arXiv research

Subspace clustering aims to cluster unlabeled data that lies in a union of low-dimensional linear subspaces. Deep subspace clustering approaches based on auto-encoders have become very popular to solve subspace clustering problems. However, the training of current deep methods converges slowly, which is much less effic…

This work simplifies Bayesian inference for neural networks by identifying influential parameter directions.

We propose Deep Closed-Form Subspace Clustering (DCFSC), a new embarrassingly simple model for subspace clustering with learning non-linear mapping. Compared with the previous deep subspace clustering (DSC) techniques, our DCFSC does not have any parameters at all for the self-expressive layer. Instead, DCFSC utilizes …

The random subspace method, known as the pillar of random forests, is good at making precise and robust predictions. However, there is not a straightforward way yet to combine it with deep learning. In this paper, we therefore propose Neural Random Subspace (NRS), a novel deep learning based random subspace method. In …

A new model classifies surface anomalies in 3D point cloud data.

Bayesian inference was once a gold standard for learning with neural networks, providing accurate full predictive distributions and well calibrated uncertainty. However, scaling Bayesian inference techniques to deep neural networks is challenging due to the high dimensionality of the parameter space. In this paper, we …

This paper proposes a novel deep subspace clustering approach which uses convolutional autoencoders to transform input images into new representations lying on a union of linear subspaces. The first contribution of our work is to insert multiple fully-connected linear layers between the encoder layers and their corresp…

Over the past decade a wide spectrum of machine learning models have been developed to model the neurodegenerative diseases, associating biomarkers, especially non-intrusive neuroimaging markers, with key clinical scores measuring the cognitive status of patients. Multi-task learning (MTL) has been commonly utilized by…

New framework explains neural network behavior through geometric postulates.

A new method tackles bilevel optimization using Lanczos process for efficient hyper-gradient computation.

Datasets with significant proportions of noisy (incorrect) class labels present challenges for training accurate Deep Neural Networks (DNNs). We propose a new perspective for understanding DNN generalization for such datasets, by investigating the dimensionality of the deep representation subspace of training samples. …

SGD updates align with a low-rank subspace but do not lead to further loss reduction.

A new method learns multiple subspaces from data.

P-OCS detects OOD samples in a low-dimensional subspace, outperforming existing methods.

LR-EDNN reduces PDE solver complexity by limiting network weights to low-rank subspace.

We show that in a variety of large-scale deep learning scenarios the gradient dynamically converges to a very small subspace after a short period of training. The subspace is spanned by a few top eigenvectors of the Hessian (equal to the number of classes in the dataset), and is mostly preserved over long periods of tr…

This paper extends neural collapse to regression problems, revealing key features and structures.

Deep ensembles have been empirically shown to be a promising approach for improving accuracy, uncertainty and out-of-distribution robustness of deep learning models. While deep ensembles were theoretically motivated by the bootstrap, non-bootstrap ensembles trained with just random initialization also perform well in p…

Variational autoencoders (VAEs) are widely used deep generative models capable of learning unsupervised latent representations of data. Such representations are often difficult to interpret or control. We consider the problem of unsupervised learning of features correlated to specific labels in a dataset. We propose a …

Symmetry transformations induce invariances which are frequently described with deep latent variable models. In many complex domains, such as the chemical space, invariances can be observed, yet the corresponding symmetry transformation cannot be formulated analytically. We propose to learn the symmetry transformation …

New method disentangles hidden data structures using HSIC and supervision.

Learning informative representations of data is one of the primary goals of deep learning, but there is still little understanding as to what representations a neural network actually learns. To better understand this, subspace match was recently proposed as a method for assessing the similarity of the representations …

New algorithm learns principal subspace from random samples.

IntroVAC learns interpretable latent subspaces for better image quality.

Modern machine learning algorithms have been adopted in a range of signal-processing applications spanning computer vision, natural language processing, and artificial intelligence. Many relevant problems involve subspace-structured features, orthogonality constrained or low-rank constrained objective functions, or sub…

The inputs of deep neural network (DNN) from real-world data usually come with uncertainties. Yet, it is challenging to propagate the uncertainty in the input features to the DNN predictions at a low computational cost. This work employs a gradient-based subspace method and response surface technique to accelerate the …

Researchers use active subspaces to quantify uncertainty in deep generative models for molecular design.

In this paper, we investigate the unsupervised deep representation learning issue and technically propose a novel framework called Deep Self-representative Concept Factorization Network (DSCF-Net), for clustering deep features. To improve the representation and clustering abilities, DSCF-Net explicitly considers discov…

Kernel sparsity ("dying ReLUs") and lack of diversity are commonly observed in CNN kernels, which decreases model capacity. Drawing inspiration from information theory and wireless communications, we demonstrate the intersection of coding theory and deep learning through the Grassmannian subspace packing problem in CNN…

Efficiently compress overparameterized deep models by focusing on low-dimensional learning dynamics.

PED-ANOVA efficiently calculates HP importance in arbitrary subspaces.

The autoencoder is an effective unsupervised learning model which is widely used in deep learning. It is well known that an autoencoder with a single fully-connected hidden layer, a linear activation function and a squared error cost function trains weights that span the same subspace as the one spanned by the principa…

It is widely believed that learning good representations is one of the main reasons for the success of deep neural networks. Although highly intuitive, there is a lack of theory and systematic approach quantitatively characterizing what representations do deep neural networks learn. In this work, we move a tiny step to…

A new method compresses NLP networks by using multiple subspaces instead of a single one.

Study efficient estimation of hidden subspaces in Gaussian Multi-index models.

A new machine learning methodology, called successive subspace learning (SSL), is introduced in this work. SSL contains four key ingredients: 1) successive near-to-far neighborhood expansion; 2) unsupervised dimension reduction via subspace approximation; 3) supervised dimension reduction via label-assisted regression …

In this paper, we propose a second order optimization method to learn models where both the dimensionality of the parameter space and the number of training samples is high. In our method, we construct on each iteration a Krylov subspace formed by the gradient and an approximation to the Hessian matrix, and then use a …

ASGD outperforms SGD in overparameterized linear regression, especially in subspaces of small eigenvalues.

We investigate the effect of the dimensionality of the representations learned in Deep Neural Networks (DNNs) on their robustness to input perturbations, both adversarial and random. To achieve low dimensionality of learned representations, we propose an easy-to-use, end-to-end trainable, low-rank regularizer (LR) that…

We examine Deep Canonically Correlated LSTMs as a way to learn nonlinear transformations of variable length sequences and embed them into a correlated, fixed dimensional space. We use LSTMs to transform multi-view time-series data non-linearly while learning temporal relationships within the data. We then perform corre…

Bayesian method for semi-structured models accounts for both types of uncertainty.

Deep linear networks oscillate beyond the edge of stability in a predictable manner.

Understanding and characterizing the subspaces of adversarial examples aid in studying the robustness of deep neural networks (DNNs) to adversarial perturbations. Very recently, Ma et al. (ICLR 2018) proposed to use local intrinsic dimensionality (LID) in layer-wise hidden representations of DNNs to study adversarial s…

A problem of considerable importance within the field of uncertainty quantification (UQ) is the development of efficient methods for the construction of accurate surrogate models. Such efforts are particularly important to applications constrained by high-dimensional uncertain parameter spaces. The difficulty of accura…

We present SEBOOST, a technique for boosting the performance of existing stochastic optimization methods. SEBOOST applies a secondary optimization process in the subspace spanned by the last steps and descent directions. The method was inspired by the SESOP optimization method for large-scale problems, and has been ada…

Bayesian optimization guided by experimenter intuition and beliefs.

Paper proposes Roweisposes for 3D action recognition using generalized eigenvalue problem.

We show that the classification performance of graph convolutional networks (GCNs) is related to the alignment between features, graph, and ground truth, which we quantify using a subspace alignment measure (SAM) corresponding to the Frobenius norm of the matrix of pairwise chordal distances between three subspaces ass…