Adapting Without Gradients: Affine Statistics Transport and What Its Certificate Can Tell You

Test-time adaptation (TTA) typically assumes that model parameters can be updated at inference time. This assumption is restrictive for inference-only accelerators, frozen or third-party models, and memory-constrained deployments, and standard BatchNorm-based TTA configurations may also become inactive on architectures without BatchNorm. We study adaptation when the learned model must remain frozen. We introduce CASTER, a gradient-free method that stores source class statistics in a discriminative subspace, estimates a class-shared affine transformation from target-batch moments, and analytically transports the source class distributions before classification. CASTER requires no backward pass, optimizer state, or stored source feature bank. Across four backbones and seven datasets, it outperforms k-NN on identical frozen features in 27 of 28 backbone-dataset settings while retaining a median of 18x less state. Affine transport is not always reliable. On ImageNet-C, where batches contain only 64 samples for 1000 classes, unconditional transport loses 21.2 top-1 points. We therefore introduce an empirical residual-to-margin transportability certificate. Across 307 evaluation cells, every transport losing more than 10 points has certificate value above 3.9, although benign and destructive regimes are not perfectly separated. Gating converts an average $-3.35$-point effect of unconditional transport into a +1.69-point gain, and performance remains within 0.3 points of the best threshold over a broad threshold range. Finally, we show that this certificate is mechanism-specific: when applied to Tent, it accepts only $4.3\%$ of updates and preserves 0.6% of Tent's available gain. These results position CASTER as a lightweight adaptation mechanism for frozen-model deployment, together with an explicit account of when its safety signal is informative and when it is not.

SpikeWorld: Fast-State Adaptation for Frozen Spiking World Models

A predictive model receives a self-supervised signal whenever the consequence of an action is observed. Using that signal after deployment is difficult when dynamics and semantics share parameters: freezing prevents adaptation, whereas weight updates require optimizer state and may alter the learned representation. Here we introduce SpikeWorld, a 1.45M-parameter sparse spiking model jointly trained for heterogeneous sensory prediction, semantics, image-text binding and action-conditioned dynamics. At deployment, all trained parameters are frozen. Delayed next-state residuals update two external paths: cumulative fixed-bank losses select the bounded action correction, while route-specific residual matrices refine next-state prediction. Neither path uses labels, teacher outputs, rewards, success signals or the true shift value. Joint optimization improves action next-state MSE by 17.10\% while also improving multimodal prediction, semantic accuracy and image-text retrieval. On held-out shear and attenuation streams, the combined external state improves aggregate prediction by 5.48\% and 30.01\%; its fixed-bank action path improves tracking by 24.20\% and 3.94\%, respectively. In a six-arm study comprising 450 new Meta-World trajectories (75 per arm), SpikeWorld raises frozen-policy reward by 7.90 (95\% CI [2.48, 14.06]); the 13.33-point success difference is descriptive (CI [0, 40]). For identical sensory inputs, model parameters and inherited semantic outputs remain bitwise unchanged. A 16-byte RLS estimator obtains the highest non-oracle reward on linear attenuation, showing that the contribution is not superior linear identification, but its integration with a frozen multimodal spiking checkpoint. Reference code is publicly available at https://github.com/Oooorca/SpikeWorld.

Open-Ended Scenario Reasoning for Specialist Model Adaptation

Process industries have accumulated validated specialist models, yet sensor drift, feedstock variation, and regime switching cause these models to degrade systematically in new scenarios. Collecting new labeled data and retraining is costly, while continuing with the original model incurs persistent bias. Existing adaptation methods require modifying model parameters with sufficient labeled data, making rapid response on deployed systems difficult. Using LLMs as direct predictors risks hallucinations and uncontrollable outputs. Such predictors also cannot incorporate unstructured scenario knowledge from the field. To address these limitations, this article proposes Reasoning-Driven Open Adaptation for Specialist Models (ROAM), a framework that uses LLM world knowledge and reasoning to adapt frozen specialist models to unseen scenarios without retraining. ROAM confines all corrections to a low-dimensional, semantically interpretable latent space. LLM-generated scenario judgments and online observations are fused under a unified probabilistic framework. A risk-constrained mechanism suppresses corrections under unreliable LLM evidence or abrupt scenario shifts and falls back to the original frozen model when evidence is insufficient. Experiments on a mineral thickening process and the public IndPenSim penicillin fermentation dataset show that ROAM reduces MAE by over 20\% in major shift settings such as hidden shifts with only 839 additional parameters and under 0.02\,ms per-step overhead. These results indicate that LLM reasoning can be turned into a conservative adaptation signal for industrial models already in service.