Predictive Processing Across Temporal Frames via Potential-Flow Contracts

Predictive Processing Across Temporal Frames via Potential-Flow Contracts

This note is a first-gate spec for a concrete idea:

• predictive processing across temporal frames,
• graph-neural operators for cross-frame message passing,
• and potential-flow contracts that constrain admissible transitions.

The target is not poetic coherence. The target is a model that can be implemented, audited, and falsified.

1) Scope and framing

I use “atemporal latent space” in a strict technical sense:

a time-index-agnostic latent manifold used to align states from multiple temporal frames without asserting that time is unreal.

This is a modeling coordinate system, not a metaphysical claim.

2) Core entities (state)

Let temporal frames be indexed by k ∈ {fast, meso, slow} (or integer indices in implementation).

Each frame has:

• x_k(t): observable/state variables at frame k
• b_k(t): predictive belief state at frame k
• z_k(t): latent embedding of frame state in shared manifold Z

Cross-frame graph:

• G = (V, E) where vertices are frames or frame-subsystems
• edges (i, j) denote allowed coupling and message transfer

This is the state definition gate.

3) Potential-flow contract (contract)

For each admissible edge (i, j), define a contract C_ij with:

1. Potential function Φ_ij(z_i, z_j)

   • scores compatibility and directional “flow pressure” between embeddings.

2. Flow constraint

   • transferred message m_ij must satisfy bounded budget and continuity constraints:
   • norm/energy bound,
   • rate-of-change bound,
   • optional conservation-like surrogate (probability mass, information budget, or task-specific invariant).

3. Latency and distortion terms

   • every transfer tracks latency τ_ij and distortion δ_ij.

4. Admissibility rule

   • transfer is valid only if contract residual r_ij is below threshold ε_ij.

Intuition: the model can pass signal across frames, but only through lawful channels with explicit error accounting.

This is the contract definition gate.

4) Graph-neural transition operator (operator)

A graph-neural operator F_θ performs update steps:

1. Encode each frame state to latent: z_k = Enc_θ(x_k, b_k)
2. For each edge (i, j), propose message m_ij = Msg_θ(z_i, z_j)
3. Project/prox message into contract-feasible set:
   • m_ij* = Proj_{C_ij}(m_ij)
4. Aggregate messages per node and update latent/state:
   • z_j' = Upd_θ(z_j, Σ_i m_ij*)
   • b_j' = BeliefUpdate(z_j', x_j)

Training/inference objective includes:

• prediction loss across frames,
• contract-violation penalty,
• latency/distortion penalty,
• optional cross-scale consistency term.

This is the operator definition gate.

5) Boundary conditions and failure modes (boundary)

The model is declared out-of-regime when any of the following persist:

1. Contract collapse: violation rate exceeds threshold for sustained windows.
2. Temporal drift explosion: cross-frame predictions decorrelate faster than baseline.
3. Mode-locking: one frame dominates and suppresses useful multi-scale coupling.
4. Latency debt: useful signal arrives too late to improve target predictions.
5. Degenerate latent geometry: embeddings collapse or become non-informative under probing.

These are explicit failure conditions, not edge-case footnotes.

This is the boundary gate.

6) Evaluation metrics (metric)

Minimum metric set:

• Cross-frame prediction error (MAE/MSE/NLL by frame and jointly)
• Contract violation rate (fraction of edges/time steps with r_ij > ε_ij)
• Coherence gain over baseline (single-scale RNN/Transformer or unconstrained GNN)
• Latency-adjusted utility (performance delta conditioned on transfer delay)
• Ablation lift
  • remove contract projection,
  • remove shared latent manifold,
  • remove multi-frame coupling,
  • compare degradation.

Success requires improvement on predictive quality and bounded violation dynamics.

This is the metric gate.

7) Minimal falsification protocol

A claim that this architecture improves temporal coherence should be rejected if:

• unconstrained baseline matches or outperforms with equal compute/data,
• contract terms do not measurably reduce pathological transitions,
• gains disappear under out-of-distribution temporal perturbations,
• performance depends on hand-tuned thresholds with no robustness window.

8) Claim tiers

Defensible now

• Multiscale predictive processing can be formalized as graph-coupled frame updates.
• Contract-constrained message passing is implementable.
• Latency/distortion accounting is necessary for honest temporal coupling claims.

Plausible but unproven

• Potential-flow contracts improve stability and interpretability versus unconstrained coupling.
• A shared time-index-agnostic latent manifold improves cross-frame transfer efficiency.

Speculative

• This framing captures a deep principle of intelligence beyond the tested task family.
• Contract geometry learned here will generalize broadly across domains without substantial redesign.

9) First-gate checklist

• State specified (x_k, b_k, z_k, graph G)
• Contract specified (Φ_ij, bounds, admissibility residual)
• Operator specified (Enc/Msg/Proj/Upd pipeline)
• Boundary specified (five explicit failure classes)
• Metric specified (prediction, violations, coherence, latency, ablations)

This passes the first gate for promotion into Sandy Chaos documentation as a formal draft, pending implementation notes.