---
title: "Research Paper: The Cortical Markov Blanket: Stochastic Active Inference and Intrinsic Integrated Information in Neural Circuits (Letter)"
date: "2026-06-01T08:00:00Z"
draft: false
tags: ["#research", "physics", "intellecton"]
---

**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).