Related papers: Efficient reconstruction of multidimensional rando…
The energy landscape of high-dimensional non-convex optimization problems is crucial to understanding the effectiveness of modern deep neural network architectures. Recent works have experimentally shown that two different solutions found…
We provide new convergence guarantees in Wasserstein distance for diffusion-based generative models, covering both stochastic (DDPM-like) and deterministic (DDIM-like) sampling methods. We introduce a simple framework to analyze…
Distributionally robust optimization has emerged as an attractive way to train robust machine learning models, capturing data uncertainty and distribution shifts. Recent statistical analyses have proved that generalization guarantees of…
Lack of ground-truth MR images impedes the common supervised training of neural networks for image reconstruction. To cope with this challenge, this paper leverages unpaired adversarial training for reconstruction networks, where the inputs…
We consider learning two layer neural networks using stochastic gradient descent. The mean-field description of this learning dynamics approximates the evolution of the network weights by an evolution in the space of probability…
Deep neural networks often require copious amount of labeled-data to train their scads of parameters. Training larger and deeper networks is hard without appropriate regularization, particularly while using a small dataset. Laterally,…
We present a novel multiscale super-resolution framework (SRLBM) that applies deep learning directly to the mesoscopic density distribution functions of the lattice Boltzmann method for high-fidelity flow reconstruction. Two neural network…
Domain shifts in the training data are common in practical applications of machine learning; they occur for instance when the data is coming from different sources. Ideally, a ML model should work well independently of these shifts, for…
Score matching provides an effective approach to learning flexible unnormalized models, but its scalability is limited by the need to evaluate a second-order derivative. In this paper, we present a scalable approximation to a general family…
We study the machine learning task for models with operators mapping between the Wasserstein space of probability measures and a space of functions, like e.g. in mean-field games/control problems. Two classes of neural networks, based on…
We analyze the Wasserstein distance ($W$-distance) between two probability distributions associated with two multidimensional jump-diffusion processes. Specifically, we analyze a temporally decoupled squared $W_2$-distance, which provides…
Despite the strong predictive performance achieved by machine learning models across many application domains, assessing their trustworthiness through reliable estimates of predictive confidence remains a critical challenge. This issue…
It is well-known that deep neural networks (DNNs) have shown remarkable success in many fields. However, when adding an imperceptible magnitude perturbation on the model input, the model performance might get rapid decrease. To address this…
Deep neural networks (DNNs) achieve remarkable performance on a wide range of tasks, yet their mathematical analysis remains fragmented: stability and generalization are typically studied in disparate frameworks and on a case-by-case basis.…
Machine learning has made tremendous progress in recent years, with models matching or even surpassing humans on a series of specialized tasks. One key element behind the progress of machine learning in recent years has been the ability to…
We study the convergence of gradient flow for the training of deep neural networks. If Residual Neural Networks are a popular example of very deep architectures, their training constitutes a challenging optimization problem due notably to…
Stochastic differential equations (SDEs) are a staple of mathematical modelling of temporal dynamics. However, a fundamental limitation has been that such models have typically been relatively inflexible, which recent work introducing…
Disentangling polysemantic neurons is at the core of many current approaches to interpretability of large language models. Here we attempt to study how disentanglement can be used to understand performance, particularly under weight…
Stochastic Gradient Descent (SGD) has proven to be remarkably effective in optimizing deep neural networks that employ ever-larger numbers of parameters. Yet, improving the efficiency of large-scale optimization remains a vital and highly…
This paper contributes to a development of randomized methods for neural networks. The proposed learner model is generated incrementally by stochastic configuration (SC) algorithms, termed as Stochastic Configuration Networks (SCNs). In…