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Francesco Rigoli

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  • A single variational principle—minimizing variational free energy via gradient descent on a Markov decision process (MDP) generative model—is sufficient to derive neuronal dynamics that reproduce, without hand-tuning, more than 10 well-characterized empirical phenomena simultaneously: repetition suppression, mismatch negativity, violation responses (peaking ~200 ms in peristimulus time allowing 100 ms conduction delays), place-cell activity, phase precession, theta sequences, theta-gamma coupling (at ~4 Hz theta with nested gamma), evidence accumulation with race-to-bound stepping dynamics, and transfer of dopamine responses from unconditioned to conditioned stimuli. The method introduced is an active inference process theory grounded in belief propagation over discrete-time MDP generative models, where neuronal firing rates encode categorical state expectations, membrane potentials encode their logarithms, and postsynaptic currents correspond to free-energy gradients (state prediction errors). Simulations use outcomes sampled every 250 ms, eight hidden states over four locations and two contexts, and utilities of ±3 nats for rewarding versus unrewarding outcomes (~20-fold preference ratio). Dopamine is formalized as encoding precision (inverse temperature γ) with a postsynaptic time constant of ~1 s (κ₁/κ₂ = 1/64 per 16 ms iteration). Because a gradient descent constitutes a valid description of neuronal activity, variational free energy functions as a Lyapunov function for neuronal dynamics, implying that neural activity conforms to Hamilton's principle of least action and that a single imperative—free energy minimization—unifies perception, action, learning, and neuromodulatory signaling within one coherent process theory.

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