Intrinsic-Noise Consolidation: A Doob-Barrier-Conditioned Diffusion Turns Analog Device Noise into a Continual-Learning Resource

On analog neuromorphic hardware, intrinsic device noise is normally an accuracy tax. We ask whether it can instead be made to consolidate memories. We cast per-synapse consolidation as a Doob h-transform: condition each weight’s stochastic dynamics on the event of never crossing a memory-critical barrier around its consolidated value. The conditioned diffusion acquires an extra drift σ2 ∂w log h — a restoring force toward the memory that is amplified by the noise variance itself, and diverges at the barrier. We are explicit about what is and is not new. The anchored-consolidation drift−s(w−µ) that our rule also contains is not ours: it is the small-noise limit of Ornstein–Uhlenbeck Adaptation [Garcia Fernandez et al., 2024], the variance-scaled anchor of MESU [Bonnet et al., 2025], and the Fisher penalty of EWC [Kirkpatrick et al., 2017], and we surrender it as a re-derivation. Our claim is the conjunction of (a) the Doob barrier-conditioning as a synaptic rule — to our knowledge unclaimed; every h-transform use we found is generative modeling or Schr¨odinger bridges, none synaptic — and (b) a falsifiable, load-bearing prediction: increasing the intrinsic noise non-monotonically improves sequential-task retention, an inverted-U these anchored-drift methods cannot produce. We pre-registered this as a go/no-go gate and it passes: on single-head Split-MNIST (8 seeds) the barrier-conditioned rule lifts retention by 10.9 percentage points at an interior optimum σ∗ = 0.02 (paired Wilcoxon p= 0.004 vs. zero noise and vs. high noise), while the matched OU, EWC and MESU anchors are monotone-decreasing in noise. Ablating the conditioning removes the effect; the optimum tracks the barrier; the inverted-U survives a device-faithful BrainScaleS-2 noise model (colored, multiplicative, fixed-pattern, 6-bit) and reproduces on a second task stream. It also survives the hardware-faithful realization in which the noise enters the forward pass (the analog MAC) rather than the weights, with the retention optimum tunable to a device’s few-percent intrinsic noise. At its optimum the rule is the strongest rehearsal-free consolidation method we test — matching MESU and significantly beating OU and EWC; plain replay, which stores data, scores higher but exhibits none of the mechanism. We further measure the intrinsic noise on real BrainScaleS-2 silicon (chip hxcube7fpga3chip61 1): it is additive and trial-to-trial-independent, with a coefficient of variation up to 12.0% that the chip’s num sends knob averages as ≈1/√N — the benign noise class the mechanism needs, at a reachable amplitude — and the inverted-U survives an emulation calibrated to it. Finally we run the rule on real BrainScaleS-2 silicon with the chip in the training loop: its own intrinsic noise, steered by the barrier-conditioning, retains a prior task 15.6 points better than the matched unconditioned control at matched average accuracy — a stability-plasticity shift, not a net-accuracy win (single seed, one operating point; retention measured, energy modelled). Within these limits the mechanism reframes analog noise from a tax into a consolidation dividend that a von-Neumann accelerator must spend energy to generate.