LLM-Guided Task-Semantic Field Factorization for Industrial Process Forecasting

# LLM-Guided Task-Semantic Field Factorization for Industrial Process Forecasting
Source: [https://arxiv.org/html/2607.06623](https://arxiv.org/html/2607.06623)
\\IEEEmembershipStudent Member, IEEERunda Jia[https://orcid.org/0000-0002-8586-243X](https://orcid.org/0000-0002-8586-243X)\{\}^\{\\lx@orcidlink\{0000\-0002\-8586\-243X\}\{\\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, Mingxuan Ren, and Dakuo He are with the College of Information Science and Engineering, Northeastern University, Shenyang 110004, China \(e\-mail: youchengzong@stumail\.neu\.edu\.cn; jiarunda@ise\.neu\.edu\.cn; renmx@mails\.neu\.edu\.cn; hedakuo@ise\.neu\.edu\.cn\)\.

###### Abstract

Process industries rely on time\-series forecasting and soft sensing to estimate quality variables that are hard to measure online\. Labeled data are scarce, operating regimes change frequently, and retraining models or rebuilding alignment pipelines for each scenario is costly\. Such settings often provide variable tables and process documents that record variable names, units, physical meanings, and process roles\. However, standard time\-series backbones usually treat inputs as anonymous numerical columns\. Existing text\-enhanced methods also rarely make the semantic\-logical relations between input variables and the prediction target available to the model within each numerical window\. To address this problem, this article proposes Task\-Semantic Field Factorization \(TSF\), a large language model \(LLM\)\-guided framework\. TSF builds a task\-semantic field from task protocols and variable documents before training and uses the LLM only for offline semantic construction\. Online training and inference remain with conventional time\-series backbones\. During training and inference, the current numerical window activates variable semantics, so semantic information participates in each prediction and supports adaptation to different prediction targets and operating shifts\. On multiple complex industrial forecasting and soft\-sensing tasks, TSF reduces MAE by 6\.4% on average in improved settings, with the largest reduction reaching 25\.5%\. It adds only about 1\.8–3\.0k parameters, with less than 0\.008 ms/step of additional online inference overhead\. These results show that TSF turns existing process documents into measurable forecasting gains across backbones and semantic generators while remaining lightweight for deployment\.

\{IEEEkeywords\}

large language models, industrial process forecasting, soft sensing, variable semantics, semantic input factorization\.

## 1Introduction

Process industries rely on time\-series forecasting and soft sensing to estimate quality variables that are hard to measure online\. These predictions directly affect safety margins, product quality, energy use, and production efficiency\. Work on soft sensing and metallurgy decision support shows that data\-driven models are now widely used in industrial informatics\[[20](https://arxiv.org/html/2607.06623#bib.bib1),[28](https://arxiv.org/html/2607.06623#bib.bib12)\]\. In real deployments, however, data conditions remain restrictive: high\-quality labels are scarce, operating conditions change frequently, and retraining models or rebuilding alignment pipelines for each scenario is costly\. Meanwhile, variable tables and process documents are usually already available\. They record variable names, units, physical meanings, sampling attributes, and process roles\. These documents are a natural source of prior knowledge, but they often remain outside the prediction process\.

This gap is most visible at the input layer\. Multivariate time\-series backbones can learn temporal dependence, but their inputs are usually just column\-ordered numerical windows\. In industrial tasks, however, a variable is not an anonymous number\. It also carries units, control meaning, and a relation to the target variable\. When samples are limited, the model needs to recognize these relations in the current window rather than only memorize the numerical shape of each column\. Therefore, the relation between input variables and the prediction target should be visible before the window enters the backbone\.

Studies on large language models \(LLMs\) and text\-augmented time series show that language information can assist time\-series modeling\[[7](https://arxiv.org/html/2607.06623#bib.bib27),[11](https://arxiv.org/html/2607.06623#bib.bib25),[15](https://arxiv.org/html/2607.06623#bib.bib30)\]\. Metadata and variable\-semantics methods further show that dataset descriptions and variable descriptions can provide useful forecasting priors\. These studies show that variable descriptions need not remain passive documentation\. Existing designs often introduce semantics through prompts, metadata, alignment modules, or knowledge structures, but those semantics usually stay at the edge of the forecasting pipeline\. For industrial regression, the key is to let the current numerical window activate these relations and reveal which variable relations are active in each prediction\.[fig\.1](https://arxiv.org/html/2607.06623#S1.F1)illustrates this shift\.

![Refer to caption](https://arxiv.org/html/2607.06623v1/x1.png)Figure 1:Paradigm transition for variable semantics in industrial forecasting\. \(a\) Conventional numerical forecasting only processes sensor\-value windows, leaving variable documents outside the model\. \(b\) LLM\-based and text\-augmented forecasting introduces semantic guidance, but the link to the current numerical window can still remain loose\. \(c\) TSF first turns task protocols and variable descriptions into task\-aware semantics, and then lets the current window activate these semantics before the backbone\.To address this, we propose LLM\-Guided Task\-Semantic Field Factorization \(TSF\)\. Before training, TSF turns task protocols, variable descriptions, and process background into task\-aware variable semantics, and the current numerical window activates these semantics at prediction time\. In this way, the prediction backbone can adapt dynamically to changing task scenarios and operating conditions by relying on input variables whose semantics are properly understood\.

The main contributions are as follows\.

- •We propose TSF, which uses an LLM’s world knowledge and reasoning to help models identify semantic\-logical relations between input variables and the prediction target\.
- •We introduce the task\-semantic field, which activates variable semantics from the task definition and the current numerical window, and helps the model adapt to different prediction targets and operating shifts\.
- •On multiple complex industrial forecasting and soft\-sensing tasks, TSF improves performance across different backbones and semantic generators, with additional online inference overhead below 0\.008 ms/step\.

The remainder of this paper is organized as follows\.[section2](https://arxiv.org/html/2607.06623#S2)reviews related work\.[section3](https://arxiv.org/html/2607.06623#S3)presents the method\.[section4](https://arxiv.org/html/2607.06623#S4)reports the experiments\.[section5](https://arxiv.org/html/2607.06623#S5)concludes the paper\.

## 2Related Work

### 2\.1Numerical Backbones and Missing Input Semantics

Industrial time\-series forecasting and soft sensing are often limited by data conditions before backbone capacity\. High\-quality labels are costly, fault and cross\-regime samples are sparse, and real deployments face confidentiality and maintenance constraints\. Existing studies have used LSTM and Transformer models for soft sensing\[[25](https://arxiv.org/html/2607.06623#bib.bib2),[5](https://arxiv.org/html/2607.06623#bib.bib3)\], and numerical backbones have also been applied to material\-pressure prediction\[[30](https://arxiv.org/html/2607.06623#bib.bib17)\]\. These results show that numerical backbones can learn industrial dynamics, but the inputs they receive are usually already reduced to numerical channels\. Before variables reach the model, their names, units, process roles, and relations to the prediction target are often absent from the input\. TSF therefore shifts attention to the input interface before the backbone, so that the forecaster can see industrial variables with their task semantics retained before modeling temporal dependence\.

### 2\.2LLM Interfaces for Time\-Series Forecasting

Recent studies use LLMs to supplement the semantic context missing from numerical windows\. Some methods place the LLM inside the prediction loop and forecast through prompt learning, direct generation, or input reprogramming\[[23](https://arxiv.org/html/2607.06623#bib.bib28),[7](https://arxiv.org/html/2607.06623#bib.bib27)\]\. Other methods reprogram pre\-trained models as forecasters or cast time\-series forecasting as an autoregressive generation problem\[[11](https://arxiv.org/html/2607.06623#bib.bib25),[27](https://arxiv.org/html/2607.06623#bib.bib26),[15](https://arxiv.org/html/2607.06623#bib.bib30)\]\. Some approaches reduce dependence on generation and align time\-series representations with textual information, including cross\-modality matching and text prototypes\[[12](https://arxiv.org/html/2607.06623#bib.bib24),[19](https://arxiv.org/html/2607.06623#bib.bib29)\]\. Broader zero\-shot foundation\-model applications give a similar message\. Pre\-trained capability is more reliable when it is tied to the target task and input context\[[18](https://arxiv.org/html/2607.06623#bib.bib19)\]\. This semantic benefit also comes with computational cost\. Controlled studies show that the extra cost of an LLM does not always translate into better forecasting performance\[[21](https://arxiv.org/html/2607.06623#bib.bib16)\]\. TSF follows this cost\-aware view\. It uses the LLM only during offline semantic construction, while a numerical forecaster handles training and inference\.

### 2\.3Variable Semantics as Input Priors

In parallel with LLM\-based forecasting interfaces, industrial studies have also used variable semantics and domain knowledge as forecasting priors\. Related methods have supported battery health estimation, load forecasting, and non\-stationary alignment\[[1](https://arxiv.org/html/2607.06623#bib.bib13),[2](https://arxiv.org/html/2607.06623#bib.bib14),[4](https://arxiv.org/html/2607.06623#bib.bib21)\]\. Other studies use LLMs or knowledge structures to support causal graph representation, zero\-shot fault diagnosis, and knowledge\-graph\-assisted diagnosis\[[24](https://arxiv.org/html/2607.06623#bib.bib20),[9](https://arxiv.org/html/2607.06623#bib.bib22),[13](https://arxiv.org/html/2607.06623#bib.bib15)\]\. These results show that variable descriptions, process knowledge, and semantic relations can improve industrial modeling\. However, many implementations still depend on extra textual inputs, explicit graph structures, or dedicated reasoning modules\. TSF keeps the prior on the input side\. It compresses variable descriptions into a frozen direction matrix before training\. The current numerical window then activates this matrix as a task\-semantic field, which is fed to a standard backbone\. In this way, existing sensor tables and variable documents can become input\-side priors without paired corpora or online knowledge\-graph maintenance\.

## 3Method

### 3\.1Problem Setup and Semantic Directions

We first define each prediction sample and the semantic objects fixed before training\. Each sample is identified by an instance indexnnand a prediction timett\. The window length isLL, and the number of input variables isdd\. For this sample, let𝐱n,ℓ∈ℝ1×d\\mathbf\{x\}\_\{n,\\ell\}\\in\\mathbb\{R\}^\{1\\times d\}denote the row vector at timeℓ\\ellwithin the window\. Each column corresponds to one input variable\. The history windowXn,tX\_\{n,t\}is formed by stacking theLLrows fromt−L\+1t\-L\+1tott\. The target is𝐲n,t∈ℝr\\mathbf\{y\}\_\{n,t\}\\in\\mathbb\{R\}^\{r\}\.

Xn,t=\[𝐱n,t−L\+1⋯𝐱n,t\]∈ℝL×d,𝐲n,t∈ℝr\.X\_\{n,t\}=\\begin\{bmatrix\}\\mathbf\{x\}\_\{n,t\-L\+1\}\\\\ \\cdots\\\\ \\mathbf\{x\}\_\{n,t\}\\end\{bmatrix\}\\in\\mathbb\{R\}^\{L\\times d\},\\qquad\\mathbf\{y\}\_\{n,t\}\\in\\mathbb\{R\}^\{r\}\.\(1\)Here,rris the output dimension of the current task\. We useX~n,t\\tilde\{X\}\_\{n,t\}for the window normalized with training\-set statistics, and all input mappings below operate onX~n,t\\tilde\{X\}\_\{n,t\}\.

TSF draws semantics from a task protocol𝒯\\mathcal\{T\}fixed before training\. We define𝒯=\(ℬ,𝒢,ℐ,𝒞\)\\mathcal\{T\}=\(\\mathcal\{B\},\\mathcal\{G\},\\mathcal\{I\},\\mathcal\{C\}\)\. Here,ℬ\\mathcal\{B\}is the process background,𝒢\\mathcal\{G\}is the target and window specification, andℐ\\mathcal\{I\}describes information availability and excluded information\. The variable metadata𝒞=\(c1,…,cd\)\\mathcal\{C\}=\(c\_\{1\},\\ldots,c\_\{d\}\)follows the input\-column order\.

𝒯=\(ℬ,𝒢,ℐ,𝒞\),𝒞=\(c1,…,cd\)\.\\mathcal\{T\}=\(\\mathcal\{B\},\\mathcal\{G\},\\mathcal\{I\},\\mathcal\{C\}\),\\qquad\\mathcal\{C\}=\(c\_\{1\},\\ldots,c\_\{d\}\)\.\(2\)This protocol records the dataset profile, optional domain context, variable names, units, sampling attributes, process roles, and target definitions\. It excludes test\-set statistics, future labels, prediction errors, and trained\-model states\.

An offline semantic generatorFϕF\_\{\\phi\}automatically maps𝒯\\mathcal\{T\}to semantic cards, whereϕ\\phidenotes the LLM and prompt configuration chosen before training\. The output\(z1,…,zd\)\(z\_\{1\},\\ldots,z\_\{d\}\)follows the same order as the input variables, whereziz\_\{i\}is the semantic card of theii\-th variable\.

\(z1,…,zd\)=Fϕ​\(𝒯\)\.\(z\_\{1\},\\ldots,z\_\{d\}\)=F\_\{\\phi\}\(\\mathcal\{T\}\)\.\(3\)Each semantic cardziz\_\{i\}describes the name, unit, physical meaning, process role, information role, temporal relation, and main coupling relations of theii\-th variable in the current task\. The semantic cards are then converted into variable\-semantic directions\.

The deterministic text rendererRRconverts the semantic cardziz\_\{i\}into a compact English phraseuiu\_\{i\}\. The embedding modelEψE\_\{\\psi\}then mapsuiu\_\{i\}to a vector, whereψ\\psidenotes the frozen parameters of this embedding model\. The normalized row vector𝐯i∈ℝ1×k\\mathbf\{v\}\_\{i\}\\in\\mathbb\{R\}^\{1\\times k\}defines the variable\-semantic direction of theii\-th variable, andkkis the semantic\-direction dimension\.

ui=R​\(zi\),𝐯i=Eψ​\(ui\)‖Eψ​\(ui\)‖2∈ℝ1×k\.u\_\{i\}=R\(z\_\{i\}\),\\qquad\\mathbf\{v\}\_\{i\}=\\frac\{E\_\{\\psi\}\(u\_\{i\}\)\}\{\\left\\lVert E\_\{\\psi\}\(u\_\{i\}\)\\right\\rVert\_\{2\}\}\\in\\mathbb\{R\}^\{1\\times k\}\.\(4\)Stacking all variable\-semantic directions in input\-column order gives the variable\-semantic direction matrixVV\.

V=\[𝐯1⋯𝐯d\]∈ℝd×k\.V=\\begin\{bmatrix\}\\mathbf\{v\}\_\{1\}\\\\ \\cdots\\\\ \\mathbf\{v\}\_\{d\}\\end\{bmatrix\}\\in\\mathbb\{R\}^\{d\\times k\}\.\(5\)After construction,VVremains unchanged during training, validation, and testing\.[fig\.2](https://arxiv.org/html/2607.06623#S3.F2)summarizes offline semantic construction and the computation path used in training and inference\.

![Refer to caption](https://arxiv.org/html/2607.06623v1/x2.png)Figure 2:TSF workflow\. Offline construction maps the task protocol and ordered variable metadata to semantic cards, rendered phrases, embeddings, and the frozen variable\-semantic direction matrixVV\. During training and inference, the normalized window activates the task\-semantic fieldS=X~​VS=\\tilde\{X\}V\. The constrained dual\-path adapter combines the semantic field, raw\-value path, and shared bias into the backbone inputZZ; the inset expands this factorization\.
### 3\.2Task\-Semantic Field Factorization

With the variable\-semantic direction matrixVVconstructed, TSF activates it using the current numerical state\. For any time indexℓ\\ellin the window,𝐱~n,ℓ∈ℝ1×d\\tilde\{\\mathbf\{x\}\}\_\{n,\\ell\}\\in\\mathbb\{R\}^\{1\\times d\}denotes the normalized input row, andx~n,ℓ,i\\tilde\{x\}\_\{n,\\ell,i\}is itsii\-th element\. The corresponding row\-wise task\-semantic field vector𝐬n,ℓ\\mathbf\{s\}\_\{n,\\ell\}is a value\-weighted sum of the variable\-semantic directions\.

𝐬n,ℓ=𝐱~n,ℓ​V=∑i=1dx~n,ℓ,i​𝐯i∈ℝ1×k\.\\mathbf\{s\}\_\{n,\\ell\}=\\tilde\{\\mathbf\{x\}\}\_\{n,\\ell\}V=\\sum\_\{i=1\}^\{d\}\\tilde\{x\}\_\{n,\\ell,i\}\\mathbf\{v\}\_\{i\}\\in\\mathbb\{R\}^\{1\\times k\}\.\(6\)Stacking allLLrow\-wise vectors𝐬n,ℓ\\mathbf\{s\}\_\{n,\\ell\}in temporal order gives the window\-level task\-semantic fieldSn,t∈ℝL×kS\_\{n,t\}\\in\\mathbb\{R\}^\{L\\times k\}\.

Sn,t=X~n,t​V\.S\_\{n,t\}=\\tilde\{X\}\_\{n,t\}V\.\(7\)BecauseVVremains unchanged whileX~n,t\\tilde\{X\}\_\{n,t\}varies across samples,Sn,tS\_\{n,t\}represents the task semantics activated by the current window\.

TSF then uses a dual\-path input adapter before the backbone to preserve the raw\-value channels and introduce the semantic\-field projection\. In the raw\-value path, the diagonal matrixDDpreserves per\-variable scaling, where𝜶∈ℝd\\bm\{\\alpha\}\\in\\mathbb\{R\}^\{d\}is a learnable per\-variable scale vector\. The semantic\-field path uses a learnable projectionB∈ℝk×dB\\in\\mathbb\{R\}^\{k\\times d\}\. The vector𝐛∈ℝd\\mathbf\{b\}\\in\\mathbb\{R\}^\{d\}is the bias, and𝟏L∈ℝL\\mathbf\{1\}\_\{L\}\\in\\mathbb\{R\}^\{L\}copies this bias to every time step in the window\.

D=diag⁡\(𝜶\),𝜶∈ℝd,B∈ℝk×d,𝐛∈ℝd,𝟏L∈ℝL\.\\begin\{gathered\}D=\\operatorname\{diag\}\(\\bm\{\\alpha\}\),\\quad\\bm\{\\alpha\}\\in\\mathbb\{R\}^\{d\},\\quad B\\in\\mathbb\{R\}^\{k\\times d\},\\\\ \\mathbf\{b\}\\in\\mathbb\{R\}^\{d\},\\quad\\mathbf\{1\}\_\{L\}\\in\\mathbb\{R\}^\{L\}\.\\end\{gathered\}\(8\)The backbone input representationZn,t∈ℝL×dZ\_\{n,t\}\\in\\mathbb\{R\}^\{L\\times d\}has the same time length and variable dimension as the original input window\.

Zn,t=X~n,t​D\+Sn,t​B\+𝟏L​𝐛⊤\.Z\_\{n,t\}=\\tilde\{X\}\_\{n,t\}D\+S\_\{n,t\}B\+\\mathbf\{1\}\_\{L\}\\mathbf\{b\}^\{\\top\}\.\(9\)From left to right, the three terms correspond to the raw\-value path, the semantic\-field projection path, and the bias shared across time steps\. SubstitutingSn,t=X~n,t​VS\_\{n,t\}=\\tilde\{X\}\_\{n,t\}Vgives the constrained structure of the pre\-backbone input mapping\.

Zn,t=X~n,t​\(D\+V​B\)\+𝟏L​𝐛⊤\.Z\_\{n,t\}=\\tilde\{X\}\_\{n,t\}\(D\+VB\)\+\\mathbf\{1\}\_\{L\}\\mathbf\{b\}^\{\\top\}\.\(10\)This equivalent form shows that cross\-variable mixing comes from the productV​BVBof the frozen variable\-semantic directionsVVand the learnable projectionBB, while the diagonal termDDpreserves each variable’s numerical channel\.[Figure3](https://arxiv.org/html/2607.06623#S3.F3)compares this constrained map with free input mixing\. A free layer learns an arbitrary matrixWW, whereas TSF restricts the map to the diagonal residualDDand the semantically constrained productV​BVB\.

![Refer to caption](https://arxiv.org/html/2607.06623v1/x3.png)Figure 3:Free input mixing versus TSF\-constrained input factorization\. \(a\) A conventional pre\-backbone layer learns an arbitrary dense matrixWWand formsX~​W\\tilde\{X\}W\. \(b\) TSF usesZ=X~​\(D\+V​B\)\+𝟏L​𝐛⊤Z=\\tilde\{X\}\(D\+VB\)\+\\mathbf\{1\}\_\{L\}\\mathbf\{b\}^\{\\top\}, whereDDpreserves per\-variable numerical channels andV​BVBconstrains cross\-variable mixing through the frozen variable\-semantic directionsVVand the learnable projectionBB\.
### 3\.3Training and Inference

After the input adapter formsZn,tZ\_\{n,t\}, TSF can connect to any time\-series backbone that accepts anL×dL\\times dwindow representation\. LetGθG\_\{\\theta\}denote the backbone together with its prediction head\. Its learnable parameters are included inθ\\theta, and its prediction is written as𝐲^n,t\\hat\{\\mathbf\{y\}\}\_\{n,t\}\.

𝐲^n,t=Gθ​\(Zn,t\)\.\\hat\{\\mathbf\{y\}\}\_\{n,t\}=G\_\{\\theta\}\(Z\_\{n,t\}\)\.\(11\)The training index set isℐtrain\\mathcal\{I\}\_\{\\mathrm\{train\}\}, and the supervised regression loss isℒ\\mathcal\{L\}\. The trainable parameter set isΘ=\{θ,B,𝜶,𝐛\}\\Theta=\\\{\\theta,B,\\bm\{\\alpha\},\\mathbf\{b\}\\\}, where𝜶\\bm\{\\alpha\}determines the raw\-value path throughD=diag⁡\(𝜶\)D=\\operatorname\{diag\}\(\\bm\{\\alpha\}\)\. The empirical risk minimization objective is

Θ∗=arg⁡minΘ⁡1\|ℐtrain\|​∑\(n,t\)∈ℐtrainℒ​\(Gθ​\(Zn,t\),𝐲n,t\),\\Theta^\{\\ast\}=\\arg\\min\_\{\\Theta\}\\frac\{1\}\{\|\\mathcal\{I\}\_\{\\mathrm\{train\}\}\|\}\\sum\_\{\(n,t\)\\in\\mathcal\{I\}\_\{\\mathrm\{train\}\}\}\\mathcal\{L\}\\big\(G\_\{\\theta\}\(Z\_\{n,t\}\),\\mathbf\{y\}\_\{n,t\}\\big\),\(12\)During training,FϕF\_\{\\phi\},RR,EψE\_\{\\psi\}, andVVremain unchanged\. Only the backbone parameters, semantic\-field projection, raw\-value path scales, and bias are learned\. At inference, TSF reuses the sameVVand computesX~n,t\\tilde\{X\}\_\{n,t\},Sn,tS\_\{n,t\},Zn,tZ\_\{n,t\}, andGθ​\(Zn,t\)G\_\{\\theta\}\(Z\_\{n,t\}\)in order\. The only role of the test set is final evaluation\. Normalization\-statistic estimation, semantic\-card generation, embedding generation, and model selection are completed outside the test set\. For a fair comparison, the baseline receivesX~n,t\\tilde\{X\}\_\{n,t\}directly, while TSF receivesZn,tZ\_\{n,t\}\. Both use the same data split, normalization strategy, backbone architecture, and training budget\. Thus, the only model change introduced by TSF is semantic input factorization before the backbone\.

## 4Experiments

This section evaluates TSF on three industrial forecasting and soft\-sensing tasks\.

### 4\.1Experimental Settings

All methods are evaluated in the same implementation and under the same training protocol\. For each dataset–backbone pair, Base and \+TSF share the data split, normalization, backbone configuration, training budget, and model\-selection rule\. The test set is never used for tuning\. All experiments were run on a workstation 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\. The main result tables report means and standard deviations over three independent runs\. For reproducibility, the source code is available at[https://github\.com/mituan\-ai/TSF\_open](https://github.com/mituan-ai/TSF_open)\.[table1](https://arxiv.org/html/2607.06623#S4.T1)summarizes the experimental settings\.

Table 1:Common training, evaluation, and TSF semantic construction settings for all experiments\. For each dataset–backbone pair, Base and \+TSF share the same split, optimizer, training budget, and model\-selection rule\.NameSettingOptimizerAdamWLearning rate10\-3LossMSEMax epochs300Early stoppingpatience40LR schedulertypeReduceLROnPlateaudecay factor0\.5patience15Weight decay10\-4Gradient clipping1\.0Batch size64Semantic dimensionkk128Semantic\-card generatorDeepSeek\-v4\-pro \(max\)Embedding modeltext\-embedding\-v4The main results report mean absolute error \(MAE↓\\downarrow\), root mean squared error \(RMSE↓\\downarrow\), coefficient of determination \(R2R^\{2\}↑\\uparrow\), and per\-step inference time \(ms/step↓\\downarrow\)\. Parameter count and peak RSS memory are reported in the online\-cost analysis\. The comparison covers eight common time\-series backbones\. They include GRU and LSTM\[[3](https://arxiv.org/html/2607.06623#bib.bib4),[10](https://arxiv.org/html/2607.06623#bib.bib5)\], Transformer and Informer\[[22](https://arxiv.org/html/2607.06623#bib.bib6),[26](https://arxiv.org/html/2607.06623#bib.bib7)\], Mamba and iTransformer\[[8](https://arxiv.org/html/2607.06623#bib.bib11),[14](https://arxiv.org/html/2607.06623#bib.bib8)\], and PatchTST and ModernTCN\[[17](https://arxiv.org/html/2607.06623#bib.bib9),[16](https://arxiv.org/html/2607.06623#bib.bib10)\]\. For each dataset and backbone, Base and \+TSF differ only in the input adapter\.

### 4\.2Datasets

The experiments use three datasets from steel metallurgy, tailings thickening dewatering, and fed\-batch fermentation\. They cover future temperature forecasting, current underflow\-concentration soft sensing, and assay\-time penicillin\-concentration estimation\. The sources include both private plant data and a public simulation benchmark\.[table2](https://arxiv.org/html/2607.06623#S4.T2)gives the variables, targets, and predefined splits for each dataset\. All training, validation, and test splits are fixed before training at the process, scenario, or batch level\. Training data mainly come from routine or near\-domain operation, while test data contain complete held\-out processes, near\-domain references, and unseen control or fault regimes\. This protocol avoids the easier random\-window split, which can leak information through the same run or adjacent windows\.

Table 2:Dataset protocols used in the TSF experiments\. The table lists input variables, sampling intervals, window lengths, prediction targets, and fixed train/validation/test splits for each process\.ItemDescriptionLadle PreheatingInputVariables14Sampling interval5minutesInput window60stepsTargetLadle temperature over the next 5 stepsSplits24 training processes15,236samples5 validation processes2,500samples3 held\-out test processes2,104samplesThickener DewateringInputVariables5Sampling interval1minuteInput window30stepsTargetUnderflow concentration at the current stepSplits5 training mild\-jitter scenarios1,355samples1 validation mild\-jitter scenario271samples1 near\-domain test scenario271samples12 far\-domain test scenarios3,252samplesIndPenSimInputVariables23Sampling interval12minutesInput window120stepsTargetAssay\-time penicillin concentrationSplits24 training recipe\-controlled batches451samples5 validation recipe\-controlled batches90samples1 same\-family recipe\-controlled test batch19samples2 near\-domain operator\-controlled test batches38samples12 far\-domain advanced process control \(APC\) or fault test batches220samples![Refer to caption](https://arxiv.org/html/2607.06623v1/figure/industrial_sites.png)Figure 4:On\-site views of the two plant processes\. \(a\) Ladle preheating at a steel plant in Maanshan, China\. \(b\) Tailings thickening dewatering at a plant in Nanjing, China\.The ladle preheating dataset comes from a private steel\-metallurgy process that has also been used in variable ladle\-preheating trend prediction\[[29](https://arxiv.org/html/2607.06623#bib.bib18)\]\. The task predicts future ladle inner temperature from fuel\-gas, air\-side, combustion\-state, and historical\-temperature variables\. The split is made by complete preheating processes; each test process is an independent run, but no explicit scenario labels or external regime descriptions are provided\. The thickener dewatering dataset comes from a tailings thickening dewatering process\. The task estimates current underflow concentration from feed, pressure, and operating\-phase variables\. Training and validation data come from mild\-jitter scenarios, while the test set includes a near\-domain reference and far\-domain operating shifts\. The IndPenSim dataset is drawn from the public IndPenSim V3 penicillin fed\-batch fermentation simulator\[[6](https://arxiv.org/html/2607.06623#bib.bib23)\]\. The task estimates offline penicillin concentration from the online process window before each assay time\. Training batches use recipe\-controlled operation, while test batches cover same\-family recipes, operator control, advanced process control \(APC\) operation, and fault conditions\.

### 4\.3Main Results

[table3](https://arxiv.org/html/2607.06623#S4.T3),[table4](https://arxiv.org/html/2607.06623#S4.T4), and[table5](https://arxiv.org/html/2607.06623#S4.T5)compare the forecasting performance of Base and \+TSF on the three test sets\. These sets include the held\-out processes and scenario\-shifted samples defined in[table2](https://arxiv.org/html/2607.06623#S4.T2)\.

Table 3:Quantitative comparison on the ladle preheating dataset\. Accuracy metrics report the mean and standard deviation over three runs; arrows indicate the preferred direction, and Time is per\-step inference time in ms\.BackboneSettingMAE↓\\downarrowRMSE↓\\downarrowR2↑\\uparrowTime \(ms\)↓\\downarrowGRUBase0\.018±0\.00010\.031±0\.00020\.991±0\.00010\.0035\+TSF0\.016±0\.00080\.030±0\.00090\.991±0\.00050\.0037LSTMBase0\.017±0\.00080\.029±0\.00030\.991±0\.00020\.0040\+TSF0\.018±0\.00080\.030±0\.00130\.991±0\.00080\.0042TransformerBase0\.020±0\.00110\.033±0\.00110\.990±0\.00070\.0065\+TSF0\.020±0\.00070\.033±0\.00070\.989±0\.00050\.0078InformerBase0\.027±0\.00130\.044±0\.00330\.981±0\.00280\.0588\+TSF0\.026±0\.00230\.041±0\.00210\.983±0\.00170\.0603MambaBase0\.021±0\.00060\.034±0\.00130\.989±0\.00090\.0184\+TSF0\.018±0\.00090\.031±0\.00080\.990±0\.00050\.0196iTransformerBase0\.020±0\.00190\.033±0\.00270\.989±0\.00180\.0068\+TSF0\.023±0\.00130\.039±0\.00340\.985±0\.00270\.0082PatchTSTBase0\.037±0\.00580\.064±0\.01170\.959±0\.01540\.0482\+TSF0\.035±0\.00200\.059±0\.00350\.966±0\.00410\.0554ModernTCNBase0\.025±0\.00220\.038±0\.00250\.986±0\.00190\.0089\+TSF0\.022±0\.00050\.036±0\.00100\.987±0\.00070\.0106Table 4:Quantitative comparison on the thickener dewatering dataset\. Accuracy metrics report the mean and standard deviation over three runs; arrows indicate the preferred direction, and Time is per\-step inference time in ms\.BackboneSettingMAE↓\\downarrowRMSE↓\\downarrowR2↑\\uparrowTime \(ms\)↓\\downarrowGRUBase0\.013±0\.00010\.030±0\.00010\.225±0\.00420\.0053\+TSF0\.013±0\.00000\.030±0\.00000\.226±0\.00050\.0079LSTMBase0\.014±0\.00010\.030±0\.00000\.221±0\.00130\.0050\+TSF0\.013±0\.00010\.030±0\.00000\.223±0\.00160\.0079TransformerBase0\.015±0\.00000\.030±0\.00000\.209±0\.00130\.0140\+TSF0\.014±0\.00030\.030±0\.00010\.214±0\.00660\.0169InformerBase0\.014±0\.00000\.030±0\.00000\.204±0\.00140\.1334\+TSF0\.014±0\.00020\.030±0\.00000\.208±0\.00140\.1408MambaBase0\.015±0\.00010\.030±0\.00000\.196±0\.00200\.0371\+TSF0\.015±0\.00020\.030±0\.00000\.201±0\.00220\.0405iTransformerBase0\.014±0\.00020\.031±0\.00000\.193±0\.00190\.0142\+TSF0\.014±0\.00010\.030±0\.00000\.210±0\.00220\.0171PatchTSTBase0\.014±0\.00010\.030±0\.00000\.200±0\.00200\.0146\+TSF0\.015±0\.00010\.031±0\.00010\.182±0\.00430\.0177ModernTCNBase0\.015±0\.00010\.030±0\.00000\.204±0\.00070\.0141\+TSF0\.015±0\.00010\.030±0\.00000\.201±0\.00170\.0172Table 5:Quantitative comparison on the IndPenSim dataset\. Accuracy metrics report the mean and standard deviation over three runs; arrows indicate the preferred direction, and Time is per\-step inference time in ms\.BackboneSettingMAE↓\\downarrowRMSE↓\\downarrowR2↑\\uparrowTime \(ms\)↓\\downarrowGRUBase2\.391±0\.07923\.655±0\.04530\.828±0\.00430\.0073\+TSF2\.370±0\.17423\.601±0\.22010\.833±0\.02060\.0087LSTMBase2\.507±0\.17814\.022±0\.32640\.791±0\.03390\.0074\+TSF2\.479±0\.11773\.813±0\.12940\.813±0\.01260\.0092TransformerBase2\.623±0\.25813\.900±0\.36880\.803±0\.03800\.0149\+TSF2\.385±0\.23023\.561±0\.27600\.836±0\.02570\.0173InformerBase2\.957±0\.71614\.043±0\.77610\.785±0\.07940\.1359\+TSF2\.620±0\.43303\.691±0\.41640\.823±0\.03940\.1385MambaBase2\.888±0\.09644\.375±0\.14760\.754±0\.01640\.0407\+TSF2\.867±0\.24654\.308±0\.21680\.761±0\.02430\.0446iTransformerBase3\.890±0\.42425\.515±0\.51780\.607±0\.07370\.0158\+TSF2\.900±0\.58234\.061±0\.54170\.786±0\.05740\.0191PatchTSTBase2\.514±0\.37503\.730±0\.53940\.819±0\.05330\.2132\+TSF2\.995±0\.43794\.116±0\.36860\.781±0\.03990\.2141ModernTCNBase2\.341±0\.36583\.537±0\.40110\.838±0\.03730\.0153\+TSF2\.026±0\.08623\.212±0\.08880\.867±0\.00730\.0185The benefit of \+TSF is most visible when variable\-level task semantics can complement limited training coverage\. The clearest case is IndPenSim, where training uses only recipe\-controlled batches while most test batches follow unseen operator\-controlled, APC, or fault regimes\. On this task, \+TSF reduces MAE on heterogeneous backbones such as iTransformer, ModernTCN, Informer, and Transformer, with the largest reduction reaching 25\.5%\.

On ladle preheating and thickener dewatering, the gains of \+TSF are smaller and more backbone\-dependent, but several combinations still improve\. When \+TSF improves over the corresponding backbone, MAE is reduced by 6\.4% on average\. The ladle test set consists of complete held\-out processes without explicit scenario labels, while thickener dewatering includes far\-domain shifts beyond the mild\-jitter training regime\. The results therefore support a more cautious conclusion: TSF is most valuable when variable\-level task semantics can complement limited training coverage\.

The online overhead of \+TSF remains small\. The average increments are about 0\.0019, 0\.0035, and 0\.0024 ms/step on the three datasets, and the largest increment is below 0\.008 ms/step\.

### 4\.4Qualitative Analysis

[fig\.5](https://arxiv.org/html/2607.06623#S4.F5)compares GRU and GRU \+ TSF on two representative tasks\.

![Refer to caption](https://arxiv.org/html/2607.06623v1/x4.png)Figure 5:Qualitative comparison on ladle preheating and IndPenSim\. The top row gives fifth\-step ladle\-temperature forecasts, 30 min ahead, for three ladle processes; insets enlarge high\-temperature regions\. The bottom row gives assay\-time penicillin\-concentration estimates for three IndPenSim anomaly cases\.On ladle preheating, GRU \+ TSF stays closer to the measured temperature in all three curves, especially by reducing sustained errors during heating rises and high\-temperature plateaus\. On IndPenSim, GRU \+ TSF keeps estimates closer to the assay measurements under substrate\-feed and aeration anomalies and reduces offsets around peak and post\-peak regions\. These visible corrections are consistent with the quantitative gains and keep the predictions closer to key process patterns such as stage changes, peaks, and plateaus\.

### 4\.5Ablation Studies

[table6](https://arxiv.org/html/2607.06623#S4.T6)reports key ablations of the TSF input adapter and separately examines semantic content, variable correspondence, the raw\-value path, and constrained factorization\.

Table 6:Ablation study of the TSF input adapter on ladle preheating and IndPenSim\. Results use GRU and ModernTCN, report MAE mean and standard deviation over three runs, and isolate semantic content, variable–semantic match, the raw\-value path, and constrained factorization; lower is better\.SemanticcontentVariable–semanticmatchRaw\-valuepathConstrainedfactorizationLadle PreheatingIndPenSimGRUModernTCNGRUModernTCN––Raw input–0\.018±0\.00010\.025±0\.00222\.391±0\.07922\.341±0\.3658Random directions✓Diagonal✓0\.017±0\.00040\.025±0\.00122\.520±0\.08752\.330±0\.2232Metadata descriptions✓Diagonal✓0\.017±0\.00050\.024±0\.00132\.473±0\.11942\.057±0\.0932Semantic cardsShuffledDiagonal✓0\.017±0\.00040\.025±0\.00202\.442±0\.07082\.398±0\.2788Semantic cards✓–✓0\.017±0\.00040\.023±0\.00252\.617±0\.11902\.468±0\.1484Semantic cards✓Full matrix–0\.017±0\.00050\.023±0\.00042\.392±0\.02172\.421±0\.2113Semantic cards✓Diagonal✓0\.016±0\.00080\.022±0\.00052\.370±0\.17422\.026±0\.0862Full TSF achieves the lowest mean MAE in all four dataset–backbone pairs\. Absolute ladle errors are already small, but full TSF still has the lowest mean\. On IndPenSim\-ModernTCN, MAE drops from 2\.341 with the raw input to 2\.026 with full TSF\. The random\-direction variant keeps the same adapter form but removes task semantics, and it underperforms full TSF in all four columns\. The main gain is tied to task\-aware semantic directions rather than adapter size alone\.

LLM\-generated semantic cards and correct variable correspondence further shape this result\. For IndPenSim\-ModernTCN, basic metadata yields 2\.057, full semantic cards reduce it to 2\.026, and shuffled correspondence raises it to 2\.398\. GRU follows the same trend\. This comparison locates the useful signal in variable\-specific semantic directions matched to the prediction task\.

The raw\-value path and constrained factorization make this semantic gain more reliable\. Removing the raw\-value path weakens both IndPenSim backbones, which indicates that the numerical identity of each variable still needs to be preserved\. The free full\-matrix variant also underperforms full TSF, with an MAE of 2\.421 on IndPenSim\-ModernTCN\. The diagonal numerical path keeps the original variables, and semantic factorization guides cross\-variable mixing\. Together, they let TSF use semantic priors while keeping a clear input structure\.

### 4\.6Task\-Semantic Field Visualization

[fig\.6](https://arxiv.org/html/2607.06623#S4.F6)visualizes the task\-semantic field in the IndPenSim\-ModernTCN run\.

![Refer to caption](https://arxiv.org/html/2607.06623v1/x5.png)Figure 6:Runtime task\-semantic field analysis on IndPenSim\-ModernTCN\. \(a\) PCA state atlas of raw normalized input windows\. \(b\) Runtime task\-semantic field atlas formed byS=X~​VS=\\tilde\{X\}V\. \(c\) Semantic intervention intensityρ=‖S​B‖/\(‖X~​D‖\+‖S​B‖\)\\rho=\\\|SB\\\|/\(\\\|\\tilde\{X\}D\\\|\+\\\|SB\\\|\), measuring the semantic projection relative to the numerical residual path at the sample level\. \(d\) Sample\-level absolute\-error reduction of TSF over the raw\-input backbone, where positive values indicate lower TSF error\. \(e\) Activation\-weighted variable couplings in far\-domain samples; node colors denote variable roles, edge widths denote coupling strength, and edge colors denote far/train enrichment\. \(f\) Counterfactual semantic\-channel importance from masking one semantic channel at a time on far\-domain samples\.Compared with the raw input space, the task\-semantic field explains a larger fraction of the two\-dimensional principal\-component variance and spreads far\-domain samples over a broader semantic region\. The semantic\-path intervention intensity varies across this space, showing that the contribution ofS​BSBchanges with the current window state\. The corresponding error\-reduction map shows gains across several far\-domain regions\. This pattern indicates that the runtime semantic structure formed by TSF is aligned with actual forecasting improvement rather than simply copying the raw numerical geometry\.

This structure can also be traced to process variables and semantic channels\. The far\-domain activation\-weighted couplings concentrate around temperature, pressure, sugar feed, PAA feed, heating/cooling, dissolved oxygen, and off\-gas variables, which correspond to thermal state, substrate supply, precursor addition, gas\-liquid transfer, and metabolic intensity in fermentation\. Counterfactual channel masking further shows that important channels are associated with directions such asco2\_out/batch time, water\-for\-injection/volume, CER/OUR, dumped broth/volume, and temperature/oil flow\. TSF therefore does more than add capacity to the input layer\. It turns variable semantics fixed before training into a runtime input structure that is activated by the current window, supports intervention, and is associated with forecasting gain\.

### 4\.7Sensitivity Analysis

We analyze TSF sensitivity along three factors: semantic dimension, semantic\-card generator, and embedding model, as shown in[fig\.7](https://arxiv.org/html/2607.06623#S4.F7)\.

![Refer to caption](https://arxiv.org/html/2607.06623v1/x6.png)Figure 7:Sensitivity analysis of TSF across semantic dimension, semantic\-card generator, and embedding model\. Values are relative MAE with respect to the default setting in each panel\. Shaded bands and error bars denote standard deviations over three runs; gray dashed lines mark the default setting\.The semantic dimension does not show a monotonic trend\. The defaultk=128k=128gives a stable operating point, while the best value changes with the dataset and backbone\. On IndPenSim\-ModernTCN, the relative MAE atk=256k=256rises to about 1\.17, showing that an overly large semantic space can weaken some dataset–backbone pairs\. The other pairs are less sensitive tokk\. We therefore usek=128k=128as the default to balance semantic capacity and training stability\.

With text\-embedding\-v4 fixed, semantic cards generated by different LLMs can all support TSF\. The changes on ladle preheating are small, while IndPenSim\-ModernTCN is more sensitive to the semantic\-card source\. GPT\-5\.5 gives a higher relative MAE than the default in this pair, whereas Claude Opus 4\.7 and Gemini 3\.1 Pro are closer to the default result\. This result indicates that TSF is not tied to a single semantic generator, but tasks with larger distribution shifts remain sensitive to semantic\-card quality\.

Changing the embedding model directly changes the semantic\-direction space\. The two alternative embeddings remain competitive on ladle preheating, but both give higher relative MAE than the default on IndPenSim\-ModernTCN, with a larger increase for gemini\-embedding\-2\-preview\. Compared with LLM replacement, embedding replacement more directly changes the geometry among variable directions\.

### 4\.8Computational Efficiency

To evaluate online deployment cost,[table7](https://arxiv.org/html/2607.06623#S4.T7)reports model size, per\-step inference time, and peak\-memory change after adding the TSF input adapter to the same backbone\.

Table 7:Online deployment cost of the TSF input adapter\. The table reports backbone and adapter parameter counts \(×103\\times 10^\{3\}\), per\-step inference time in ms, and Peak RSS increase relative to the base backbone\. LLM semantic\-card generation and embedding generation are not counted in per\-step inference\.Model Size↓\\downarrowDeployment Cost↓\\downarrowBackboneBackbone\( × 103\)Adapter\( × 103\)Base InferenceTime \(ms/step\)\+TSF InferenceTime \(ms/step\)Peak RSSIncrease \(MB\)Ladle PreheatingGRU88\.6131\.8200\.00350\.00370\.22ModernTCN78\.3411\.8200\.00890\.01064\.61IndPenSimGRU90\.8172\.9900\.00730\.008715\.23ModernTCN78\.8172\.9900\.01530\.01850\.74The results show that TSF has low online cost because semantic construction is moved before training and only a small input adapter remains online\. This design adds task semantics without changing the backbone inference pipeline\. The slowest \+TSF timing is still only 0\.0185 ms/step, far below the sampling intervals of the industrial tasks\. Peak RSS changes do not create a new deployment bottleneck\.

## 5Conclusion

This article presented TSF, a framework that equips numerical time\-series models with task\-aware variable semantics from process documents\. It represents LLM\-derived process knowledge as semantic\-logical relations between input variables and the prediction target and activates these relations with the current numerical window\. Variable semantics therefore move from external documentation into the prediction process and support adaptation to different prediction targets and operating shifts\. Across multiple complex industrial forecasting and soft\-sensing tasks, experimental results show that TSF reduces forecasting error when variable semantics can complement limited training coverage\. In improved settings, \+TSF reduces MAE by 6\.4% on average; on IndPenSim, the largest reduction reaches 25\.5%\. The online adapter adds only about 1\.8–3\.0k parameters, with less than 0\.008 ms/step of additional online inference overhead\. These results show that TSF can turn existing process documents into deployable forecasting gains across backbones and semantic generators\.

TSF still depends on usable task protocols, variable tables, and process descriptions\. When these inputs are missing, inconsistent, or insufficient, the semantic cards should be validated before deployment\. Future work will improve semantic\-card quality control, use on\-site logs and multimodal process records to fill gaps in incomplete protocols, and evaluate TSF in longer\-term industrial deployments\.

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