Read the equation
The next state is a linear transformation of the current state plus independent zero-mean Gaussian noise with identity covariance. At stationarity, the covariance solves the discrete Lyapunov equation shown alongside it. The benchmark scales W to spectral radius 0.9, which ensures a unique finite covariance for this stable linear system.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| X_t | n-dimensional network state |
| W | Recurrent weight matrix |
| epsilon_t | Independent Gaussian innovation |
| Sigma | Stationary covariance |
| I | Identity innovation covariance |
How it works
Read the definition from its right-hand expression to the quantity on the left. Its surrounding source records the intended input, state, or parameter context. Where the source leaves an operation unspecified, this page preserves that gap.
Assumptions & limits
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Original context
Read the surrounding source passage
Can classical and variational quantum search recover the \emph{normalized} minimum-information partition (MIP) when an exhaustive reference is available? This operationalizes the information-integration question motivating the author's broader manuscript [6], without reusing its historical scores as new evidence. The prototype evaluates synthetic \emph{linear stochastic recurrent neural-network models}; it does not train language models, analyze biological recordings, or establish subjective experience. Stochastic interaction is a specific observational information-loss measure [1], not the full IIT 3.0/4.0 formalism.
[Context excerpt; full source linked.]Exact original notation
X_{t+1}=WX_t+\varepsilon_t,\quad \varepsilon_t\sim\mathcal N(0,I),
\qquad \Sigma=W\Sigma W^\top+I.Related builds
Sources & provenance
X_{t+1}=WX_t+\varepsilon_t,\quad \varepsilon_t\sim\mathcal N(0,I), \qquad \Sigma=W\Sigma W^\top+I.
X_{t+1}=WX_t+\varepsilon_t,\quad \varepsilon_t\sim\mathcal N(0,I), \qquad \Sigma=W\Sigma W^\top+I.