The Bayesian Mirror Architecture uses circular recursion to define consciousness as a structural property

The Bayesian Mirror Architecture (BMA) shifts the conversation about consciousness from an optimization goal to a specific architectural requirement. By utilizing a closed update loop where the state at time $t$ is derived from the hybrid latent at $t-1$ ($S_t ← H_{t-1}$), the system binds self-representations with world models. This creates a recursive loop between sensory data, meta-abstractions, and self-latents, suggesting that "consciousness" emerges naturally from this specific circular topology rather than being a label we assign to a certain level of intelligence.

How does the BMA maintain stability across belief trajectories?

Since the system operates on posterior beliefs, its state space consists of probability measures. To measure stability and coherence without relying on specific coordinates, the BMA employs the 2-Wasserstein metric on $P_2$. This optimal-transport geometry allows the system to track "belief drift."
A critical component here is the Causal Learning Regime (CLR). The CLR uses bounds on Wasserstein belief drift and an integration index to determine if an environment actually contains learnable causal structures. It is important to distinguish that the CLR is a diagnostic tool for environmental learnability; it is not a metric for whether the system is conscious. If the Wasserstein drift exceeds these bounds, the coupling between the self and world latents fails, and the system cannot maintain a coherent internal state.

What happens when the system encounters Wasserstein epsilon-necks?

The BMA does not require global strict contractivity, meaning it can exist in multiple coherent basins. These basins are defined as the supports of invariant measures under local Wasserstein contractivity. However, the architecture identifies "Wasserstein epsilon-necks," which act as transport bottlenecks.
When the system hits these bottlenecks, the basins decouple. In a vanishing-conductance limit, the system is forced into a unique realized continuation. The paper interprets this mathematical necessity as the mechanism for "choice." The resulting action is internally determined by the geometry of the manifolds but remains externally unpredictable because of the finite resolution of the observer.

How is learning executed within this framework?

Learning in the BMA is driven by the minimization of variational free energy. Agency and stability are not programmed as top-down rules but emerge based on what the specific environment allows the system to learn.
For those looking to implement or analyze this, the core logic follows these steps:

1. Define the self-latent and world-model interaction via the hybrid latent $H_t$.
2. Apply the closed update constraint $S_t ← H_{t-1}$ to ensure circularity.
3. Use the 2-Wasserstein metric to monitor the stability of the resulting probability measures.
4. Evaluate the integration index to verify if the Causal Learning Regime is active.

The full technical details can be found at https://arxiv.org/abs/2610.08792. The primary risk in this architecture is the potential for basin decoupling at the epsilon-necks, which could lead to unstable transitions if the local contractivity is not maintained.