Related papers: Computational Mechanics of Input-Output Processes:…

Contemporary machine learning optimizes for predictive accuracy, yet systems that achieve state of the art performance remain causally opaque: their internal representations provide no principled handle for intervention. We can retrain such…

Computational modeling helps neuroscientists to integrate and explain experimental data obtained through neurophysiological and anatomical studies, thus providing a mechanism by which we can better understand and predict the principles of…

In the study of quantum computation, data is represented in terms of linear operators which form a generalized model of probability, and computations are most commonly described as products of unitary transformations, which are the…

We introduce a formal definition of Wolfram's notion of computational process based on cellular automata, a physics-like model of computation. There is a natural classification of these processes into decidable, intermediate and complete.…

Previously, we showed that computational mechanic's causal states -- predictively-equivalent trajectory classes for a stochastic dynamical system -- can be cast into a reproducing kernel Hilbert space. The result is a widely-applicable…

Physical processes are computations only when we use them to externalize thought. Computation is the performance of one or more fixed processes within a contingent environment. We reformulate the Church-Turing thesis so that it applies to…

Quantum mechanics, the fundamental theory that governs the behaviour of matter and energy at microscopic scales, forms the foundation of quantum computing and quantum information science. As quantum technologies progress, software engineers…

Simulations of stochastic processes play an important role in the quantitative sciences, enabling the characterisation of complex systems. Recent work has established a quantum advantage in stochastic simulation, leading to quantum devices…

Structured prediction tasks pose a fundamental trade-off between the need for model complexity to increase predictive power and the limited computational resources for inference in the exponentially-sized output spaces such models require.…

Mechanistic Interpretability (MI) aims to reverse-engineer model behaviors by identifying functional sub-networks. Yet, the scientific validity of these findings depends on their stability. In this work, we argue that circuit discovery is…

We use the system of p-adic numbers for the description of information processes. Basic objects of our models are so called transformers of information, basic processes are information processes, the statistics are information statistics…

Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…

This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…

Continuous-time stochastic processes pervade everyday experience, and the simulation of models of these processes is of great utility. Classical models of systems operating in continuous-time must typically track an unbounded amount of…

In this paper, we explore statistical versus computational trade-off to address a basic question in the application of a distributed algorithm: what is the minimal computational cost in obtaining statistical optimality? In smoothing spline…

There is a growing consensus that physics majors need to learn computational skills, but many departments are still devoid of computation in their physics curriculum. Some departments may lack the resources or commitment to create a…

This article introduces both a new algorithm for reconstructing epsilon-machines from data, as well as the decisional states. These are defined as the internal states of a system that lead to the same decision, based on a user-provided…

We introduce an algebra qCCS of pure quantum processes in which no classical data is involved, communications by moving quantum states physically are allowed, and computations is modeled by super-operators. An operational semantics of qCCS…

We merge computational mechanics' definition of causal states (predictively-equivalent histories) with reproducing-kernel Hilbert space (RKHS) representation inference. The result is a widely-applicable method that infers causal structure…

Any physical process can be represented as a quantum channel mapping an initial state to a final state. Hence it can be characterized from the point of view of communication theory, i.e., in terms of its ability to transfer information.…