36 citations · 128 across the 27 of their papers we have counts for
9 papers · 1 filter
Verifying the Union of Manifolds Hypothesis for Image Data
Bradley C. A. Brown, Anthony L. Caterini, Brendan Leigh Ross +2
Deep learning has had tremendous success at learning low-dimensional representations of high-dimensional data. This success would be impossible if there was no hidden low-dimension…
Neural Implicit Manifold Learning for Topology-Aware Density Estimation
Brendan Leigh Ross, Gabriel Loaiza-Ganem, Anthony L. Caterini +1
Natural data observed in is often constrained to an -dimensional manifold , where . This work focuses on the task of building theoretically pr…
Diagnosing and Fixing Manifold Overfitting in Deep Generative Models
Gabriel Loaiza-Ganem, Brendan Leigh Ross, Jesse C. Cresswell +1
Likelihood-based, or explicit, deep generative models use neural networks to construct flexible high-dimensional densities. This formulation directly contradicts the manifold hypot…
Entropic Issues in Likelihood-Based OOD Detection
Anthony L. Caterini, Gabriel Loaiza-Ganem
Deep generative models trained by maximum likelihood remain very popular methods for reasoning about data probabilistically. However, it has been observed that they can assign high…
Rectangular Flows for Manifold Learning
Anthony L. Caterini, Gabriel Loaiza-Ganem, Geoff Pleiss +1
Normalizing flows are invertible neural networks with tractable change-of-volume terms, which allow optimization of their parameters to be efficiently performed via maximum likelih…
Variational Inference with Continuously-Indexed Normalizing Flows
Anthony Caterini, Rob Cornish, Dino Sejdinovic +1
Continuously-indexed flows (CIFs) have recently achieved improvements over baseline normalizing flows on a variety of density estimation tasks. CIFs do not possess a closed-form ma…
Relaxing Bijectivity Constraints with Continuously Indexed Normalising Flows
Rob Cornish, Anthony L. Caterini, George Deligiannidis +1
We show that normalising flows become pathological when used to model targets whose supports have complicated topologies. In this scenario, we prove that a flow must become arbitra…
A Novel Representation of Neural Networks
Anthony Caterini, Dong Eui Chang
Deep Neural Networks (DNNs) have become very popular for prediction in many areas. Their strength is in representation with a high number of parameters that are commonly learned vi…
A Geometric Framework for Convolutional Neural Networks
Anthony L. Caterini, Dong Eui Chang
In this paper, a geometric framework for neural networks is proposed. This framework uses the inner product space structure underlying the parameter set to perform gradient descent…