In this paper, we propose a novel model for high-dimensional data, called the Hybrid Orthogonal Projection and Estimation (HOPE) model, which combines a linear orthogonal projection and a finite mixture model under a unified generative modeling framework. The HOPE model itself can be learned unsupervised from unlabelled data based on the maximum likelihood estimation as well as discriminatively from labelled data. More interestingly, we have shown the proposed HOPE models are closely related to neural networks (NNs) in a sense that each hidden layer can be reformulated as a HOPE model. As a result, the HOPE framework can be used as a novel tool to probe why and how NNs work, more importantly, to learn NNs in either supervised or unsupervised ways. In this work, we have investigated the HOPE framework to learn NNs for several standard tasks, including image recognition on MNIST and speech recognition on TIMIT. Experimental results have shown that the HOPE framework yields significant performance gains over the current state-of-the-art methods in various types of NN learning problems, including unsupervised feature learning, supervised or semi-supervised learning.
Tsinghua University（清华大学）；Institute for AI Industry Research, Tsinghua University（清华大学人工智能产业研究院）；Beijing National Research Center for Information Science and Technology（北京信息科学与技术国家研究中心）；Beijing Academy of Artificial Intelligence（北京人工智能研究院）；International Innovation Center of Tsinghua University（清华大学国际创新中心）；Quan Cheng Laboratory（泉城实验室）
Continual learning aims to avoid catastrophic forgetting and effectively leverage learned experiences to master new knowledge. Existing gradient projection approaches impose hard constraints on the optimization space for new tasks to minimize interference, which simultaneously hinders forward knowledge transfer. To address this issue, recent methods reuse frozen parameters with a growing network, resulting in high computational costs. Thus, it remains a challenge whether we can improve forward knowledge transfer for gradient projection approaches using a fixed network architecture. In this wor…
Predictive models are increasingly deployed for the purpose of determining access to services such as credit, insurance, and employment. Despite potential gains in productivity and efficiency, several potential problems have yet to be addressed, particularly the potential for unintentional discrimination. We present an iterative procedure, based on orthogonal projection of input attributes, for enabling interpretability of black-box predictive models. Through our iterative procedure, one can quantify the relative dependence of a black-box model on its input attributes.The relative significance…
University of Vienna（维也纳大学）；Medical University of Vienna（维也纳医科大学）；Brno University of Technology（布尔诺理工大学）
The use of orthogonal projections on high-dimensional input and target data in learning frameworks is studied. First, we investigate the relations between two standard objectives in dimension reduction, preservation of variance and of pairwise relative distances. Investigations of their asymptotic correlation as well as numerical experiments show that a projection does usually not satisfy both objectives at once. In a standard classification problem we determine projections on the input data that balance the objectives and compare subsequent results. Next, we extend our application of orthogon…
Tsinghua University（清华大学）；University of Reading（雷丁大学）；Shandong University of Science and Technology（山东科技大学）
By integrating two powerful methods of density reduction and intrinsic dimensionality estimation, a new data-driven method, referred to as OLPP-MLE (orthogonal locality preserving projection-maximum likelihood estimation), is introduced for process monitoring. OLPP is utilized for dimensionality reduction, which provides better locality preserving power than locality preserving projection. Then, the MLE is adopted to estimate intrinsic dimensionality of OLPP. Within the proposed OLPP-MLE, two new static measures for fault detection $T_{\scriptscriptstyle {OLPP}}^2$ and ${\rm SPE}_{\scriptscrip…
Muon-OGD: Muon-based Spectral Orthogonal Gradient Projection for LLM Continual Learning
Purdue University（普渡大学）；Brown University（布朗大学）；Massachusetts Institute of Technology（麻省理工学院）；University of California, Irvine（加州大学 Irvine 分校）；Utah State University（犹他州立大学）；Harvard University（哈佛大学）
Hebbian Learning based Orthogonal Projection for Continual Learning of Spiking Neural Networks
School of Intelligence Science and Technology, Peking University（北京大学智能科学与技术学院）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Shenzhen Research Institute of Big Data（深圳大数据研究院）；School of Public Health, Peking University（北京大学公共卫生学院）；Institute for Artificial Intelligence, Peking University（北京大学人工智能研究院）；Peng Cheng Laboratory（鹏城实验室）
Principal component analysis (PCA) is an unsupervised method for learning low-dimensional features with orthogonal projections. Multilinear PCA methods extend PCA to deal with multidimensional data (tensors) directly via tensor-to-tensor projection or tensor-to-vector projection (TVP). However, under the TVP setting, it is difficult to develop an effective multilinear PCA method with the orthogonality constraint. This paper tackles this problem by proposing a novel Semi-Orthogonal Multilinear PCA (SO-MPCA) approach. SO-MPCA learns low-dimensional features directly from tensors via TVP by impos…
In a linear stochastic bandit model, each arm is a vector in an Euclidean space and the observed return at each time step is an unknown linear function of the chosen arm at that time step. In this paper, we investigate the problem of learning the best arm in a linear stochastic bandit model, where each arm's expected reward is an unknown linear function of the projection of the arm onto a subspace. We call this the projection reward. Unlike the classical linear bandit problem in which the observed return corresponds to the reward, the projection reward at each time step is unobservable. Such a…
ESAT-STADIUS；KU Leuven（鲁汶大学）；Department of Computer Science（计算机科学系）；University of Toronto（多伦多大学）
Neural ordinary differential equations (Neural ODEs) are an effective framework for learning dynamical systems from irregularly sampled time series data. These models provide a continuous-time latent representation of the underlying dynamical system where new observations at arbitrary time points can be used to update the latent representation of the dynamical system. Existing parameterizations for the dynamics functions of Neural ODEs limit the ability of the model to retain global information about the time series; specifically, a piece-wise integration of the latent process between observat…
Probabilistic Analysis of Least Squares, Orthogonal Projection, and QR Factorization Algorithms Subject to Gaussian Noise
Department of Computer Science, University of Saskatchewan（萨斯喀彻温大学计算机科学系）；Department of Applied Mathematics, University of Colorado Denver（科罗拉多大学丹佛分校应用数学系）；Department of Mathematics, The University of Tulsa（塔尔萨大学数学系）
Structured pruning is an effective compression technique to reduce the computation of neural networks, which is usually achieved by adding perturbations to reduce network parameters at the cost of slightly increasing training loss. A more reasonable approach is to find a sparse minimizer along the flat minimum valley found by optimizers, i.e. stochastic gradient descent, which keeps the training loss constant. To achieve this goal, we propose the structured directional pruning based on orthogonal projecting the perturbations onto the flat minimum valley. We also propose a fast solver sDprun an…
Orthogonal Subspace Projection for Continual Machine Unlearning via SVD-Based LoRA
Institute for Digital Technologies, Loughborough University, UK（伦敦大学数字技术研究所，英国）；School of Artificial Intelligent Medicine, Guilin Medical University（桂林医学院人工智能医学院）
Scalable Heterogeneous Graph Learning via Heterogeneous-aware Orthogonal Prototype Experts
National Engineering Research Center for Big Data Technology；System Lab, Cluster；Grid Computing Lab, School of Computer Science；Technology, Huazhong University of Science；DIRO, Université de Montréal \& Mila \& Canada CIFAR AI Chair, Canada
Privacy-Aware Video Anomaly Detection through Orthogonal Subspace Projection
School of Engineering and Built Environment, Griffith University（格里菲斯大学工程与环境学院）；School of Computer Science and Engineering, University of New South Wales（新南威尔士大学计算机科学与工程学院）；School of Information and Communication Technology, Griffith University（格里菲斯大学信息与通信技术学院）
GoQuant: Geometric Orthogonal Residual Projection for Multiplier-Free Power-of-Two Transformer Quantization
Information Systems Technology and Design（信息系统技术与设计）；Singapore University of Technology and Design（新加坡科技设计大学）；Institute of High Performance Computing (IHPC)（高性能计算研究所）；Agency for Science, Technology and Research (A*STAR)（科技研究局）
In neural networks, continual learning results in gradient interference among sequential tasks, leading to catastrophic forgetting of old tasks while learning new ones. This issue is addressed in recent methods by storing the important gradient spaces for old tasks and updating the model orthogonally during new tasks. However, such restrictive orthogonal gradient updates hamper the learning capability of the new tasks resulting in sub-optimal performance. To improve new learning while minimizing forgetting, in this paper we propose a Scaled Gradient Projection (SGP) method, where we combine th…
