Open-Ended Scenario Reasoning for Specialist Model Adaptation

# Open-Ended Scenario Reasoning for Specialist Model Adaptation
Source: [https://arxiv.org/html/2607.06625](https://arxiv.org/html/2607.06625)
Youcheng Zong[https://orcid.org/0009-0008-6795-8412](https://orcid.org/0009-0008-6795-8412)\{\}^\{\\lx@orcidlink\{0009\-0008\-6795\-8412\}\{\\orcidlogo\}\}, , Runda Jia[https://orcid.org/0000-0002-8586-243X](https://orcid.org/0000-0002-8586-243X)\{\}^\{\\lx@orcidlink\{0000\-0002\-8586\-243X\}\{\\orcidlogo\}\}, Ranmeng Lin[https://orcid.org/0009-0006-3829-4472](https://orcid.org/0009-0006-3829-4472)\{\}^\{\\lx@orcidlink\{0009\-0006\-3829\-4472\}\{\\orcidlogo\}\}, Mingxuan Ren[https://orcid.org/0009-0001-0172-5914](https://orcid.org/0009-0001-0172-5914)\{\}^\{\\lx@orcidlink\{0009\-0001\-0172\-5914\}\{\\orcidlogo\}\}, and Dakuo He[https://orcid.org/0000-0001-8303-529X](https://orcid.org/0000-0001-8303-529X)\{\}^\{\\lx@orcidlink\{0000\-0001\-8303\-529X\}\{\\orcidlogo\}\}This work was supported by the Fundamental Research Funds for the Central Universities, China \(N26GFZ006\)\.\(Corresponding author: Runda Jia\.\)Youcheng Zong, Runda Jia, Ranmeng Lin, Mingxuan Ren, and Dakuo He are with the College of Information Science and Engineering, Northeastern University, Shenyang 110004, China \(e\-mail: youchengzong@stumail\.neu\.edu\.cn; jiarunda@ise\.neu\.edu\.cn; linrm@mails\.neu\.edu\.cn; renmx@mails\.neu\.edu\.cn; hedakuo@ise\.neu\.edu\.cn\)\.The source code is available at[https://github\.com/mituan\-ai/ROAM\_open](https://github.com/mituan-ai/ROAM_open)\.

###### Abstract

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\.

## Note to Practitioners

This paper is motivated by a practical problem in process plants: key variables such as quality, concentration, or yield are often not measured continuously, so automation systems rely on soft sensors for online estimates\. These models are validated before deployment, but their estimates can slowly drift from the real process after sensor drift, feedstock changes, equipment maintenance, or control\-policy switching\. New sampling, laboratory analysis, and retraining may take hours or days\. During this period, biased estimates can affect control, alarms, and production scheduling\. ROAM is intended as an adaptation layer outside the existing soft sensor\. It reads shift logs, maintenance records, and a small set of process signals at the start of a new operating interval, then judges whether the current error is more likely due to measurement bias, scaling change, load change, dynamic\-response change, or output\-relation change\. ROAM then applies only a bounded correction to the model output\. When records are unclear, signals conflict, or the new state is too far from known operation, it reduces the correction or returns to the original model\. The practical value is to keep validated model assets in service while reducing persistent bias early in abnormal or new conditions, improving the reliability of quality estimates and reducing the need for urgent retraining\. The current approach still needs usable field records and assumes that the dominant operating condition does not change frequently within one interval\. Future work should connect alarm sequences, inspection images, maintenance systems, and operator feedback, and test the method in longer closed\-loop production\. Beyond thickening dewatering and fermentation, the same idea may support energy\-load forecasting, equipment\-health monitoring, and other automation applications where existing model certification must be preserved\.

## IIntroduction

Process industries including mineral processing, petrochemicals, and biopharmaceuticals have accumulated validated data\-driven specialist models for soft sensing of critical quality variables\[[17](https://arxiv.org/html/2607.06625#bib.bib21),[34](https://arxiv.org/html/2607.06625#bib.bib2),[10](https://arxiv.org/html/2607.06625#bib.bib3),[24](https://arxiv.org/html/2607.06625#bib.bib26)\]\. Related studies have addressed key modeling constraints such as dynamic modeling, foundation\-model transfer, missing data, partial labels, and physical consistency\[[32](https://arxiv.org/html/2607.06625#bib.bib32),[22](https://arxiv.org/html/2607.06625#bib.bib33),[30](https://arxiv.org/html/2607.06625#bib.bib34)\]\. These models perform well under their training conditions but degrade systematically once sensor drift, feedstock variation, regime switching, or equipment aging introduces distribution shifts\[[25](https://arxiv.org/html/2607.06625#bib.bib1)\]\. In mineral thickening dewatering, for instance, soft sensing of underflow concentration directly governs dewatering efficiency and tailings storage safety\. Shift sources including feedstock properties, settling dynamics, and observation pathways act on the same model simultaneously\. Relabeling and retraining are costly with narrow engineering windows, while continuing with the original model incurs systematic bias\. This dilemma is common across process industries\[[39](https://arxiv.org/html/2607.06625#bib.bib24)\]\.

Field engineers often possess scenario\-level knowledge such as ore\-grade decline or reagent\-formula changes, recorded in maintenance logs and shift reports, yet the deployed model has no mechanism to consume such evidence\. Existing adaptation strategies sidestep this problem at three levels\. Parameter\-update methods such as transfer learning, domain adaptation, and meta\-learning assume modifiable parameters, violating the frozen constraint and drawing signals solely from data distributions\[[1](https://arxiv.org/html/2607.06625#bib.bib12),[35](https://arxiv.org/html/2607.06625#bib.bib11),[9](https://arxiv.org/html/2607.06625#bib.bib22)\]\. LLM\-based methods place the LLM inside the prediction loop without uncertainty control\[[3](https://arxiv.org/html/2607.06625#bib.bib13),[6](https://arxiv.org/html/2607.06625#bib.bib14)\]\. Post\-hoc interpretability methods decouple diagnosis from adaptation entirely\[[15](https://arxiv.org/html/2607.06625#bib.bib19)\]\. These blind spots converge on one root cause: the open\-ended evidence gap\. Scenario knowledge exists as unstructured, uncertain text, yet safe adaptation demands structured, uncertainty\-quantified corrections\. Bridging this gap requires a paradigm shift from updating model parameters to updating beliefs about the scenario state\.

![Refer to caption](https://arxiv.org/html/2607.06625v1/x1.png)Figure 1:Adaptation paradigms for industrial specialist models\. \(a\) Parameter\-update methods modifyθ\\thetadirectly, risking regression on validated behavior with no entry point for open\-ended textual evidence\. \(b\) LLM\-as\-predictor approaches embed the LLM in the prediction loop without explicit uncertainty control\. \(c\) ROAM freezesθ\\thetaand uses the LLM only as an out\-of\-loop prior engine\. Adaptation is confined to a low\-dimensional semantic latent correction, fused by Bayesian posterior updating and filtered through multi\-layer risk gating\. The system falls back to the baseline prediction when evidence is insufficient\.As illustrated in[fig\.1](https://arxiv.org/html/2607.06625#S1.F1)\(c\), we propose Reasoning\-Driven Open Adaptation for Specialist Models \(ROAM\), which recasts adaptation as a belief\-update problem\. ROAM constrains all adaptation degrees of freedom to a semantically anchored, low\-dimensional latent space\. The LLM serves solely as an external structured prior engine that produces belief judgments with calibrated uncertainty, without entering the prediction pipeline\. Semantic priors and heterogeneous online observations are fused through Bayesian posterior updating within a single probabilistic framework\. The entire adaptation chain is designed to be conservative: the system falls back to the original frozen prediction when evidence is scarce\. This decoupled design allows independent upgrades of the LLM and the specialist model without mutual revalidation\. The main contributions are as follows\.

- •We propose ROAM, a framework that uses LLM world knowledge and reasoning to enable frozen models to adapt to unseen scenarios without retraining\.
- •We introduce a risk\-constrained mechanism that suppresses unreliable corrections under LLM hallucinations, insufficient evidence, or abrupt scenario shifts, and supports fallback to the original frozen model\.
- •On both a thickening dewatering process and a penicillin fermentation benchmark, ROAM yields substantial cross\-backbone gains in major shift settings with only∼\\sim0\.02 ms of additional inference overhead\.

The remainder of this paper is organized as follows\.[sectionII](https://arxiv.org/html/2607.06625#S2)reviews related work,[sectionIII](https://arxiv.org/html/2607.06625#S3)presents the proposed ROAM framework,[sectionIV](https://arxiv.org/html/2607.06625#S4)reports experimental results, and[sectionV](https://arxiv.org/html/2607.06625#S5)concludes this article\.

## IIRelated Work

### II\-AParameter\-update adaptation

Transfer learning adapts to target domains by fine\-tuning parameters\[[1](https://arxiv.org/html/2607.06625#bib.bib12)\], and domain adaptation aligns feature distributions to reduce cross\-domain discrepancy\[[35](https://arxiv.org/html/2607.06625#bib.bib11)\]\. Cross\-domain industrial diagnosis further uses prototypes or transferable features to reduce domain gaps\[[2](https://arxiv.org/html/2607.06625#bib.bib35)\]\. Meta\-learning acquires rapid adaptation capability through episodic training\[[38](https://arxiv.org/html/2607.06625#bib.bib25)\], and online learning together with test\-time adaptation continuously updates parameters at deployment\[[28](https://arxiv.org/html/2607.06625#bib.bib23)\]\. These methods rest on the premise that model parameters are legitimate degrees of freedom for adaptation\. In industrial deployments, however, specialist models are frozen after validation; parameter modification invalidates certification and introduces regression risk\[[25](https://arxiv.org/html/2607.06625#bib.bib1)\]\. Even if parameters were updatable, adaptation signals come entirely from data distributions, with no mechanism to exploit scenario knowledge in textual form\.

### II\-BLLMs in industrial prediction

Recent studies introduce LLMs into industrial prediction and decision support from three perspectives\. The first treats the LLM as part of the prediction model, using fine\-tuning, adapters, or cross\-modal alignment to connect textual factors or semantic embeddings with battery health estimation, load forecasting, nonstationary time\-series prediction, and fault diagnosis\[[3](https://arxiv.org/html/2607.06625#bib.bib13),[6](https://arxiv.org/html/2607.06625#bib.bib14),[8](https://arxiv.org/html/2607.06625#bib.bib28),[13](https://arxiv.org/html/2607.06625#bib.bib29)\]\. The second uses LLMs as offline knowledge sources, providing physics\-informed priors for graph neural networks or constructing industrial knowledge graphs\[[31](https://arxiv.org/html/2607.06625#bib.bib27),[19](https://arxiv.org/html/2607.06625#bib.bib15)\]\. The third focuses on human\-AI collaborative decision support, where LLMs integrate field knowledge and generate operational suggestions for complex industrial processes such as metallurgy\[[37](https://arxiv.org/html/2607.06625#bib.bib30)\]\. At the same time, recent analysis suggests that the practical gain of LLMs over simpler baselines in time\-series forecasting should be assessed carefully\[[26](https://arxiv.org/html/2607.06625#bib.bib20)\]\. Industrial diagnosis work that fuses multimodal evidence and dynamic variable dependencies further shows that open\-ended evidence can support field\-state judgment, but such evidence usually supports diagnosis or classification rather than conservative correction of frozen predictive models\[[29](https://arxiv.org/html/2607.06625#bib.bib36),[21](https://arxiv.org/html/2607.06625#bib.bib37)\]\. These directions show that LLMs can provide complementary semantic, knowledge\-level, and decision\-level information, but they do not solve the structured\-belief problem required for safe adaptation\. Prediction\-in\-the\-loop methods usually lack explicit uncertainty control\. Offline knowledge\-injection methods mainly use static knowledge during training\. Human\-AI collaborative systems emphasize operational suggestions, but do not directly provide an auditable correction mechanism for frozen predictive models\. Therefore, an LLM’s semantic judgment \(e\.g\., “sensor drift has occurred”\) must still be converted into a structured belief with confidence and boundaries\. Otherwise, coupling the LLM with the specialist model means that upgrading either component requires revalidating the whole system\.

### II\-CInterpretability, uncertainty, and safety

XAI\-FD combines adversarial autoencoders with SHAP for post\-hoc attribution\[[15](https://arxiv.org/html/2607.06625#bib.bib19)\], and CDGNN separates causal and bias substructures through a causal disentangled graph neural network\[[20](https://arxiv.org/html/2607.06625#bib.bib16)\]\. These methods treat interpretability as a post\-hoc analysis layer: the explanation does not influence adaptation, and no closed\-loop mechanism translates diagnosis into correction\. Bayesian methods, probabilistic ensembles, and statistical feature learning provide principled tools for uncertainty quantification and online fault diagnosis in industrial processes\[[4](https://arxiv.org/html/2607.06625#bib.bib17),[16](https://arxiv.org/html/2607.06625#bib.bib18),[33](https://arxiv.org/html/2607.06625#bib.bib38),[18](https://arxiv.org/html/2607.06625#bib.bib39)\]\. Existing Bayesian approaches, however, quantify uncertainty in model parameters or outputs, not in the adaptation process itself\. Few methods incorporate safety into the adaptation design or automatically suppress corrections when evidence is insufficient or contradictory\. ROAM is among the first frameworks that place the LLM outside the prediction loop as a structured prior engine, perform online evidence fusion through Bayesian posterior updating at deployment, and ensure safe fallback via multi\-layer risk gating\.[sectionIII](https://arxiv.org/html/2607.06625#S3)details the framework\.

## IIIMethod

### III\-AOverview

ROAM consists of an offline phase and an online phase\. The offline phase learns a set of low\-capacity linear mappings on training scenarios, establishing an adaptation manifold from backbone hidden states to a five\-dimensional semantic latent space \([sectionIII\-C](https://arxiv.org/html/2607.06625#S3.SS3)\)\. The online phase executes three stages for each new episode: semantic prior construction \([sectionIII\-B](https://arxiv.org/html/2607.06625#S3.SS2)\), structured posterior updating \([sectionIII\-D](https://arxiv.org/html/2607.06625#S3.SS4)\), and output correction with risk gating \([sectionIII\-E](https://arxiv.org/html/2607.06625#S3.SS5)\)\.

Letfθf\_\{\\theta\}be a sequence regressor \(specialist model\) trained offline on a limited set of scenarios and frozen at deployment, with parametersθ\\thetathat are never updated after deployment\.fθf\_\{\\theta\}takes a sliding window𝐱t−W\+1:t\\mathbf\{x\}\_\{t\-W\+1:t\}\(WWis the window length\) as input and produces a scalar predictiony^t0\\hat\{y\}\_\{t\}^\{0\}and an internal hidden state𝐡t\\mathbf\{h\}\_\{t\}\. ROAM estimates and compensates for residual environmental effects using open\-ended scenario evidence and online observations, without modifyingθ\\theta\.

We partition the deployment timeline into episodes\. An episoderris a contiguous operating interval during which the scenario state is approximately stationary\. Episode boundaries are triggered by external events \(e\.g\., operating\-condition switching, maintenance intervention, or operator judgment\), and the posterior is reset to a freshly constructed prior at the start of each new episode\. For each episoderr, we introduce a low\-dimensional corrective latent𝐳r∈ℝ5\\mathbf\{z\}\_\{r\}\\in\\mathbb\{R\}^\{5\}, with each dimension anchored to a common source of industrial mismatch\.[tableI](https://arxiv.org/html/2607.06625#S3.T1)lists the semantic definition and industrial correspondence of each axis\.

TABLE I:Semantic axes of the 5\-D corrective latent space\. Each axis corresponds to a common source of mismatch in industrial deployment\.AxisSymbolSemanticIndustrial Correspondencebiasz1z\_\{1\}fixed offset in observationssensor zero\-point drift, static measurement biasscalez2z\_\{2\}proportional distortionsensor range drift, observation scaling changeloadz3z\_\{3\}hidden load variationupstream feed property change, latent exogenous disturbancedynamicsz4z\_\{4\}response rate changeprocess inertia variation, post\-switching temporal dynamicsreadoutz5z\_\{5\}output mapping driftbaseline readout shift, hidden\-state\-to\-target relation changeIn addition, the system maintains an observation anomaly scoreτr∈\[0,1\]\\tau\_\{r\}\\in\[0,1\]\(not a dimension of𝐳r\\mathbf\{z\}\_\{r\}but an episode\-level gating variable\) that gates the strength of observation\-related corrections\. A higherτr\\tau\_\{r\}indicates greater anomaly in the current observation pathway, leading to stronger suppression of observation\-side corrections\.

Together, all adaptation degrees of freedom are constrained to a semantically anchored, low\-dimensional manifold \(𝐳r\\mathbf\{z\}\_\{r\}andτr\\tau\_\{r\}\), reducing the risk that over\-adaptation disturbs the frozen backbone’s established behavior\.

![Refer to caption](https://arxiv.org/html/2607.06625v1/x2.png)Figure 2:Overview of the ROAM framework\. The left half shows the offline phase, which synthesizes anchors from training\-episode residuals and alternates corrective\-latent inference with linear\-mapping refitting to produce a frozen latent adapter and support geometry\. The right half shows the online phase\. It constructs a Gaussian prior from LLM\-derived semantic judgments, fuses delayed labels, observation anomaly features, and process diagnostics via Bayesian posterior updating, and applies multi\-layer risk gating to yield the adapted prediction\.
### III\-BSemantic Prior Construction via LLM Reasoning

ROAM uses a large language model \(LLM\) as a prior engine to convert open\-ended evidence available at the episode start into structured prior judgments on the five semantic axes\. The prior engine does not participate in the prediction pipeline—it only provides prior beliefs\.

The prior engine input has three temporally legal parts \(no future information is used\)\. \(1\) Open evidence: scenario\-level text from operation logs, maintenance records, and upstream descriptions\. \(2\) Episode\-start structured context: task\-specific exogenous context available at the episode boundary\. \(3\) First\-window diagnostics: a single forward pass of the frozen backbone on the first complete window before any labels arrive, extracting numerically defined anomaly signals such as feature\-drift scores and hidden\-state statistics shifts\.

The prior engine outputs a structured judgment for each of the six semantic axes \(five corrective axes plus trust\): directiondk∈\[−1,1\]d\_\{k\}\\in\[\-1,1\], strengthsk∈\[0,1\]s\_\{k\}\\in\[0,1\], confidenceck∈\[0,1\]c\_\{k\}\\in\[0,1\], a natural\-language rationale, and a global uncertaintyu∈\[0,1\]u\\in\[0,1\]\.

For the five corrective axes, we construct a local Gaussian priorp​\(𝐳r\)=𝒩​\(𝝁0,𝚺0\)p\(\\mathbf\{z\}\_\{r\}\)=\\mathcal\{N\}\(\\bm\{\\mu\}\_\{0\},\\bm\{\\Sigma\}\_\{0\}\)as follows:

μ0,k\\displaystyle\\mu\_\{0,k\}=\\displaystyle=dk⋅sk,\\displaystyle d\_\{k\}\\cdot s\_\{k\},\(1\)σ0,k2\\displaystyle\\sigma\_\{0,k\}^\{2\}=\\displaystyle=σmin2\+\(σmax2−σmin2\)⋅\(1−ck\)\+u2,\\displaystyle\\sigma\_\{\\min\}^\{2\}\+\(\\sigma\_\{\\max\}^\{2\}\-\\sigma\_\{\\min\}^\{2\}\)\\cdot\\frac\{\(1\-c\_\{k\}\)\+u\}\{2\},\(2\)𝚺0\\displaystyle\\bm\{\\Sigma\}\_\{0\}=\\displaystyle=diag​\(σ0,12,…,σ0,52\)\.\\displaystyle\\mathrm\{diag\}\(\\sigma\_\{0,1\}^\{2\},\\ldots,\\sigma\_\{0,5\}^\{2\}\)\.\(3\)Higher confidence and lower global uncertainty yield smaller prior variance, giving the prior stronger influence on the posterior; otherwise the prior becomes diffuse and the posterior relies more on online evidence\.

For the trust axis, the negative direction is clipped to zero, and the product of strength and direction yieldsτprior∈\[0,1\]\\tau\_\{\\text\{prior\}\}\\in\[0,1\]\. A learned anomaly head \(trained offline; see[sectionIII\-C](https://arxiv.org/html/2607.06625#S3.SS3)\) also estimates a diagnostic anomaly scoreτdiag∈\[0,1\]\\tau\_\{\\text\{diag\}\}\\in\[0,1\]from the first\-window observation features\. The episode\-level observation anomaly score fuses both sources:

τr\\displaystyle\\tau\_\{r\}=\\displaystyle=1−\(1−τprior\)​\(1−τdiag\)\.\\displaystyle 1\-\(1\-\\tau\_\{\\text\{prior\}\}\)\(1\-\\tau\_\{\\text\{diag\}\}\)\.\(4\)τr\\tau\_\{r\}remains constant throughout the episode and only affects the gating strength of observation\-side corrections\.

### III\-COffline Learning: Semantic\-Anchored Adaptation Manifold

The offline phase learns a set of low\-capacity linear mappings so that each direction of the five\-dimensional latent explains one interpretable class of industrial mismatch\. It also learns diagnostic heads and the training\-distribution support geometry\.

Training data comes from two sources\. Synthetic anchors apply controlled perturbations to training samples, including observation bias, observation scaling, dynamics acceleration/deceleration, and observation delay\. These perturbations produce perturbed samples along known semantic directions that provide the geometric skeleton for the bias, scale, and dynamics axes\.

The semantic alignment of the load and readout axes comes mainly from the residual and context structure of real training episodes, because these two types of mismatch are difficult to synthesize via simple signal\-level perturbations\. Real training episode residual sequences provide backbone prediction residuals, observation features, summary features, and context features\. By alternating corrective\-latent inference with linear\-mapping refitting, the adaptation manifold aligns with both the semantic directions of synthetic anchors and the residual structure of real data\.

The offline phase produces a latent adapter model with the following learnable components:

Axis coefficient mapping𝐛t=𝐖​𝐡~t\+𝐚\\mathbf\{b\}\_\{t\}=\\mathbf\{W\}\\tilde\{\\mathbf\{h\}\}\_\{t\}\+\\mathbf\{a\}: a linear projection from the standardized backbone hidden state𝐡~t\\tilde\{\\mathbf\{h\}\}\_\{t\}\(zero\-mean, unit\-variance normalization using training\-set statistics\) to a five\-dimensional axis coefficient vector\.

Observation heads: map observation anomaly features \(prediction deviation, feature drift, channel sensitivity shift, etc\.\) to latent observations in the bias/scale subspace, and simultaneously estimate the scalar anomaly scoreτdiag\\tau\_\{\\text\{diag\}\}\.

Nominal summary prediction: predicts the expected summary features under the training distribution from hidden states; the online phase uses the residual between actual and nominal summaries as dynamics evidence\.

Load / dynamics / readout subspace heads: estimate latent observations for each subspace from the corresponding context or residualized features\.

Support geometry: the set of support latents formed by synthetic anchor latents and inferred training episode corrective latents, standardized to approximately zero mean and unit diagonal covariance\. The online phase measures deviation from the training distribution via the nearest distance from the posterior mean to the support latents\.

For example, the axis coefficient mapping is fitted by ridge regression:

min𝐖,𝐚​∑t‖et−\(𝐖​𝐡~t\+𝐚\)⊤​𝐳r‖2\+λ​‖𝐖‖F2,\\displaystyle\\min\_\{\\mathbf\{W\},\\mathbf\{a\}\}\\sum\_\{t\}\\\|e\_\{t\}\-\(\\mathbf\{W\}\\tilde\{\\mathbf\{h\}\}\_\{t\}\+\\mathbf\{a\}\)^\{\\top\}\\mathbf\{z\}\_\{r\}\\\|^\{2\}\+\\lambda\\\|\\mathbf\{W\}\\\|\_\{F\}^\{2\},\(5\)whereet=yt−y^t0e\_\{t\}=y\_\{t\}\-\\hat\{y\}\_\{t\}^\{0\}is the backbone residual and𝐳r\\mathbf\{z\}\_\{r\}is the current episode’s corrective latent \(known for synthetic anchors, inferred by alternation for real episodes\)\. The observation heads, summary prediction head, and subspace heads all adopt a similar linear regression form, but differ in their input features and target subspaces\.

Joint training first fits the initial axis coefficient mapping and diagnostic heads on synthetic anchors\. If training episode data are available, ROAM alternates corrective\-latent inference with mapping refitting forNiterN\_\{\\text\{iter\}\}rounds until the mapping residual stabilizes\. All linear heads are then jointly refitted on the combined set of anchors and training episodes\. Every mapping is linear, and all offline\-learned components are fully frozen during online adaptation\.

### III\-DOnline Posterior Update: Structured Evidence Fusion

The online phase maintains a Gaussian posterior𝒩​\(𝝁r,𝚺r\)\\mathcal\{N\}\(\\bm\{\\mu\}\_\{r\},\\bm\{\\Sigma\}\_\{r\}\)over𝐳r\\mathbf\{z\}\_\{r\}, initialized from the prior\(𝝁0,𝚺0\)\(\\bm\{\\mu\}\_\{0\},\\bm\{\\Sigma\}\_\{0\}\)constructed in[sectionIII\-B](https://arxiv.org/html/2607.06625#S3.SS2)\. As the episode progresses, three types of heterogeneous evidence are fused into the posterior through different pathways, with each type acting only on its corresponding semantic subspace\.[fig\.3](https://arxiv.org/html/2607.06625#S3.F3)illustrates the complete data flow from prior construction to the final conservative correction\.

![Refer to caption](https://arxiv.org/html/2607.06625v1/x3.png)Figure 3:Online posterior update and conservative correction\. \(A\) The LLM prior engine processes open\-ended evidence, structured context, and first\-window diagnostics once per episode to produce a Gaussian prior and an observation anomaly scoreτr\\tau\_\{r\}\. \(B\) Delayed labels, observation anomaly features, and process diagnostics each update the shared posterior within their respective semantic subspaces at each prediction step\. \(C\) Posterior uncertainty and support distance are extracted for risk control\. \(D\) Subspace corrections pass through multi\-layer risk gating to yield the adapted prediction; dashed arrows indicate fallback to the frozen baseline when evidence is insufficient\.Delayed label residuals\.When historical labels are revealed after a delay ofΔ\\Deltasteps, we compute the residualet=yt−y^t0e\_\{t\}=y\_\{t\}\-\\hat\{y\}\_\{t\}^\{0\}and perform a standard linear\-Gaussian Kalman single\-step update using the current axis coefficient vector𝐛t\\mathbf\{b\}\_\{t\}as the observation matrix:

𝐊t\\displaystyle\\mathbf\{K\}\_\{t\}=\\displaystyle=𝚺r​𝐛t𝐛t⊤​𝚺r​𝐛t\+σy2,\\displaystyle\\frac\{\\bm\{\\Sigma\}\_\{r\}\\mathbf\{b\}\_\{t\}\}\{\\mathbf\{b\}\_\{t\}^\{\\top\}\\bm\{\\Sigma\}\_\{r\}\\mathbf\{b\}\_\{t\}\+\\sigma\_\{y\}^\{2\}\},\(6\)𝝁r\\displaystyle\\bm\{\\mu\}\_\{r\}←\\displaystyle\\leftarrow𝝁r\+𝐊t​\(et−𝐛t⊤​𝝁r\),\\displaystyle\\bm\{\\mu\}\_\{r\}\+\\mathbf\{K\}\_\{t\}\(e\_\{t\}\-\\mathbf\{b\}\_\{t\}^\{\\top\}\\bm\{\\mu\}\_\{r\}\),\(7\)𝚺r\\displaystyle\\bm\{\\Sigma\}\_\{r\}←\\displaystyle\\leftarrow𝚺r−𝐊t​𝐛t⊤​𝚺r,\\displaystyle\\bm\{\\Sigma\}\_\{r\}\-\\mathbf\{K\}\_\{t\}\\mathbf\{b\}\_\{t\}^\{\\top\}\\bm\{\\Sigma\}\_\{r\},\(8\)where𝐊t\\mathbf\{K\}\_\{t\}is the Kalman gain andσy2\\sigma\_\{y\}^\{2\}is the label observation noise variance\. This is the most direct evidence source—real labels drive the latent toward the direction that explains the residual\.

Subspace Gaussian update\.Both observation and process evidence are fused into the posterior via the following general form, an analogous Gaussian update restricted to index setℐ\\mathcal\{I\}\. Let𝐳~\\tilde\{\\mathbf\{z\}\}denote the latent observation in that subspace andσ2\\sigma^\{2\}the observation noise variance:

𝐊ℐ\\displaystyle\\mathbf\{K\}\_\{\\mathcal\{I\}\}=\\displaystyle=𝚺r​\[ℐ,ℐ\]​\(𝚺r​\[ℐ,ℐ\]\+σ2​𝐈\)−1,\\displaystyle\\bm\{\\Sigma\}\_\{r\}\[\\mathcal\{I\},\\mathcal\{I\}\]\\big\(\\bm\{\\Sigma\}\_\{r\}\[\\mathcal\{I\},\\mathcal\{I\}\]\+\\sigma^\{2\}\\mathbf\{I\}\\big\)^\{\-1\},\(9\)𝝁r​\[ℐ\]\\displaystyle\\bm\{\\mu\}\_\{r\}\[\\mathcal\{I\}\]←\\displaystyle\\leftarrow𝝁r​\[ℐ\]\+𝐊ℐ​\(𝐳~−𝝁r​\[ℐ\]\),\\displaystyle\\bm\{\\mu\}\_\{r\}\[\\mathcal\{I\}\]\+\\mathbf\{K\}\_\{\\mathcal\{I\}\}\\big\(\\tilde\{\\mathbf\{z\}\}\-\\bm\{\\mu\}\_\{r\}\[\\mathcal\{I\}\]\\big\),\(10\)𝚺r​\[ℐ,ℐ\]\\displaystyle\\bm\{\\Sigma\}\_\{r\}\[\\mathcal\{I\},\\mathcal\{I\}\]←\\displaystyle\\leftarrow\(𝐈−𝐊ℐ\)​𝚺r​\[ℐ,ℐ\]\.\\displaystyle\(\\mathbf\{I\}\-\\mathbf\{K\}\_\{\\mathcal\{I\}\}\)\\bm\{\\Sigma\}\_\{r\}\[\\mathcal\{I\},\\mathcal\{I\}\]\.\(11\)This update modifies only the components of𝝁r\\bm\{\\mu\}\_\{r\}and𝚺r\\bm\{\\Sigma\}\_\{r\}at indicesℐ\\mathcal\{I\}; all other dimensions remain unchanged\.

Observation anomaly evidence\.Observation anomaly features \(feature drift, channel sensitivity shift, etc\.\) are mapped by the learned observation head to a latent observation𝐳~obs\\tilde\{\\mathbf\{z\}\}\_\{\\text\{obs\}\}in the bias/scale subspace\. After averaging buffered features over a predefined update interval, the subspace update above is applied withℐobs=\{1,2\}\\mathcal\{I\}\_\{\\text\{obs\}\}=\\\{1,2\\\}\. The effective noise variance of observation evidence is amplified byτr\\tau\_\{r\}:

σobs,eff2\\displaystyle\\sigma\_\{\\text\{obs,eff\}\}^\{2\}=\\displaystyle=σobs2​\(1\+τr\),\\displaystyle\\sigma\_\{\\text\{obs\}\}^\{2\}\(1\+\\tau\_\{r\}\),\(12\)so that higher observation anomaly weakens the pull of observation evidence on the posterior\.

Process diagnostic evidence\.Process\-related evidence is split into three independent subspace channels, each using the subspace update in[eq\.9](https://arxiv.org/html/2607.06625#S3.E9)–[eq\.11](https://arxiv.org/html/2607.06625#S3.E11)\. \(i\) Dynamics evidence comes from the residual between the current window’s summary features and the nominal summary prediction; the dynamics head maps it to updatez4z\_\{4\}with noise varianceσdyn2\\sigma\_\{\\text\{dyn\}\}^\{2\}\. \(ii\) Readout evidence comes from the interaction between residuals and context features; the readout head maps it to updatez5z\_\{5\}with noise varianceσread2\\sigma\_\{\\text\{read\}\}^\{2\}\. \(iii\) Load evidence comes from context features combined with the current residual mean; the load head maps it to updatez3z\_\{3\}with noise varianceσload2\\sigma\_\{\\text\{load\}\}^\{2\}\. Like observation evidence, process evidence is buffered and batch\-updated at predefined intervals\.

At each prediction step, two types of geometric quantities are derived from the posterior for risk control: the posterior trace, measuring uncertainty magnitude separately on the observation and process subspaces; and the support distance, the Euclidean distance from the posterior mean to the nearest support latent, measuring deviation from the training distribution\.

### III\-EOutput Correction and Risk Gating

Given the posterior\(𝝁r,𝚺r\)\(\\bm\{\\mu\}\_\{r\},\\bm\{\\Sigma\}\_\{r\}\)and the current axis coefficients𝐛t\\mathbf\{b\}\_\{t\}, ROAM computes corrections via subspace dot products and applies them to the baseline prediction through multi\-layer gating \(Block D in[fig\.3](https://arxiv.org/html/2607.06625#S3.F3)\)\. Let the baseline prediction bey^t0\\hat\{y\}\_\{t\}^\{0\}\. The axis coefficient mapping yields𝐛t∈ℝ5\\mathbf\{b\}\_\{t\}\\in\\mathbb\{R\}^\{5\}, split into an observation part𝐛tobs\\mathbf\{b\}\_\{t\}^\{\\text\{obs\}\}\(bias/scale axes\) and a process part𝐛tproc\\mathbf\{b\}\_\{t\}^\{\\text\{proc\}\}\(load/dynamics/readout axes\)\. The subspace corrections are:

cobs\\displaystyle c\_\{\\text\{obs\}\}=\\displaystyle=\(𝐛tobs\)⊤​𝝁robs,\\displaystyle\(\\mathbf\{b\}\_\{t\}^\{\\text\{obs\}\}\)^\{\\top\}\\bm\{\\mu\}\_\{r\}^\{\\text\{obs\}\},\(13\)cproc\\displaystyle c\_\{\\text\{proc\}\}=\\displaystyle=\(𝐛tproc\)⊤​𝝁rproc,\\displaystyle\(\\mathbf\{b\}\_\{t\}^\{\\text\{proc\}\}\)^\{\\top\}\\bm\{\\mu\}\_\{r\}^\{\\text\{proc\}\},\(14\)where𝝁robs\\bm\{\\mu\}\_\{r\}^\{\\text\{obs\}\}and𝝁rproc\\bm\{\\mu\}\_\{r\}^\{\\text\{proc\}\}are the posterior mean projected onto the corresponding subspaces\.

Each subspace has an effect strength coefficient that approaches zero when the posterior mean is small relative to the uncertainty—even if the correction direction is correct, insufficient confidence prevents large corrections:

αobs\\displaystyle\\alpha\_\{\\text\{obs\}\}=\\displaystyle=‖𝝁robs‖‖𝝁robs‖\+tr​\(𝚺robs\)\+ϵ,\\displaystyle\\frac\{\\\|\\bm\{\\mu\}\_\{r\}^\{\\text\{obs\}\}\\\|\}\{\\\|\\bm\{\\mu\}\_\{r\}^\{\\text\{obs\}\}\\\|\+\\sqrt\{\\mathrm\{tr\}\(\\bm\{\\Sigma\}\_\{r\}^\{\\text\{obs\}\}\)\}\+\\epsilon\},\(15\)withαproc\\alpha\_\{\\text\{proc\}\}defined analogously andϵ\>0\\epsilon\>0a small constant for numerical stability\.

The base gating coefficientγ\\gammais jointly determined by the posterior covariance trace and the support distance:

γ=exp\(−η1⋅tr\(𝚺robs\)−η2⋅tr\(𝚺rproc\)\\displaystyle\\gamma=\\exp\\\!\\Big\(\{\-\}\\eta\_\{1\}\\cdot\\mathrm\{tr\}\(\\bm\{\\Sigma\}\_\{r\}^\{\\text\{obs\}\}\)\-\\eta\_\{2\}\\cdot\\mathrm\{tr\}\(\\bm\{\\Sigma\}\_\{r\}^\{\\text\{proc\}\}\)−β1⋅dobs−β2⋅dproc\),\\displaystyle\\qquad\\qquad\{\-\}\\beta\_\{1\}\\cdot d\_\{\\text\{obs\}\}\-\\beta\_\{2\}\\cdot d\_\{\\text\{proc\}\}\\Big\),\(16\)wheredobsd\_\{\\text\{obs\}\}anddprocd\_\{\\text\{proc\}\}denote the nearest support\-latent distances computed in the observation and process subspaces, respectively \(measuring deviation from the training distribution\), andη1,η2,β1,β2\\eta\_\{1\},\\eta\_\{2\},\\beta\_\{1\},\\beta\_\{2\}are hyperparameters\. The observation\-side and process\-side gating coefficients are:

γobs\\displaystyle\\gamma\_\{\\text\{obs\}\}=\\displaystyle=γ1\+τr,γproc=γ\.\\displaystyle\\frac\{\\gamma\}\{1\+\\tau\_\{r\}\},\\qquad\\gamma\_\{\\text\{proc\}\}=\\gamma\.\(17\)The observation anomaly scoreτr\\tau\_\{r\}suppresses only observation\-related corrections\. The final adapted prediction is:

y^t\\displaystyle\\hat\{y\}\_\{t\}=\\displaystyle=y^t0\+γobs⋅αobs⋅cobs\+γproc⋅αproc⋅cproc\.\\displaystyle\\hat\{y\}\_\{t\}^\{0\}\+\\gamma\_\{\\text\{obs\}\}\\cdot\\alpha\_\{\\text\{obs\}\}\\cdot c\_\{\\text\{obs\}\}\+\\gamma\_\{\\text\{proc\}\}\\cdot\\alpha\_\{\\text\{proc\}\}\\cdot c\_\{\\text\{proc\}\}\.\(18\)
Prior diffusion, effect strength suppression, gating decay, and trust gating cascade to drive the system toward no\-op under uncertainty, i\.e\., it degrades to the original backbone prediction\. All prior judgments, posterior updates, and gating coefficients can be logged for post\-hoc inspection\.

## IVExperiments

We evaluate ROAM on two industrial processes\.

### IV\-AExperimental Settings

All backbones and ROAM components are trained and evaluated in the same codebase with identical hyperparameters\. No per\-dataset or per\-backbone tuning is applied\. Experiments run on a workstation equipped with an Intel Xeon 8470Q CPU, 90 GB RAM, and a single NVIDIA RTX 5090 GPU \(32 GB\)\. The implementation uses Python 3\.14, PyTorch 2\.11\.0, and CUDA 13\.0\. Main results report the mean over three independent runs\. Each backbone is trained with Adam \(lr =1×10−31\{\\times\}10^\{\-3\}\) for a fixed budget of 300 epochs and then frozen\. The ROAM offline adapter is fitted on the frozen backbone via ridge regression \(λ=0\.001\\lambda\{=\}0\.001\) with 3 alternating iterations over synthetic anchors and real episodes\. The online prior engine uses DeepSeek\-V3\.2\-Thinking\. No post\-processing is applied at inference\.

We report three metrics: mean absolute error \(MAE↓\\downarrow\), root mean squared error \(RMSE↓\\downarrow\), and coefficient of determination \(R2R^\{2\}↑\\uparrow\)\. Efficiency is measured by per\-step inference time \(ms/step↓\\downarrow\)\. To validate the backbone\-agnostic design, we test seven backbones spanning four architecture families: classic ML \(SVR\[[23](https://arxiv.org/html/2607.06625#bib.bib4)\]and XGBoost\[[5](https://arxiv.org/html/2607.06625#bib.bib5)\]\), recurrent models \(GRU\[[7](https://arxiv.org/html/2607.06625#bib.bib6)\]and LSTM\[[14](https://arxiv.org/html/2607.06625#bib.bib7)\]\), attention\-based models \(Transformer\[[27](https://arxiv.org/html/2607.06625#bib.bib8)\]and Informer\[[36](https://arxiv.org/html/2607.06625#bib.bib9)\]\), and a state\-space model \(Mamba\[[12](https://arxiv.org/html/2607.06625#bib.bib10)\]\)\. All backbones share the same ROAM adapter configuration and evaluation protocol\.

### IV\-BDatasets

We validate ROAM on two industrial processes\. In both environments, the training set contains only standard production runs, so that the model learns exclusively nominal process dynamics without exposure to any shift or fault condition\. This design provides a stricter test of adaptation capability\. Each test set reserves one in\-distribution scenario as a baseline control\.[tableII](https://arxiv.org/html/2607.06625#S4.T2)gives the full taxonomy\.

TABLE II:Scenario taxonomy for the thickening and IndPenSim environments, organized by train/test split and shift category\.UsageCategoryScenario DescriptionThickening Dewatering \(19 scenarios\)TrainNominalFeed jitter variations under nominal conditions×\\times6TestSame\-familyHeld\-out nominal feed\-jitterVisible shiftSustained high upstream loadSustained low upstream loadHidden shiftDischarge efficiency dropSlurry property shiftFeed solids ratio shiftFlocculant dosing failureMedia permeability lossActuator deadtime / gain lossRestart inventory shiftObservation shiftPressure sensor biasFlow scale errorPressure signal delayIndPenSim Penicillin Fermentation \(44 scenarios\)TrainRecipe controlStandard recipe\-based control×\\times29TestSame\-familyHeld\-out standard\-recipeOperator controlOperator\-controlled process×\\times2Control\-regimeRaman\-assisted advanced process control×\\times2Process faultSubstrate feed anomaly×\\times3pH measurement drift×\\times2Cooling / thermal anomaly×\\times2Aeration anomaly×\\times3The thickening dewatering environment originates from a No\. 7 tailings thickener \(diameter 50 m\) at a plant in Nanjing, China\. The soft\-sensing target is minute\-level underflow concentrationcufc\_\{\\text\{uf\}\}\. The thickener dewaters tailings slurry via gravity settling and flocculation, and underflow concentration directly governs downstream filter\-press efficiency and tailings storage safety\. Model inputs are feed flow, mid\-level and bottom pressures, and two phase indicators \(5 variables\), with each episode spanning 300 minutes\. Six training scenarios cover nominal feed jitter, and fourteen test scenarios span a baseline control, a same\-family generalization check, and shift scenarios grouped by visibility\.[fig\.4](https://arxiv.org/html/2607.06625#S4.F4)shows the system inputs, the digital\-twin interface, and on\-site deployment views\.

![Refer to caption](https://arxiv.org/html/2607.06625v1/figure/thickening_site.png)Figure 4:No\. 7 tailings thickening dewatering site at a plant in Nanjing, China, showing system input signals, the digital\-twin interface, and on\-site deployment views\.The IndPenSim environment is drawn from the publicly available IndPenSim V3 dataset\[[11](https://arxiv.org/html/2607.06625#bib.bib31)\], which simulates an industrial\-scale penicillin fed\-batch fermentation process\. The process cultivatesPenicillium chrysogenumin a bioreactor under controlled temperature, pH, dissolved oxygen, and feeding strategies\. The soft\-sensing target is offline penicillin concentration\. Model inputs comprise 23 online process variables with a window length of 120 steps\. Twenty\-nine training batches cover standard recipe\-based control\. Fifteen test scenarios span a baseline control, operator\-controlled runs, Raman\-assisted APC runs, and process faults\.

### IV\-CMain Results

[tableIII](https://arxiv.org/html/2607.06625#S4.T3)and[tableIV](https://arxiv.org/html/2607.06625#S4.T4)report MAE, RMSE,R2R^\{2\}, and per\-step inference time for each method across scenario categories\.

TABLE III:Quantitative comparison in the thickening environment across seven backbones\. MAE and RMSE are in units of × 103\. Best per column in bold\.Same\-familyVisible shiftHidden shiftObservation shiftBackboneSettingMAE↓\\downarrowRMSE↓\\downarrowR2R^\{2\}↑\\uparrowMAE↓\\downarrowRMSE↓\\downarrowR2R^\{2\}↑\\uparrowMAE↓\\downarrowRMSE↓\\downarrowR2R^\{2\}↑\\uparrowMAE↓\\downarrowRMSE↓\\downarrowR2R^\{2\}↑\\uparrowInference Time \(ms/step\)↓\\downarrowSVRBase0\.1880\.2310\.9996911\.18312\.963\-0\.0368524\.21941\.5720\.129185\.2557\.6850\.662670\.144\+ROAM0\.1850\.2270\.999708\.51810\.0020\.3827919\.68437\.0190\.309494\.1226\.0130\.793490\.151XGBoostBase0\.0470\.0610\.999980\.0590\.0790\.9999623\.12840\.6300\.168220\.0510\.0650\.999980\.255\+ROAM0\.0470\.0610\.999980\.0600\.0800\.9999618\.88836\.1200\.342630\.0590\.0780\.999970\.270GRUBase0\.0270\.0340\.999990\.6720\.8460\.9955922\.95740\.3910\.177962\.3413\.4820\.930731\.532\+ROAM0\.0230\.0310\.999990\.5510\.7540\.9964918\.32935\.1540\.377321\.7522\.7520\.956741\.538LSTMBase0\.0360\.0580\.999980\.9681\.3000\.9895723\.01440\.4430\.175842\.9074\.3920\.889840\.584\+ROAM0\.0370\.0570\.999980\.7541\.0570\.9931118\.28235\.0210\.382022\.1413\.2340\.940270\.589TransformerBase0\.0570\.0820\.999963\.8904\.5740\.8709022\.97740\.4240\.176602\.5023\.5530\.927891\.170\+ROAM0\.0550\.0780\.999973\.6684\.3710\.8821418\.29835\.1150\.378682\.6654\.5680\.880781\.186InformerBase0\.4000\.4930\.998610\.8370\.9640\.9942724\.39841\.4840\.132881\.8243\.5140\.929457\.845\+ROAM0\.3820\.4700\.998740\.7110\.8190\.9958719\.38236\.0790\.344111\.4302\.6870\.958757\.858MambaBase0\.0190\.0231\.000007\.3168\.4750\.5568422\.84240\.3030\.181543\.4004\.1920\.899648\.716\+ROAM0\.0180\.0231\.000005\.3696\.3790\.7489018\.15034\.8910\.386582\.7253\.3220\.936988\.736TABLE IV:Quantitative comparison on the IndPenSim environment across seven backbones\. Best per column in bold\.Same\-familyOperator controlControl\-regimeProcess faultBackboneSettingMAE↓\\downarrowRMSE↓\\downarrowR2R^\{2\}↑\\uparrowMAE↓\\downarrowRMSE↓\\downarrowR2R^\{2\}↑\\uparrowMAE↓\\downarrowRMSE↓\\downarrowR2R^\{2\}↑\\uparrowMAE↓\\downarrowRMSE↓\\downarrowR2R^\{2\}↑\\uparrowInference Time \(ms/step\)↓\\downarrowSVRBase1\.6752\.1580\.810362\.1753\.9940\.821971\.7272\.3620\.942523\.3604\.4310\.723750\.638\+ROAM1\.5962\.0420\.830281\.7972\.9980\.899701\.5162\.1070\.954242\.7753\.6650\.811010\.650XGBoostBase1\.3451\.9600\.843640\.8601\.4660\.976011\.1271\.6350\.972453\.2124\.5210\.712460\.283\+ROAM1\.1591\.7500\.875360\.8471\.4500\.976531\.0501\.4520\.978262\.4203\.3200\.844940\.301GRUBase0\.9281\.2270\.938750\.9251\.1970\.984001\.3001\.8280\.965582\.9654\.2670\.743800\.529\+ROAM0\.9381\.2320\.938180\.8971\.1710\.984691\.2291\.6810\.970892\.6403\.7360\.803650\.534LSTMBase0\.8651\.1600\.945202\.4424\.1070\.811751\.4701\.8760\.963733\.0704\.5650\.706760\.565\+ROAM0\.8041\.0820\.952381\.7912\.8680\.908221\.3461\.7320\.969072\.8434\.0840\.765330\.569TransformerBase1\.0341\.3130\.929792\.2013\.4790\.864923\.0795\.2070\.720542\.6963\.7420\.803021\.115\+ROAM0\.9921\.2620\.935171\.9082\.8740\.907802\.5114\.3360\.806212\.3643\.2950\.847281\.129InformerBase0\.8151\.0530\.954872\.3553\.6890\.848081\.0861\.3880\.980152\.0663\.1660\.859007\.387\+ROAM0\.8061\.0100\.958431\.9963\.0590\.895531\.1301\.4210\.979181\.8212\.5830\.906127\.399MambaBase1\.6302\.1940\.804033\.0304\.3480\.788973\.0235\.5830\.678763\.8015\.1100\.6325826\.615\+ROAM1\.4902\.0850\.823062\.6323\.5600\.858562\.6884\.4920\.792083\.3714\.6680\.6934226\.655In the thickening environment, same\-family performance is near saturation for all backbones, and ROAM introduces negligible change\. The gains concentrate on hidden shift\. Base hidden\-shift MAE falls within a narrow 22\.8–24\.4 band across all seven backbones, dropping consistently to 18\.2–19\.7 with ROAM, a reduction of roughly 20%, with Mamba\+ROAM reaching the lowest value\. The tight clustering of Base scores shows that hidden shift is a backbone\-agnostic bottleneck: changes in load, dynamics, or readout are barely visible in raw channels, so all backbones degrade to a similar level\.

Visible\-shift and observation\-shift Base MAEs, by contrast, vary by orders of magnitude across backbones\. XGBoost Base already achieves lower MAE than every other backbone’s \+ROAM on both categories, because the shift signal is encoded in the input features\. Observation\-shift improvements are weaker and less uniform than hidden\-shift gains\. Some corruptions are absorbed by backbone robustness, and ROAM intervenes only where the posterior carries sufficient evidence\.

IndPenSim confirms the pattern under harder conditions: absolute errors are larger and backbone rankings are less stable\. The clearest gains appear in operator\-control and process\-fault scenarios, where retraining data are scarcest\. The control\-regime column is mixed; some regime changes are already encoded in trajectories and handled by sequence models alone\. Inference time sets an engineering bound: tree models and GRU/LSTM keep overhead practical, while Informer and Mamba cost substantially more\. Across both datasets, ROAM delivers its gains where mismatch is hidden and retraining is impractical\. The added cost scales with the backbone’s own computational footprint\.

### IV\-DQualitative Results

[fig\.5](https://arxiv.org/html/2607.06625#S4.F5)compares the GRU backbone and GRU\+ROAM on eight representative IndPenSim anomaly scenarios\.

![Refer to caption](https://arxiv.org/html/2607.06625v1/x4.png)Figure 5:Prediction curves on eight representative IndPenSim anomaly scenarios comparing GRU \(Base\) and GRU\+ROAM\. Lower strips report the final posterior on five semantic axes and the trust scoreτr\\tau\_\{r\}; serrated ends mark out\-of\-range values\.In the substrate\-feed and aeration anomalies \(A–C, G, H\), the frozen backbone overestimates penicillin concentration and ROAM pulls the prediction back toward ground truth\. The posterior concentrates on the readout axis with only minor bias, load, or scale corrections\. These shifts are mainly output\-mapping mismatch\. D and E are smoother\. The backbone already captures the main batch trend and ROAM makes only selective corrections\. F has the largestτr\\tau\_\{r\}among the eight scenarios, and a positive readout posterior still provides partial compensation\. H is the hardest case\. The readout posterior reaches the display limit, yet ROAM only partially closes the gap\. This result exposes the boundary of low\-capacity external correction under severe aeration mismatch\.

### IV\-EAblation Studies

[tableV](https://arxiv.org/html/2607.06625#S4.T5)ablates ROAM in the thickening environment\. Var\. A is the frozen GRU baseline reused from Main Results, and Var\. I is the full system\. Variants B–I share the same base artifact and progressively enable label\-residual updates, observation and process evidence, LLM prior, risk gate, trust gate, and subspace decoupling\.

TABLE V:Component ablation in the thickening environment \(GRU backbone\)\. Var\. A is the frozen baseline and Var\. I is the full ROAM system\. In the subspace update mode each evidence channel updates only its designated axes, whereas in the full mode all channels update the entire 5\-D latent\.Evidence channelMAE \( × 103\)↓\\downarrowVariantPrior sourceLabelresidualObservationevidenceProcessevidenceRisk gateTrust gateτr\\tau\_\{r\}Update spaceSame\-familyVisible shiftHidden shiftObservation shiftA––––––subspace0\.0270\.67222\.9572\.341B–✓\\checkmark––✓\\checkmark✓\\checkmarksubspace0\.0260\.66120\.4612\.197C–✓\\checkmark✓\\checkmark–✓\\checkmark✓\\checkmarksubspace0\.0260\.58320\.1042\.121D–✓\\checkmark–✓\\checkmark✓\\checkmark✓\\checkmarksubspace0\.0250\.63819\.0772\.003Eflat✓\\checkmark✓\\checkmark✓\\checkmark✓\\checkmark✓\\checkmarksubspace0\.0240\.55618\.4681\.862FLLM✓\\checkmark✓\\checkmark✓\\checkmark✓\\checkmark–subspace0\.0240\.55218\.3441\.841GLLM✓\\checkmark✓\\checkmark✓\\checkmark––subspace0\.0240\.7315\.3061\.725HLLM✓\\checkmark✓\\checkmark✓\\checkmark✓\\checkmark✓\\checkmarkfull0\.0260\.60417\.7951\.975ILLM✓\\checkmark✓\\checkmark✓\\checkmark✓\\checkmark✓\\checkmarksubspace0\.0230\.55118\.3291\.752A→\\toB shows that online posterior updating is the primary source of gain, with the largest improvement on hidden\-shift scenarios\. B→\\toC mainly improves visible shifts while B→\\toD mainly improves hidden and observation shifts, confirming that the two channels act on separated latent subspaces\. Observation evidence corrects bias/scale axes and process evidence corrects load/dynamics/readout axes\. D→\\toE completes all three channels under a flat prior and yields consistent improvement across categories\. E→\\toI replaces the flat prior with LLM semantics and mainly provides directional initialization for the hidden axes\. The remaining columns change little because label\-residual and evidence channels already deliver most of the adaptation benefit\.

F and I differ only in the trust gate\. Removing it yields marginal improvement, indicating that the gate is a conservatism mechanism that suppresses unreliable observation updates at a slight accuracy cost\. G further removes the risk gate and achieves the best MAE on same\-family, hidden, and observation shifts, but causes visible\-shift over\-correction\. H and I differ only in update space\. Full\-space updating improves hidden\-shift recovery but raises error elsewhere due to cross\-axis interference\. Subspace decoupling keeps each axis’s correction isolated\. Both gating and subspace choices trade per\-category aggressiveness for cross\-scenario balance\.

Var\. I is the most balanced configuration\. It retains the LLM prior’s hidden\-axis initialization while avoiding the over\-correction of G and the cross\-axis interference of H\. Standard deviations across three LLM repeats remain below 0\.050\.

### IV\-FAnalysis and Discussion

We examine parameter sensitivity, LLM sensitivity, adaptation paradigm comparison, and computational efficiency\.

#### IV\-F1Parameter Sensitivity

[fig\.6](https://arxiv.org/html/2607.06625#S4.F6)presents a one\-at\-a\-time sensitivity analysis of four hyperparameters for the GRU\+ROAM configuration in the thickening environment\.

![Refer to caption](https://arxiv.org/html/2607.06625v1/x5.png)Figure 6:One\-at\-a\-time sensitivity analysis of four ROAM hyperparameters \(σmax2\\sigma\_\{\\max\}^\{2\},σy2\\sigma\_\{y\}^\{2\},Δu\\Delta\_\{u\},λg\\lambda\_\{g\}\) in the thickening environment \(GRU backbone\)\. Each subplot reports MAE across four scenario categories\.All four hyperparameters show cross\-category trade\-offs\.σmax2\\sigma\_\{\\max\}^\{2\}andσy2\\sigma\_\{y\}^\{2\}have moderate effects, with each shift category improving at the expense of others\.Δu\\Delta\_\{u\}andλg\\lambda\_\{g\}have larger effects\. A short update interval amplifies short\-term fluctuations and raises same\-family MAE\. The trade\-off is most pronounced inλg\\lambda\_\{g\}\. Relaxing the gate substantially improves hidden shift but worsens visible shift, and tightening reverses the trend\. The defaults yield the best compromise across all four categories\.

#### IV\-F2LLM Sensitivity

To analyze the sensitivity of ROAM to different LLMs,[fig\.7](https://arxiv.org/html/2607.06625#S4.F7)fixes the GRU backbone and swaps only the prior engine across DeepSeek, GPT, Gemini, and Claude\.

![Refer to caption](https://arxiv.org/html/2607.06625v1/x6.png)Figure 7:Relative MAE of LLM prior engines in the thickening environment with a fixed GRU backbone\. Each shift category is normalized by the DeepSeek\-V3\.2 result\. The dashed line marks parity at 1\.00\.All bars fall within a narrow 0\.95 to 1\.05 band, and the largest deviation across four shift categories does not exceed 5%\. This is because the LLM only provides the initial prior\. Subsequent online updates are driven by observations, and the initial differences among LLMs vanish within a few steps\. The results confirm that ROAM maintains stable adaptation performance across all four representative LLMs\.

#### IV\-F3Adaptation Paradigm Comparison

Scenario shifts fall within the classic scope of transfer learning, meta\-learning, and online fine\-tuning\.[tableVI](https://arxiv.org/html/2607.06625#S4.T6)benchmarks ROAM against these established paradigms in the thickening environment\.

TABLE VI:Adaptation paradigm comparison in the thickening environment \(GRU backbone\)\. MAE in units of × 103; best per column in bold\.StrategySame\-familyVisible shiftHidden shiftObservation shiftFrozen backbone0\.0270\.67222\.9572\.341Last\-layer fine\-tune0\.0230\.54922\.5661\.983Full\-model fine\-tune0\.0260\.47522\.9032\.289MAML0\.0220\.51021\.4471\.960ROAM0\.0230\.55118\.3291\.752Both fine\-tuning variants improve visible\- and observation\-shift MAE but leave hidden\-shift MAE near the frozen\-backbone level\. This confirms that gradient updates exploit observable distributional changes but cannot capture unobserved process\-logic shifts\. MAML narrows the hidden\-shift gap further than either fine\-tuning variant but still falls well short of ROAM, indicating that data\-driven meta\-learning alone cannot compensate when the underlying process logic changes\.

ROAM achieves the best hidden\-shift and observation\-shift MAE without updating backbone parameters or degrading same\-family performance, while full\-model fine\-tuning leads only on visible shift\. Open\-ended textual evidence supplies scenario\-level information that gradient signals cannot access, enabling the best overall adaptation with a fully frozen backbone\.

#### IV\-F4Computational Efficiency

[tableVII](https://arxiv.org/html/2607.06625#S4.T7)reports per\-step deployment cost in the thickening environment\. Each episode invokes the language model only once at the start to construct the semantic prior\.

TABLE VII:Per\-step deployment cost in the thickening environment\. Peak RSS is the memory increment over the base model\. For SVR and XGBoost, backbone parameters include all stored support vectors or tree nodes\.Parameters \( × 103\)↓\\downarrowDeployment Cost↓\\downarrowBackboneBackboneAdapterBase InferenceTime \(ms/step\)\+ROAM InferenceTime \(ms/step\)Peak RSS \(MB\)SVR73\.4890\.2630\.1440\.1510\.130XGBoost7\.7450\.2630\.2550\.270<\{<\}0\.001GRU0\.3690\.1671\.5321\.538<\{<\}0\.001LSTM0\.4890\.1670\.5840\.589<\{<\}0\.001Transformer86\.7210\.8391\.1701\.186<\{<\}0\.001Informer170\.4330\.8397\.8457\.8580\.542Mamba3283\.9690\.8398\.7168\.736<\{<\}0\.001The adapter adds at most 839 parameters\. In the thickening environment, per\-step inference time increases by under 0\.02 ms across all backbones, requiring no additional forward pass or gradient computation\. Peak RSS increment stays below 0\.001 MB for five of seven backbones, while SVR and Informer add only 0\.130 and 0\.542 MB\. Relative to millisecond\-level industrial sampling intervals, the total overhead is negligible\.

## VConclusion

This article proposes ROAM, a framework that uses LLM world knowledge and reasoning to adapt frozen specialist models to unseen scenarios without retraining\. ROAM keeps all backbone parameters frozen and fuses LLM\-generated scenario judgments with online observations in a low\-dimensional semantic correction space\. This allows deployed models to respond to new operating conditions\. When evidence is insufficient or LLM outputs are unreliable, a risk\-constrained mechanism suppresses corrections and reverts the system to the original model prediction\. This mechanism provides empirical risk control rather than a pointwise monotonic\-improvement guarantee for every backbone and scenario\. Experiments on a mineral thickening process and the IndPenSim penicillin fermentation dataset show that ROAM substantially reduces error in major shift settings, especially hidden shifts where MAE decreases by over 20%\. The entire adaptation requires only 839 additional parameters and under 0\.02 ms per\-step overhead\. Existing model assets need not be rebuilt because backbone parameters stay frozen\. Every judgment and correction during adaptation is logged and auditable for field\-level traceability\.

Correction effectiveness decreases when multiple shift sources change drastically at the same time\. The LLM prior carries limited information when textual scenario descriptions are unavailable on site, and this remains a bottleneck for cross\-industry deployment\. Future work will explore fusing multimodal evidence such as images to reduce reliance on textual logs\. We will also introduce nonlinear semantic mappings for more complex shift patterns and extend the framework to other metallurgical stages for broader industrial validation\.

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