Related papers: A Compositional Account of Generalized Reversible …
Compositional generalization is a crucial step towards developing data-efficient intelligent machines that generalize in human-like ways. In this work, we tackle a challenging form of distribution shift, termed compositional shift, where…
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…
A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This…
Our starting point is a particular `canvas' aimed to `draw' theories of physics, which has symmetric monoidal categories as its mathematical backbone. In this paper we consider the conceptual foundations for this canvas, and how these can…
A basic postulate of modern compositional approaches to generalised physical theories is the generalised Born rule, in which probabilities are postulated to be computable from the composition of states and effects. In this paper we consider…
Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of weak distribution or generalised random variable, and the same…
This work examines approaches to making computational models reversible. Broadly speaking, transforming a computational model into a reversible one, i.e. reversibilizing it, means extending its operational semantics conservatively in a way…
The one-body reduced density matrix $\gamma$ plays a fundamental role in describing and predicting quantum features of bosonic systems, such as Bose-Einstein condensation. The recently proposed reduced density matrix functional theory for…
We introduce a novel framework for decomposing interventional causal effects into synergistic, redundant, and unique components, building on the intuition of Partial Information Decomposition (PID) and the principle of M\"obius inversion.…
This paper generalizes the Maurer--Pontil framework of finite-dimensional lossy coding schemes to the setting where a high-dimensional random vector is mapped to an element of a compact set of latent representations in a lower-dimensional…
Categorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier…
We introduce structured decompositions, category-theoretic structures which simultaneously generalize notions from graph theory (including treewidth, layered treewidth, co-treewidth, graph decomposition width, tree independence number,…
For a commutative ring $A$, we have the category of (bounded-below) chain complexes of $A$-modules $Ch_{+}(A\mymod)$, a closed symmetric monoidal category with a compatible stable Quillen model structure. The associated homotopy category is…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
For a long time, people have been focusing on how to extract more information, such as off-diagonal observables, from the quantum Monte Carlo (QMC) simulation of the partition function, but there have been numerous difficulties, and many of…
In the reductionistic approach, mechanisms are divided into simpler parts interconnected in some standard way (e.g. by a mechanical transmission). We explore the possibility of porting reductionism in quantum operations. Conceptually, first…
Process theories provide a powerful framework for describing compositional structures across diverse fields, from quantum mechanics to computational linguistics. Traditionally, they have been formalized using symmetric monoidal categories…
Software frequently converts data from one representation to another and vice versa. Naively specifying both conversion directions separately is error prone and introduces conceptual duplication. Instead, bidirectional programming…
We present a new framework for recycling independent variational approximations to Gaussian processes. The main contribution is the construction of variational ensembles given a dictionary of fitted Gaussian processes without revisiting any…
Causal nonseparability refers to processes where events take place in a coherent superposition of different causal orders. These may be the key resource for experimental violations of causal inequalities and have been recently identified as…