相关论文: An entropy-optimal path to humble AI

Modern language model-based AI systems are remarkably powerful, yet their capabilities remain fundamentally capped by their human creators in three key ways. First, although a model's weights can be updated via fine-tuning, acquiring new…

The majority of data assimilation (DA) methods in the geosciences are based on Gaussian assumptions. While these assumptions facilitate efficient algorithms, they cause analysis biases and subsequent forecast degradations. Non-parametric,…

We describe the implementation of a new approach to the numerical evaluation of the effects of non-cold relics on the evolution of cosmological perturbations. The Boltzmann hierarchies used to compute the contributions of these relics to…

Restricted Boltzmann machines are undirected neural networks which have been shown to be effective in many applications, including serving as initializations for training deep multi-layer neural networks. One of the main reasons for their…

Cloud-related parameterizations remain a leading source of uncertainty in climate projections. Although machine learning holds promise for Earth system models (ESMs), many data-driven parameterizations lack interpretability, physical…

Almost all fields of science rely upon statistical inference to estimate unknown parameters in theoretical and computational models. While the performance of modern computer hardware continues to grow, the computational requirements for the…

Functions that are not differentiable in the classical sense have become a central tool in modern mathematical models for imaging, inverse problems, machine learning, and optimal control of differential equations. These models are…

We study the classic online learning problem of predicting with expert advice, and propose a truly parameter-free and adaptive algorithm that achieves several objectives simultaneously without using any prior information. The main component…

Data-driven machine learning models for weather forecasting have made transformational progress in the last 1-2 years, with state-of-the-art ones now outperforming the best physics-based models for a wide range of skill scores. Given the…

High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…

Choosing the optimization algorithm that performs best on a given machine learning problem is often delicate, and there is no guarantee that current state-of-the-art algorithms will perform well across all tasks. Consequently, the more…

Computing equilibrium states in condensed-matter many-body systems, such as solvated proteins, is a long-standing challenge. Lacking methods for generating statistically independent equilibrium samples in "one shot", vast computational…

Maximum likelihood estimation of energy-based models is a challenging problem due to the intractability of the log-likelihood gradient. In this work, we propose learning both the energy function and an amortized approximate sampling…

We introduce an efficient method for learning linear models from uncertain data, where uncertainty is represented as a set of possible variations in the data, leading to predictive multiplicity. Our approach leverages abstract…

The study of complex systems is limited by the fact that only few variables are accessible for modeling and sampling, which are not necessarily the most relevant ones to explain the systems behavior. In addition, empirical data typically…

This paper develops a unified framework for evaluating the optimal degree of task automation. Moving beyond binary automate-or-not assessments, we model automation intensity as a continuous choice in which firms minimize costs by selecting…

Traditional maximum entropy and sparsity-based algorithms for analytic continuation often suffer from the ill-posed kernel matrix or demand tremendous computation time for parameter tuning. Here we propose a neural network method by convex…

Tool-using agents based on Large Language Models (LLMs) excel in tasks such as mathematical reasoning and multi-hop question answering. However, in long trajectories, agents often trigger excessive and low-quality tool calls, increasing…

A Boltzmann machine is a stochastic neural network that has been extensively used in the layers of deep architectures for modern machine learning applications. In this paper, we develop a Boltzmann machine that is capable of modelling…

We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and…