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Noor Sajid

Publications and source records attributed to Noor Sajid.

At least 19 recordsLinked to original sources
arXiv2025

Dissociating model architectures from inference computations

Parr et al., 2025 examines how auto-regressive and deep temporal models differ in their treatment of non-Markovian sequence modelling. Building on this, we highlight the need for dissociating model architectures, i.e., how the predictive distribution factorises, from the computations invoked at inference. We demonstrate that deep temporal computations are mimicked by autoregressive models by structuring context access during iterative inference. Using a transformer trained on next-token prediction, we show that inducing hierarchical temporal factorisation during iterative inference maintains predictive capacity while instantiating fewer computations. This emphasises that processes for constructing and refining predictions are not necessarily bound to their underlying model architectures.

q-bio.NC↗
arXiv2025

Model alignment using inter-modal bridges

Foundation models have demonstrated remarkable performance across modalities such as language and vision. However, model reuse across distinct modalities (e.g., text and vision) remains limited due to the difficulty of aligning internal representations. Existing methods require extensive paired training data or are constrained to specific domains. We introduce a semi-supervised approach for model alignment via conditional flow matching. The conditional flow between latent spaces of different modalities (e.g., text-to-image or biological-to-artificial neuronal activity) can be learned in two settings: ($1$) solving a (balanced or unbalanced) optimal transport problem with an inter-space bridge cost, and ($2$) performing memory-efficient alignment using labelled exemplars. Despite being constrained by the original models' capacity, our method--under both settings--matches downstream task performance of end-to-end trained models on object recognition and image generation tasks across MNIST, ImageNet, and \cite{majaj2015simple} datasets, particularly when labelled training data is scarce ($<20\%$). Our method provides a data-efficient solution for inter-modal model alignment with minimal supervision.

cs.LG↗
arXiv2024

A broken duet: multistable dynamics of dyadic interactions

Misunderstandings in dyadic interactions often persist despite our best efforts, particularly between native and non-native speakers, resembling a broken duet that refuses to harmonise. This paper delves into the computational mechanisms underpinning these misunderstandings through the lens of the broken Lorenz system -- a continuous dynamical model. By manipulating a specific parameter regime, we induce bistability within the Lorenz equations, thereby confining trajectories to distinct attractors based on initial conditions. This mirrors the persistence of divergent interpretations that often result in misunderstandings. Our simulations reveal that differing prior beliefs between interlocutors result in misaligned generative models, leading to stable yet divergent states of understanding when exposed to the same percept. Specifically, native speakers equipped with precise (i.e., overconfident) priors expect inputs to align closely with their internal models, thus struggling with unexpected variations. Conversely, non-native speakers with imprecise (i.e., less confident) priors exhibit a greater capacity to adjust and accommodate unforeseen inputs. Our results underscore the important role of generative models in facilitating mutual understanding (i.e., establishing a shared narrative) and highlight the necessity of accounting for multistable dynamics in dyadic interactions.

q-bio.NC↗
arXiv2024

Active Inference as a Model of Agency

Is there a canonical way to think of agency beyond reward maximisation? In this paper, we show that any type of behaviour complying with physically sound assumptions about how macroscopic biological agents interact with the world canonically integrates exploration and exploitation in the sense of minimising risk and ambiguity about states of the world. This description, known as active inference, refines the free energy principle, a popular descriptive framework for action and perception originating in neuroscience. Active inference provides a normative Bayesian framework to simulate and model agency that is widely used in behavioural neuroscience, reinforcement learning (RL) and robotics. The usefulness of active inference for RL is three-fold. \emph{a}) Active inference provides a principled solution to the exploration-exploitation dilemma that usefully simulates biological agency. \emph{b}) It provides an explainable recipe to simulate behaviour, whence behaviour follows as an explainable mixture of exploration and exploitation under a generative world model, and all differences in behaviour are explicit in differences in world model. \emph{c}) This framework is universal in the sense that it is theoretically possible to rewrite any RL algorithm conforming to the descriptive assumptions of active inference as an active inference algorithm. Thus, active inference can be used as a tool to uncover and compare the commitments and assumptions of more specific models of agency.

cs.AI↗
arXiv2023

Supervised structure learning

This paper concerns structure learning or discovery of discrete generative models. It focuses on Bayesian model selection and the assimilation of training data or content, with a special emphasis on the order in which data are ingested. A key move - in the ensuing schemes - is to place priors on the selection of models, based upon expected free energy. In this setting, expected free energy reduces to a constrained mutual information, where the constraints inherit from priors over outcomes (i.e., preferred outcomes). The resulting scheme is first used to perform image classification on the MNIST dataset to illustrate the basic idea, and then tested on a more challenging problem of discovering models with dynamics, using a simple sprite-based visual disentanglement paradigm and the Tower of Hanoi (cf., blocks world) problem. In these examples, generative models are constructed autodidactically to recover (i.e., disentangle) the factorial structure of latent states - and their characteristic paths or dynamics.

cs.LG↗
arXiv2023

Hierarchical generative modelling for autonomous robots

Humans can produce complex whole-body motions when interacting with their surroundings, by planning, executing and combining individual limb movements. We investigated this fundamental aspect of motor control in the setting of autonomous robotic operations. We approach this problem by hierarchical generative modelling equipped with multi-level planning-for autonomous task completion-that mimics the deep temporal architecture of human motor control. Here, temporal depth refers to the nested time scales at which successive levels of a forward or generative model unfold, for example, delivering an object requires a global plan to contextualise the fast coordination of multiple local movements of limbs. This separation of temporal scales also motivates robotics and control. Specifically, to achieve versatile sensorimotor control, it is advantageous to hierarchically structure the planning and low-level motor control of individual limbs. We use numerical and physical simulation to conduct experiments and to establish the efficacy of this formulation. Using a hierarchical generative model, we show how a humanoid robot can autonomously complete a complex task that necessitates a holistic use of locomotion, manipulation, and grasping. Specifically, we demonstrate the ability of a humanoid robot that can retrieve and transport a box, open and walk through a door to reach the destination, approach and kick a football, while showing robust performance in presence of body damage and ground irregularities. Our findings demonstrated the effectiveness of using human-inspired motor control algorithms, and our method provides a viable hierarchical architecture for the autonomous completion of challenging goal-directed tasks.

cs.RO↗
arXiv2023

On efficient computation in active inference

Despite being recognized as neurobiologically plausible, active inference faces difficulties when employed to simulate intelligent behaviour in complex environments due to its computational cost and the difficulty of specifying an appropriate target distribution for the agent. This paper introduces two solutions that work in concert to address these limitations. First, we present a novel planning algorithm for finite temporal horizons with drastically lower computational complexity. Second, inspired by Z-learning from control theory literature, we simplify the process of setting an appropriate target distribution for new and existing active inference planning schemes. Our first approach leverages the dynamic programming algorithm, known for its computational efficiency, to minimize the cost function used in planning through the Bellman-optimality principle. Accordingly, our algorithm recursively assesses the expected free energy of actions in the reverse temporal order. This improves computational efficiency by orders of magnitude and allows precise model learning and planning, even under uncertain conditions. Our method simplifies the planning process and shows meaningful behaviour even when specifying only the agent's final goal state. The proposed solutions make defining a target distribution from a goal state straightforward compared to the more complicated task of defining a temporally informed target distribution. The effectiveness of these methods is tested and demonstrated through simulations in standard grid-world tasks. These advances create new opportunities for various applications.

cs.LG↗
arXiv2023

The free energy principle made simpler but not too simple

This paper provides a concise description of the free energy principle, starting from a formulation of random dynamical systems in terms of a Langevin equation and ending with a Bayesian mechanics that can be read as a physics of sentience. It rehearses the key steps using standard results from statistical physics. These steps entail (i) establishing a particular partition of states based upon conditional independencies that inherit from sparsely coupled dynamics, (ii) unpacking the implications of this partition in terms of Bayesian inference and (iii) describing the paths of particular states with a variational principle of least action. Teleologically, the free energy principle offers a normative account of self-organisation in terms of optimal Bayesian design and decision-making, in the sense of maximising marginal likelihood or Bayesian model evidence. In summary, starting from a description of the world in terms of random dynamical systems, we end up with a description of self-organisation as sentient behaviour that can be interpreted as self-evidencing; namely, self-assembly, autopoiesis or active inference.

cond-mat.stat-mech↗
arXiv2022

Bistable perception, precision and neuromodulation

Bistable perception follows from observing a static, ambiguous, (visual) stimulus with two possible interpretations. Here, we present an active (Bayesian) inference account of bistable perception and posit that perceptual transitions between different interpretations (i.e., inferences) of the same stimulus ensue from specific eye movements that shift the focus to a different visual feature. Formally, these inferences are a consequence of precision control that determines how confident beliefs are and change the frequency with which one can perceive - and alternate between - two distinct percepts. We hypothesised that there are multiple, but distinct, ways in which precision modulation can interact to give rise to a similar frequency of bistable perception. We validated this using numerical simulations of the Necker's cube paradigm and demonstrate the multiple routes that underwrite the frequency of perceptual alternation. Our results provide an (enactive) computational account of the intricate precision balance underwriting bistable perception. Importantly, these precision parameters can be considered the computational homologues of particular neurotransmitters - i.e., acetylcholine, noradrenaline, dopamine - that have been previously implicated in controlling bistable perception, providing a computational link between the neurochemistry and perception.

q-bio.NC↗
arXiv2022

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.

cs.LG↗
arXiv2022

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.

cs.AI↗
arXiv2022

Reclaiming saliency: rhythmic precision-modulated action and perception

Computational models of visual attention in artificial intelligence and robotics have been inspired by the concept of a saliency map. These models account for the mutual information between the (current) visual information and its estimated causes. However, they fail to consider the circular causality between perception and action. In other words, they do not consider where to sample next, given current beliefs. Here, we reclaim salience as an active inference process that relies on two basic principles: uncertainty minimisation and rhythmic scheduling. For this, we make a distinction between attention and salience. Briefly, we associate attention with precision control, i.e., the confidence with which beliefs can be updated given sampled sensory data, and salience with uncertainty minimisation that underwrites the selection of future sensory data. Using this, we propose a new account of attention based on rhythmic precision-modulation and discuss its potential in robotics, providing numerical experiments that showcase advantages of precision-modulation for state and noise estimation, system identification and action selection for informative path planning.

cs.RO↗
arXiv2021

Active inference, Bayesian optimal design, and expected utility

Active inference, a corollary of the free energy principle, is a formal way of describing the behavior of certain kinds of random dynamical systems that have the appearance of sentience. In this chapter, we describe how active inference combines Bayesian decision theory and optimal Bayesian design principles under a single imperative to minimize expected free energy. It is this aspect of active inference that allows for the natural emergence of information-seeking behavior. When removing prior outcomes preferences from expected free energy, active inference reduces to optimal Bayesian design, i.e., information gain maximization. Conversely, active inference reduces to Bayesian decision theory in the absence of ambiguity and relative risk, i.e., expected utility maximization. Using these limiting cases, we illustrate how behaviors differ when agents select actions that optimize expected utility, expected information gain, and expected free energy. Our T-maze simulations show optimizing expected free energy produces goal-directed information-seeking behavior while optimizing expected utility induces purely exploitive behavior and maximizing information gain engenders intrinsically motivated behavior.

stat.ML↗
arXiv2021

Active Inference for Stochastic Control

Active inference has emerged as an alternative approach to control problems given its intuitive (probabilistic) formalism. However, despite its theoretical utility, computational implementations have largely been restricted to low-dimensional, deterministic settings. This paper highlights that this is a consequence of the inability to adequately model stochastic transition dynamics, particularly when an extensive policy (i.e., action trajectory) space must be evaluated during planning. Fortunately, recent advancements propose a modified planning algorithm for finite temporal horizons. We build upon this work to assess the utility of active inference for a stochastic control setting. For this, we simulate the classic windy grid-world task with additional complexities, namely: 1) environment stochasticity; 2) learning of transition dynamics; and 3) partial observability. Our results demonstrate the advantage of using active inference, compared to reinforcement learning, in both deterministic and stochastic settings.

cs.LG↗
arXiv2021

Exploration and preference satisfaction trade-off in reward-free learning

Biological agents have meaningful interactions with their environment despite the absence of immediate reward signals. In such instances, the agent can learn preferred modes of behaviour that lead to predictable states -- necessary for survival. In this paper, we pursue the notion that this learnt behaviour can be a consequence of reward-free preference learning that ensures an appropriate trade-off between exploration and preference satisfaction. For this, we introduce a model-based Bayesian agent equipped with a preference learning mechanism (pepper) using conjugate priors. These conjugate priors are used to augment the expected free energy planner for learning preferences over states (or outcomes) across time. Importantly, our approach enables the agent to learn preferences that encourage adaptive behaviour at test time. We illustrate this in the OpenAI Gym FrozenLake and the 3D mini-world environments -- with and without volatility. Given a constant environment, these agents learn confident (i.e., precise) preferences and act to satisfy them. Conversely, in a volatile setting, perpetual preference uncertainty maintains exploratory behaviour. Our experiments suggest that learnable (reward-free) preferences entail a trade-off between exploration and preference satisfaction. Pepper offers a straightforward framework suitable for designing adaptive agents when reward functions cannot be predefined as in real environments.

cs.AI↗
arXiv2021

Bayesian brains and the Rényi divergence

Under the Bayesian brain hypothesis, behavioural variations can be attributed to different priors over generative model parameters. This provides a formal explanation for why individuals exhibit inconsistent behavioural preferences when confronted with similar choices. For example, greedy preferences are a consequence of confident (or precise) beliefs over certain outcomes. Here, we offer an alternative account of behavioural variability using Rényi divergences and their associated variational bounds. Rényi bounds are analogous to the variational free energy (or evidence lower bound) and can be derived under the same assumptions. Importantly, these bounds provide a formal way to establish behavioural differences through an $α$ parameter, given fixed priors. This rests on changes in $α$ that alter the bound (on a continuous scale), inducing different posterior estimates and consequent variations in behaviour. Thus, it looks as if individuals have different priors, and have reached different conclusions. More specifically, $α\to 0^{+}$ optimisation leads to mass-covering variational estimates and increased variability in choice behaviour. Furthermore, $α\to + \infty$ optimisation leads to mass-seeking variational posteriors and greedy preferences. We exemplify this formulation through simulations of the multi-armed bandit task. We note that these $α$ parameterisations may be especially relevant, i.e., shape preferences, when the true posterior is not in the same family of distributions as the assumed (simpler) approximate density, which may be the case in many real-world scenarios. The ensuing departure from vanilla variational inference provides a potentially useful explanation for differences in behavioural preferences of biological (or artificial) agents under the assumption that the brain performs variational Bayesian inference.

q-bio.NC↗
arXiv2020

Active inference: demystified and compared

Active inference is a first principle account of how autonomous agents operate in dynamic, non-stationary environments. This problem is also considered in reinforcement learning (RL), but limited work exists on comparing the two approaches on the same discrete-state environments. In this paper, we provide: 1) an accessible overview of the discrete-state formulation of active inference, highlighting natural behaviors in active inference that are generally engineered in RL; 2) an explicit discrete-state comparison between active inference and RL on an OpenAI gym baseline. We begin by providing a condensed overview of the active inference literature, in particular viewing the various natural behaviors of active inference agents through the lens of RL. We show that by operating in a pure belief-based setting, active inference agents can carry out epistemic exploration, and account for uncertainty about their environment in a Bayes-optimal fashion. Furthermore, we show that the reliance on an explicit reward signal in RL is removed in active inference, where reward can simply be treated as another observation; even in the total absence of rewards, agent behaviors are learned through preference learning. We make these properties explicit by showing two scenarios in which active inference agents can infer behaviors in reward-free environments compared to both Q-learning and Bayesian model-based RL agents; by placing zero prior preferences over rewards and by learning the prior preferences over the observations corresponding to reward. We conclude by noting that this formalism can be applied to more complex settings if appropriate generative models can be formulated. In short, we aim to demystify the behavior of active inference agents by presenting an accessible discrete state-space and time formulation, and demonstrate these behaviors in a OpenAI gym environment, alongside RL agents.

cs.AI↗
arXiv2020

Deep active inference agents using Monte-Carlo methods

Active inference is a Bayesian framework for understanding biological intelligence. The underlying theory brings together perception and action under one single imperative: minimizing free energy. However, despite its theoretical utility in explaining intelligence, computational implementations have been restricted to low-dimensional and idealized situations. In this paper, we present a neural architecture for building deep active inference agents operating in complex, continuous state-spaces using multiple forms of Monte-Carlo (MC) sampling. For this, we introduce a number of techniques, novel to active inference. These include: i) selecting free-energy-optimal policies via MC tree search, ii) approximating this optimal policy distribution via a feed-forward `habitual' network, iii) predicting future parameter belief updates using MC dropouts and, finally, iv) optimizing state transition precision (a high-end form of attention). Our approach enables agents to learn environmental dynamics efficiently, while maintaining task performance, in relation to reward-based counterparts. We illustrate this in a new toy environment, based on the dSprites data-set, and demonstrate that active inference agents automatically create disentangled representations that are apt for modeling state transitions. In a more complex Animal-AI environment, our agents (using the same neural architecture) are able to simulate future state transitions and actions (i.e., plan), to evince reward-directed navigation - despite temporary suspension of visual input. These results show that deep active inference - equipped with MC methods - provides a flexible framework to develop biologically-inspired intelligent agents, with applications in both machine learning and cognitive science.

q-bio.NC↗