Zobrazeno 1 - 10
of 221
pro vyhledávání: '"Biau Gérard"'
Attention-based models, such as Transformer, excel across various tasks but lack a comprehensive theoretical understanding, especially regarding token-wise sparsity and internal linear representations. To address this gap, we introduce the single-loc
Externí odkaz:
http://arxiv.org/abs/2410.01537
Physics-informed machine learning typically integrates physical priors into the learning process by minimizing a loss function that includes both a data-driven term and a partial differential equation (PDE) regularization. Building on the formulation
Externí odkaz:
http://arxiv.org/abs/2409.13786
Physics-informed machine learning combines the expressiveness of data-based approaches with the interpretability of physical models. In this context, we consider a general regression problem where the empirical risk is regularized by a partial differ
Externí odkaz:
http://arxiv.org/abs/2402.07514
Residual neural networks are state-of-the-art deep learning models. Their continuous-depth analog, neural ordinary differential equations (ODEs), are also widely used. Despite their success, the link between the discrete and continuous models still l
Externí odkaz:
http://arxiv.org/abs/2309.01213
Physics-informed neural networks (PINNs) are a promising approach that combines the power of neural networks with the interpretability of physical modeling. PINNs have shown good practical performance in solving partial differential equations (PDEs)
Externí odkaz:
http://arxiv.org/abs/2305.01240
The signature is a representation of a path as an infinite sequence of its iterated integrals. Under certain assumptions, the signature characterizes the path, up to translation and reparameterization. Therefore, a crucial question of interest is the
Externí odkaz:
http://arxiv.org/abs/2304.01862
Deep ResNets are recognized for achieving state-of-the-art results in complex machine learning tasks. However, the remarkable performance of these architectures relies on a training procedure that needs to be carefully crafted to avoid vanishing or e
Externí odkaz:
http://arxiv.org/abs/2206.06929
The mathematical forces at work behind Generative Adversarial Networks raise challenging theoretical issues. Motivated by the important question of characterizing the geometrical properties of the generated distributions, we provide a thorough analys
Externí odkaz:
http://arxiv.org/abs/2201.02824
Building on the interpretation of a recurrent neural network (RNN) as a continuous-time neural differential equation, we show, under appropriate conditions, that the solution of a RNN can be viewed as a linear function of a specific feature set of th
Externí odkaz:
http://arxiv.org/abs/2106.01202