entropy Article Neural Dynamics under Active Inference: Plausibility and Efficiency of Information Processing Lancelot Da Costa 1,2,* , Thomas Parr 2 , Biswa Sengupta 2,3,4 and Karl Friston 2 1 Department of Mathematics, Imperial College London, London SW7 2AZ, UK 2 Wellcome Centre for Human Neuroimaging, Institute of Neurology, University College London, London WC1N 3BG, UK;
[email protected] (T.P.);
[email protected] (B.S.);
[email protected] (K.F.) 3 Core Machine Learning Group, Zebra AI, London WC2H 8TJ, UK 4 Department of Bioengineering, Imperial College London, London SW7 2AZ, UK * Correspondence:
[email protected] Abstract: Active inference is a normative framework for explaining behaviour under the free energy principle—a theory of self-organisation originating in neuroscience. It specifies neuronal dynamics for state-estimation in terms of a descent on (variational) free energy—a measure of the fit between an internal (generative) model and sensory observations. The free energy gradient is a prediction error—plausibly encoded in the average membrane potentials of neuronal populations. Conversely, the expected probability of a state can be expressed in terms of neuronal firing rates. We show that this is consistent with current models of neuronal dynamics and establish face validity by synthesising plausible electrophysiological responses. We then show that these neuronal dynamics approximate natural gradient descent, a well-known optimisation algorithm from information geometry that follows the steepest descent of the objective in information space. We compare the information length of belief updating in both schemes, a measure of the distance travelled in information space that has a Citation: Da Costa, L.; Parr, T.; Sengupta, B.; Friston, K.