intrinsic-noise-consolidation-doob

name	intrinsic-noise-consolidation-doob
description	Doob h-transform barrier-conditioned diffusion for continual learning on analog neuromorphic hardware. Converts intrinsic device noise from accuracy tax to consolidation dividend. Activation: Doob h-transform, barrier conditioning, analog noise, neuromorphic continual learning, BrainScaleS-2, intrinsic noise consolidation, inverted-U retention
metadata	{"arxiv_id":"2607.06924","published":"2026-07-08","authors":"Gunner Levi Howe","tags":["neuromorphic","continual-learning","doob-h-transform","analog-noise","brain-scale-s-2","synaptic-plasticity"]}

Intrinsic-Noise Consolidation via Doob Barrier-Conditioned Diffusion

Core Innovation

Transform analog neuromorphic device noise from an accuracy tax into a memory consolidation resource using Doob h-transform barrier conditioning. The conditioned diffusion acquires a restoring force σ²∂_w log h that is amplified by the noise variance itself and diverges at memory-critical barriers.

Key Theoretical Contribution

Doob h-Transform as Synaptic Rule

• Cast per-synapse consolidation as conditioning weight dynamics on never crossing memory-critical barrier at μ±b
• Ground-state h-transform: h(w) = cos(π(w-μ)/2b)
• Conditioned drift: σ²∂_w log h(w) — noise-powered restoring force
• Barrier half-width: b_i = b₀/√(1 + s_i/median(s)) — high-Fisher synapses get tight barriers

Novelty Claims (Explicit)

1. Doob barrier-conditioning as synaptic rule — first use in synaptic/plasticity/continual-learning (all prior h-transform uses are generative modeling or Schrödinger bridges)
2. Falsifiable prediction: intrinsic noise non-monotonically improves sequential-task retention (inverted-U curve) — anchored-drift methods (OU, EWC, MESU) cannot produce this

What is NOT Novel

• Anchored drift term -s(w-μ) is small-noise limit of OUA/MESU/EWC — explicitly surrendered as re-derivation

Methodology

Weight Dynamics (Euler-Maruyama)

dw = [-s(w-μ) + σ²∂_w log h(w)]dt + σ dW

• First term: anchored drift (known from OUA/MESU/EWC)
• Second term: Doob barrier conditioning (novel)
• All methods receive identical injected noise at matched σ

Experimental Validation

• E0-E4 (GPU emulation): Split-MNIST domain-incremental, 5 binary tasks, MLP 784-100-100-2

  • Retention inverted-U: 10.9 pts lift at σ*=0.02 (p=0.004, 8 seeds)
  • OU/EWC/MESU anchors are monotone-decreasing in noise
  • Ablating conditioning (κ:1→0) flattens curve — effect is from conditioning, not generic noise

• E2 (Device-faithful): BSS-2 noise model (colored AR(1) + multiplicative + fixed-pattern + 6-bit quantization)

  • Inverted-U survives on continual Yin-Yang benchmark

• E5 (Real silicon measurement): BrainScaleS-2 chip hxcube7fpga3chip61_1

  • Intrinsic noise is additive, trial-to-trial independent
  • CV up to 12.0%, num_sends knob averages as ≈1/√N
  • Benign noise class at reachable amplitude

• E7 (On-chip training): Real BrainScaleS-2 with analog MAC in training loop

  • Chip's own intrinsic noise + barrier conditioning retains prior task 15.6 pts better than unconditioned control
  • Single-seed proof of concept; retention measured, energy modeled

Baselines

• OUA (Ornstein-Uhlenbeck Adaptation)
• EWC (Elastic Weight Consolidation)
• MESU (Bayesian continual learning)
• Benna-Fusi complex synapses
• Plain replay (stores data, lacks mechanism)

Key Results

1. Inverted-U retention curve: Noise helps retention up to optimum σ*, then hurts — unique to barrier-conditioned rule
2. Rehearsal-free: Strongest rehearsal-free consolidation method tested (ties MESU, beats OU/EWC)
3. Energy argument: Analog substrate pays no energy to generate noise (it's intrinsic); digital accelerator must spend energy to inject it
4. Hardware validation: Mechanism works on real BrainScaleS-2 silicon with device's own noise

Pitfalls

Pre-Registration as Go/No-Go Gate

The inverted-U prediction was pre-registered as a hard go/no-go gate. If noise did not help retention beyond unconditioned anchor, the mechanism reduces to OUA/MESU and there is no paper. It passed.

Single-Seed On-Chip Result

E7 (real silicon training) is single-seed, one operating point. Retention measured, energy modeled but not directly measured. Replication across seeds and chips needed.

Emulation vs. Silicon

E0-E4 are GPU emulations. E2 uses device-faithful noise model but is still emulation. Only E5 (noise measurement) and E7 (on-chip training) are real-silicon results.

Fair Comparison

All methods receive identical injected noise at matched σ. Methods differ only in drift term. This isolates barrier conditioning effect rather than generic noise effect.

Applications

• Analog neuromorphic hardware: BrainScaleS-2, other analog accelerators with intrinsic noise
• Continual learning: Sequential task retention without rehearsal
• Energy-efficient consolidation: Leverage intrinsic noise instead of injecting artificial noise
• Stability-plasticity balance: Barrier conditioning provides tunable trade-off

Related Work

• OUA (Garcia Fernandez et al., 2024): Mean-reverting OU diffusion — exactly the anchored drift term, but no barrier or first-passage conditioning
• MESU (Bonnet et al., 2025): Bayesian continual learning with variance-scaled anchor — treats device read-noise as sampling resource, never as retention optimum
• EWC (Kirkpatrick et al., 2017): Static Fisher-weighted quadratic anchor — deterministic ancestor
• ANV (Xie et al., 2021): Injects artificial neural variability to reduce forgetting — but variability is injected (digital regularizer), benefit is monotone, no barrier
• Benna-Fusi (2016): Multi-timescale cascade synapses — consolidates without barrier via deterministic cascade

References

• arXiv:2607.06924 — Full paper with proofs, experimental details, and energy model
• BrainScaleS-2: Pehle et al., 2022; Weis et al., 2020
• Doob h-transform: Classical stochastic process theory
• Continual learning benchmarks: Split-MNIST, Yin-Yang (Kriener et al., 2022)