Noor Sajid
London School of Economics and Political Science, Government, Graduate Student
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... more
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...
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Recent advances in neuroscience have characterised brain function using mathematical formalisms and first principles that may be usefully applied elsewhere. In this paper, we explain how active inference—a well-known description of... more
Recent advances in neuroscience have characterised brain function using mathematical formalisms and first principles that may be usefully applied elsewhere. In this paper, we explain how active inference—a well-known description of sentient behaviour from neuroscience—can be exploited in robotics. In short, active inference leverages the processes thought to underwrite human behaviour to build effective autonomous systems. These systems show state-of-the-art performance in several robotics settings; we highlight these and explain how this framework may be used to advance robotics.
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Under the Bayesian brain hypothesis, behavioral variations can be attributed to different priors over generative model parameters. This provides a formal explanation for why individuals exhibit inconsistent behavioral preferences when... more
Under the Bayesian brain hypothesis, behavioral variations can be attributed to different priors over generative model parameters. This provides a formal explanation for why individuals exhibit inconsistent behavioral 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 behavioral 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 behavioral 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 behavior. Thus, it looks as if individuals have different priors and have reached different co...
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Biological agents have meaningful interactions with their environment despite the absence of a reward signal. In such instances, the agent can learn preferred modes of behaviour that lead to predictable states -- necessary for survival.... more
Biological agents have meaningful interactions with their environment despite the absence of a reward signal. 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 confid...
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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... more
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 environmenta...
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Active inference is a first (Bayesian) principles account of how autonomous agents might operate in dynamic, non-stationary environments. The optimization of congruent formulations of the free energy functional (variational and expected),... more
Active inference is a first (Bayesian) principles account of how autonomous agents might operate in dynamic, non-stationary environments. The optimization of congruent formulations of the free energy functional (variational and expected), in active inference, enables agents to make inferences about the environment and select optimal behaviors. The agent achieves this by evaluating (sensory) evidence in relation to its internal generative model that entails beliefs about future (hidden) states and sequence of actions that it can choose. In contrast to analogous frameworks $-$ by operating in a pure belief-based setting (free energy functional of beliefs about states) $-$ active inference agents can carry out epistemic exploration and naturally account for uncertainty about their environment. Through this review, we disambiguate these properties, by providing a condensed overview of the theory underpinning active inference. A T-maze simulation is used to demonstrate how these behavior...
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Biological forms depend on a progressive specialization of pluripotent stem cells. The differentiation of these cells in their spatial and functional environment defines the organism itself; however, cellular mutations may disrupt the... more
Biological forms depend on a progressive specialization of pluripotent stem cells. The differentiation of these cells in their spatial and functional environment defines the organism itself; however, cellular mutations may disrupt the mutual balance between a cell and its niche, where cell proliferation and specialization are released from their autopoietic homeostasis. This induces the construction of cancer niches and maintains their survival. In this paper, we characterise cancer niche construction as a direct consequence of interactions between clusters of cancer and healthy cells. Explicitly, we evaluate these higher-order interactions between niches of cancer and healthy cells using Kikuchi approximations to the free energy. Kikuchi’s free energy is measured in terms of changes to the sum of energies of baseline clusters of cells (or nodes) minus the energies of overcounted cluster intersections (and interactions of interactions, etc.). We posit that these changes in energy no...
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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... more
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, Pepper 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 confi...
Research Interests:
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... more
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 environmenta...
Research Interests:
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... more
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 optimizi...
One third of stroke survivors have language difficulties. Emerging evidence suggests that their likelihood of recovery depends mainly on the damage to language centers. Thus previous research for predicting language recovery post-stroke... more
One third of stroke survivors have language difficulties. Emerging evidence suggests that their likelihood of recovery depends mainly on the damage to language centers. Thus previous research for predicting language recovery post-stroke has focused on identifying damaged regions of the brain. In this paper, we introduce a novel method where we only make use of stitched 2-dimensional cross-sections of raw MRI scans in a deep convolutional neural network setup to predict language recovery post-stroke. Our results show: a) the proposed model that only uses MRI scans has comparable performance to models that are dependent on lesion specific information; b) the features learned by our model are complementary to the lesion specific information and the combination of both appear to outperform previously reported results in similar settings. We further analyse the CNN model for understanding regions in brain that are responsible for arriving at these predictions using gradient based salienc...
Active inference is a normative framework for generating behaviour based upon the free energy principle, a theory of self-organisation. This framework has been successfully used to solve reinforcement learning and stochastic control... more
Active inference is a normative framework for generating behaviour based upon the free energy principle, a theory of self-organisation. This framework has been successfully used to solve reinforcement learning and stochastic control problems, yet, the formal relation between active inference and reward maximisation has not been fully explicated. In this paper, we consider the relation between active inference and dynamic programming under the Bellman equation, which underlies many approaches to reinforcement learning and control. We show that, on partially observable Markov decision processes, dynamic programming is a limiting case of active inference. In active inference, agents select actions to minimise expected free energy. In the absence of ambiguity about states, this reduces to matching expected states with a target distribution encoding the agent's preferences. When target states correspond to rewarding states, this maximises expected reward, as in reinforcement learning...
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Humans can produce complex movements when interacting with their surroundings. This relies on the planning of various movements and subsequent execution. In this paper, we investigated this fundamental aspect of motor control in the... more
Humans can produce complex movements when interacting with their surroundings. This relies on the planning of various movements and subsequent execution. In this paper, we investigated this fundamental aspect of motor control in the setting of autonomous robotic operations. We consider hierarchical generative modelling—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, the apprehension and delivery of an object requires both a global plan that contextualises the fast coordination of multiple local limb movements. This separation of temporal scales can also be motivated from a robotics and control perspective. Specifically, to ensure versatile sensorimotor control, it is necessary to hierarchically structure high-level planning and low-level motor control of individual limbs. We use numerical experiments ...
Paradoxical lesions are secondary brain lesions that ameliorate functional deficits caused by the initial insult. This effect has been explained in several ways; particularly by the reduction of functional inhibition, or by increases in... more
Paradoxical lesions are secondary brain lesions that ameliorate functional deficits caused by the initial insult. This effect has been explained in several ways; particularly by the reduction of functional inhibition, or by increases in the excitatory-to-inhibitory synaptic balance within perilesional tissue. In this article, we simulate how and when a modification of the excitatory–inhibitory balance triggers the reversal of a functional deficit caused by a primary lesion. For this, we introduce in-silico lesions to an active inference model of auditory word repetition. The first in-silico lesion simulated damage to the extrinsic (between regions) connectivity causing a functional deficit that did not fully resolve over 100 trials of a word repetition task. The second lesion was implemented in the intrinsic (within region) connectivity, compromising the model’s ability to rebalance excitatory–inhibitory connections during learning. We found that when the second lesion was mild, the...
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The active visual system comprises the visual cortices, cerebral attention networks, and oculomotor system. While fascinating in its own right, it is also an important model for sensorimotor networks in general. A prominent approach to... more
The active visual system comprises the visual cortices, cerebral attention networks, and oculomotor system. While fascinating in its own right, it is also an important model for sensorimotor networks in general. A prominent approach to studying this system is active inference—which assumes the brain makes use of an internal (generative) model to predict proprioceptive and visual input. This approach treats action as ensuring sensations conform to predictions (i.e., by moving the eyes) and posits that visual percepts are the consequence of updating predictions to conform to sensations. Under active inference, the challenge is to identify the form of the generative model that makes these predictions—and thus directs behavior. In this paper, we provide an overview of the generative models that the brain must employ to engage in active vision. This means specifying the processes that explain retinal cell activity and proprioceptive information from oculomotor muscle fibers. In addition ...
Active inference is a first principle account of how autonomous agents operate in dynamic, nonstationary environments. This problem is also considered in reinforcement learning, but limited work exists on comparing the two approaches on... more
Active inference is a first principle account of how autonomous agents operate in dynamic, nonstationary environments. This problem is also considered in reinforcement learning, but limited work exists on comparing the two approaches on the same discrete-state environments. In this letter, 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 reinforcement learning, and (2) an explicit discrete-state comparison between active inference and reinforcement learning 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 reinforcement learning. 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 Bay...
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The segregation of neural processing into distinct streams has been interpreted by some as evidence in favour of a modular view of brain function. This implies a set of specialised ‘modules’, each of which performs a specific kind of... more
The segregation of neural processing into distinct streams has been interpreted by some as evidence in favour of a modular view of brain function. This implies a set of specialised ‘modules’, each of which performs a specific kind of computation in isolation of other brain systems, before sharing the result of this operation with other modules. In light of a modern understanding of stochastic non-equilibrium systems, like the brain, a simpler and more parsimonious explanation presents itself. Formulating the evolution of a non-equilibrium steady state system in terms of its density dynamics reveals that such systems appear on average to perform a gradient ascent on their steady state density. If this steady state implies a sufficiently sparse conditional independency structure, this endorses a mean-field dynamical formulation. This decomposes the density over all states in a system into the product of marginal probabilities for those states. This factorisation lends the system a mod...
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This paper introduces active listening, as a unified framework for synthesising and recognising speech. The notion of active listening inherits from active inference, which considers perception and action under one universal imperative:... more
This paper introduces active listening, as a unified framework for synthesising and recognising speech. The notion of active listening inherits from active inference, which considers perception and action under one universal imperative: to maximise the evidence for our (generative) models of the world. First, we describe a generative model of spoken words that simulates (i) how discrete lexical, prosodic, and speaker attributes give rise to continuous acoustic signals; and conversely (ii) how continuous acoustic signals are recognised as words. The ‘active’ aspect involves (covertly) segmenting spoken sentences and borrows ideas from active vision. It casts speech segmentation as the selection of internal actions, corresponding to the placement of word boundaries. Practically, word boundaries are selected that maximise the evidence for an internal model of how individual words are generated. We establish face validity by simulating speech recognition and showing how the inferred con...
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Understanding the aetiology of the diverse recovery patterns in bilingual aphasia is a theoretical challenge with implications for treatment. Loss of control over intact language networks provides a parsimonious starting point that can be... more
Understanding the aetiology of the diverse recovery patterns in bilingual aphasia is a theoretical challenge with implications for treatment. Loss of control over intact language networks provides a parsimonious starting point that can be tested using in-silico lesions. We simulated a complex recovery pattern (alternate antagonism and paradoxical translation) to test the hypothesis—from an established hierarchical control model—that loss of control was mediated by constraints on neuromodulatory resources. We used active (Bayesian) inference to simulate a selective loss of sensory precision; i.e., confidence in the causes of sensations. This in-silico lesion altered the precision of beliefs about task relevant states, including appropriate actions, and reproduced exactly the recovery pattern of interest. As sensory precision has been linked to acetylcholine release, these simulations endorse the conjecture that loss of neuromodulatory control can explain this atypical recovery patter...
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The notions of degeneracy and redundancy are important constructs in many areas, ranging from genomics through to network science. Degeneracy finds a powerful role in neuroscience, explaining key aspects of distributed processing and... more
The notions of degeneracy and redundancy are important constructs in many areas, ranging from genomics through to network science. Degeneracy finds a powerful role in neuroscience, explaining key aspects of distributed processing and structure–function relationships in the brain. For example, degeneracy accounts for the superadditive effect of lesions on functional deficits in terms of a “many-to-one” structure–function mapping. In this paper, we offer a principled account of degeneracy and redundancy, when function is operationalized in terms of active inference, namely, a formulation of perception and action as belief updating under generative models of the world. In brief, “degeneracy” is quantified by the “entropy” of posterior beliefs about the causes of sensations, while “redundancy” is the “complexity” cost incurred by forming those beliefs. From this perspective, degeneracy and redundancy are complementary: Active inference tries to minimize redundancy while maintaining dege...
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This paper presents a biologically plausible generative model and inference scheme that is capable of simulating the generation and comprehension of language, when synthetic subjects talk to each other. Building on active inference... more
This paper presents a biologically plausible generative model and inference scheme that is capable of simulating the generation and comprehension of language, when synthetic subjects talk to each other. Building on active inference formulations of dyadic interactions, we simulate linguistic exchange to explore generative models that support dialogues. These models employ high-order interactions among abstract (discrete) states in deep (hierarchical) models. The sequential nature of language processing mandates generative models with a particular factorial structure—necessary to accommodate the rich combinatorics of language. We illustrate this by simulating a synthetic subject who can play the ‘Twenty Questions’ game. In this game, synthetic subjects take the role of the questioner or answerer, using the same generative model. This simulation setup is used to illustrate some key architectural points and demonstrate that many behavioural and neurophysiological correlates of language ...
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Functional recovery after brain damage varies widely and depends on many factors, including lesion site and extent. When a neuronal system is damaged, recovery may occur by engaging residual (e.g., perilesional) components. When damage is... more
Functional recovery after brain damage varies widely and depends on many factors, including lesion site and extent. When a neuronal system is damaged, recovery may occur by engaging residual (e.g., perilesional) components. When damage is extensive, recovery depends on the availability of other intact neural structures that can reproduce the same functional output (i.e., degeneracy). A system’s response to damage may occur rapidly, require learning or both. Here, we simulate functional recovery from four different types of lesions, using a generative model of word repetition that comprised a default premorbid system and a less used alternative system. The synthetic lesions (i) completely disengaged the premorbid system, leaving the alternative system intact, (ii) partially damaged both premorbid and alternative systems, and (iii) limited the experience-dependent plasticity of both. The results, across 1000 trials, demonstrate that (i) a complete disconnection of the premorbid system...