Overview
Information topography is the geometry of how information flows through a complex system. These Part III / MPhil projects develop the mathematical foundations of that geometry — from Fisher conductance and open inaccessible games to geometries of agency and good-regulator conditions — with L172 IEI as the shared prerequisite. Related group programme: Information Topography.
Prerequisite
L172 Information, Energy and Intelligence (IEI), or equivalent preparation in information theory, maximum entropy, and information geometry.
Projects in this theme
Fisher Conductance as a Predictive Information Topography
Supervisor: Neil D. Lawrence
Prerequisite: L172 Information, Energy and Intelligence (IEI), or equivalent preparation in information theory, maximum entropy, and information geometry.
Information theory characterises what can be transmitted through a channel, but does not explain how communication structure arises. The inaccessible game (Lawrence, 2025) derives a dynamical system from information-theoretic axioms in which the Fisher information matrix acts as a state-dependent conductance tensor — an information topography. Existing demonstrations from the inaccessible game are largely descriptive: GENERIC-like structure appears, bottlenecks can be visualised. This project asks the sharper question required for a generative theory: does the conductance geometry predict where bottlenecks form and how the topography reorganises under controlled interventions? The project builds on the open-source companion library tig-code and on the classical equivalence between steepest entropy ascent and GENERIC dissipation (Montefusco, Consonni and Beretta, 2015). Success means pre-registered predictions from the Fisher geometry that outperform naive baselines.
Opening the Inaccessible Game without External Adjudication
Supervisor: Neil D. Lawrence
Prerequisite: L172 Information, Energy and Intelligence (IEI), or equivalent preparation in information theory, maximum entropy, and information geometry.
The inaccessible game is deliberately closed and agent-free: marginal entropy conservation $\sum_i h_i = C$ and maximum-entropy production generate an information topography without pre-specified channels. Real organisations and agentic systems are open — they exchange information with an environment. Recent work on steepest entropy ascent in composite systems (Ray and Beretta, 2025) shows how hard it is to open a thermodynamically consistent dynamics without violating no-signaling or smuggling in an external referee. This project asks whether the inaccessible game can be opened in a way that remains internally adjudicable, preserves (a suitable generalisation of) conservation structure, and still produces a reorganising topography under changing external information demand. A rigorous negative result — characterising an obstruction — is an acceptable and publishable outcome.
