A5000475430- Computability, Logic, AI Algorithms
- Philosophy and History of Science
- Neural dynamics and brain function
- Embodied and Extended Cognition
- Nanopore and Nanochannel Transport Studies
- Complex Systems and Time Series Analysis
- Semantic Web and Ontologies
- Bayesian Modeling and Causal Inference
- Machine Learning and Algorithms
- Statistical Mechanics and Entropy
- Electrostatics and Colloid Interactions
- Advanced Memory and Neural Computing
- DNA and Nucleic Acid Chemistry
- Language and cultural evolution
- Cognitive Science and Education Research
- Force Microscopy Techniques and Applications
- Neural Networks and Applications
- Memory and Neural Mechanisms
- Logic, Reasoning, and Knowledge
- AI-based Problem Solving and Planning
- Ferroelectric and Negative Capacitance Devices
- Blind Source Separation Techniques
- Biomedical Text Mining and Ontologies
- Advanced Polymer Synthesis and Characterization
- Topological and Geometric Data Analysis
Topos Institute
2022-2024
University of Oxford
2018-2024
VERSES (United States)
2023-2024
Topos
2022-2024
Oxford Centre for Computational Neuroscience
2021
University of Gothenburg
2015-2018
Codeplay (United Kingdom)
2018
This white paper lays out a vision of research and development in the field artificial intelligence for next decade (and beyond). Its denouement is cyber-physical ecosystem natural synthetic sense-making, which humans are integral participants—what we call “shared intelligence.” premised on active inference, formulation adaptive behavior that can be read as physics intelligence, inherits from self-organization. In this context, understand capacity to accumulate evidence generative model...
In this paper, we unite concepts from Husserlian phenomenology, the active inference framework in theoretical biology, and category theory mathematics to develop a comprehensive for understanding social action premised on shared goals. We begin with an overview of focusing aspects inner time-consciousness, namely, retention, primal impression, protention. then review as formal approach modeling agent behavior based variational (approximate Bayesian) inference. Expanding upon Husserl’s model...
This white paper lays out a vision of research and development in the field artificial intelligence for next decade (and beyond). Its denouement is cyber-physical ecosystem natural synthetic sense-making, which humans are integral participants -- what we call ''shared intelligence''. premised on active inference, formulation adaptive behavior that can be read as physics intelligence, inherits from self-organization. In this context, understand capacity to accumulate evidence generative model...
Bayes' rule tells us how to invert a causal process in order update our beliefs light of new evidence. If the is believed have complex compositional structure, we may ask whether composing inversions component processes gives same belief as inversion whole. We answer this question affirmatively, showing that relevant structure precisely lens pattern, and can think Bayesian particular instance state-dependent morphism corresponding fibred category. define general notion (mixed) lens, discuss...
Theoretical results for the extension of a polymer confined to channel are usually derived in limit infinite contour length. But experimental studies and simulations DNA molecules nanochannels not necessarily this asymptotic limit. We calculate statistics span end-to-end distance semiflexible finite length extended de Gennes regime, exploiting fact that problem can be mapped one-dimensional weakly self-avoiding random walk. The thus obtained compare favourably with pruned-enriched Rosenbluth...
We present a categorical formulation of the cognitive frameworks Predictive Processing and Active Inference, expressed in terms string diagrams interpreted monoidal category with copying discarding. This includes diagrammatic accounts generative models, Bayesian updating, perception, planning, active inference, free energy. In particular we derivation formula for inference via energy minimisation, establish compositionality property energy, allowing to be applied at all levels an agent's...
If a semiflexible polymer confined to narrow channel bends around by 180°, the is said exhibit hairpin. The equilibrium extension statistics of are well understood when hairpins vanishingly rare or they plentiful. Here, we analyze in intermediate situation via experiments with DNA coated protein RecA, which enhances stiffness molecule approximately one order magnitude. We find that distribution highly non-Gaussian, good agreement Monte-Carlo simulations discrete wormlike chains. develop...
ABSTRACT Spiking Neural Network (SNN) simulations require internal variables – such as the membrane voltages of individual neurons and their synaptic inputs to be updated on a sub-millisecond resolution. As result, single second simulation time requires many thousands update calculations per neuron. Furthermore, increases in scale SNN models have, accordingly, led manyfold runtime simulations. Existing solutions this problem include high performance CPU based simulators capable multithreaded...
Bayes' rule tells us how to invert a causal process in order update our beliefs light of new evidence. If the is believed have complex compositional structure, we may observe that inversion whole can be computed piecewise terms component processes. We study structure this rule, noting it relates lens pattern functional programming. Working suitably general axiomatic presentation category Markov kernels, see think Bayesian as particular instance state-dependent morphism fibred category....
We present categories of open dynamical systems with general time evolution as coalgebras opindexed by polynomial interfaces, and show how this extends the coalgebraic framework to capture common scientific applications such ordinary differential equations, Markov processes, random systems. then extend Spivak's operad Org setting, construct associated monoidal whose morphisms represent hierarchical systems; when their interfaces are simple, these supply canonical comonoid structures....
We introduce the concepts of Bayesian lens, characterizing bidirectional structure exact inference, and statistical game, formalizing optimization objectives approximate inference problems. prove that inversions compose according to compositional lens pattern, exemplify games with a number classic concepts, from maximum likelihood estimation generalized variational methods. This paper is first in series laying foundations for account theory active we therefore pay particular attention...
In probabilistic modelling, joint distributions are often of more interest than their marginals, but the standard composition stochastic channels is defined by marginalization. Recently, notion 'copy-composition' was introduced in order to circumvent this problem and express chain rule relative entropy fibrationally, while that goal achieved, copy-composition lacked a satisfactory origin story. Here, we supply such story for two tools: directed undirected graphical models. We explain...
We introduce structured active inference, a large generalization and formalization of inference using the tools categorical systems theory. cast generative models formally as "on an interface", with latter being compositional abstraction usual notion Markov blanket; agents are then 'controllers' for their models, dual to them. This opens landscape new horizons, such as: interfaces (e.g. 'mode-dependence', or that interact computer APIs); can manage other agents; 'meta-agents', use change...
In this paper, we unite concepts from Husserlian phenomenology, the active inference framework in theoretical biology, and category theory mathematics to develop a comprehensive for understanding social action premised on shared goals. We begin with an overview of focusing aspects inner time consciousness, namely, retention, primal impression, protention. then review as formal approach modeling agent behavior, based variational (approximate Bayesian) inference. Expanding upon Husserl’s model...
We define a categorical notion of cybernetic system as dynamical realisation generalized open game, along with coherence condition. show that this captures wide class systems in computational neuroscience and statistical machine learning, exposes their compositional structure, gives an abstract justification for the bidirectional structure empirically observed cortical circuits. Our construction is built on observation Bayesian updates compose optically, fact which we prove way, via fibred...
We present categories of open dynamical systems with general time evolution as coalgebras opindexed by polynomial interfaces, and show how this extends the coalgebraic framework to capture common scientific applications such ordinary differential equations, Markov processes, random systems. then extend Spivak's operad Org setting, construct associated monoidal whose morphisms represent hierarchical systems; when their interfaces are simple, these supply canonical comonoid structures....
We extend our earlier work on the compositional structure of cybernetic systems in order to account for embodiment such systems. All their interactions proceed through bodies' boundaries: sensations impinge surfaces, and actions correspond changes configurations. formalize this morphological perspective using polynomial functors. The 'internal universes' are shown constitute an indexed category statistical games over polynomials; dynamics form behaviours. characterize 'active inference...
Place and head-direction (HD) cells are fundamental to maintaining accurate representations of location heading in the mammalian brain across sensory conditions, thought underlie path integration-the ability maintain an representation during motion dark. Substantial evidence suggests that both populations spatial function as attractor networks, but their developmental mechanisms poorly understood. We present simulations a fully self-organizing network model this process using...
We characterize a number of well known systems approximate inference as loss models: lax sections 2-fibrations statistical games, constructed by attaching internally-defined functions to Bayesian lenses. Our examples include the relative entropy, which constitutes strict section, and whose chain rule is formalized horizontal composition 2-fibration. In order capture this compositional structure, we first introduce notion 'copy-composition', alongside corresponding bicategories through...
State-of-the art machine learning systems typically depend on energetically costly gradient-descent over a curated task-specific data set. Despite their successes, these methods are not well suited to building fully autonomous such as may employ energy-efficient accelerators targeted by OpenCL. By contrast, the brain uses low-energy local rules discover causal structure of an environment, forming semantically rich representations without supervision, and therefore exhibiting required...
Despite ample evidence that our concepts, cognitive architecture, and mathematics itself are all deeply compositional, few models take advantage of this structure. We therefore propose a radically compositional approach to computational neuroscience, drawing on the methods applied category theory. describe how these tools grant us means overcome complexity improve interpretability, supply rigorous common language for scientific modelling, analogous type theories computer science. As case...