Publications related to Softmax function

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Nicolas Henri Bernard Flammarion, Hristo Georgiev Papazov, Scott William Pesme

In this work, we investigate the effect of momentum on the optimisation trajectory of gradient descent. We leverage a continuous-time approach in the analysis of momentum gradient descent with step size

\gamma

and momentum parameter

\beta

that allows u ...

2024

On the number of regions of piecewise linear neural networks

Michaël Unser, Alexis Marie Frederic Goujon

Many feedforward neural networks (NNs) generate continuous and piecewise-linear (CPWL) mappings. Specifically, they partition the input domain into regions on which the mapping is affine. The number of these so-called linear regions offers a natural metric ...

2024

Deep Learning Theory Through the Lens of Diagonal Linear Networks

Scott William Pesme

In this PhD manuscript, we explore optimisation phenomena which occur in complex neural networks through the lens of

2

-layer diagonal linear networks. This rudimentary architecture, which consists of a two layer feedforward linear network with a diagonal ...

EPFL2024

Benign Overfitting in Deep Neural Networks under Lazy Training

Volkan Cevher, Grigorios Chrysos, Fanghui Liu, Zhenyu Zhu

This paper focuses on over-parameterized deep neural networks (DNNs) with ReLU activation functions and proves that when the data distribution is well-separated, DNNs can achieve Bayesoptimal test error for classification while obtaining (nearly) zero-trai ...

2023

A Theory of Finite-Width Neural Networks: Generalization, Scaling Laws, and the Loss Landscape

Berfin Simsek

Deep learning has achieved remarkable success in various challenging tasks such as generating images from natural language or engaging in lengthy conversations with humans.The success in practice stems from the ability to successfully train massive neural ...

EPFL2023

Inverse Reinforcement Learning of Pedestrian-Robot Coordination

Aude Billard, David Julian Gonon

We apply inverse reinforcement learning (IRL) with a novel cost feature to the problem of robot navigation in human crowds. Consistent with prior empirical work on pedestrian behavior, the feature anticipates collisions between agents. We efficiently learn ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023

From Kernel Methods to Neural Networks: A Unifying Variational Formulation

Michaël Unser

The minimization of a data-fidelity term and an additive regularization functional gives rise to a powerful framework for supervised learning. In this paper, we present a unifying regularization functional that depends on an operator L\documentclass[12pt]{ ...

New York2023

Penalising the biases in norm regularisation enforces sparsity

Nicolas Henri Bernard Flammarion, Etienne Patrice Boursier

Controlling the parameters' norm often yields good generalisation when training neural networks. Beyond simple intuitions, the relation between parameters' norm and obtained estimators theoretically remains misunderstood. For one hidden ReLU layer networks ...

2023

ReLU Neural Network Galerkin BEM

Fernando José Henriquez Barraza

We introduce Neural Network (NN for short) approximation architectures for the numerical solution of Boundary Integral Equations (BIEs for short). We exemplify the proposed NN approach for the boundary reduction of the potential problem in two spatial dime ...

SPRINGER/PLENUM PUBLISHERS2023

Towards Stable and Efficient Adversarial Training against $l_1$ Bounded Adversarial Attacks

Sabine Süsstrunk, Mathieu Salzmann, Yulun Jiang, Chen Liu, Zhuoyi Huang

We address the problem of stably and efficiently training a deep neural network robust to adversarial perturbations bounded by an

l_1

norm. We demonstrate that achieving robustness against

l_1

-bounded perturbations is more challenging than in the

l_2

...

2023

Softmax function

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Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

On the number of regions of piecewise linear neural networks

Deep Learning Theory Through the Lens of Diagonal Linear Networks

Benign Overfitting in Deep Neural Networks under Lazy Training

A Theory of Finite-Width Neural Networks: Generalization, Scaling Laws, and the Loss Landscape

Inverse Reinforcement Learning of Pedestrian-Robot Coordination

From Kernel Methods to Neural Networks: A Unifying Variational Formulation

Penalising the biases in norm regularisation enforces sparsity

ReLU Neural Network Galerkin BEM

Towards Stable and Efficient Adversarial Training against $l_1$ Bounded Adversarial Attacks

On the number of regions of piecewise linear neural networks

Deep Learning Theory Through the Lens of Diagonal Linear Networks

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

ReLU Neural Network Galerkin BEM

Penalising the biases in norm regularisation enforces sparsity

Benign Overfitting in Deep Neural Networks under Lazy Training

A Theory of Finite-Width Neural Networks: Generalization, Scaling Laws, and the Loss Landscape

Inverse Reinforcement Learning of Pedestrian-Robot Coordination

From Kernel Methods to Neural Networks: A Unifying Variational Formulation

Towards Stable and Efficient Adversarial Training against $l_1$ Bounded Adversarial Attacks