相关论文: Uniqueness of MAP estimates for inverse problems u…

The information metric provides a unique notion of distance along any continuous family of physical theories, placing two theories further apart the more distinguishable they are. As such, the information metric is typically singular at…

Traditional machine learning relies on explicit models and domain assumptions, limiting flexibility and interpretability. We introduce a model-free framework using surprisal (information theoretic uncertainty) to directly analyze and…

Effective Field Theory (EFT) extensions of the Standard Model are tools to compute observables $\big(e.g.$ cross sections with partonic center-of-mass energy $\sqrt{\hat{s}}\,\big)$ as a systematically improvable expansion suppressed by a…

Inferential models (IMs) are data-dependent, imprecise-probabilistic structures designed to quantify uncertainty about unknowns. As the name suggests, the focus has been on uncertainty quantification for inference and on its reliability…

Recent advances in reconstruction methods for inverse problems leverage powerful data-driven models, e.g., deep neural networks. These techniques have demonstrated state-of-the-art performances for several imaging tasks, but they often do…

In our previous arXiv papers (more systematically the informational conception is presented in the paper "The Information as Absolute", 2010) it was rigorously shown that Matter in our Universe - and Universe as a whole - are some…

We present an information-theoretic framework for understanding overfitting and underfitting in machine learning and prove the formal undecidability of determining whether an arbitrary classification algorithm will overfit a dataset.…

Multivariate time series forecasting is a pivotal task in several domains, including financial planning, medical diagnostics, and climate science. This paper presents the Neural Fourier Transform (NFT) algorithm, which combines…

Many studies of possible new physics employ effective field theory (EFT), whereby corrections to the Standard Model take the form of higher-dimensional operators, suppressed by a large energy scale. Fits of such a theory to data typically…

We introduce an information-theoretic framework that views learning as universal prediction under log loss, characterized through regret bounds. Central to the framework is an effective notion of architecture-based model complexity, defined…

Information theory is built on probability measures and by definition a probability measure has total mass 1. Probability measures are used to model uncertainty, and one may ask how important it is that the total mass is one. We claim that…

Probing heavy new physics beyond the Standard Model (SM) increasingly relies on global effective field theory (EFT) likelihoods. We introduce differentiable, multi-scale EFT likelihoods that combine renormalization-group evolution,…

We derive exact inversion identities satisfied by the transfer matrix of inhomogeneous interaction-round-a-face (IRF) models with arbitrary boundary conditions using the underlying integrable structure and crossing properties of the local…

We develop a foundational framework for inverse problems governed by evolutionary partial differential equations (PDEs) on the Wasserstein space of probability measures. While the forward problems for such transport-type PDEs have been…

We establish guarantees for the unique recovery of vector fields and transport maps from finite measure-valued data, yielding new insights into generative models, data-driven dynamical systems, and PDE inverse problems. In particular, we…

A field theory is developed based on the idea that the effective action of yet unknown fundamental theory, at energy scale below M_{p} has the form of expansion in two measures: S=\intd^{4}x[\Phi L_{1}+\sqrt{-g}L_{2}] where the new measure…

The most fundamental problem in statistics is the inference of an unknown probability distribution from a finite number of samples. For a specific observed data set, answers to the following questions would be desirable: (1) Estimation:…

Conformal Prediction (CP) is a distribution-free uncertainty estimation framework that constructs prediction sets guaranteed to contain the true answer with a user-specified probability. Intuitively, the size of the prediction set encodes a…

Integrated information theory (IIT) is a theoretical framework that provides a quantitative measure to estimate when a physical system is conscious, its degree of consciousness, and the complexity of the qualia space that the system is…

Deep learning is renowned for its theory-practice gap, whereby principled theory typically fails to provide much beneficial guidance for implementation in practice. This has been highlighted recently by the benign overfitting phenomenon:…