Formalization of Hopfield Networks (WIP) #664
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mkaratarakis
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This PR enhances the `NeuralNetwork` framework to support polymorphic activation values (`σ`), enabling flexible modeling of diverse neuron types (e.g., `R`, `SignumType`, `Bool`). It introduces a helper map `m : σ → R` for numeric computations and refines state definitions and update mechanisms for clarity and correctness. Key Changes 1. **Polymorphic Activation Values**: `σ` parameter added to `NeuralNetwork`, with `m` for numeric mapping. 2. **State Enhancements**: Added `State.out` for numeric outputs and `onlyUi` for consistent non-input activations. 3. **Improved Update Mechanisms**: Refined `Up`, `workPhase`, and `seqStates` for generalized updates. 4. **Backward Compatibility**: Existing Hopfield networks remain functional with `σ := R` and `m := id`. No breaking changes.
Add reversibility (detailed balance) for Markov kernels and show it implies invariance
…rgySpec abstractions This file builds a general interface for two-state neural networks, provides three concrete Hopfield-style instances, develops a one-site Gibbs update kernel, and proves convergence of this kernel to a deterministic zero-temperature limit as `β → ∞` (equivalently, `T → 0+`).
…iled balance and invariance for gibbs random kernel, etc. major refactor with proof of detailed balance /reversibility) and invariance (stationary) for our general TwoState random Gibbs kernel. This covers, with one general API, most of specific discrete HN and BM in the literature
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