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08/18/2023
Capacity Bounds for Hyperbolic Neural Network Representations of Latent Tree Structures
We study the representation capacity of deep hyperbolic neural networks ...
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04/24/2023
A Transfer Principle: Universal Approximators Between Metric Spaces From Euclidean Universal Approximators
We build universal approximators of continuous maps between arbitrary Po...
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02/17/2023
Generative Ornstein-Uhlenbeck Markets via Geometric Deep Learning
We consider the problem of simultaneously approximating the conditional ...
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11/02/2022
Instance-Dependent Generalization Bounds via Optimal Transport
Existing generalization bounds fail to explain crucial factors that driv...
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10/24/2022
Designing Universal Causal Deep Learning Models: The Case of Infinite-Dimensional Dynamical Systems from Stochastic Analysis
Deep learning (DL) is becoming indispensable to contemporary stochastic ...
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09/14/2022
Small Transformers Compute Universal Metric Embeddings
We study representations of data from an arbitrary metric space 𝒳 in the...
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04/24/2022
Piecewise-Linear Activations or Analytic Activation Functions: Which Produce More Expressive Neural Networks?
Many currently available universal approximation theorems affirm that de...
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01/31/2022
Metric Hypertransformers are Universal Adapted Maps
We introduce a universal class of geometric deep learning models, called...
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10/07/2021
Universal Approximation Under Constraints is Possible with Transformers
Many practical problems need the output of a machine learning model to s...
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05/17/2021
Universal Regular Conditional Distributions
We introduce a general framework for approximating regular conditional d...
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01/13/2021
Quantitative Rates and Fundamental Obstructions to Non-Euclidean Universal Approximation with Deep Narrow Feed-Forward Networks
By incorporating structured pairs of non-trainable input and output laye...
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12/31/2020
Optimizing Optimizers: Regret-optimal gradient descent algorithms
The need for fast and robust optimization algorithms are of critical imp...
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10/29/2020
Overcoming The Limitations of Neural Networks in Composite-Pattern Learning with Architopes
The effectiveness of neural networks in solving complex problems is well...
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06/24/2020
Architopes: An Architecture Modification for Composite Pattern Learning, Increased Expressiveness, and Reduced Training Time
We introduce a simple neural network architecture modification that enab...
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06/03/2020
Non-Euclidean Universal Approximation
Modifications to a neural network's input and output layers are often re...
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10/08/2019
Universal Approximation Theorems
The universal approximation theorem established the density of specific ...
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08/31/2018
The NEU Meta-Algorithm for Geometric Learning with Applications in Finance
We introduce a meta-algorithm, called non-Euclidean upgrading (NEU), whi...
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10/16/2017
Geometric Learning and Filtering in Finance
We develop a method for incorporating relevant non-Euclidean geometric i...
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10/14/2017