相关论文: Pattern theory: the mathematics of perception

In this paper we investigate the existence of a separation principle between model identification and control design in the context of model predictive control. First, we clarify that such a separation principle holds asymptotically in the…

Within the biological, physical, and social sciences, there are two broad quantitative traditions: statistical and mathematical modeling. Both traditions have the common pursuit of advancing our scientific knowledge, but these traditions…

Perception, in theoretical neuroscience, has been modeled as the encoding of external stimuli into internal signals, which are then decoded. The Bayesian mean is an important decoder, as it is optimal for purposes of both estimation and…

The past decades have seen enormous improvements in computational inference based on statistical models, with continual enhancement in a wide range of computational tools, in competition. In Bayesian inference, first and foremost, MCMC…

An overview is given about the statistical physics of neural networks generating and analysing time series. Storage capacity, bit and sequence generation, prediction error, antipredictable sequences, interacting perceptrons and the…

These notes introduce the theory of susceptibilities as developed in [arXiv:2504.18274, arXiv:2601.12703] for interpreting neural networks. The susceptibility of an observable $\phi$ to a data perturbation is defined as a derivative of a…

This paper develops a Bayesian mechanics for adaptive systems. Firstly, we model the interface between a system and its environment with a Markov blanket. This affords conditions under which states internal to the blanket encode information…

Bayesian probability theory is used to analyze the oft-made assumption that humans are typical observers in the universe. Some theoretical calculations make the {\it selection fallacy} that we are randomly chosen from a class of objects by…

Recent research in computational linguistics has developed algorithms which associate matrices with adjectives and verbs, based on the distribution of words in a corpus of text. These matrices are linear operators on a vector space of…

We present a model of speech perception which takes into account effects of correlations between sounds. Words in this model correspond to the attractors of a suitably chosen descent dynamics. The resulting lexicon is rich in short words,…

Stacking is a widely used model averaging technique that asymptotically yields optimal predictions among linear averages. We show that stacking is most effective when model predictive performance is heterogeneous in inputs, and we can…

Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…

What is it to interpret the outputs of an opaque machine learning model. One approach is to develop interpretable machine learning techniques. These techniques aim to show how machine learning models function by providing either model…

Agents acting in the natural world aim at selecting appropriate actions based on noisy and partial sensory observations. Many behaviors leading to decision mak- ing and action selection in a closed loop setting are naturally phrased within…

Statistical modeling is a key component in the extraction of physical results from lattice field theory calculations. Although the general models used are often strongly motivated by physics, many model variations can frequently be…

We present a learning theory for the training of a linear system operator having an input compositional variable and propose a Bayesian inversion method for inferring the unknown variable from an output of a noisy linear system. We assume…

Mathematical models are increasingly a part of microbiological research. Here, we share our perspective on how modeling advances the discipline by: (i) enforcing logical consistency, (ii) enabling quantitative prediction, (iii) extracting…

Two different approaches to dealing with probabilistic knowledge are examined -models and inductive inference. Examples of the first are: influence diagrams [1], Bayesian networks [2], log-linear models [3, 4]. Examples of the second are:…

Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge…

Non-Bayesian social learning theory provides a framework for distributed inference of a group of agents interacting over a social network by sequentially communicating and updating beliefs about the unknown state of the world through…