Memory Imprint Model¶

Purpose¶

Track cumulative exposure history per oscillator. The imprint vector M_k modulates coupling and phase lag, encoding long-term adaptation.

Dynamics¶

M_k(t + dt) = M_k(t) * exp(-decay_rate * dt) + exposure_k * dt
M_k = clip(M_k, 0, saturation)

decay_rate: Exponential forgetting rate. Higher = faster fade.
saturation: Upper bound on imprint magnitude. Prevents runaway accumulation.
exposure_k: Instantaneous exposure signal for oscillator k.

Modulation¶

Coupling modulation¶

K_ij_effective = K_ij * (1 + M_i)

Oscillators with high imprint couple more strongly. Row-wise scaling of Knm.

Lag modulation¶

alpha_ij_effective = alpha_ij + M_i

High imprint shifts the phase lag, introducing a directional bias.

Configuring modulation targets¶

The binding spec imprint_model.modulates list controls which knobs are affected:

imprint_model:
  decay_rate: 0.01
  saturation: 2.0
  modulates: ["K", "alpha"]

Attribution¶

ImprintState.attribution maps source labels to contribution magnitudes. Tracks where exposure came from for audit and explainability.

Lifecycle¶

Initialise M_k = 0 for all oscillators.
Each step: call ImprintModel.update(state, exposure, dt).
Before UPDE integration: apply modulation via modulate_coupling() and/or modulate_lag().
Attribution updated alongside exposure sources.

When to Use¶

Enable the imprint model when the system has history-dependent coupling -- habituation, sensitisation, learning, or drift adaptation. Omit when coupling is time-invariant.