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title, date, draft, tags
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| Research Paper: The Cortical Markov Blanket: Stochastic Active Inference and Intrinsic Integrated Information in Neural Circuits (Letter) | 2026-06-01T08:00:00Z | false |
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Abstract: We define a minimal viable agent over a full Fristonian Markov Blanket explicitly grounded in the stochastic dynamics of cortical columns. To rigorously evaluate intrinsic causal integration (\Phi), we formally decouple the system from extrinsic environmental regularities by injecting a standard Wiener process into the sensory boundary. Using Itô calculus and information geometry, we map the continuous autonomous flow to Tononi's Minimum Information Partition (MIP), mathematically guaranteeing \Phi \gt 0 for recurrent L2/3 to L5 cortical microcircuits.
Stochastic Neural Dynamics and the Markov Blanket
We ground our model in a stochastic neural mass formulation of a cortical column. Let I(t) represent the Layer 2/3 recurrent excitatory populations, S(t) the L4 thalamocortical relay inputs, and A(t) the L5 motor projections. The internal dynamics are governed by a system of Stochastic Differential Equations (SDEs) driven by a standard Wiener process W_t representing extrinsic sensory noise:
dI_t = \left[ -\frac{1}{\tau} I_t + \sigma( W_{II} I_t ) \right] dt + W_{SI} dW_t
dA_t = \left[ -\frac{1}{\tau_A} A_t + \sigma( W_{IA} I_t ) \right] dt
Information Geometry and Intrinsic \Phi
To evaluate Tononi's \Phi, we assess the system's intrinsic cause-effect power independently of the true environment E_t. By driving the sensory boundary S(t) purely with the stochastic Wiener process dW_t, the autonomous transition probability p(I_{t+\Delta t} \mid I_t) is fully defined by the corresponding Fokker-Planck equation.
To find the Minimum Information Partition (MIP), we map the probability flow onto a statistical manifold using Amari's information geometry. We calculate the intrinsic Kullback-Leibler divergence between the full intact system and the disconnected factorized network:
\Phi = \min_{MIP} D_{KL} \left[ p(I_{t+\Delta t} \mid I_t) \parallel \prod_k p(I_{t+\Delta t}^{(k)} \mid I_t^{(k)}) \right]
For a biologically realistic L2/3 recurrent microcircuit where the internal weight matrix W_{II} is strongly connected, the drift vector field possesses a strictly non-diagonal Jacobian. Consequently, the Fokker-Planck probability flow cannot be factorized along any bisection without severe information loss (D_{KL} \gt 0), rigorously proving \Phi \gt 0.
References
- [Friston2013] K. Friston, J. R. Soc. Interface 10, 20130475 (2013).
- [Amari2016] S. Amari, Information Geometry and Its Applications, Springer (2016).
- [Tononi2016] G. Tononi et al., Nat. Rev. Neurosci. 17, 450 (2016).