Constraint-Weighted State Selection: Geometry and Memory Shape Realized States
This article proposes a new model called Constraint-Weighted State Selection (CWSS) that extends standard entropy-driven models by considering how constraint geometry and accumulated history actively bias which allowed states get realized.
Why it matters
CWSS provides a more nuanced view of how constraints and history can actively influence which states get realized in complex systems, with potential applications in machine learning, physics, and other domains.
Key Points
- 1CWSS introduces a constraint cost term that captures the geometric expense of a state, along with a memory coupling term that amplifies this cost based on history
- 2The model includes a dynamical memory variable that tracks accumulated constraint load, leading to non-Markovian behavior
- 3CWSS predicts several signatures not captured by pure entropy-driven or Markovian models, including geometric bias, history-dependent drift, and disorder-load correspondence
Details
The core idea of CWSS is to modify the standard probability distribution over states by including two additional exponential terms: one for the constraint cost (geometric expense) of each state, and another for the accumulated constraint load modulated by the memory coupling. This turns constraints from static walls into a time-dependent, geometry-aware filter that shapes the realized distribution. The model also includes a dynamical memory variable that tracks the accumulated constraint load, leading to non-Markovian behavior. CWSS is shown to predict several signatures not captured by standard models, such as geometric bias in state selection, history-dependent drift, threshold-based redistribution, and a quantitative link between observable disorder and future constraint pressure.
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