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P98: Bayesian mechanics in the brain under the free-energy principle
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**Chang Sub Kim**

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In the field of neurosciences, the free-energy principle (FEP) stipulates that all viable organisms cognize and behave using probabilistic models embodied in their brain in a manner that ensures their adaptive fitness in the environment [1]. Here, we report on our recent theoretical study that supports the use of the FEP as a more physically plausible theory, based on the principle of least action [2].

We recapitulate the FEP carefully [3] and evaluate that some technical facets in its conventional formalism require reformulation with finesse [4]. Accordingly, we articulate the FEP as living organisms minimize the sensory uncertainty, which is the average surprisal over a temporal horizon, and reformulate the recognition dynamics of the brain's ability for actively inferring the external causes of sensory inputs. We effectively cast the Bayesian inversion problem in the organism's brain to find the optimal neural trajectories by minimizing the time integral of the informational free energy (IFE), which is the upper bound of the long-term average surprisal. Specifically, we abstain from i) the non-Newtonian extension of continuous states, which yields the generalized motion, by recursively taking higher- order derivatives of the sensory observation and state equations, and ii) the heuristic gradient-descent minimization of the IFE in a moving frame of reference in a generalized-state space by viewing the nonequilibrium dynamics of brain states as drift-diffusion flows that locally conserve the probability density.

The advantage of our formulation is that only bare variables (positions) and their first-order derivatives (velocities) are used in the Bayesian neural computation, thereby dismissing the need for the extra-physical assumptions. Bare variables are an organism's representations of the causal environment, and their conjugate momenta resemble the precision-weighted prediction errors in a predictive coding language [5]. Furthermore, we consider the sensory-data-generating dynamics to be nonstationary on an equal footing with intra- and inter-hierarchical-level dynamics in a neuronally based biophysical model. Consequently, our theory delivers a natural account of the descending predictions and ascending prediction errors in the brain's hierarchical message-passing structure (Fig. 1). The ensuing neural circuitry may be related to the alpha-beta and gamma rhythms that characterize the feedback and feed-forward influences, respectively, in the primate visual cortex [6].

**References **

[1] Friston K. The free-energy principle: a unified brain theory?. Nature Reviews Neuroscience. 2010, 11, 127--138.

[2] Landau L P, Lifshitz E M. Classical Mechanics. 3rd edition. Amsterdam: Elsevier Ltd.; 1976.

[3] Buckley C L & Kim C S, McGregor S, Seth A K. The free energy principle for action and perception: A mathematical review. Journal of Mathematical Psychology. 2017, 81, 55--79;

[4] Kim C S. Recognition dynamics in the brain under the free energy principle. Neural Computation. 2018, 30, 2616-2659; .

[5] Rao R P N, Ballard D H. Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects. Nature Neuroscience. 1999, 2(1), 79--87.

[6] Michalareas G, Vezoli J, van Pelt S, et al. Alpha-beta and gamma rhythms subserve feedback and feedforward influences among human visual cortical areas. Neuron. 2016, 89, 384-397.

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To join the video meeting, click this link: https://meet.google.com/wtq-nrpp-emw

In the field of neurosciences, the free-energy principle (FEP) stipulates that all viable organisms cognize and behave using probabilistic models embodied in their brain in a manner that ensures their adaptive fitness in the environment [1]. Here, we report on our recent theoretical study that supports the use of the FEP as a more physically plausible theory, based on the principle of least action [2].

We recapitulate the FEP carefully [3] and evaluate that some technical facets in its conventional formalism require reformulation with finesse [4]. Accordingly, we articulate the FEP as living organisms minimize the sensory uncertainty, which is the average surprisal over a temporal horizon, and reformulate the recognition dynamics of the brain's ability for actively inferring the external causes of sensory inputs. We effectively cast the Bayesian inversion problem in the organism's brain to find the optimal neural trajectories by minimizing the time integral of the informational free energy (IFE), which is the upper bound of the long-term average surprisal. Specifically, we abstain from i) the non-Newtonian extension of continuous states, which yields the generalized motion, by recursively taking higher- order derivatives of the sensory observation and state equations, and ii) the heuristic gradient-descent minimization of the IFE in a moving frame of reference in a generalized-state space by viewing the nonequilibrium dynamics of brain states as drift-diffusion flows that locally conserve the probability density.

The advantage of our formulation is that only bare variables (positions) and their first-order derivatives (velocities) are used in the Bayesian neural computation, thereby dismissing the need for the extra-physical assumptions. Bare variables are an organism's representations of the causal environment, and their conjugate momenta resemble the precision-weighted prediction errors in a predictive coding language [5]. Furthermore, we consider the sensory-data-generating dynamics to be nonstationary on an equal footing with intra- and inter-hierarchical-level dynamics in a neuronally based biophysical model. Consequently, our theory delivers a natural account of the descending predictions and ascending prediction errors in the brain's hierarchical message-passing structure (Fig. 1). The ensuing neural circuitry may be related to the alpha-beta and gamma rhythms that characterize the feedback and feed-forward influences, respectively, in the primate visual cortex [6].

[1] Friston K. The free-energy principle: a unified brain theory?. Nature Reviews Neuroscience. 2010, 11, 127--138.

[2] Landau L P, Lifshitz E M. Classical Mechanics. 3rd edition. Amsterdam: Elsevier Ltd.; 1976.

[3] Buckley C L & Kim C S, McGregor S, Seth A K. The free energy principle for action and perception: A mathematical review. Journal of Mathematical Psychology. 2017, 81, 55--79;

[4] Kim C S. Recognition dynamics in the brain under the free energy principle. Neural Computation. 2018, 30, 2616-2659; .

[5] Rao R P N, Ballard D H. Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects. Nature Neuroscience. 1999, 2(1), 79--87.

[6] Michalareas G, Vezoli J, van Pelt S, et al. Alpha-beta and gamma rhythms subserve feedback and feedforward influences among human visual cortical areas. Neuron. 2016, 89, 384-397.

Sunday July 19, 2020 7:00pm - 8:00pm CEST

Slot 02

Slot 02