Available Projects

Action-Sufficiency Audits for LLM Belief Bottlenecks

Supervisors: Neil D. Lawrence, Christian Cabrera Jojoa

Prerequisite: L172 Information, Energy and Intelligence (IEI), or equivalent preparation in information theory, maximum entropy, and information geometry.

Long-horizon LLM agents cannot keep full histories in context. Recent systems compress interaction into belief states or summaries: ABBEL maintains natural-language belief bottlenecks; CoACT optimises observation compression for next-action preservation (NAP); other work uses mutual-information rate between raw context and compression as a proxy for compressor quality (ABBEL, arXiv:2512.20111; CoACT, arXiv:2607.02911; information-theoretic agentic design, arXiv:2512.21720). Passing NAP or improving accuracy is not the same as preserving an action-sufficient representation: a summary $R = f(O)$ such that $p(y\mid o, a) = p(y\mid R, a)$ for consequences $y$ of available actions. Summaries can preserve the next click while discarding distinctions needed for later escalation — a microscopic form of agentic debt. This project builds audits that separate those failure modes.

Causal Information-Flow Instrumentation for Multi-Agent LLM Systems

Supervisors: Neil D. Lawrence, Christian Cabrera Jojoa

Prerequisite: L172 Information, Energy and Intelligence (IEI), or equivalent preparation in information theory, maximum entropy, and information geometry.

Multi-agent LLM systems are fully instrumentable: every message, tool call, and memory write can be logged. Transfer entropy and directed information are the natural language for directed flow, with recent estimators (TREET; AGM-TE) and early applications to LLM-MAS cascade monitoring. Separately, causal audits of latent channels show that end-task performance does not identify whether receivers actually use transmitted content (message permute / drop / other-example interventions). An information topography needs topographic quantities — conductance proxies, saturation, judgement-junction load — that survive causal checks. This project builds that instrumentation layer on DOAgent-quality traces and refuses to treat a TE heatmap as a result.

Escalation as Conductance Intervention — Measuring Agentic Debt

Supervisors: Neil D. Lawrence, Christian Cabrera Jojoa

Prerequisite: L172 Information, Energy and Intelligence (IEI), or equivalent preparation in information theory, maximum entropy, and information geometry.

Knowledge hierarchies escalate exceptions upward so scarce expertise handles hard cases (Garicano, 2000). Generative AI changes that calculus: automation versus augmentation shifts who faces routine work and who absorbs exceptions (recent organisation-theory models of GenAI in knowledge economies). In engineering, multi-agent systems add relays that act as information bottlenecks — helpful when they remove noise, harmful when they drop task-critical context — while governance layers such as the Organizational Control Layer (OCL) separate proposal generation from environment-facing execution. What is missing is a topographic experiment: encode escalation as a conductance constraint, measure whether the judgement junction is actually exercised, and quantify agentic debt when institutional escalation paths exist on paper but are bypassed in the realised communication graph (parallel channels, aggressive summarisation, prompt injection).

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.

Homeostatic Regulators in Multi-Agent Environments

Supervisors: Joery de Vries, Neil D. Lawrence

Prerequisite: L172 Information, Energy and Intelligence (IEI), or equivalent preparation in information theory, maximum entropy, and information geometry.

Conant and Ashby’s good regulator theorem concerns a regulator that holds an outcome steady against a disturbance. Its success criterion is the entropy of the outcome, which is different from the classical notion of reward in reinforcement learning: it is a concave objective over the occupancy polytope, so an optimal single regulator is deterministic. This project asks what happens when the disturbance is another regulator. Several agents share an environment and each minimises the entropy of its own outcome under its own reference measure. From any agent’s viewpoint the other agents are structured, adaptive disturbances. Refinements of the theorem, notably Wentworth’s, say the regulator must carry a posterior over its disturbance, thus the notion of “model” that Conant and Ashby’s theorem implies is a posterior over the other agents’ policies. We will try to answer whether this posterior is necessary, and whether the joint problem is Nash. The working hypothesis is that competing regulators partition the state space into per-agent stable niches, which remains to be verified experimentally.

Illegible Protocols under Bandwidth — The Monitorability Frontier

Supervisors: Neil D. Lawrence, Christian Cabrera Jojoa

Prerequisite: L172 Information, Energy and Intelligence (IEI), or equivalent preparation in information theory, maximum entropy, and information geometry.

Classical emergent-communication work showed agents invent efficient but opaque codes under bandwidth limits. LLM multi-agent systems inherit the risk in a new form: under token budgets they can drift from English into shorter protocols even in fully cooperative settings (e.g. GlossoGen); vision-language referential games produce covert signalling; steganography literature studies adversarial opacity. Efficiency work (AgentPrune, Agora-style protocols) reduces redundancy but rarely measures loss of human monitorability — or whether illegibility is merely displaced into tools and memory. The question here is can a communication topography predict loss of monitorable language, and can harnesses preserve judgement without killing performance?

Interface-Junction Diagnostics on Organisational Event Logs

Supervisor: Neil D. Lawrence

Prerequisite: L172 Information, Energy and Intelligence (IEI), or equivalent preparation in information theory, maximum entropy, and information geometry.

Process mining recovers process models, bottlenecks, and organisational handoff networks from event logs; recent work adds LLM assistance and BPMN extensions for human–agent collaboration. Hand-off design literature stresses confidence thresholds, accountability, and escalation rules when AI enters hybrid workflows. This project hypothesises that AI adoption outcomes follow from what deployment does to interface junctions — points where format, authority, or fidelity changes between human and machine regimes — and proposes a three-axis diagnostic (sensing, modelling, amplification capacity) grounded in the Viable System Model and the Good Regulator condition. This project makes that diagnostic computational on public event logs, with falsifiable predictions about interventions.

Interpretable Machine Learning for Intensive Care Decision Support

Supervisors: Christian Cabrera Jojoa, Neil D. Lawrence

Intensive care units (ICUs) generate vast volumes of patient data, yet clinicians often lack tools to translate this data into timely, trustworthy decisions. The aICU project, which aims to support safe, interpretable, and clinically meaningful decision-making by establishing a standardised pipeline for developing, evaluating, and deploying AI in critical care. This project proposes to reproduce existing machine learning models that address specific ICU problems (e.g., mortality prediction, sepsis detection, ventilator weaning, or length-of-stay estimation) and then investigate interpretability methods to make the model predictions understandable to clinicians.

Interpretable Multi-Agent Systems with DOAgent

Supervisors: Christian Cabrera Jojoa, Neil D. Lawrence

Multi-agent systems (MAS) and Self-Adaptive Systems (SAS) are used across robotics, resource management, and autonomous computing, yet understanding why agents make particular decisions remains an open challenge. When multiple agents interact through shared environments, the resulting behaviour is difficult to trace, attribute, and explain. DOAgent is a Python library that addresses this gap by treating shared data as the primary interface between agents, automatically recording decisions, state transitions, and contributions so that agent behaviour can be analysed after execution. This project proposes to reproduce an existing multi-agent or self-adaptive system from the literature using DOAgent, and then explore interpretability approaches on the recorded agent interactions.

Machine Learning (Bayesian Methodology, Inference and Applications)

Supervisor: Carl Henrik Ek

Students interested to work with me should come up with a grain of an idea before reaching out. If there is a match I would be happy to discuss to flesh out the details and create a project out of it. I always believed that part of doing a project is coming up with ideas and angles ripe for exploration.

I am broadly interested in probabilistic machine learning and applications in climate science.

Multi-objective optimisation of cloud infrastructure

Supervisors: Andrei Paleyes, Neil D. Lawrence

Machine learning (ML) and optimisation techniques are increasingly used to help solve decision-making problems that would be difficult or time-consuming to address manually. One such problem is the configuration of cloud infrastructure, where many deployment parameters can affect several competing objectives at the same time. This project investigates the use of multi-objective optimisation to automatically explore different cloud infrastructure configurations defined through Infrastructure-as-Code templates. Our aim will be to build a fully automated system that identifies a range of Pareto-optimal configurations that represent different trade-offs between the objectives being considered. Such a system can help reduce the time and cost required to create efficient cloud deployments while providing a better understanding of the available configuration choices.

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.

Testing Good Regulator Notions in Agentic Loops

Supervisors: Neil D. Lawrence, Christian Cabrera Jojoa

Prerequisite: L172 Information, Energy and Intelligence (IEI), or equivalent preparation in information theory, maximum entropy, and information geometry.

Conant and Ashby’s Good Regulator Theorem is often quoted as “every good regulator must be a model of the system,” but the bare result mainly yields determinism $H(A\mid S)=0$ among minimal entropy-minimising policies, this is a weak sense of “model.” Recent work strengthens or reframes the claim: Wentworth’s Gooder Regulator (information bottleneck forcing an internal posterior), Virgo et al. (2025) on observer-attributed belief updating for embodied agents, and algorithmic / internal-model principles from control theory. Parallel work on action-sufficient representations argues that a regulator need only preserve distinctions that matter for action consequences. Agentic AI systems have generated excitement, alongside them the term “world models,” is used usually without saying what definition is meant. This project builds a controllable agentic loop and tests which operational definition of “has a model” predicts out-of-distribution failure — and when a checkpoint looks like judgement but is only a frozen attenuator (agentic debt).

Three Geometries of Agency — Crooks, Wasserstein, and Schrödinger Bridges

Supervisors: Neil D. Lawrence, Christian Cabrera Jojoa

Prerequisite: L172 Information, Energy and Intelligence (IEI), or equivalent preparation in information theory, maximum entropy, and information geometry.

The IEI module treats intelligent agency as transport of probability mass and distinguishes three geometries that must not be collapsed: (1) Fisher–Rao / Crooks thermodynamic length (near-equilibrium, dissipation bounded by $\mathcal{L}^2/\tau$); (2) Wasserstein (minimum ground-cost mass transport); (3) Schrödinger bridge (maximum-entropy interpolation; discrete MaxEnt coupling via Sinkhorn). Machine learning has made Schrödinger bridges practical generative tools (Sinkhorn bridges with statistical rates; LightSB-M; SB flow for unpaired translation), usually without asking which geometry explains an agent’s belief updates under metabolic or information cost. This project treats the three geometries as competing scientific explanations of agency, not as interchangeable samplers.

What Does a Good Regulator Need to Know?

Supervisors: Joery de Vries, Neil D. Lawrence

Prerequisite: L172 Information, Energy and Intelligence (IEI), or equivalent preparation in information theory, maximum entropy, and information geometry.

Conant and Ashby’s (1970) good regulator theorem says a successful regulator must be a model of its system. Which model depends on what the regulator observes: Wentworth’s (2021) “gooder regulator” for instance requires the belief state. Since a good regulator objective minimises the entropy of a regulated outcome this adds a secondary dependence during learning due to concavity of the optimization problem. Similar to convex RL, it can be solved by a sequence of linear rewards built from the occupancy of the outcome features. Although the agent converges to a single deterministic policy, during learning its representation must support every reward in the sequence. Therefore, reusing what it learned under earlier rewards while staying focused on what the objective makes relevant is crucial. For instance, the successor features of the outcome suffice for this. Despite much work on state abstraction, self-predictive representations and sensorimotor world models, it is unclear what a good regulator needs to represent while it learns. This project investigates what acting and learning require for good regulators in the language of state abstractions of Li, Walsh and Littman (2006) and of Ni et al. (2024), and what combination of latent world-model loss delivers all aspects.

5asideCHESS Engine and Tablebase

Supervisor: Radzim Sendyka

The idea of this project is to build an Engine and Tablebase for a Cambridge-based smaller variant of the classic game. This project would be carried out in contact with Ross Smith from 5asideCHESS, an organisation focused on improving social connections. Offered to motivated students passionate about machine learning and chess.

Interpretable Machine Learning for Intensive Care Decision Support

Supervisors: Christian Cabrera Jojoa, Neil D. Lawrence

Intensive care units (ICUs) generate vast volumes of patient data, yet clinicians often lack tools to translate this data into timely, trustworthy decisions. The aICU project, which aims to support safe, interpretable, and clinically meaningful decision-making by establishing a standardised pipeline for developing, evaluating, and deploying AI in critical care. This project proposes to reproduce existing machine learning models that address specific ICU problems (e.g., mortality prediction, sepsis detection, ventilator weaning, or length-of-stay estimation) and then investigate interpretability methods to make the model predictions understandable to clinicians.

Interpretable Multi-Agent Systems with DOAgent

Supervisors: Christian Cabrera Jojoa, Neil D. Lawrence

Multi-agent systems (MAS) and Self-Adaptive Systems (SAS) are used across robotics, resource management, and autonomous computing, yet understanding why agents make particular decisions remains an open challenge. When multiple agents interact through shared environments, the resulting behaviour is difficult to trace, attribute, and explain. DOAgent is a Python library that addresses this gap by treating shared data as the primary interface between agents, automatically recording decisions, state transitions, and contributions so that agent behaviour can be analysed after execution. This project proposes to reproduce an existing multi-agent or self-adaptive system from the literature using DOAgent, and then explore interpretability approaches on the recorded agent interactions.

Machine Learning (Bayesian Methodology, Inference and Applications)

Supervisor: Carl Henrik Ek

Students interested to work with me should come up with a grain of an idea before reaching out. If there is a match I would be happy to discuss to flesh out the details and create a project out of it. I always believed that part of doing a project is coming up with ideas and angles ripe for exploration.

I am broadly interested in probabilistic machine learning and applications in climate science.