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

arXiv: https://arxiv.org/abs/2607.06924 · HTML: https://mlsanity.com/paper/2607.06924/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 18 references that are in the map.
- First posted on arXiv 8 Jul 2026.

## Builds on (most cited first, 12 of 12)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Simulating Diffusion Bridges with Score Matching](https://mlsanity.com/paper/2111.07243/) (2021)
- [Artificial Neural Variability for Deep Learning: On Overfitting, Noise Memorization, and Catastrophic Forgetting](https://mlsanity.com/paper/2011.06220/) (2020)
- [Doob's Lagrangian: A Sample-Efficient Variational Approach to Transition Path Sampling](https://mlsanity.com/paper/2410.07974/) (2024)
- [h-Edit: Effective and Flexible Diffusion-Based Editing via Doob's h-Transform](https://mlsanity.com/paper/2503.02187/) (2025)
- [Reflected Schr"odinger Bridge for Constrained Generative Modeling](https://mlsanity.com/paper/2401.03228/) (2024)
- [Bayesian continual learning and forgetting in neural networks](https://mlsanity.com/paper/2504.13569/) (2025)
- [Ornstein-Uhlenbeck Adaptation as a Mechanism for Learning in Brains and Machines](https://mlsanity.com/paper/2410.13563/) (2024)
- [Noise-Aware Training of Neuromorphic Dynamic Device Networks](https://mlsanity.com/paper/2401.07387/) (2024)
- [Inference with Artificial Neural Networks on Analog Neuromorphic Hardware](https://mlsanity.com/paper/2006.13177/) (2020)
- [Probabilistic Metaplasticity for Continual Learning with Memristors](https://mlsanity.com/paper/2403.08718/) (2024)
- [Internal noise in hardware deep and recurrent neural networks helps with learning](https://mlsanity.com/paper/2504.13778/) (2025)

## Built on by (most cited first, 1 of 1)

- [A Noise Optimum in Rehearsal-Free Continual Learning: Isolation, Mechanism, and Scope](https://mlsanity.com/paper/2609.20162/) (2026)

## Abstract (arXiv)

On analog neuromorphic hardware, intrinsic device noise is normally an accuracy tax. We ask whether it can instead consolidate memories. We cast per-synapse consolidation as a Doob h-transform: condition each weight's stochastic dynamics on never crossing a memory-critical barrier around its consolidated value. The conditioned diffusion gains an extra drift sigma^2 d/dw log h, a restoring force amplified by the noise variance itself that diverges at the barrier. We are explicit about novelty: the anchored drift -s(w-mu) our rule also contains is not ours (the limit of OUA, MESU, and EWC), and we surrender it. We claim only 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, none synaptic), and (b) a falsifiable prediction: increasing intrinsic noise non-monotonically improves sequential-task retention, an inverted-U that anchored-drift methods cannot produce. We pre-registered this as a go/no-go gate; it passes. On single-head Split-MNIST (8 seeds) the rule lifts retention 10.9 points at an interior optimum (paired Wilcoxon p=0.004), while matched OU/EWC/MESU anchors are monotone. Ablating the conditioning removes the effect; the optimum tracks the barrier; the inverted-U survives a second task stream and the realization where noise enters the forward pass. We then measure the intrinsic noise on real BrainScaleS-2 silicon (additive, trial-to-trial independent, tunable via on-chip averaging) and run the rule on the chip with its noise in the training loop: barrier-conditioning retains a prior task 15.6 points better than the matched control at matched average accuracy, a stability-plasticity shift, not a net-accuracy win (single seed; retention measured, energy modelled). Intrinsic analog noise thus becomes a consolidation dividend a digital accelerator must spend energy to generate.