# Fast geometric learning with symbolic matrices

@inproceedings{Feydy2020FastGL, title={Fast geometric learning with symbolic matrices}, author={Jean Feydy and Joan Alexis Glaun{\`e}s and Benjamin Charlier and Michael M. Bronstein}, booktitle={Neural Information Processing Systems}, year={2020} }

Geometric methods rely on tensors that can be encoded using a symbolic formula and data arrays, such as kernel and distance matrices. We present an extension for standard machine learning frameworks that provides comprehensive support for this abstraction on CPUs and GPUs: our toolbox combines a versatile, transparent user interface with fast runtimes and low memory usage. Unlike general purpose acceleration frameworks such as XLA, our library turns generic Python code into binaries whose…

## 19 Citations

### Memory Safe Computations with XLA Compiler

- Computer ScienceArXiv
- 2022

An XLA compiler extension 1 is developed that adjusts the computational data-ﬂow representation of an algorithm according to a user-speciﬁed memory limit and shows that k-nearest neighbour and sparse Gaussian process regression methods can be run at a much larger scale on a single device, where standard implementations would have failed.

### Low-Precision Arithmetic for Fast Gaussian Processes

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### Fast end-to-end learning on protein surfaces

- Computer Science, BiologybioRxiv
- 2020

A new framework for deep learning on protein structures that addresses limitations including the need to pre-compute the input features and mesh connectivities and achieves state-of-the-art performance with much faster run times and fewer parameters than previous models.

### GNPM: Geometric-Aware Neural Parametric Models

- Computer ScienceArXiv
- 2022

We propose Geometric Neural Parametric Models (GNPM), a learned parametric model that takes into account the local structure of data to learn disentangled shape and pose latent spaces of 4D dynamics,…

### Unbalanced Optimal Transport, from Theory to Numerics

- Computer ScienceArXiv
- 2022

How unbalanced OT, entropic regularization and GW can work hand-in-hand to turn OT into efficient geometric loss functions for data sciences is explained.

### Convex transport potential selection with semi-dual criterion

- Computer Science
- 2021

This work proposes to leverage the Brenier formulation of OT to perform Optimal Transport in a stochastic setting and can identify the potential that is closest to the true OT map between the source and the target and observes that this selected potential is not the one that performs best for the downstream transfer classification task.

### Accurate Point Cloud Registration with Robust Optimal Transport

- Computer Science, Environmental ScienceNeurIPS
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It is shown that recent OT solvers improve both optimization-based and deep learning methods for point cloud registration, boosting accuracy at an affordable computational cost and providing a new key method for the computer vision toolbox.

### Neural Monge Map estimation and its applications

- Computer Science
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This work presents a scalable algorithm based on a weak form of the optimal transport problem, thus it only requires samples from the marginals instead of their analytic expres-sions, and can accommodate optimal transport between two distributions with different dimensions.

### Sinkhorn Divergences for Unbalanced Optimal Transport

- Computer ScienceArXiv
- 2019

The formulation of Sinkhorn divergences is extended to the unbalanced setting of arbitrary positive measures, providing both theoretical and algorithmic advances, and a linear rate of convergence is shown, under mild assumptions, independent of the number of samples.

### Bayesian Optimization with High-Dimensional Outputs

- Computer ScienceNeurIPS
- 2021

This work devise an efficient technique for exact multitask GP sampling that combines exploiting Kronecker structure in the covariance matrices with Matheron’s identity, allowing it to perform Bayesian Optimization using exact multi-task GP models with tens of thousands of correlated outputs.

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