Related papers: Mathematical Foundations for a Compositional Accou…

Compositionality is believed to be fundamental to intelligence. In humans, it underlies the structure of thought, language, and higher-level reasoning. In AI, compositional representations can enable a powerful form of out-of-distribution…

Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be…

Modern data analysis increasingly requires flexible conditional inference P(X_B | X_A) where (X_A, X_B) is an arbitrary partition of observed variable X. Existing approaches are either restricted to a fixed conditioning structure or depend…

Causal inference can be formalized as Bayesian inference that combines a prior distribution over causal models and likelihoods that account for both observations and interventions. We show that it is possible to implement this approach…

In a published paper [Sengupta, 2016], we have proposed that the brain (and other self-organized biological and artificial systems) can be characterized via the mathematical apparatus of a gauge theory. The picture that emerges from this…

The framework of causal models provides a principled approach to causal reasoning, applied today across many scientific domains. Here we present this framework in the language of string diagrams, interpreted formally using category theory.…

Experiments that study neural encoding of stimuli at the level of individual neurons typically choose a small set of features present in the world --- contrast and luminance for vision, pitch and intensity for sound --- and assemble a…

The compositionality degree of multiword expressions indicates to what extent the meaning of a phrase can be derived from the meaning of its constituents and their grammatical relations. Prediction of (non)-compositionality is a task that…

We extend the open games framework for compositional game theory to encompass also mixed strategies, making essential use of the discrete probability distribution monad. We show that the resulting games form a symmetric monoidal category,…

The parametric bootstrap can be used for the efficient computation of Bayes posterior distributions. Importance sampling formulas take on an easy form relating to the deviance in exponential families and are particularly simple starting…

Multi-dimensional functional data arises in numerous modern scientific experimental and observational studies. In this paper we focus on longitudinal functional data, a structured form of multidimensional functional data. Operating within a…

We introduce a graphical framework for Bayesian inference that is sufficiently general to accommodate not just the standard case but also recent proposals for a theory of quantum Bayesian inference wherein one considers density operators…

Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has…

Many dynamical systems -- from robots interacting with their surroundings to large-scale multiphysics systems -- involve a number of interacting subsystems. Toward the objective of learning composite models of such systems from data, we…

In many applications, smooth processes generate data that is recorded under a variety of observation regimes, such as dense, sparse or fragmented observations that are often contaminated with error. The statistical goal of registering and…

The world is fundamentally compositional, so it is natural to think of visual recognition as the recognition of basic visually primitives that are composed according to well-defined rules. This strategy allows us to recognize unseen complex…

A Bayesian pseudocoreset is a compact synthetic dataset summarizing essential information of a large-scale dataset and thus can be used as a proxy dataset for scalable Bayesian inference. Typically, a Bayesian pseudocoreset is constructed…

Algorithmicists are well-aware that fast dynamic programming algorithms are very often the correct choice when computing on compositional (or even recursive) graphs. Here we initiate the study of how to generalize this folklore intuition to…

Bayesian inference is an effective approach for solving statistical learning problems especially with uncertainty and incompleteness. However, inference efficiencies are physically limited by the bottlenecks of conventional computing…

The ability to compose parts to form a more complex whole, and to analyze a whole as a combination of elements, is desirable across disciplines. This workshop bring together researchers applying compositional approaches to physics, NLP,…