A5076934946- Neural Networks and Applications
- Probabilistic and Robust Engineering Design
- Game Theory and Applications
- Auction Theory and Applications
- Model Reduction and Neural Networks
- Advanced Bandit Algorithms Research
- Advanced Multi-Objective Optimization Algorithms
- Advanced Numerical Analysis Techniques
- Image and Signal Denoising Methods
École Polytechnique Fédérale de Lausanne
2020-2022
Recent studies show that a reproducing kernel Hilbert space (RKHS) is not suitable to model functions by neural networks as the curse of dimensionality (CoD) cannot be evaded when trying approximate even single ReLU neuron (Bach, 2017). In this paper, we study function for over-parameterized two-layer with bounded norms (e.g., path norm, Barron norm) in perspective sample complexity and generalization properties. First, norm (as well able obtain width-independence bounds, which allows...
We provide an algorithm to generate trajectories of sparse stochastic processes that are solutions linear ordinary differential equations driven by Lévy white noises. A recent paper showed these limits in law generalized compound-Poisson processes. Based on this result, we derive off-the-grid generates arbitrarily close approximations the target process. Our method relies a B-spline representation illustrate numerically validity our approach.
Polynomial neural networks (PNNs) have been recently shown to be particularly effective at image generation and face recognition, where high-frequency information is critical. Previous studies revealed that demonstrate a $\textit{spectral bias}$ towards low-frequency functions, which yields faster learning of components during training. Inspired by such studies, we conduct spectral analysis the Neural Tangent Kernel (NTK) PNNs. We find $\Pi$-Net family, i.e., proposed parametrization PNNs,...
We introduce an online learning algorithm in the bandit feedback model that, once adopted by all agents of a congestion game, results game-dynamics that converge to $\epsilon$-approximate Nash Equilibrium polynomial number rounds with respect $1/\epsilon$, players and available resources. The proposed also guarantees sublinear regret any agent adopting it. As result, our work answers open question from arXiv:2206.01880 extends recent arXiv:2306.15543 model. additionally establish can be...