Search Results for author: Justin Solomon

Found 47 papers, 30 papers with code

Sampling with Mollified Interaction Energy Descent

no code implementations24 Oct 2022 Lingxiao Li, Qiang Liu, Anna Korba, Mikhail Yurochkin, Justin Solomon

These energies rely on mollifier functions -- smooth approximations of the Dirac delta originated from PDE theory.

Outlier-Robust Group Inference via Gradient Space Clustering

1 code implementation13 Oct 2022 Yuchen Zeng, Kristjan Greenewald, Kangwook Lee, Justin Solomon, Mikhail Yurochkin

Traditional machine learning models focus on achieving good performance on the overall training distribution, but they often underperform on minority groups.

Riemannian Metric Learning via Optimal Transport

no code implementations18 May 2022 Christopher Scarvelis, Justin Solomon

We introduce an optimal transport-based model for learning a metric tensor from cross-sectional samples of evolving probability measures on a common Riemannian manifold.

Metric Learning

Symmetric Volume Maps: Order-Invariant Volumetric Mesh Correspondence with Free Boundary

1 code implementation5 Feb 2022 S. Mazdak Abulnaga, Oded Stein, Polina Golland, Justin Solomon

Although shape correspondence is a central problem in geometry processing, most methods for this task apply only to two-dimensional surfaces.

Log-Euclidean Signatures for Intrinsic Distances Between Unaligned Datasets

1 code implementation3 Feb 2022 Tal Shnitzer, Mikhail Yurochkin, Kristjan Greenewald, Justin Solomon

We use manifold learning to compare the intrinsic geometric structures of different datasets by comparing their diffusion operators, symmetric positive-definite (SPD) matrices that relate to approximations of the continuous Laplace-Beltrami operator from discrete samples.

Rewiring with Positional Encodings for Graph Neural Networks

no code implementations29 Jan 2022 Rickard Brüel-Gabrielsson, Mikhail Yurochkin, Justin Solomon

As a conservative alternative, we use positional encodings to expand receptive fields to $r$-hop neighborhoods.

Learning Proximal Operators to Discover Multiple Optima

no code implementations28 Jan 2022 Lingxiao Li, Noam Aigerman, Vladimir G. Kim, Jiajin Li, Kristjan Greenewald, Mikhail Yurochkin, Justin Solomon

We present an end-to-end method to learn the proximal operator of a family of training problems so that multiple local minima can be quickly obtained from initial guesses by iterating the learned operator, emulating the proximal-point algorithm that has fast convergence.

object-detection Object Detection

Wassersplines for Neural Vector Field--Controlled Animation

no code implementations28 Jan 2022 Paul Zhang, Dmitriy Smirnov, Justin Solomon

Trajectories are then computed by advecting keyframes through the velocity field.

DeepCurrents: Learning Implicit Representations of Shapes with Boundaries

1 code implementation CVPR 2022 David Palmer, Dmitriy Smirnov, Stephanie Wang, Albert Chern, Justin Solomon

Recent techniques have been successful in reconstructing surfaces as level sets of learned functions (such as signed distance fields) parameterized by deep neural networks.

Volumetric Parameterization of the Placenta to a Flattened Template

1 code implementation15 Nov 2021 S. Mazdak Abulnaga, Esra Abaci Turk, Mikhail Bessmeltsev, P. Ellen Grant, Justin Solomon, Polina Golland

However, due to the curved and highly variable in vivo shape of the placenta, interpreting and visualizing these images is difficult.

Anatomy Local Distortion

Object DGCNN: 3D Object Detection using Dynamic Graphs

1 code implementation NeurIPS 2021 Yue Wang, Justin Solomon

Our method models 3D object detection as message passing on a dynamic graph, generalizing the DGCNN framework to predict a set of objects.

2D object detection 3D Object Detection +3

DETR3D: 3D Object Detection from Multi-view Images via 3D-to-2D Queries

1 code implementation13 Oct 2021 Yue Wang, Vitor Guizilini, Tianyuan Zhang, Yilun Wang, Hang Zhao, Justin Solomon

This top-down approach outperforms its bottom-up counterpart in which object bounding box prediction follows per-pixel depth estimation, since it does not suffer from the compounding error introduced by a depth prediction model.

3D Object Detection Autonomous Driving +3

$k$-Mixup Regularization for Deep Learning via Optimal Transport

no code implementations29 Sep 2021 Kristjan Greenewald, Anming Gu, Mikhail Yurochkin, Justin Solomon, Edward Chien

To better leverage the structure of the data, we extend mixup to $k$-mixup by perturbing $k$-batches of training points in the direction of other $k$-batches using displacement interpolation, i. e. interpolation under the Wasserstein metric.

Adversarial Robustness

Polygonal Building Extraction by Frame Field Learning

1 code implementation CVPR 2021 Nicolas Girard, Dmitriy Smirnov, Justin Solomon, Yuliya Tarabalka

While state of the art image segmentation models typically output segmentations in raster format, applications in geographic information systems often require vector polygons.

Image Segmentation Multi-Task Learning +1

k-Mixup Regularization for Deep Learning via Optimal Transport

no code implementations5 Jun 2021 Kristjan Greenewald, Anming Gu, Mikhail Yurochkin, Justin Solomon, Edward Chien

Mixup is a popular regularization technique for training deep neural networks that can improve generalization and increase adversarial robustness.

Adversarial Robustness

Do Neural Optimal Transport Solvers Work? A Continuous Wasserstein-2 Benchmark

3 code implementations NeurIPS 2021 Alexander Korotin, Lingxiao Li, Aude Genevay, Justin Solomon, Alexander Filippov, Evgeny Burnaev

Despite the recent popularity of neural network-based solvers for optimal transport (OT), there is no standard quantitative way to evaluate their performance.

Image Generation

Large-Scale Wasserstein Gradient Flows

3 code implementations NeurIPS 2021 Petr Mokrov, Alexander Korotin, Lingxiao Li, Aude Genevay, Justin Solomon, Evgeny Burnaev

Specifically, Fokker-Planck equations, which model the diffusion of probability measures, can be understood as gradient descent over entropy functionals in Wasserstein space.

MarioNette: Self-Supervised Sprite Learning

1 code implementation NeurIPS 2021 Dmitriy Smirnov, Michael Gharbi, Matthew Fisher, Vitor Guizilini, Alexei A. Efros, Justin Solomon

Artists and video game designers often construct 2D animations using libraries of sprites -- textured patches of objects and characters.

Improving Approximate Optimal Transport Distances using Quantization

no code implementations25 Feb 2021 Gaspard Beugnot, Aude Genevay, Kristjan Greenewald, Justin Solomon

Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden.

Quantization

Continuous Wasserstein-2 Barycenter Estimation without Minimax Optimization

2 code implementations ICLR 2021 Alexander Korotin, Lingxiao Li, Justin Solomon, Evgeny Burnaev

Wasserstein barycenters provide a geometric notion of the weighted average of probability measures based on optimal transport.

Outlier Robust Optimal Transport

no code implementations1 Jan 2021 Debarghya Mukherjee, Aritra Guha, Justin Solomon, Yuekai Sun, Mikhail Yurochkin

In light of recent advances in solving the OT problem, OT distances are widely used as loss functions in minimum distance estimation.

Outlier Detection

$k$-Variance: A Clustered Notion of Variance

no code implementations13 Dec 2020 Justin Solomon, Kristjan Greenewald, Haikady N. Nagaraja

We introduce $k$-variance, a generalization of variance built on the machinery of random bipartite matchings.

Empirical Sampling of Connected Graph Partitions for Redistricting

1 code implementation8 Dec 2020 Lorenzo Najt, Daryl DeFord, Justin Solomon

Second, we analyze the robustness of the qualitative properties of typical districting plans with respect to score functions and a certain lattice-like graph, called the state-dual graph, that is used as a discretization of geographic regions in most districting analysis.

Physics and Society Statistical Mechanics 62P25, 82-05 K.4.1; G.3

Redistricting Algorithms

no code implementations18 Nov 2020 Amariah Becker, Justin Solomon

Why not have a computer just draw a map?

Data Structures and Algorithms Computers and Society K.4.0

Multi-Frame to Single-Frame: Knowledge Distillation for 3D Object Detection

no code implementations24 Sep 2020 Yue Wang, Alireza Fathi, Jiajun Wu, Thomas Funkhouser, Justin Solomon

A common dilemma in 3D object detection for autonomous driving is that high-quality, dense point clouds are only available during training, but not testing.

3D Object Detection Autonomous Driving +2

Continuous Regularized Wasserstein Barycenters

1 code implementation NeurIPS 2020 Lingxiao Li, Aude Genevay, Mikhail Yurochkin, Justin Solomon

Leveraging a new dual formulation for the regularized Wasserstein barycenter problem, we introduce a stochastic algorithm that constructs a continuous approximation of the barycenter.

Model Fusion with Kullback--Leibler Divergence

1 code implementation ICML 2020 Sebastian Claici, Mikhail Yurochkin, Soumya Ghosh, Justin Solomon

Our algorithm relies on a mean field assumption for both the fused model and the individual dataset posteriors and proceeds using a simple assign-and-average approach.

Federated Learning

Polygonal Building Segmentation by Frame Field Learning

2 code implementations30 Apr 2020 Nicolas Girard, Dmitriy Smirnov, Justin Solomon, Yuliya Tarabalka

While state of the art image segmentation models typically output segmentations in raster format, applications in geographic information systems often require vector polygons.

Image Segmentation Multi-Task Learning +1

Incorporating Unlabeled Data into Distributionally Robust Learning

no code implementations16 Dec 2019 Charlie Frogner, Sebastian Claici, Edward Chien, Justin Solomon

We examine the performance of this new formulation on 14 real datasets and find that it often yields effective classifiers with nontrivial performance guarantees in situations where conventional DRL produces neither.

Active Learning

Alleviating Label Switching with Optimal Transport

1 code implementation NeurIPS 2019 Pierre Monteiller, Sebastian Claici, Edward Chien, Farzaneh Mirzazadeh, Justin Solomon, Mikhail Yurochkin

Label switching is a phenomenon arising in mixture model posterior inference that prevents one from meaningfully assessing posterior statistics using standard Monte Carlo procedures.

Recombination: A family of Markov chains for redistricting

4 code implementations31 Oct 2019 Daryl DeFord, Moon Duchin, Justin Solomon

Redistricting is the problem of partitioning a set of geographical units into a fixed number of districts, subject to a list of often-vague rules and priorities.

Computers and Society Physics and Society 60J10, 05C70, 91F10

Algebraic Representations for Volumetric Frame Fields

1 code implementation15 Aug 2019 David Palmer, David Bommes, Justin Solomon

A key challenge in extending these methods to three dimensions, however, is representation of field values.

Graphics

Hierarchical Optimal Transport for Document Representation

1 code implementation NeurIPS 2019 Mikhail Yurochkin, Sebastian Claici, Edward Chien, Farzaneh Mirzazadeh, Justin Solomon

The ability to measure similarity between documents enables intelligent summarization and analysis of large corpora.

Learning Embeddings into Entropic Wasserstein Spaces

2 code implementations8 May 2019 Charlie Frogner, Farzaneh Mirzazadeh, Justin Solomon

Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions.

Dimensionality Reduction

Learning Entropic Wasserstein Embeddings

no code implementations ICLR 2019 Charlie Frogner, Farzaneh Mirzazadeh, Justin Solomon

Despite their prevalence, Euclidean embeddings of data are fundamentally limited in their ability to capture latent semantic structures, which need not conform to Euclidean spatial assumptions.

Dimensionality Reduction

Deep Parametric Shape Predictions using Distance Fields

1 code implementation CVPR 2020 Dmitriy Smirnov, Matthew Fisher, Vladimir G. Kim, Richard Zhang, Justin Solomon

Many tasks in graphics and vision demand machinery for converting shapes into consistent representations with sparse sets of parameters; these representations facilitate rendering, editing, and storage.

Placental Flattening via Volumetric Parameterization

1 code implementation12 Mar 2019 S. Mazdak Abulnaga, Esra Abaci Turk, Mikhail Bessmeltsev, P. Ellen Grant, Justin Solomon, Polina Golland

We formulate our method as a map from the in vivo shape to a flattened template that minimizes the symmetric Dirichlet energy to control distortion throughout the volume.

Anatomy

Dynamical Optimal Transport on Discrete Surfaces

1 code implementation19 Sep 2018 Hugo Lavenant, Sebastian Claici, Edward Chien, Justin Solomon

We propose a technique for interpolating between probability distributions on discrete surfaces, based on the theory of optimal transport.

Analysis of PDEs Numerical Analysis Numerical Analysis Optimization and Control

Wasserstein Measure Coresets

no code implementations18 May 2018 Sebastian Claici, Aude Genevay, Justin Solomon

The proliferation of large data sets and Bayesian inference techniques motivates demand for better data sparsification.

Bayesian Inference

Gerrymandering and Compactness: Implementation Flexibility and Abuse

1 code implementation7 Mar 2018 Richard Barnes, Justin Solomon

As a case study demonstrating the effect, we show that commonly-used measures of geometric compactness for district boundaries are affected by several factors irrelevant to fairness or compliance with civil rights law.

Computers and Society Computational Geometry

Stochastic Wasserstein Barycenters

3 code implementations ICML 2018 Sebastian Claici, Edward Chien, Justin Solomon

We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport.

Optimal Transport on Discrete Domains

no code implementations23 Jan 2018 Justin Solomon

Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold.

Steklov Spectral Geometry for Extrinsic Shape Analysis

1 code implementation21 Jul 2017 Yu Wang, Mirela Ben-Chen, Iosif Polterovich, Justin Solomon

We propose using the Dirichlet-to-Neumann operator as an extrinsic alternative to the Laplacian for spectral geometry processing and shape analysis.

Graphics

Parallel Streaming Wasserstein Barycenters

1 code implementation NeurIPS 2017 Matthew Staib, Sebastian Claici, Justin Solomon, Stefanie Jegelka

Our method is even robust to nonstationary input distributions and produces a barycenter estimate that tracks the input measures over time.

Bayesian Inference

Quantum Optimal Transport for Tensor Field Processing

1 code implementation20 Dec 2016 Gabriel Peyré, Lenaïc Chizat, François-Xavier Vialard, Justin Solomon

This "quantum" formulation of OT (Q-OT) corresponds to a relaxed version of the classical Kantorovich transport problem, where the fidelity between the input PSD-valued measures is captured using the geometry of the Von-Neumann quantum entropy.

Graphics

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