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Researcher profile

Lancelot Da Costa

Lancelot Da Costa contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Artificial IntelligenceMachine LearningNeurons and Cognitionmath.OCmath.STStatistics Theorycond-mat.stat-mechmath.DGmath.PRnlin.AO

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Published work

9 published item(s)

preprint2026arXiv

Learning POMDP World Models from Observations with Language-Model Priors

Whether navigating a building, operating a robot, or playing a game, an agent that acts effectively in an environment must first learn an internal model of how that environment works. Partially-observable Markov decision processes (POMDPs) provide a flexible modeling class for such internal world models, but learning them from observation-action trajectories alone is challenging and typically requires extensive environment interaction. We ask whether language-model priors can reduce costly interaction by leveraging prior knowledge, and introduce \emph{Pinductor} (POMDP-inductor): an LLM proposes candidate POMDP models from a few observation-action trajectories and iteratively refines them to optimize a belief-based likelihood score. Despite using strictly less information, \emph{Pinductor} matches the performance and sample efficiency of LLM-based POMDP learning methods that assume privileged access to the hidden state, while significantly surpassing the sample efficiency of tabular POMDP baselines. Further results show that performance scales with LLM capability and degrades gracefully as semantic information about the environment is withheld. Together, these results position language-model priors as a practical tool for sample-efficient world-model learning under partial observability, and a step toward generalist agents in real-world environments. Code is available at https://github.com/atomresearch/pinductor.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Sample Path Regularity of Gaussian Processes from the Covariance Kernel

Gaussian processes (GPs) are the most common formalism for defining probability distributions over spaces of functions. While applications of GPs are myriad, a comprehensive understanding of GP sample paths, i.e. the function spaces over which they define a probability measure, is lacking. In practice, GPs are not constructed through a probability measure, but instead through a mean function and a covariance kernel. In this paper we provide necessary and sufficient conditions on the covariance kernel for the sample paths of the corresponding GP to attain a given regularity. We focus primarily on Hölder regularity as it grants particularly straightforward conditions, which simplify further in the cases of stationary and isotropic GPs. We then demonstrate that our results allow for novel and unusually tight characterisations of the sample path regularities of the GPs commonly used in machine learning applications, such as the Matérn GPs.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Branching Time Active Inference: the theory and its generality

Over the last 10 to 15 years, active inference has helped to explain various brain mechanisms from habit formation to dopaminergic discharge and even modelling curiosity. However, the current implementations suffer from an exponential (space and time) complexity class when computing the prior over all the possible policies up to the time-horizon. Fountas et al (2020) used Monte Carlo tree search to address this problem, leading to impressive results in two different tasks. In this paper, we present an alternative framework that aims to unify tree search and active inference by casting planning as a structure learning problem. Two tree search algorithms are then presented. The first propagates the expected free energy forward in time (i.e., towards the leaves), while the second propagates it backward (i.e., towards the root). Then, we demonstrate that forward and backward propagations are related to active inference and sophisticated inference, respectively, thereby clarifying the differences between those two planning strategies.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents

In this chapter, we identify fundamental geometric structures that underlie the problems of sampling, optimisation, inference and adaptive decision-making. Based on this identification, we derive algorithms that exploit these geometric structures to solve these problems efficiently. We show that a wide range of geometric theories emerge naturally in these fields, ranging from measure-preserving processes, information divergences, Poisson geometry, and geometric integration. Specifically, we explain how (i) leveraging the symplectic geometry of Hamiltonian systems enable us to construct (accelerated) sampling and optimisation methods, (ii) the theory of Hilbertian subspaces and Stein operators provides a general methodology to obtain robust estimators, (iii) preserving the information geometry of decision-making yields adaptive agents that perform active inference. Throughout, we emphasise the rich connections between these fields; e.g., inference draws on sampling and optimisation, and adaptive decision-making assesses decisions by inferring their counterfactual consequences. Our exposition provides a conceptual overview of underlying ideas, rather than a technical discussion, which can be found in the references herein.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Modelling non-reinforced preferences using selective attention

How can artificial agents learn non-reinforced preferences to continuously adapt their behaviour to a changing environment? We decompose this question into two challenges: ($i$) encoding diverse memories and ($ii$) selectively attending to these for preference formation. Our proposed \emph{no}n-\emph{re}inforced preference learning mechanism using selective attention, \textsc{Nore}, addresses both by leveraging the agent's world model to collect a diverse set of experiences which are interleaved with imagined roll-outs to encode memories. These memories are selectively attended to, using attention and gating blocks, to update agent's preferences. We validate \textsc{Nore} in a modified OpenAI Gym FrozenLake environment (without any external signal) with and without volatility under a fixed model of the environment -- and compare its behaviour to \textsc{Pepper}, a Hebbian preference learning mechanism. We demonstrate that \textsc{Nore} provides a straightforward framework to induce exploratory preferences in the absence of external signals.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Reward Maximisation through Discrete Active Inference

Active inference is a probabilistic framework for modelling the behaviour of biological and artificial agents, which derives from the principle of minimising free energy. In recent years, this framework has successfully been applied to a variety of situations where the goal was to maximise reward, offering comparable and sometimes superior performance to alternative approaches. In this paper, we clarify the connection between reward maximisation and active inference by demonstrating how and when active inference agents perform actions that are optimal for maximising reward. Precisely, we show the conditions under which active inference produces the optimal solution to the Bellman equation--a formulation that underlies several approaches to model-based reinforcement learning and control. On partially observed Markov decision processes, the standard active inference scheme can produce Bellman optimal actions for planning horizons of 1, but not beyond. In contrast, a recently developed recursive active inference scheme (sophisticated inference) can produce Bellman optimal actions on any finite temporal horizon. We append the analysis with a discussion of the broader relationship between active inference and reinforcement learning.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Sparse coupling and Markov blankets: A comment on "How particular is the physics of the Free Energy Principle?" by Aguilera, Millidge, Tschantz and Buckley

In this commentary, we respond to a technical analysis of the Free Energy Principle (hereafter: FEP) presented in "How particular is the physics of the Free Energy Principle" by Aguilera et al. In the target article, the authors analyzed certain sparsely coupled stochastic differential equations whose non-equilibrium steady-state densities are claimed--in previous FEP literature--to have a Markov blanket. The authors demonstrate that in general, Markov blankets are not guaranteed to follow from sparse coupling. The current commentary explains the relationship between sparse coupling and Markov blankets in the case of Gaussian steady-state densities. We precisely derive conditions under which causal coupling leads--or does not lead--to Markov blankets. Importantly, our derivations hold for both linear and non-linear stochastic differential equations. This result may shed light on the sorts of systems which we expect to have Markov blankets. Future work should focus on verifying whether these sorts of constraints are satisfied in realistic models of sparsely coupled systems.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Active inference on discrete state-spaces: a synthesis

Active inference is a normative principle underwriting perception, action, planning, decision-making and learning in biological or artificial agents. From its inception, its associated process theory has grown to incorporate complex generative models, enabling simulation of a wide range of complex behaviours. Due to successive developments in active inference, it is often difficult to see how its underlying principle relates to process theories and practical implementation. In this paper, we try to bridge this gap by providing a complete mathematical synthesis of active inference on discrete state-space models. This technical summary provides an overview of the theory, derives neuronal dynamics from first principles and relates this dynamics to biological processes. Furthermore, this paper provides a fundamental building block needed to understand active inference for mixed generative models; allowing continuous sensations to inform discrete representations. This paper may be used as follows: to guide research towards outstanding challenges, a practical guide on how to implement active inference to simulate experimental behaviour, or a pointer towards various in-silico neurophysiological responses that may be used to make empirical predictions.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Sophisticated Inference

Active inference offers a first principle account of sentient behaviour, from which special and important cases can be derived, e.g., reinforcement learning, active learning, Bayes optimal inference, Bayes optimal design, etc. Active inference resolves the exploitation-exploration dilemma in relation to prior preferences, by placing information gain on the same footing as reward or value. In brief, active inference replaces value functions with functionals of (Bayesian) beliefs, in the form of an expected (variational) free energy. In this paper, we consider a sophisticated kind of active inference, using a recursive form of expected free energy. Sophistication describes the degree to which an agent has beliefs about beliefs. We consider agents with beliefs about the counterfactual consequences of action for states of affairs and beliefs about those latent states. In other words, we move from simply considering beliefs about 'what would happen if I did that' to 'what would I believe about what would happen if I did that'. The recursive form of the free energy functional effectively implements a deep tree search over actions and outcomes in the future. Crucially, this search is over sequences of belief states, as opposed to states per se. We illustrate the competence of this scheme, using numerical simulations of deep decision problems.

0 citations0 reviewsNo code linkedOpen access