Related papers: Thermodynamically Optimal Regularization under Inf…

Modern deep reinforcement learning (RL) algorithms are motivated by either the generalised policy iteration (GPI) or trust-region learning (TRL) frameworks. However, algorithms that strictly respect these theoretical frameworks have proven…

Implicit Neural Representations (INRs) have emerged as a powerful tool for geometric representation, yet their suitability for physics-based simulation remains underexplored. While metrics like Hausdorff distance quantify surface…

Proximal Policy Optimization (PPO) is widely used in reinforcement learning due to its strong empirical performance, yet it lacks formal guarantees for policy improvement and convergence. PPO's clipped surrogate objective is motivated by a…

Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…

Recent advances in deep learning theory have evoked the study of generalizability across different local minima of deep neural networks (DNNs). While current work focused on either discovering properties of good local minima or developing…

Regularization is a central tool for addressing ill-posedness in inverse problems and statistical estimation, with the choice of a suitable penalty often determining the reliability and interpretability of downstream solutions. While recent…

The concept of Rao-Blackwellization is employed to improve predictions of artificial neural networks by physical information. The error norm and the proof of improvement are transferred from the original statistical concept to a…

We propose a regularization framework inspired by thermodynamic work for guiding pre-trained probability flow generative models (e.g., continuous normalizing flows or diffusion models) by minimizing excess work, a concept rooted in…

A thermodynamic formalism describing the efficiency of information learning is proposed, which is applicable for stochastic thermodynamic systems with multiple internal degree of freedom. The learning rate, entropy production rate (EPR),…

We study the informational underpinnings of thermodynamics and statistical mechanics, using an abstract framework, general probabilistic theories, capable of describing arbitrary physical theories. This allows one to abstract the…

We derive upper bounds on the generalization error of a learning algorithm in terms of the mutual information between its input and output. The bounds provide an information-theoretic understanding of generalization in learning problems,…

The efficacy of mathematical models heavily depends on the quality of the training data, yet collecting sufficient data is often expensive and challenging. Many modeling applications require inferring parameters only as a means to predict…

Unsupervised representation learning methods are widely used for gaining insight into high-dimensional, unstructured, or structured data. In some cases, users may have prior topological knowledge about the data, such as a known cluster…

Robust optimization (RO) is a common approach to tractably obtain safeguarding solutions for optimization problems with uncertain constraints. In this paper, we study a statistical framework to integrate data into RO, based on learning a…

Reward maximization, safe exploration, and intrinsic motivation are often studied as separate objectives in reinforcement learning (RL). We present a unified geometric framework, that views these goals as instances of a single optimization…

Trustworthy machine learning aims at combating distributional uncertainties in training data distributions compared to population distributions. Typical treatment frameworks include the Bayesian approach, (min-max) distributionally robust…

We propose a physics-based regularization technique for function learning, inspired by statistical mechanics. By drawing an analogy between optimizing the parameters of an interpolator and minimizing the energy of a system, we introduce…

Topological optimization finds a material density distribution minimizing a functional of the solution of a partial differential equation (PDE), subject to a set of constraints (typically, a bound on the volume or mass of the material).…

Despite a variety of available techniques the issue of the proper regularization parameter choice for inverse problems still remains one of the biggest challenges. The main difficulty lies in constructing a rule, allowing to compute the…

We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…