Related papers: Dimensionless learning based on information

The principles of statistical mechanics and information theory play an important role in learning and have inspired both theory and the design of numerous machine learning algorithms. The new aspect in this paper is a focus on integrating…

Diffusion models (DMs) have become dominant in visual generation but suffer performance drop when tested on resolutions that differ from the training scale, whether lower or higher. In fact, the key challenge in generating variable-scale…

The identification of universal properties from minimally processed data sets is one goal of machine learning techniques applied to statistical physics. Here, we study how the minimum number of variables needed to accurately describe the…

We present a numerical framework for recovering unknown non-autonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the non-autonomous nature of the system, our method transforms the solution state…

High-dimensional data are ubiquitous in contemporary science and finding methods to compress them is one of the primary goals of machine learning. Given a dataset lying in a high-dimensional space (in principle hundreds to several thousands…

We make two theoretical contributions to disentanglement learning by (a) defining precise semantics of disentangled representations, and (b) establishing robust metrics for evaluation. First, we characterize the concept "disentangled…

A low-dimensional dynamical system is observed in an experiment as a high-dimensional signal; for example, a video of a chaotic pendulums system. Assuming that we know the dynamical model up to some unknown parameters, can we estimate the…

High-fidelity simulation of complex physical systems is exorbitantly expensive and inaccessible across spatiotemporal scales. Recently, there has been an increasing interest in leveraging deep learning to augment scientific data based on…

In Machine Learning (ML), a regression algorithm aims to minimize a loss function based on data. An assessment method in this context seeks to quantify the discrepancy between the optimal response for an input-output system and the estimate…

The principle of maximum entropy is a broadly applicable technique for computing a distribution with the least amount of information possible while constrained to match empirically estimated feature expectations. However, in many real-world…

The "curse of dimensionality" is a well-known problem in pattern recognition. A widely used approach to tackling the problem is a group of subspace methods, where the original features are projected onto a new space. The lower dimensional…

In this paper, we focus on learning a linear time-invariant (LTI) model with low-dimensional latent variables but high-dimensional observations. We provide an algorithm that recovers the high-dimensional features, i.e. column space of the…

Autonomous multi-agent systems are fundamentally fragile: they struggle to solve the Hayekian Information problem (eliciting dispersed private knowledge) and the Hurwiczian Incentive problem (aligning local actions with global objectives),…

Recent model-free reinforcement learning algorithms have proposed incorporating learned dynamics models as a source of additional data with the intention of reducing sample complexity. Such methods hold the promise of incorporating imagined…

Recently, we have demonstrated that our approach is a highly effective tool while analysing complex phenomena existing in networks of coupled nonlinear systems. In the present article we present the results of our investigations into a…

Metric learning aims at finding a suitable distance metric over the input space, to improve the performance of distance-based learning algorithms. In high-dimensional settings, it can also serve as dimensionality reduction by imposing a…

Parameter-free algorithms are online learning algorithms that do not require setting learning rates. They achieve optimal regret with respect to the distance between the initial point and any competitor. Yet, parameter-free algorithms do…

In this paper, we introduce an innovative approach for addressing Bayesian inverse problems through the utilization of physics-informed invertible neural networks (PI-INN). The PI-INN framework encompasses two sub-networks: an invertible…

Despite their apparent diversity, modern machine learning methods can be reduced to a remarkably simple core principle: learning is achieved by continuously optimizing parameters to minimize or maximize a scalar objective function. This…

Large scale dynamical systems (e.g. many nonlinear coupled differential equations) can often be summarized in terms of only a few state variables (a few equations), a trait that reduces complexity and facilitates exploration of behavioral…