119 citations · 338 across the 22 of their papers we have counts for
23 papers
Thermalizing Stochastic Programs
Mirko Amico, Andraž Jelinčič, Colin Oscar Nancarrow +6
We present a set of tools for mapping general stochastic programs to thermodynamic hardware designed for energy-efficient stochastic sampling. Given a target stochastic program exp…
On two differing geometric descriptions of the passage from microscopy to macroscopy in Markov diffusion theory
Dalton A R Sakthivadivel
In various disparate settings one studies how random processes give way to parabolic partial differential equations and in turn to functional inequalities involving gradients and v…
The nonequilibrium statistical mechanics of Markov interacting particles
Dalton A R Sakthivadivel
We consider coupled stochastic systems decomposed into exterior, boundary, and interior variables, with the boundary variables sometimes carrying the directed structure of a sensor…
Completions of complexes of differential modules on singular schemes
Bruno Borić, Dalton A R Sakthivadivel
Spencer cohomology theory studies the cohomology of chain complexes of modules over the ring of differential operators of a smooth analytic space. In this paper we gi…
The relation of bias with risk in empirically constrained inferences
Dalton A R Sakthivadivel
We give some results relating asymptotic characterisations of maximum entropy probability measures to characterisations of Bayes optimal classifiers. Our main theorems show that ma…
Resilience and adaptability in self-evidencing systems
Mahault Albarracin, Dalton A R Sakthivadivel
In this paper we will articulate a view of resilience under the free energy principle and vice versa. The free energy principle is about existence and identity, and resilience is t…
Topological constraints on self-organisation in locally interacting systems
Francesco Sacco, Dalton A R Sakthivadivel, Michael Levin
All intelligence is collective intelligence, in the sense that it is made of parts which must align with respect to system-level goals. Understanding the dynamics which facilitate…
From bordisms of three-manifolds to domain walls between topological orders
Yu Leon Liu, Dalton A R Sakthivadivel
We study a correspondence between spin three-manifolds and bosonic abelian topological orders. Let be a spin three-manifold. We can define a -dimensional topological ord…
A framework for the use of generative modelling in non-equilibrium statistical mechanics
Karl J Friston, Maxwell J D Ramstead, Dalton A R Sakthivadivel
We discuss an approach to mathematically modelling systems made of objects that are coupled together, using generative models of the dependence relationships between states (or tra…
Functorial Statistical Physics: Feynman--Kac Formulae and Information Geometries
Dalton A R Sakthivadivel
The main results of this paper comprise proofs of the following two related facts: (i) the Feynman--Kac formula is a functor , namely, between a stochastic differential equati…
Designing Ecosystems of Intelligence from First Principles
Karl J Friston, Maxwell J D Ramstead, Alex B Kiefer +17
This white paper lays out a vision of research and development in the field of artificial intelligence for the next decade (and beyond). Its denouement is a cyber-physical ecosyste…
Path integrals, particular kinds, and strange things
Karl Friston, Lancelot Da Costa, Dalton A. R. Sakthivadivel +4
This paper describes a path integral formulation of the free energy principle. The ensuing account expresses the paths or trajectories that a particle takes as it evolves over time…
Weak Markov Blankets in High-Dimensional, Sparsely-Coupled Random Dynamical Systems
Dalton A R Sakthivadivel
This paper formulates a notion of high-dimensional random dynamical systems that couple to another system, like an embedding environment, in such a way that each system engages in…
On the map-territory fallacy fallacy
Maxwell J D Ramstead, Dalton A R Sakthivadivel, Karl J Friston
This paper presents a meta-theory of the usage of the free energy principle (FEP) and examines its scope in the modelling of physical systems. We consider the so-called `map-territ…
A Worked Example of the Bayesian Mechanics of Classical Objects
Dalton A R Sakthivadivel
Bayesian mechanics is a new approach to studying the mathematics and physics of interacting stochastic processes. Here, we provide a worked example of a physical mechanics for clas…
Regarding Flows Under the Free Energy Principle: A Comment on "How Particular is the Physics of the Free Energy Principle?" by Aguilera, Millidge, Tschantz, and Buckley
Dalton A R Sakthivadivel
In a recent technical critique of the free energy principle (FEP) due to Aguilera-Millidge-Tschantz-Buckley, it is argued that there are a number of instances where the FEP$\unicod…
On Bayesian Mechanics: A Physics of and by Beliefs
Maxwell J. D. Ramstead, Dalton A. R. Sakthivadivel, Conor Heins +5
The aim of this paper is to introduce a field of study that has emerged over the last decade called Bayesian mechanics. Bayesian mechanics is a probabilistic mechanics, comprising…
Some Minimal Notes on Notation and Minima: A Comment on "How Particular is the Physics of the Free Energy Principle?" by Aguilera, Millidge, Tschantz, and Buckley
Maxwell J D Ramstead, Dalton A R Sakthivadivel
We comment on a technical critique of the free energy principle in linear systems by Aguilera, Millidge, Tschantz, and Buckley, entitled "How Particular is the Physics of the Free…
Towards a Geometry and Analysis for Bayesian Mechanics
Dalton A R Sakthivadivel
In this paper, a simple case of Bayesian mechanics under the free energy principle is formulated in axiomatic terms. We argue that any dynamical system with constraints on its dyna…
Entropy-Maximising Diffusions Satisfy a Parallel Transport Law
Dalton A R Sakthivadivel
We show that the principle of maximum entropy, a variational method appearing in statistical inference, statistical physics, and the analysis of stochastic dynamical systems, admit…
Characterising the Non-Equilibrium Dynamics of a Neural Cell
Dalton A R Sakthivadivel
We examine the dynamical evolution of the state of a neurone, with particular care to the non-equilibrium nature of the forces influencing its movement in state space. We combine n…
Formalising the Use of the Activation Function in Neural Inference
Dalton A R Sakthivadivel
We investigate how the activation function can be used to describe neural firing in an abstract way, and in turn, why it works well in artificial neural networks. We discuss how a…
Magnetisation and mean field theory in the Ising model
Dalton A R Sakthivadivel
In this set of notes, a complete, pedagogical tutorial for applying mean field theory to the two-dimensional Ising model is presented. Beginning with the motivation and basis for m…