Search Results for author: Matthew Trager

Found 14 papers, 3 papers with code

Geometry of Linear Convolutional Networks

no code implementations3 Aug 2021 Kathlén Kohn, Thomas Merkh, Guido Montúfar, Matthew Trager

We study the family of functions that are represented by a linear convolutional neural network (LCN).

Symmetry Breaking in Symmetric Tensor Decomposition

no code implementations10 Mar 2021 Yossi Arjevani, Joan Bruna, Michael Field, Joe Kileel, Matthew Trager, Francis Williams

In this note, we consider the optimization problem associated with computing the rank decomposition of a symmetric tensor.

Tensor Decomposition

Neural Splines: Fitting 3D Surfaces with Infinitely-Wide Neural Networks

1 code implementation CVPR 2021 Francis Williams, Matthew Trager, Joan Bruna, Denis Zorin

We present Neural Splines, a technique for 3D surface reconstruction that is based on random feature kernels arising from infinitely-wide shallow ReLU networks.

Surface Reconstruction

Pure and Spurious Critical Points: a Geometric Study of Linear Networks

no code implementations ICLR 2020 Matthew Trager, Kathlén Kohn, Joan Bruna

The critical locus of the loss function of a neural network is determined by the geometry of the functional space and by the parameterization of this space by the network's weights.

Gradient Dynamics of Shallow Univariate ReLU Networks

no code implementations NeurIPS 2019 Francis Williams, Matthew Trager, Claudio Silva, Daniele Panozzo, Denis Zorin, Joan Bruna

We show that the gradient dynamics of such networks are determined by the gradient flow in a non-redundant parameterization of the network function.

Coordinate-Free Carlsson-Weinshall Duality and Relative Multi-View Geometry

no code implementations CVPR 2019 Matthew Trager, Martial Hebert, Jean Ponce

We present a coordinate-free description of Carlsson-Weinshall duality between scene points and camera pinholes and use it to derive a new characterization of primal/dual multi-view geometry.

On the Expressive Power of Deep Polynomial Neural Networks

1 code implementation NeurIPS 2019 Joe Kileel, Matthew Trager, Joan Bruna

We study deep neural networks with polynomial activations, particularly their expressive power.

On the Solvability of Viewing Graphs

1 code implementation ECCV 2018 Matthew Trager, Brian Osserman, Jean Ponce

A set of fundamental matrices relating pairs of cameras in some configuration can be represented as edges of a "viewing graph".

Consistent sets of lines with no colorful incidence

no code implementations16 Mar 2018 Boris Bukh, Xavier Goaoc, Alfredo Hubard, Matthew Trager

We consider incidences among colored sets of lines in $\mathbb{R}^d$ and examine whether the existence of certain concurrences between lines of $k$ colors force the existence of at least one concurrence between lines of $k+1$ colors.

3D Reconstruction

Changing Views on Curves and Surfaces

no code implementations6 Jul 2017 Kathlén Kohn, Bernd Sturmfels, Matthew Trager

Visual events in computer vision are studied from the perspective of algebraic geometry.

General models for rational cameras and the case of two-slit projections

no code implementations CVPR 2017 Matthew Trager, Bernd Sturmfels, John Canny, Martial Hebert, Jean Ponce

The rational camera model recently introduced in [19] provides a general methodology for studying abstract nonlinear imaging systems and their multi-view geometry.

Congruences and Concurrent Lines in Multi-View Geometry

no code implementations21 Aug 2016 Jean Ponce, Bernd Sturmfels, Matthew Trager

We present a new framework for multi-view geometry in computer vision.

Consistency of Silhouettes and Their Duals

no code implementations CVPR 2016 Matthew Trager, Martial Hebert, Jean Ponce

Silhouettes provide rich information on three-dimensional shape, since the intersection of the associated visual cones generates the "visual hull", which encloses and approximates the original shape.

Camera Calibration Object Recognition

The Joint Image Handbook

no code implementations ICCV 2015 Matthew Trager, Martial Hebert, Jean Ponce

Given multiple perspective photographs, point correspondences form the "joint image", effectively a replica of three dimensional space distributed across its two-dimensional projections.

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