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Found 21 papers, 5 papers with code
OTAD: An Optimal Transport-Induced Robust Model for Agnostic Adversarial Attack
OTAD opens a novel avenue for developing reliable and secure deep learning systems through the regularity of optimal transport maps.
Analytical Solution of a Three-layer Network with a Matrix Exponential Activation Function
In practice, deeper networks tend to be more powerful than shallow ones, but this has not been understood theoretically.
Progressive Feedforward Collapse of ResNet Training
Overall, this study extends NC to PFC to model the collapse phenomenon of intermediate layers and its dependence on the input data, shedding light on the theoretical understanding of ResNet in classification problems.
DeMatch: Deep Decomposition of Motion Field for Two-View Correspondence Learning
Specifically we first decompose the rough motion field that is contaminated by false matches into several different sub-fields which are highly smooth and contain the main energy of the original field.
Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation
To address these limitations, we propose the Monte Carlo Neural PDE Solver (MCNP Solver) for training unsupervised neural solvers via the PDEs' probabilistic representation, which regards macroscopic phenomena as ensembles of random particles.
Rethinking Influence Functions of Neural Networks in the Over-parameterized Regime
However, the classic implicit Hessian-vector product (IHVP) method for calculating IF is fragile, and theoretical analysis of IF in the context of neural networks is still lacking.
Information-theoretic Classification Accuracy: A Criterion that Guides Data-driven Combination of Ambiguous Outcome Labels in Multi-class Classification
While practitioners commonly combine ambiguous outcome labels for all data points (instances) in an ad hoc way to improve the accuracy of multi-class classification, there lacks a principled approach to guide the label combination for all data points by any optimality criterion.
Adversarial Information Bottleneck
The information bottleneck (IB) principle has been adopted to explain deep learning in terms of information compression and prediction, which are balanced by a trade-off hyperparameter.
A Mathematical Principle of Deep Learning: Learn the Geodesic Curve in the Wasserstein Space
In a word, we conclude a mathematical principle of deep learning is to learn the geodesic curve in the Wasserstein space; and deep learning is a great engineering realization of continuous transformation in high-dimensional space.
Learnable Graph-regularization for Matrix Decomposition
Low-rank approximation models of data matrices have become important machine learning and data mining tools in many fields including computer vision, text mining, bioinformatics and many others.
Tessellated Wasserstein Auto-Encoders
Non-adversarial generative models such as variational auto-encoder (VAE), Wasserstein auto-encoders with maximum mean discrepancy (WAE-MMD), sliced-Wasserstein auto-encoder (SWAE) are relatively easy to train and have less mode collapse compared to Wasserstein auto-encoder with generative adversarial network (WAE-GAN).
Distributed Bayesian Matrix Decomposition for Big Data Mining and Clustering
Such a method should scale up well, model the heterogeneous noise, and address the communication issue in a distributed system.
Towards Understanding Residual and Dilated Dense Neural Networks via Convolutional Sparse Coding
Inspired by these considerations, we propose two novel multi-layer models--residual convolutional sparse coding model (Res-CSC) and mixed-scale dense convolutional sparse coding model (MSD-CSC), which have close relationship with the residual neural network (ResNet) and mixed-scale (dilated) dense neural network (MSDNet), respectively.
Matrix Normal PCA for Interpretable Dimension Reduction and Graphical Noise Modeling
However, most of the existing methods only assume that the noise is correlated in the feature space while there may exist two-way structured noise.
Group-sparse SVD Models and Their Applications in Biological Data
We employ an alternating direction method of multipliers (ADMM) to solve the proximal operator.
Bayesian Joint Matrix Decomposition for Data Integration with Heterogeneous Noise
A few of matrix decomposition methods have been extended for such multi-view data integration and pattern discovery.
Sparse Weighted Canonical Correlation Analysis
Given two data matrices $X$ and $Y$, sparse canonical correlation analysis (SCCA) is to seek two sparse canonical vectors $u$ and $v$ to maximize the correlation between $Xu$ and $Yv$.
Sparse Deep Nonnegative Matrix Factorization
Deep learning, however, with its carefully designed hierarchical structure, is able to combine hidden features to form more representative features for pattern recognition.
A Unified Joint Matrix Factorization Framework for Data Integration
In this paper, we introduce a sparse multiple relationship data regularized joint matrix factorization (JMF) framework and two adapted prediction models for pattern recognition and data integration.
Network-regularized Sparse Logistic Regression Models for Clinical Risk Prediction and Biomarker Discovery
To address it, we introduce a novel network-regularized sparse LR model with a new penalty $\lambda \|\bm{w}\|_1 + \eta|\bm{w}|^T\bm{M}|\bm{w}|$ to consider the difference between the absolute values of the coefficients.
L0-norm Sparse Graph-regularized SVD for Biclustering
Motivated by the development of sparse coding and graph-regularized norm, we propose a novel sparse graph-regularized SVD as a powerful biclustering tool for analyzing high-dimensional data.
