[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83161-en":3,"doc-seo-83161-105":30,"detail-sidebar-cat-0-en-105":83},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},83161,2336464648746,"Skyler","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Intrinsic Noise Consolidation: Doob-Barrier-Conditioned Diffusion for Continual Learning","Intrinsic device noise in analog neuromorphic hardware is typically treated as an accuracy cost. This work investigates a contrarian goal: consolidating memories using that same noise by conditioning per-synapse stochastic dynamics on never crossing a memory-critical barrier around a consolidated value. The resulting Doob h-transform diffusion adds a noise-variance-amplified restoring drift that diverges at the barrier. A key prediction is a falsifiable inverted-U effect where increasing intrinsic noise improves sequential retention at an interior optimum, verified on Split-MNIST, and sustained under multiple device-faithful noise models and on real BrainScaleS-2 silicon.","arXiv :2607 .06924v 1 [ cs .LG] 8 Jul 2026  \nIntrinsic-Noise Consolidation: A Doob-Barrier-Conditioned Diffusion Turns Analog Device Noise into a Continual-Learning Resource  \nGunner Levi Howe  \n[gunnerlevihowe@gmail.com](gunnerlevihowe@gmail.com)  \nJuly 2026  \nAbstract  \nOn 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 asa 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 σ 2 ∂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 barrierconditioning 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, loadbearing 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](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  \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, retainsa 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;  \nretention 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.  \n1 Introduction  \nCatastrophic forgetting—the overwriting of old memories when a network learns something new— is usually fought with regularizers that anchor important weights to their consolidated values  \n[Kirkpatrick et al. , 2017 , Benna and Fusi, 2016] . On digital hardware, stochasticity is something you add deliberately and pay for. On analog neuromorphic substrates such as BrainScaleS-2 (BSS- 2) the situation is inverted: the hardware is intrinsically noisy—thermal fluctuations","cbCainB0M6WT7Hjn","https://ap.wps.com/l/cbCainB0M6WT7Hjn","pdf",446865,2,1,14,"English","en",105,"# Abstract\n# Introduction\n## Catastrophic forgetting and intrinsic noise on analog hardware\n## Anchored drift baseline (OU Adaptation, MESU, EWC limit)\n## Doob h-transform conditioning on a memory-critical barrier\n## Inverted-U prediction and contribution split","[{\"question\":\"What main prediction about intrinsic noise and retention does the paper test?\",\"answer\":\"The paper predicts a non-monotonic inverted-U relationship: increasing intrinsic noise improves sequential-task retention up to an interior optimum, after which performance declines. It contrasts this behavior with anchored methods that decrease monotonically with noise.\"}]",1784185682,35,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":78,"head_meta":80,"extra_data":82,"updated_unix":28},"intrinsic-noise-consolidation-doob-barrier-conditioned-diffusion-for-continual-learning","",{"@graph":36,"@context":77},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/intrinsic-noise-consolidation-doob-barrier-conditioned-diffusion-for-continual-learning/83161/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-20","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"What main prediction about intrinsic noise and retention does the paper test?","Question",{"text":75,"@type":76},"The paper predicts a non-monotonic inverted-U relationship: increasing intrinsic noise improves sequential-task retention up to an interior optimum, after which performance declines. It contrasts this behavior with anchored methods that decrease monotonically with noise.","Answer","https://schema.org",{"og:url":51,"og:type":79,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":81,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":84},[85,89,93,97,102,107,112,115,120,123,127],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":20,"doc_module":4,"doc_module_name":46,"category_name":90,"show_sort_weight":91,"slug":92},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Exam",70,"exam",{"id":98,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},5,"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":46,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":46,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":113,"slug":114},30,"research-report",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":46,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":98,"slug":130},19,"General","general"]