Related papers: An entropy-optimal path to humble AI

We consider adaptive finite element methods for second-order elliptic PDEs, where the arising discrete systems are not solved exactly. For contractive iterative solvers, we formulate an adaptive algorithm which monitors and steers the…

The success of any machine learning system depends critically on effective representations of data. In many cases, it is desirable that a representation scheme uncovers the parts-based, additive nature of the data. Of current representation…

In recent years, Deep-Learning Earth System Models (DL-ESMs) have emerged as promising, computationally efficient complements to traditional Earth system models. Here, we present an evaluation framework for testing DL-ESMs from a…

In many real world problems, optimization decisions have to be made with limited information. The decision maker may have no a priori or posteriori data about the often nonconvex objective function except from on a limited number of points…

The era of huge data necessitates highly efficient machine learning algorithms. Many common machine learning algorithms, however, rely on computationally intensive subroutines that are prohibitively expensive on large datasets. Oftentimes,…

The topic of deep learning has seen a surge of interest in recent years both within and outside of the field of Statistics. Deep models leverage both nonlinearity and interaction effects to provide superior predictions in many cases when…

For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…

As language models continue to grow larger, the cost of acquiring high-quality training data has increased significantly. Collecting human feedback is both expensive and time-consuming, and manual labels can be noisy, leading to an…

Contextual policy search allows adapting robotic movement primitives to different situations. For instance, a locomotion primitive might be adapted to different terrain inclinations or desired walking speeds. Such an adaptation is often…

Many engineering processes can be accurately modelled using partial differential equations (PDEs), but high dimensionality and non-convexity of the resulting systems pose limitations on their efficient optimisation. In this work, a model…

Multi-Agent Reinforcement Learning involves agents that learn together in a shared environment, leading to emergent dynamics sensitive to initial conditions and parameter variations. A Dynamical Systems approach, which studies the evolution…

Neural networks that synergistically integrate data and physical laws offer great promise in modeling dynamical systems. However, iterative gradient-based optimization of network parameters is often computationally expensive and suffers…

Maximum entropy methods, rooted in the inverse Ising/Potts problem from statistical physics, are widely used to model pairwise interactions in complex systems across disciplines such as bioinformatics and neuroscience. While successful,…

A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such…

Archetypal analysis is an unsupervised learning method for exploratory data analysis. One major challenge that limits the applicability of archetypal analysis in practice is the inherent computational complexity of the existing algorithms.…

We propose a unified data-driven framework based on inverse optimal transport that can learn adaptive, nonlinear interaction cost function from noisy and incomplete empirical matching matrix and predict new matching in various matching…

Large language models (LLMs) are reshaping how knowledge is produced, with increasing reliance on AI systems for generation, summarization, and reasoning. While prior work has studied cognitive offloading in humans and model collapse in…

Graphical models are powerful tools for modeling high-dimensional data, but learning graphical models in the presence of latent variables is well-known to be difficult. In this work we give new results for learning Restricted Boltzmann…

Weather forecasting is fundamentally challenged by the chaotic nature of the atmosphere, necessitating probabilistic approaches to quantify uncertainty. While traditional ensemble prediction (EPS) addresses this through computationally…

In this paper, we show how to transform any optimization problem that arises from fitting a machine learning model into one that (1) detects and removes contaminated data from the training set while (2) simultaneously fitting the trimmed…