks is that the formulation corresponding to the training with the supervision of both the centers and the weights is a highly non-convex optimization problem, which leads to some fundamentally difficulties for traditional optimization theory and methods. This paper presents a generalized canonical duality theory for solving this challenging problem. We demonstrate that by sequential canonical dual transformations, the nonconvex optimization problem of the RBFNN can be ref…
Convolutional Neural Networks (CNNs) compression is crucial to deploying these models in edge devices with limited resources. Existing channel pruning algorithms for CNNs have achieved plenty of success on complex models. They approach the pruning problem from various perspectives and use different metrics to guide the pruning process. However, these metrics mainly focus on the model's `outputs' or `weights' and neglect its `interpretations' information. To fill in this gap, we propose to address the channel pruning problem from a novel perspective by leveraging the interpretations of a model …
ETH Zürich（苏黎世联邦理工学院）；Beihang University（北京航空航天大学）；Singapore Management University（新加坡管理大学）
Many mobile applications demand selective execution of multiple correlated deep learning inference tasks on resource-constrained platforms. Given a set of deep neural networks, each pre-trained for a single task, it is desired that executing arbitrary combinations of tasks yields minimal computation cost. Pruning each network separately yields suboptimal computation cost due to task relatedness. A promising remedy is to merge the networks into a multitask network to eliminate redundancy across tasks before network pruning. However, pruning a multitask network combined by existing network mergi…
University of Málaga（马拉加大学）；Biomedic Research Institute of Málaga (IBIMA)（马拉加生物医学研究所 (IBIMA)）；University of Michigan（密歇根大学）
Support Vector Machines (SVMs) are still one of the most popular and precise classifiers. The Radial Basis Function (RBF) kernel has been used in SVMs to separate among classes with considerable success. However, there is an intrinsic dependence on the initial value of the kernel hyperparameter. In this work, we propose OKSVM, an algorithm that automatically learns the RBF kernel hyperparameter and adjusts the SVM weights simultaneously. The proposed optimization technique is based on a gradient descent method. We analyze the performance of our approach with respect to the classical SVM for cl…
Global optimization problems whose objective function is expensive to evaluate can be solved effectively by recursively fitting a surrogate function to function samples and minimizing an acquisition function to generate new samples. The acquisition step trades off between seeking for a new optimization vector where the surrogate is minimum (exploitation of the surrogate) and looking for regions of the feasible space that have not yet been visited and that may potentially contain better values of the objective function (exploration of the feasible space). This paper proposes a new global optimi…
We demonstrate the use of similarity domains (SDs) for shape modeling and skeleton extraction. SDs are recently proposed and they can be utilized in a neural network framework to help us analyze shapes. SDs are modeled with radial basis functions with varying shape parameters in Similarity Domains Networks (SDNs). In this paper, we demonstrate how using SDN can first help us model a pixel-based image in terms of SDs and then demonstrate how those learned SDs can be used to extract the skeleton of a shape.
Radial basis function (RBF) network is a third layered neural network that is widely used in function approximation and data classification. Here we propose a quantum model of the RBF network. Similar to the classical case, we still use the radial basis functions as the activation functions. Quantum linear algebraic techniques and coherent states can be applied to implement these functions. Differently, we define the state of the weight as a tensor product of single-qubit states. This gives a simple approach to implement the quantum RBF network in the quantum circuits. Theoretically, we prove …
The aim of this project is to develop a code to discover the optimal sigma value that maximum the F1 score and the optimal sigma value that maximizes the accuracy and to find out if they are the same. Four algorithms which can be used to solve this problem are: Genetic Regression Neural Networks (GRNNs), Radial Based Function (RBF) Neural Networks (RBFNNs), Support Vector Machines (SVMs) and Feedforward Neural Network (FFNNs).
We present a fast and numerically accurate method for expanding digitized $L \times L$ images representing functions on $[-1,1]^2$ supported on the disk $\{x \in \mathbb{R}^2 : |x|<1\}$ in the harmonics (Dirichlet Laplacian eigenfunctions) on the disk. Our method, which we refer to as the Fast Disk Harmonics Transform (FDHT), runs in $O(L^2 \log L)$ operations. This basis is also known as the Fourier-Bessel basis, and it has several computational advantages: it is orthogonal, ordered by frequency, and steerable in the sense that images expanded in the basis can be rotated by applying a diagona…
Adaptively trained Physics-informed Radial Basis Function Neural Networks for Solving Multi-asset Option Pricing Problems
College of Mathematics and Statistics, Northwest Normal University（西北师范大学数学与统计学院）；Department of Mathematics, City University of Hong Kong（香港城市大学数学系）；Department of Information Technology, Uppsala University（乌普萨拉大学信息科技系）
Laboratory of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院材料研究所计算科学与建模实验室）
The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular representations can be seen as an expansion of the symmetrized correlations of the atom density, and differ mainly by the choice of basis. Considerable effort has been dedicated to the optimization of the basis set, typically driven by heuristic considerations on the behavior of the regression target. Here we take a different, unsupervised viewpoint, aiming…
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…
City University of Hong Kong（香港城市大学）；Xi’an Jiaotong University（西安交通大学）；University of Sydney（悉尼大学）
This paper proposes a distributed weighted regularized least squares algorithm (DWRLS) based on spherical radial basis functions and spherical quadrature rules to tackle spherical data that are stored across numerous local servers and cannot be shared with each other. Via developing a novel integral operator approach, we succeed in deriving optimal approximation rates for DWRLS and theoretically demonstrate that DWRLS performs similarly as running a weighted regularized least squares algorithm with the whole data on a large enough machine. This interesting finding implies that distributed lear…
We introduce a generalization to the lottery ticket hypothesis in which the notion of "sparsity" is relaxed by choosing an arbitrary basis in the space of parameters. We present evidence that the original results reported for the canonical basis continue to hold in this broader setting. We describe how structured pruning methods, including pruning units or factorizing fully-connected layers into products of low-rank matrices, can be cast as particular instances of this "generalized" lottery ticket hypothesis. The investigations reported here are preliminary and are provided to encourage furthe…
Financial time series are characterised by their nonstationarity and autocorrelation. Even if these time series are differenced, technically ensuring their stationarity, they experience regular covariate shifts and concept drifts. Against this backdrop, we combine feature representation transfer with sequential optimisation to provide multi-horizon returns forecasts. Our online learning rbfnet outperforms a random-walk baseline and several powerful batch learners. The rbfnets we formulate are naturally designed to measure the similarity between test samples and continuously updated prototypes …
Changsha University of Science and Technology（长沙理工大学）；Hunan Provincial Key Laboratory of Intelligent Processing of Big Data on Transp（湖南省交通大数据智能处理重点实验室）
Convolutional Neural Network (CNN) is more and more widely used in various fileds, and its computation and memory-demand are also increasing significantly. In order to make it applicable to limited conditions such as embedded application, network compression comes out. Among them, researchers pay more attention to network pruning. In this paper, we encode the convolution network to obtain the similarity of different encoding nodes, and evaluate the connectivity-power among convolutional kernels on the basis of the similarity. Then impose different level of penalty according to different connec…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Parallel surrogate optimization algorithms have proven to be efficient methods for solving expensive noisy optimization problems. In this work we develop a new parallel surrogate optimization algorithm (ProSRS), using a novel tree-based "zoom strategy" to improve the efficiency of the algorithm. We prove that if ProSRS is run for sufficiently long, with probability converging to one there will be at least one point among all the evaluations that will be arbitrarily close to the global minimum. We compare our algorithm to several state-of-the-art Bayesian optimization algorithms on a suite of s…
University of Tennessee at Chattanooga（田纳西大学查塔努加分校）
In this paper, the accuracy of two mesh-free approximation approaches, the Gravity model and Radial Basis Function, are compared. The two schemes' convergence behaviors prove that RBF is faster and more accurate than the Gravity model. As a case study, the interpolation of temperature at different locations in Tennesse, USA, are compared. Delaunay mesh generation is used to create random points inside and on the border, which data can be incorporated in these locations. 49 MERRA weather stations as used as data sources to provide the temperature at a specific day and hour. The contours of inte…
Mammography is often used as the most common laboratory method for the detection of breast cancer, yet associated with the high cost and many side effects. Machine learning prediction as an alternative method has shown promising results. This paper presents a method based on a multilayer fuzzy expert system for the detection of breast cancer using an extreme learning machine (ELM) classification model integrated with radial basis function (RBF) kernel called ELM-RBF, considering the Wisconsin dataset. The performance of the proposed model is further compared with a linear-SVM model. The propos…
Université Clermont Auvergne（克莱蒙奥弗涅大学）；Clermont Auvergne INP（克莱蒙奥弗涅国立理工学院）；CNRS（法国国家科学研究中心）；Institut Pascal（帕斯卡研究所）；Laboratoire de Mathématiques Blaise Pascal（布莱士·帕斯卡数学实验室）
While reinforcement learning (RL) from raw images has been largely investigated in the last decade, existing approaches still suffer from a number of constraints. The high input dimension is often handled using either expert knowledge to extract handcrafted features or environment encoding through convolutional networks. Both solutions require numerous parameters to be optimized. In contrast, we propose a generic method to extract sparse features from raw images with few trainable parameters. We achieved this using a Radial Basis Function Network (RBFN) directly on raw image. We evaluate the p…
Resource-Efficient Pruning for Transformer via Low-Rank Importance Estimation
School of Computer Science and Technology, Guangdong University of Technology（广东工业大学计算机科学与技术学院）；College of Information and Artificial Intelligence, Yangzhou University（扬州大学信息与人工智能学院）
Interferometry can measure the shape or the material density of a system that could not be measured otherwise by recording the difference between the phase change of a signal and a reference phase. This difference is always between $-π$ and $π$ while it is the absolute phase that is required to get a true measurement. There is a long history of methods designed to recover accurately this phase from the phase "wrapped" inside $]-π,π]$. However, noise and under-sampling limit the effectiveness of most techniques and require highly sophisticated algorithms that can process imperfect measurements.…
