Publications

Canonical neural networks perform active inference

Abstract This work considers a class of canonical neural networks comprising rate coding models, wherein neural activity and plasticity minimise a common cost function—and plasticity is modulated with a certain delay. We show that such neural networks implicitly perform active inference and learning to minimise the risk associated with future outcomes. Mathematical analyses demonstrate that this biological optimisation can be cast as maximisation of model evidence, or equivalently minimisation of variational free energy, under the well-known form of a partially observed Markov decision process model. This equivalence indicates that the delayed modulation of Hebbian plasticity—accompanied with adaptation of firing thresholds—is a sufficient neuronal substrate to attain Bayes optimal control. We corroborated this proposition using numerical analyses of maze tasks. This theory offers a universal characterisation of canonical neural networks in terms of Bayesian belief updating and provides insight into the neuronal mechanisms underlying planning and adaptive behavioural control.

Testing and tracking in the UK: A dynamic causal modelling study

<ns7:p>By equipping a previously reported dynamic causal modelling of COVID-19 with an isolation state, we were able to model the effects of self-isolation consequent on testing and tracking. Specifically, we included a quarantine or isolation state occupied by people who believe they might be infected but are asymptomatic—and could only leave if they test negative. We recovered <ns7:italic>maximum posteriori</ns7:italic> estimates of the model parameters using time series of new cases, daily deaths, and tests for the UK. These parameters were used to simulate the trajectory of the outbreak in the UK over an 18-month period. Several clear-cut conclusions emerged from these simulations. For example, under plausible (graded) relaxations of social distancing, a rebound of infections is highly unlikely. The emergence of a second wave depends almost exclusively on the rate at which we lose immunity, inherited from the first wave. There exists no testing strategy that can attenuate mortality rates, other than by deferring or delaying a second wave. A testing and tracking policy—implemented at the present time—will defer any second wave beyond a time horizon of 18 months. Crucially, this deferment is within current testing capabilities (requiring an efficacy of tracing and tracking of about 20% of asymptomatic infected cases, with 50,000 tests per day). These conclusions are based upon a dynamic causal model for which we provide some construct and face validation—using a comparative analysis of the United Kingdom and Germany, supplemented with recent serological studies.</ns7:p>

Caching mechanisms for habit formation in Active Inference

A popular distinction in the human and animal learning literature is between deliberate (or willed) and habitual (or automatic) modes of control. Extensive evidence indicates that, after sufficient learning, living organisms develop behavioural habits that permit them saving computational resources. Furthermore, humans and other animals are able to transfer control from deliberate to habitual modes (and vice versa), trading off efficiently flexibility and parsimony – an ability that is currently unparalleled by artificial control systems. Here, we discuss a computational implementation of habit formation, and the transfer of control from deliberate to habitual modes (and vice versa) within Active Inference: a computational framework that merges aspects of cybernetic theory and of Bayesian inference. To model habit formation, we endow an Active Inference agent with a mechanism to "cache" (or memorize) policy probabilities from previous trials, and reuse them to skip – in part or in full – the inferential steps of deliberative processing. We exploit the fact that the relative quality of policies, conditioned upon hidden states, is constant over trials; provided that contingencies and prior preferences do not change. This means the only quantity that can change policy selection is the prior distribution over the initial state – where this prior is based upon the posterior beliefs from previous trials. Thus, an agent that caches the quality (or the probability) of policies can safely reuse cached values to save on cognitive and computational resources – unless contingencies change. Our simulations illustrate the computational benefits, but also the limits, of three caching schemes under Active Inference. They suggest that key aspects of habitual behaviour – such as perseveration – can be explained in terms of caching policy probabilities. Furthermore, they suggest that there may be many kinds (or stages) of habitual behaviour, each associated with a different caching scheme; for example, caching associated or not associated with contextual estimation. These schemes are more or less impervious to contextual and contingency changes.

Imaging the interaction: Epileptic discharges, working memory, and behavior

Interictal generalized epileptiform discharges may impair cognition. We used simultaneous video‐electroencephalography and functional imaging to quantify changes, induced by epileptiform discharges, in the task‐related activations during a spatial working‐memory paradigm. The number of epileptiform discharges increased during the task with its level of complexity, but were not significantly associated with wrong responses during the task. We observed hemodynamic responses in working‐memory related frontal‐lobe‐network, motor‐cortex, precuneus, and parietal lobes in the absence of epileptiform discharges. In the presence of epileptiform discharges during the task, task‐related hemodynamic changes were seen only in motor‐cortex, precuneus, and parietal lobes. These findings suggest that generalized epileptiform discharges during a high demanding working memory task may change the working memory‐related hemodynamic responses in frontal‐lobe‐network. Hum Brain Mapp 34:2910–2917, 2013. © 2012 Wiley Periodicals, Inc.

Dynamic causal modelling of seizure activity in a rat model