TimeThink: Eliciting Compositional Reasoning in Timeseries Large Language Models

# TimeThink: Eliciting Compositional Reasoning in Timeseries Large Language Models
Source: [https://arxiv.org/html/2609.13457](https://arxiv.org/html/2609.13457)
Arvind PillaiAffiliation:Lisa Marsch,Nicholas C\. Jacobson,Andrew CampbellYu Yvonne WuAffiliation:Dartmouth CollegeYuliang ChenAffiliation:Correspondence:[sudarshan\.regmi\.gr@dartmouth\.edu](mailto:[email protected])

###### Abstract

Timeseries multimodal large language models \(TS\-MLLMs\) have recently begun leveraging the reasoning capabilities of large language models \(LLMs\) for question\-answering tasks\. However, these models often fail to capture dynamic temporal patterns, providing only implicit reasoning that lacks the underlying explanations critical for high\-stakes applications like healthcare\. While reinforcement learning \(RL\)\-based timeseries language models aim to address this, they often fall short because they are trained on narrow, in\-distribution data and struggle with out\-of\-distribution compositional questions\. To address these challenges, we presentTimeThink, a synthetic framework for eliciting compositional timeseries reasoning\. Core timeseries primitives \(e\.g\., trend, seasonality\) are domain\-independent and can be deterministically generated\. Guided by this premise,TimeThinkfirst designs a synthetic data generator that producesatomicandcompositequestion\-answer pairs, providing objective ground truth with reasoning traces\. Building on this framework,TimeThinkemploys a reinforcement learning with verifiable rewards \(RLVR\) training strategy that encourages explicit reasoning\. Unlike template\-reliant methods, this approach enables the model to learn the underlying logic of composition rather than simply imitating traces\. Extensive experiments show thatTimeThink, trained only on synthetic data, significantly outperforms strong baselines on both synthetic and real\-world benchmarks\.111Code:[https://github\.com/sudarshanregmi/timethink](https://github.com/sudarshanregmi/timethink)

## 1Introduction

Timeseries data are ubiquitous in real\-world systems, capturing temporal dynamics across healthcare, industrial operations, and finance\. Recent timeseries multimodal large language models \(TS\-MLLMs\) adapt large language models \(LLMs\) to numerical sequences and have shown promising results on detection and question\-answering tasks\([Xie et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib8);[Zhang et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib21)\)\. Existing TS\-MLLMs differ mainly in how the numerical signal is encoded for the language model\. Some convert the series to raw text or visual plots so that an LLM or vision\-language model \(VLM\) can interpret it directly\([Yoon et al\., 2024](https://arxiv.org/html/2609.13457#bib.bib2);[Kim et al\., 2024](https://arxiv.org/html/2609.13457#bib.bib10)\)\. Others embed the series natively into the language space, training the projection on paired timeseries and language data\([Xie et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib8);[Xu et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib3);[Zhang et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib21)\)\. Across these designs, however, the model is supervised only on the final answer\. Temporal patterns such as trends, seasonality and anomalies are absorbed implicitly, and the reasoning behind a prediction is left invisible\([Li et al\., 2026](https://arxiv.org/html/2609.13457#bib.bib18)\)\. This matters because the action taken downstream of a timeseries model usually depends on which pattern triggered the prediction, not just on the prediction itself\. For example, when an equipment failure occurs in rotating machinery, a model may correctly raise an alarm from vibration, current, and temperature streams\. But it does not reveal whether the alarm stems from sustained motor load, rising bearing temperature, or a transient vibration spike\. This distinction is critical for routing maintenance to the right component\. The same holds in healthcare and other high\-stakes settings, where actions require justified diagnoses\.

These settings demand not only correct answers but the reasoning behind them\. To this end, a recent line of work uses reinforcement learning with verifiable rewards to elicit reasoning traces\([He et al\., 2026](https://arxiv.org/html/2609.13457#bib.bib11);[Guan et al\., 2026](https://arxiv.org/html/2609.13457#bib.bib16);[Ni et al\., 2026](https://arxiv.org/html/2609.13457#bib.bib19)\)\. Models such as TimeOmni\-1\([Guan et al\., 2026](https://arxiv.org/html/2609.13457#bib.bib16)\)and STReasoner\([Ni et al\., 2026](https://arxiv.org/html/2609.13457#bib.bib19)\)are optimized against outcome\-based rewards: typically exact match on multiple\-choice answers or error on a forecast\. In practice, however, the bulk of capability in these works is installed by supervised fine\-tuning \(SFT\) on reasoning templates, with reinforcement learning \(RL\) serving as a refinement pass that sharpens format compliance and offers modest accuracy gains\. Together, this recipe makes the reasoning legible at inference time and improves accuracy on the targeted tasks\.

Two limitations follow from this design\. First, because the reasoning templates are crafted or distilled per task, the resulting models are tied to the narrow band of temporal patterns covered by their training distribution \(a single forecasting target, a fixed sensor domain, or a closed set of question types\) and might not transfer to timeseries whose properties were unseen at training time\. Second, real\-world questions rarely turn on a single temporal phenomenon\. They typically require composing several at once: locating an anomaly within a seasonal trend, or correlating two variables under a non\-stationary regime\. When a question spans multiple patterns composed in novel ways, many TS\-MLLMs lose the thread and fall back to the heuristics induced by their reasoning templates\.

To address these gaps, we proposeTimeThink, a synthetic framework for eliciting compositional timeseries reasoning\. The framework begins with a synthetic data generator that combines domain\-invariant*atomic*primitives with a separate set of*sub\-skills*to form*composite*QAs\. For a small subset of examples, we use an LLM to diversify the wording and complexity of the questions and answers while preserving the programmatically generated reasoning structure and verified ground truth\. The resulting mixture of atomic and composite QAs is then used in two sequential training stages, SFT followed by reinforcement learning with verifiable rewards \(RLVR\) to enable explicit reasoning\. RLVR is driven by question\-aware rewards that decompose by answer type \(binary, categorical, numerical, and set overlap\), thereby providing denser learning signals\. We evaluateTimeThinkon both synthetic and real\-world question\-answering benchmarks, which highlight the efficacy of a synthetic\-only regime\. Our contributions:

- •TimeThink\-framework:We develop a programmatic generator for domain\-independent timeseries primitives that produces deterministic question\-aware ground truth, making RLVR tractable at scale\. We create evaluation sets containing varying compositions of timeseries primitives\. We plan to release all code, data, and models to encourage open\-source research\.
- •Timeseries compositional reasoning:We study compositional reasoning over timeseries, where answering a query requires composing learned*atomic primitives*\. To the best of our knowledge, we present the first work to train such reasoning explicitly with synthetic verifiable rewards in TS\-MLLMs\.
- •Extensive analysis:We evaluate on diverse synthetic and real\-world datasets across six tasks\. Results on compositional questions demonstrate thatTimeThinkoutperforms existing timeseries models, and further analysis showsTimeThink\(RL\) generalizes to extended temporal horizons\.

## 2Related Work

##### TS\-MLLMs without explicit reasoning\.

Existing TS\-MLLMs differ primarily in how the numerical signal is presented to the language model\. Early methods convert timeseries into strings for direct LLM processing\([Gruver et al\., 2023](https://arxiv.org/html/2609.13457#bib.bib1);[Xue and Salim, 2023](https://arxiv.org/html/2609.13457#bib.bib5);[Kim et al\., 2024](https://arxiv.org/html/2609.13457#bib.bib10)\), which suffer from token exhaustion and degraded fidelity over long sequences\([Pillai et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib4);[Spathis and Kawsar, 2024](https://arxiv.org/html/2609.13457#bib.bib7)\)\. To improve efficiency, alternative strategies use visual prompting via vision\-language models\([Yoon et al\., 2024](https://arxiv.org/html/2609.13457#bib.bib2)\), but these often pick up on surface visual patterns rather than the underlying temporal dynamics\([Merrill et al\., 2024](https://arxiv.org/html/2609.13457#bib.bib25)\)\. A more recent line treats timeseries as a native modality, projecting numerical patches directly into the LLM embedding space and aligning the two via paired data\([Jin et al\., 2023](https://arxiv.org/html/2609.13457#bib.bib9);[Xie et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib8);[Xu et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib3);[Zhang et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib21)\)\. In all three cases, models are often supervised only on final answers\. Temporal patterns are absorbed implicitly, so the model cannot expose or audit the reasoning behind a prediction\. Recent benchmarks show that even frontier LLMs struggle with synthetic timeseries questions beyond basic pattern recognition\([Cai et al\., 2024](https://arxiv.org/html/2609.13457#bib.bib27)\), with performance deteriorating further on multi\-step temporal reasoning tasks\([Li et al\., 2026](https://arxiv.org/html/2609.13457#bib.bib18)\)\.

##### Explicit reasoning over timeseries and its limits\.

A recent work\([Potosnak et al\., 2024](https://arxiv.org/html/2609.13457#bib.bib26)\)shows deep forecasters can compose temporal structure under distribution shift, but that composition is implicit and never trained for\. More recently, researchers have started to explore explicit reasoning over timeseries, following the broader RL\-for\-reasoning paradigm\([Guo et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib14);[Shao et al\., 2024](https://arxiv.org/html/2609.13457#bib.bib6)\)\. One line supervises on annotated chain\-of\-thought traces along with the final answer \(SFT\-style\), as in SenTSR\-Bench\([He et al\., 2026](https://arxiv.org/html/2609.13457#bib.bib11)\)and LLaTiSA\([Ding et al\., 2026](https://arxiv.org/html/2609.13457#bib.bib20)\)\. Another uses reinforcement learning with task\-specific rewards to elicit thinking traces during training, including STReasoner\([Ni et al\., 2026](https://arxiv.org/html/2609.13457#bib.bib19)\)and TimeOmni\-1\([Guan et al\., 2026](https://arxiv.org/html/2609.13457#bib.bib16)\)\. A parallel line applies RL to temporal reasoning over events and dates\([Liu et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib17)\)\. Two limitations curb both lines\. First, they are typically trained on relatively narrow task distributions, which can limit generalization to out\-of\-distribution timeseries\. Second, they can struggle with questions that require composing multiple temporal patterns\. What remains missing is explicit reasoning over core temporal primitives, such as trend, correlation, and seasonality with verifiable rewards\. Our work targets this gap\.

## 3TimeThink

![Refer to caption](https://arxiv.org/html/2609.13457v1/timethink_overflow.png)Figure 1:Overview ofTimeThink\.\(A, B\) Synthetic Data Generation:a programmatic generator builds Atomic QA targeting single primitives, Composite QA chaining multiple operators, andout\-of\-distribution \(OOD\) QAover unseen task axes\.\(C\) LLM\-Driven QA Evolution:templated QAs are evolved into more complex, diverse variants, with the reasoning trace \(<think\>block\) preserved so that responses stay grounded in timeseries properties\.\(D\) Training Stage Optimization:Stage 1 \(SFT\)fine\-tunes on programmatic reasoning traces at an anchor length ofT≤256T\\leq 256;Stage 2 \(RLVR\)applies GRPO to incentivize autonomous composition and extend the horizon toT≤768T\\leq 768, using a verifiable reward \(rfmt\+ransr\_\{\\mathrm\{fmt\}\}\+r\_\{\\mathrm\{ans\}\}\) over four answer categories \(binary, proximity, categorical, Set\-F1F\_\{1\}\) besides the format reward\.##### Preliminaries\.

We consider the task of question answering over multivariate timeseries\. Let𝐱=\(x1,…,xT\)∈ℝT×d\\mathbf\{x\}=\(x\_\{1\},\\dots,x\_\{T\}\)\\in\\mathbb\{R\}^\{T\\times d\}denote a timeseries of lengthTT, where each observationxt∈ℝdx\_\{t\}\\in\\mathbb\{R\}^\{d\}corresponds to a univariate \(d=1d=1\) or multivariate \(d\>1d\>1\) sequence\. Given a questionq∈𝒬q\\in\\mathcal\{Q\}about𝐱\\mathbf\{x\}, the model generates an autoregressive response𝐲=\(y1,…,y\|𝐲\|\)\\mathbf\{y\}=\(y\_\{1\},\\dots,y\_\{\|\\mathbf\{y\}\|\}\)comprising a reasoning trace and a final answer\. To facilitate the independent verification of response structure and grounding, we employ a structured output format:<think\>⋯\\cdotsanswer: \{value\}</think\>⟨\\langlepost\-think response⟩\\rangle, enabling verification of response format and answer correctness\. The conditional distributionπθ​\(𝐲∣𝐱,q\)\\pi\_\{\\theta\}\(\\mathbf\{y\}\\mid\\mathbf\{x\},q\)over output tokens is defined as:

πθ​\(𝐲∣𝐱,q\)=∏n=1\|𝐲\|πθ​\(yn∣𝐱,q,y<n\),\\pi\_\{\\theta\}\(\\mathbf\{y\}\\mid\\mathbf\{x\},q\)=\\prod\_\{n=1\}^\{\|\\mathbf\{y\}\|\}\\pi\_\{\\theta\}\(y\_\{n\}\\mid\\mathbf\{x\},q,y\_\{<n\}\),\(1\)
whereθ\\thetarepresents the model parameters\. It underlies both supervised fine\-tuning and reinforcement learning with verifiable rewards\.

Overview\.TimeThinkintroduces a synthetic framework for eliciting compositional timeseries reasoning by incorporating \(a\) synthetic data generation and \(b\) training with SFT followed by RLVR\. Data generation synthesizes and evolves atomic and composite QAs using an LLM, while training is designed to incentivize the model to compose learned atomic operations\. We describeTimeThink’s components below\.

### 3\.1Synthetic Data Generation

Timeseries reasoning has a natural compositional structure\. Questions may depend not only on a single temporal pattern but on mixtures of trends, seasonality, and others\. Answering them requires identifying primitive temporal facts and composing them through higher\-level reasoning operations\. To mimic this structure, we design a synthetic QA generator\. Unlike open\-ended language or visual reasoning, these primitives can be procedurally generated with deterministic intermediate states and exact ground truth\. Specifically, to simulate real\-world temporal patterns, we design comprehensive temporal QA generators producing*atomic*and*composite*questions\. Each composite question in our corpus is built from two kinds of operators\. An*atom operator*reads the timeseries directly and returns one fact, for example a maximum value or the position of a peak\. The atom operator setℱatom\\mathcal\{F\}\_\{\\mathrm\{atom\}\}aggregates over nine common temporal operations:Mean,Std,Percentile,ExtVal,ExtPos,EventEnum,SegEnum,PeriodandTrendClassify\. A*sub\-skill operator*takes one or more facts \(from atoms, or from sub\-skills\) and combines them into a final answer\. The*sub\-skill set*ℱop\\mathcal\{F\}\_\{\\mathrm\{op\}\}applies diverse reasoning operations to atomics:Count,Sum,Filter,Locate,Compare,Threshold,Argmax,RankandArith\. In short, atoms tell the model*what to look for*and sub\-skills*how to combine what it found*\.

Atomic QA\.An atomic QA instance is a single atom application:a=f⁡\(𝐱\)a=f\(\\mathbf\{x\}\)withf∈ℱatomf\\in\\mathcal\{F\}\_\{\\mathrm\{atom\}\}\. We refer to the outputf⁡\(𝐱\)f\(\\mathbf\{x\}\)of an atom operator as an*atomic fact*\. For example,a=ExtPos​\(𝐱\)a=\\textsc\{ExtPos\}\(\\mathbf\{x\}\)is answer to*“At which timestep does𝐱\\mathbf\{x\}reach its maximum?”*\. Atomic QAs teach the primitives thereby aligning the timeseries encoder with LLM backbone that every downstream composition will invoke\.

Composite QA\.Real\-world questions about timeseries are rarely about one pattern in isolation\. A practitioner usually asks about a mix of patterns at once, for instance comparing two segments, locating an extremum within a trend, or checking whether two signals agree on their overall shape\. Composite QAs mimic this structure: each question is built by reading several atomic facts from the timeseries and then combining them with one or more sub\-skills\. Concretely, a composite QA usesm≥1m\\geq 1atom operatorsfi∈ℱatomf\_\{i\}\\in\\mathcal\{F\}\_\{\\mathrm\{atom\}\}, each applied to𝐱\\mathbf\{x\}or to a sub\-series of𝐱\\mathbf\{x\}, to extract facts, and thenK≥1K\\geq 1sub\-skill operatorsgj∈ℱopg\_\{j\}\\in\\mathcal\{F\}\_\{\\mathrm\{op\}\}to combine those facts into the final answeraa:

f1​\(𝐱\),…,fm​\(𝐱\)⏟m​atomic facts→g1,g2,…,gKa\.\\underbrace\{f\_\{1\}\(\\mathbf\{x\}\),\\ \\ldots,\\ f\_\{m\}\(\\mathbf\{x\}\)\}\_\{m\\ \\text\{atomic facts\}\}\\;\\xrightarrow\{\\;g\_\{1\},\\,g\_\{2\},\\,\\ldots,\\,g\_\{K\}\\;\}\\;a\.For example, the question*“Is the first half of𝐱\\mathbf\{x\}on average higher than the second half?”*reflects a common real\-world question about a timeseries\. We build it by reading two atomic facts, the means of the two halves, and then combining them with a comparison:Mean​\(I1\),Mean​\(I2\)→Comparea\\textsc\{Mean\}\(I\_\{1\}\),\\ \\textsc\{Mean\}\(I\_\{2\}\)\\xrightarrow\{\\textsc\{Compare\}\}a, whereI1=\(x1,…,x⌊T/2⌋\)I\_\{1\}=\(x\_\{1\},\\dots,x\_\{\\lfloor T/2\\rfloor\}\)andI2=\(x⌊T/2⌋\+1,…,xT\)I\_\{2\}=\(x\_\{\\lfloor T/2\\rfloor\+1\},\\dots,x\_\{T\}\)denote the first and second halves of𝐱\\mathbf\{x\}\. Every composite question thus has a known programa=\(gK∘⋯∘g1\)\(f1\(𝐱\),…,fm\(𝐱\)\)a=\(g\_\{K\}\\circ\\cdots\\circ g\_\{1\}\)\(f\_\{1\}\(\\mathbf\{x\}\),\\ldots,f\_\{m\}\(\\mathbf\{x\}\)\)\. By*compositional reasoning*, we mean answering questions that require combining multiple atomic facts\. After building the QA structures above, we partition composite QA families into three splits,𝒬D\\mathcal\{Q\}\_\{\\mathrm\{D\}\},𝒬R\\mathcal\{Q\}\_\{\\mathrm\{R\}\}, and𝒬ood\\mathcal\{Q\}\_\{\\mathrm\{ood\}\}, according to the supervision each family receives\. Our training pipeline has two stages \(detailed in[Section3\.2](https://arxiv.org/html/2609.13457#S3.SS2)\): SFT on worked decompositions, followed by RLVR\. The three splits differ in how much of this pipeline each family participates in:

\(a\) Comp\-D \(CoT\-demonstrated\): a chain\-of\-thought \(CoT\) decomposition is shown during SFT, and the same composite additionally appears in the RL pool\.\(b\) Comp\-R \(reward\-only\): the composite appears only in the RL pool, so the policy is expected to solve it from the verifiable outcome reward alone\.\(c\) OOD \(held\-out\): the composite is held out from both training stages and evaluated only at test time, which measures whether compositional reasoning learned in \(a\) and \(b\) transfers to compositions the policy never saw\.

A composite QA answeraacan admit multiple equivalent decompositions, so SFT on a single CoT decomposition risks overfitting to a stylistic template, while omitting atomic QAs during RL risks primitive\-skill regression and rote memorization of composites\. We therefore mix atomic and composite QAs in both the SFT and RL phases\. The complete enumeration of every QA family is provided in[SectionD\.1](https://arxiv.org/html/2609.13457#A4.SS1)–[D\.5](https://arxiv.org/html/2609.13457#A4.SS5)\.

#### 3\.1\.1LLM\-driven QA Evolution

The generator produces questions from a fixed set of templates\. Training only on these risks memorization of form rather than learning timeseries structure\. To prevent this, we apply an LLM\-driven*question evolution*step to a small portion of training data to diversify question and answer framing \(Figure[1](https://arxiv.org/html/2609.13457#S3.F1)C\)\. Following[Xu et al\. \(2024\)](https://arxiv.org/html/2609.13457#bib.bib12), we evolve our atomic and composite templated QAs \(containing explicit reasoning breakdown\) into LLM\-enhanced QAs\. Specifically, we condition the LLM on the original question, reasoning block, and answer, and prompt it to generate a more complex question\-answer pair while preserving the same reasoning structure\. The evolution strategy is selected automatically based on the seed example\([Xu et al\., 2024](https://arxiv.org/html/2609.13457#bib.bib12)\)\. Unlike prior approaches such as ChatTS\([Xie et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib8)\), our framework preserves explicit reasoning grounding between the question and the final answer\. This keeps the model grounded in fundamental timeseries properties rather than shortcuts, and robust to elaborate rephrasings\. We additionally use question paraphrasing as a lightweight augmentation, retaining the same reasoning block and final answer\.

### 3\.2Training

Following ChatTS\([Xie et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib8)\), we adopt timeseries encoder\-fused LLM and value\-preserved timeseries normalization to train the model\. The data generator in[Section3\.1](https://arxiv.org/html/2609.13457#S3.SS1)gives us a test bed for compositional timeseries reasoning: every QA in this test bed has a known reasoning chain \(the atoms and sub\-skills that lead to the answer\) and a verifiable final answer, and the Comp\-D/Comp\-R/OOD splits separate compositions that are demonstrated, rewarded\-only, and held out respectively\. As discussed, many existing TS\-MLLMs are trained primarily with final\-answer supervision, providing no signal for producing a reasoning chain\. Therefore, to make the reasoning explicit, we design a two\-stage training framework that elicits the reasoning chain\.

Supervised Fine\-Tuning\.The first stage teaches the model what a valid reasoning chain looks like\. We fine\-tune on \(timeseries, question, target\) triples where the target is a worked chain followed by the final answer, so the model learns to emit both, in order, when prompted with a question\. In the supervised stage, we train on synthetic demonstrations𝒟SFT=\{\(𝐱\(i\),q\(i\),𝐲∗\(i\)\)\}i=1NSFT\\mathcal\{D\}\_\{\\mathrm\{SFT\}\}=\\\{\(\\mathbf\{x\}^\{\(i\)\},q^\{\(i\)\},\\mathbf\{y\}^\{\*\(i\)\}\)\\\}\_\{i=1\}^\{N\_\{\\mathrm\{SFT\}\}\}where each reference target𝐲∗\(i\)\\mathbf\{y\}^\{\*\(i\)\}is a worked reasoning trace followed by the final answer\. The SFT objective maximizes the log\-likelihood of the reference output:

ℒSFT​\(θ\)=−𝔼𝒟SFT​\[∑n=1\|𝐲∗\|log⁡πθ​\(yn∗∣𝐱,q,y<n∗\)\]\.\\mathcal\{L\}\_\{\\mathrm\{SFT\}\}\(\\theta\)=\-\\mathbb\{E\}\_\{\\mathcal\{D\}\_\{\\mathrm\{SFT\}\}\}\\Big\[\\sum\_\{n=1\}^\{\|\\mathbf\{y\}^\{\*\}\|\}\\log\\pi\_\{\\theta\}\(y\_\{n\}^\{\*\}\\mid\\mathbf\{x\},q,y\_\{<n\}^\{\*\}\)\\Big\]\.\(2\)
Reinforcement Learning with Verifiable Rewards\.The second stage refines the model’s reasoning under a verifiable reward\. The model generates its own chain on each example and is scored only on whether its final answer is correct and whether the response follows the required format\. Because the reward checks only the answer, the model is free to discover chains that go beyond the ones it imitated during SFT\. Given a timeseries and a question\(𝐱,q\)\(\\mathbf\{x\},q\), we sample a group ofGGresponses\{𝐲g\}g=1G∼πθold\(⋅∣𝐱,q\)\\\{\\mathbf\{y\}\_\{g\}\\\}\_\{g=1\}^\{G\}\\sim\\pi\_\{\\theta\_\{\\mathrm\{old\}\}\}\(\\cdot\\mid\\mathbf\{x\},q\)\. Each response is evaluated using a verifiable reward functionr⁡\(𝐱,q,𝐲\)r\(\\mathbf\{x\},q,\\mathbf\{y\}\), which decomposes into two additive components:r⁡\(𝐱,q,𝐲\)=rfmt​\(𝐲\)\+rans​\(𝐱,q,𝐲\)r\(\\mathbf\{x\},q,\\mathbf\{y\}\)=r\_\{\\mathrm\{fmt\}\}\(\\mathbf\{y\}\)\+r\_\{\\mathrm\{ans\}\}\(\\mathbf\{x\},q,\\mathbf\{y\}\), withrfmt,rans∈\[0,1\]r\_\{\\mathrm\{fmt\}\},r\_\{\\mathrm\{ans\}\}\\in\[0,1\]and hencer∈\[0,2\]r\\in\[0,2\]\. The first componentrfmtr\_\{\\mathrm\{fmt\}\}checks structural compliance for reliable extraction of predicted answer such that the response must contain exactly one<think\>\.\.\.</think\>block whose final line follows the templateanswer: \{value\}\. The accuracy component,ransr\_\{\\mathrm\{ans\}\}, performs question\-aware verification on the extracted value across four distinct categories: \(1\)Binary: exact match is required for boolean questions; \(2\)Categorical: exact match is required over a finite semantic label space; \(3\)Proximity: for numerical queries, a graded reward signal is assigned based on the distance between the predicted value and the ground truth; and \(4\)Set\-F1F\_\{1\}: partial credit is awarded for enumeration or grouping tasks by computing theF1F\_\{1\}overlap between the predicted and gold sets\. This reward design eliminates the need for manually annotated reasoning traces while still providing a rich and informative training signal\. Ultimately, we optimize the Group Relative Policy Optimization \(GRPO\) objective\([Shao et al\., 2024](https://arxiv.org/html/2609.13457#bib.bib6)\):

maxθ⁡𝔼\(𝐱,q\),𝐲g∼πθold​\[ℒGRPO​\(θ,\{r⁡\(𝐱,q,𝐲g\)\}g=1G\)\],\\resizebox\{21931650\}\{\}\{$\\displaystyle\\max\_\{\\theta\}\\,\\mathbb\{E\}\_\{\(\\mathbf\{x\},q\),\\,\\mathbf\{y\}\_\{g\}\\sim\\pi\_\{\\theta\_\{\\mathrm\{old\}\}\}\}\\big\[\\mathcal\{L\}\_\{\\mathrm\{GRPO\}\}\(\\theta,\\\{r\(\\mathbf\{x\},q,\\mathbf\{y\}\_\{g\}\)\\\}\_\{g=1\}^\{G\}\)\\big\]$\},\(3\)which normalizes rewards within each group to obtain relative advantages and updates the policy with a PPO\-style clipped surrogate plus a KL penalty against a frozen reference policyπref\\pi\_\{\\mathrm\{ref\}\}\([Guo et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib14)\)\. Hereπθold\\pi\_\{\\theta\_\{\\mathrm\{old\}\}\}denotes the rollout policy held fixed during each PPO update, whileπref\\pi\_\{\\mathrm\{ref\}\}is the SFT\-stage model frozen throughout RL\. We use the implementation provided by the verl library\([Sheng et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib13)\)\.

## 4Experiments

Task\.Our evaluation covers six task families: multiple\-choice, categorical, numerical, clustering, ranking/enumeration/ordering and description questions\.

Datasets\.We evaluate on the following datasets: \(a\) TSEvol\([Xie et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib8)\): It includes inductive \(LLM\-as\-judge score\), causal \(accuracy\) and deductive \(accuracy\) questions collected from real\-world domains\. \(b\) MCQ2\([Merrill et al\., 2024](https://arxiv.org/html/2609.13457#bib.bib25)\): It includes counterfactual MCQ questions relating to pair of timeseries\. \(c\) SenTSR\-Bench\([He et al\., 2026](https://arxiv.org/html/2609.13457#bib.bib11)\): It includes MCQ questions involving anomaly characterization \(What Happened\), cause diagnosis \(How Happened\) and action recommendation \(Suggested fix\) questions\. \(d\)TimeThinkbench: See[SectionD\.1](https://arxiv.org/html/2609.13457#A4.SS1)–[D\.5](https://arxiv.org/html/2609.13457#A4.SS5)\.

Metrics\.\(a\) Accuracy: match to ground truth; \(b\) Proximity accuracy: computed for numerical tasks asmax⁡\(0,1−\|e^−e\|/s\)\\max\\\!\\bigl\(0,\\,1\-\|\\hat\{e\}\-e\|/s\\bigr\), wheree^\\hat\{e\}is the prediction,eeis the ground truth, and the scalessis the sequence length for positional tasks andmax⁡\(\|e\|,1\)\\max\(\|e\|,1\)otherwise; \(c\) F1: computed for grouping tasks over groups extracted by the LLM judge; \(d\) Judge\-score: computed by the LLM judge \(Qwen2\.5\-72B\-Instruct\-GPTQ\-Int4\) depending on the task \(ranking, enumeration, ordering, or description\)\.

Baselines\.For general\-purpose LLMs, we use Qwen2\.5\-Instruct\-7B\([Qwen et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib22)\)and Mistral\-Instruct\-7B\-v0\.3\([Jiang et al\., 2023](https://arxiv.org/html/2609.13457#bib.bib24)\)\. For text\-based timeseries and temporal reasoning models, we include Time\-R1\-3B\([Liu et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib17)\), Time\-MQA\-7B\([Kong et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib15)\), and TimeOmni\-1\([Guan et al\., 2026](https://arxiv.org/html/2609.13457#bib.bib16)\)\. For timeseries encoder\-based approaches, we compare against ChatTS\([Xie et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib8)\)\.

Training details\.We train three variants of Qwen3\-8B\([Yang et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib23)\)augmented with a timeseries encoder\([Xie et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib8)\)on a single node with 8×\\timesNVIDIA H200 GPUs using the verl\([Sheng et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib13)\)framework\. The first variant \(equivalent to ChatTS\([Xie et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib8)\)\) is trained on answer\-only targets over our task taxonomy\. The second variant,TimeThink\(SFT\), adds chain\-of\-thought supervision\. The third variant,TimeThink\(RL\), initializes from the SFT checkpoint and applies RLVR with GRPO\([Shao et al\., 2024](https://arxiv.org/html/2609.13457#bib.bib6)\)optimization\. We use AdamW with weight decay0\.010\.01for all three post\-training stages\. Both ChatTS andTimeThink\(SFT\) use a learning rate1​e−51\\mathrm\{e\}\{\-5\}and effective batch size192192\. GRPO optimization uses learning rate1​e−61\\mathrm\{e\}\{\-6\}and effective batch size256256with 16 rollouts\. The training corpus consists entirely of synthetic data \(90K SFT samples and 110K RL samples\), with no real\-world timeseries data included\. There are 7\.5k LLM\-evolved QAs in the SFT pool, whereas there are 7\.5k question\-rephrased samples in the RL pool\.

## 5Results

In all tables,boldmarks the best score andunderlinethe second\-best\. Cross\-architecture comparisons are restricted to sequence length below256256due to the cost of text\-based models; among TS\-native models we use lengths up to15361536\.

Table 1:Performance on synthetic compositional timeseries QA\.TimeThink\(RL\) outperforms all baselines\.ModelComp\-D\(\#3,261\)Comp\-R\(\#1,948\)CategoricalNumericalClusteringOrd\./Enum\.W\. AvgCategoricalNumericalW\. AvgQwen2\.5\-Instruct\-7B0\.6780\.4740\.2630\.4840\.5600\.6560\.4720\.593Mistral\-7B\-Instruct\-v0\.30\.6240\.4060\.2790\.4320\.5070\.6560\.4220\.576Time\-MQA0\.5380\.3640\.1890\.3740\.4380\.5500\.3710\.488Time\-R10\.6050\.4360\.2330\.4870\.5110\.5970\.4090\.532TimeOmni\-10\.5740\.5170\.2470\.4030\.5120\.5520\.5470\.550ChatTS0\.5500\.6500\.4070\.5470\.5730\.5250\.4960\.515TimeThink\(SFT\)0\.7220\.6410\.7070\.7280\.6960\.5620\.4740\.532TimeThink\(RL\)0\.7710\.6680\.7120\.7500\.7310\.7220\.7540\.733

Comp\-D vs\. Comp\-R:The results in[Table1](https://arxiv.org/html/2609.13457#S5.T1), evaluated on∼\\sim5k test samples, mirror the asymmetry between the two splits\. On Comp\-D,TimeThink\(SFT\) already reaches 0\.696, since the demonstrated decompositions cover most of the reasoning the model must produce, and RL adds a further\+3\.5\+3\.5pp \(0\.696→0\.7310\.696\\to 0\.731\)\. On Comp\-R,TimeThink\(SFT\) plateaus at 0\.532, consistent with the difficulty of transferring SFT demonstrations to composite families absent from the SFT pool\. RL lifts this to 0\.733, a\+20\.1\+20\.1pp gain\. This gain shows that reward\-only training substantially improves performance on composite families that lack SFT reasoning demonstrations\. To separate the effect of RL from additional exposure to Comp\-R examples, we compare RL against rejection fine\-tuning from the same checkpoint using the same 10K prompts \([Table5](https://arxiv.org/html/2609.13457#A1.T5)\)\. RL improves Comp\-R from 0\.528 to 0\.597 compared with 0\.567 for additional SFT\. These controlled results suggest that the gains are not explained solely by additional training exposure\.

Figure 2:RL gains come from both the atomic skills \(Δa\\Delta\_\{a\}\) and the sub\-skill that composes them \(Δc\\Delta\_\{c\}\)\.Figure 3:Overall OOD performance across tasks\.TimeThink\(RL\) leads all native\-TS baselines\.OOD composition:A strictly fair OOD comparison applies only to timeseries\-native models, whose encoders are trained on a fixed distribution; text\-based baselines may have seen similar patterns during pretraining, so their OOD numbers are not directly comparable\.[Figure3](https://arxiv.org/html/2609.13457#S5.F3)reports overall OOD compositional performance \(mean over numerical, categorical and enumeration\) on∼\\sim8k test samples\. First,TimeThink\(RL\) improves over its SFT counterpart by nearly 10 pp on the OOD split \(0\.533→\\to0\.629\)\. Second, theTimeThink\(SFT\) model yields only marginal improvements over the ChatTS baseline, suggesting that imitation alone does not transfer under distribution shift\. Third, text\-based baselines at best matchTimeThink\(SFT\) despite Time\-MQA and TimeOmni\-1 being trained on timeseries data, and Time\-R1 on temporal\-reasoning data\.

Where does compositional ability come from?A composite question requires both the constituent atomic skill\(s\) and the*sub\-skill\(s\)*that combine them, so a gain on the overall composition could reflect either\. For every composition, we score its constituent atoms on their dedicated test set and compare the RL gain on atoms \(Δa\\Delta\_\{a\}\) against the gain on the composition \(Δc\\Delta\_\{c\}\) \(unweighted means\)\. Three patterns drive the reading of[Figure2](https://arxiv.org/html/2609.13457#S5.F2)and per\-composition details are in[AppendixE](https://arxiv.org/html/2609.13457#A5)\. RL improves the atomic substrate by the same amount regardless of which compositions sit on top of it, so the variance inΔc\\Delta\_\{c\}is not driven by variance inΔa\\Delta\_\{a\}\. Atomic propagation alone would predictΔc≤Δa\\Delta\_\{c\}\\leq\\Delta\_\{a\}in every row; the Comp\-R row falsifies this \(Δc=\+0\.18\>Δa=\+0\.10\\Delta\_\{c\}=\+0\.18\>\\Delta\_\{a\}=\+0\.10\)\. With atomic gain held essentially constant, the\+0\.18\+0\.18on Comp\-R against\+0\.04\+0\.04on Comp\-D reflects RL acquiring the sub\-skill that combines atoms where SFT did not demonstrate it\. The\+0\.09\+0\.09on OOD additionally indicates that this learned sub\-skill transfers to held\-out composite questions\.

Table 2:Performance on real\-world TSEvol datasets\.Trained only on synthetic QA,TimeThink\(RL\) achieves the best weighted average\.Real\-world evaluation\.On the real\-world TSEvol\([Xie et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib8)\)datasets \([Table2](https://arxiv.org/html/2609.13457#S5.T2)\),TimeThink\(RL\) achieves the best results on causal and inductive reasoning as well as on average, improving overTimeThink\(SFT\) from 0\.632 to 0\.709, while text\-based baselines such as Time\-MQA and Time\-R1 underperform general\-purpose text baselines\. RLVR on basic timeseries skills hence transfers to real\-world reasoning tasks\.

## 6Ablations and Case Studies

Figure 4:Overall performance on unseen\-length timeseries \(\[769,1536\]\[769,1536\]steps\)\.Δ\\DeltaisTimeThink\(RL\)’s gain over the best baseline\.Figure 5:Overall performance as the number of TS variables in the prompt grows\.Length generalization\.To test ifTimeThink\(RL\)’s gains transfer beyond training\-length, we evaluate on unseen range\[769,1536\]\[769,1536\]timesteps and compare overall performance againstTimeThink\(SFT\) and ChatTS\. As shown in[Figure4](https://arxiv.org/html/2609.13457#S6.F4),TimeThink\(RL\) consistently outperforms both baselines across all categories, with especially large gains on compositional tasks, whileTimeThink\(SFT\) improves over ChatTS on Comp\-D but underperforms on atomic tasks and Comp\-R\.

Sensitivity analysis w\.r\.t\. the number of timeseries\.We examine how performance changes with the number of timeseries variables in the prompt, splitting the test set into four groups: 1 variable \(UTS\), 2–4, 5–8, and≥9\\geq 9variables\.[Figure5](https://arxiv.org/html/2609.13457#S6.F5)reports overall performance for the three native timeseries variants in each group\.TimeThink\(RL\) achieves the highest accuracy across all four groups, and its improvement overTimeThink\(SFT\) grows from approximately 8 pp on UTS examples to 10 pp for prompts with≥5\\geq 5variables\. This suggests RL is particularly effective for multivariate reasoning, where the model must combine evidence across several timeseries\.

Data scaling: SFT vs RL\.A natural alternative to RL post\-training is additional SFT on the same training distribution\. We compare the two regimes in[Table3](https://arxiv.org/html/2609.13457#S6.T3)on SenTSR\-Bench\([He et al\., 2026](https://arxiv.org/html/2609.13457#bib.bib11)\)and MCQ2\([Merrill et al\., 2024](https://arxiv.org/html/2609.13457#bib.bib25)\)benchmarks\. Starting from ChatTS\([Xie et al\., 2025](https://arxiv.org/html/2609.13457#bib.bib8)\), adding 110K additional SFT samples improves SenTSR\-Bench mean accuracy by only 2\.8 pp and*regresses*MCQ2 accuracy by 8\.0 pp, consistent with SFT’s tendency to reinforce the dominant answer distribution\. In contrast, starting fromTimeThink\(SFT\), adding 10K RL samples yields larger gains:\+8\.1\+8\.1pp on SenTSR\-Bench mean accuracy and\+5\.7\+5\.7pp on MCQ2\. The RL recipe thus requires an11×11\\timessmaller data budget and only outcome\-verifiable supervision rather than reference responses\.

Reward design\.[SectionA\.8](https://arxiv.org/html/2609.13457#A1.SS8)reports two further case studies: proximity rewards beat exact\-match rewards on numerical tasks \(\+18\.4\+18\.4vs\.\+8\.4\+8\.4pp\), and rewarding composites alone is not enough, since an atomic primitive that is only indirectly rewarded degrades on OOD composites built on it\.

Table 3:Data scaling comparison in SFT vs\. RL axis\.What,HowandFixare the SenTSR\-Bench splits\.
## 7Conclusion

TimeThinkgrounds timeseries language reasoning in domain\-invariant atomic primitives \(e\.g\., trend, seasonality\) with deterministic ground truth, which removes costly annotation and makes reinforcement learning with verifiable rewards tractable\. The resulting model composes primitives autonomously, outperforming text\-based and native timeseries models on both synthetic and real\-world benchmarks, and a curriculum over sequence length carries these gains to longer horizons\. Primitive\-based reasoning is a promising route for high\-stakes domains like healthcare and finance\.

## 8Limitations

Given the scope of this work, it necessarily entails certain limitations\.TimeThinkis trained on a fixed set of synthetic atomic primitives, which may not exhaustively capture all temporal phenomena found in real\-world timeseries\. Relying on synthetic data is a necessity given the lack of real\-world datasets for compositional reasoning with precise ground truth; however, should such resources become available,TimeThinkcould benefit from training on mixed datasets\. As the primary scope of this work is to study compositional reasoning, we do not focus on injecting exhaustive knowledge or various real\-world sensor domains\. We leave this as a direction for future work\.

## 9Acknowledgments

The authors acknowledge support for this research fromEvergreen: A Generative AI and Behavioral Sensing Digital Ecosystem to Promote Student Wellness and Flourishing\.This work is made possible through philanthropic gifts to Dartmouth College dedicated to advancing AI\-supported well\-being and flourishing of college students\.

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- Zhanget al\.\(2025\)Y\. Zhang, K\. Ayush, S\. Qiao, A\. A\. Heydari, G\. Narayanswamy, M\. A\. Xu, A\. A\. Metwally, S\. Xu, J\. Garrison, X\. Xu, T\. Althoff, Y\. Liu, P\. Kohli, J\. Zhan, M\. Malhotra, S\. Patel, C\. Mascolo, X\. Liu, D\. McDuff, and Y\. YangSensorLM: learning the language of wearable sensors\.arXiv preprint arXiv:2506\.09108\.Cited by:[§1](https://arxiv.org/html/2609.13457#S1.p1.1),[§2](https://arxiv.org/html/2609.13457#S2.SS0.SSS0.Px1.p1.1)\.

## Appendix AAdditional Results

### A\.1Comparison with a Coding Agent

We also compare with a code\-interpreter agent: a 32B model given the raw values of each series and a Python interpreter allowing it to compute statistics exactly\. As[Table4](https://arxiv.org/html/2609.13457#A1.T4)shows, the agent performs well on synthetic questions, outperformingTimeThinkon two splits\. This is expected because our synthetic questions are defined by simple programs over the raw values, making code execution close to an oracle\. Thus, the agent has an advantage unavailable toTimeThinkand is not a like\-for\-like baseline; we therefore exclude it from the main results\. On real\-world data, the trend reverses: the agent scores 25\.8 on SenTSR\-Bench compared with 35\.5 forTimeThink, as these questions require reasoning beyond direct computation over the observed values\.

Table 4:Comparison with a code\-interpreter agent: Qwen2\.5\-32B\-Instruct given the raw values as text plus a Python interpreter\.TimeThinkreads the series through its encoder, without tools\.
### A\.2Additional SFT vs\. RL

Starting from the sameTimeThink\(SFT\) checkpoint, we compare additional SFT and RL using 10K additional reward\-only composite training samples\. Since reward\-only composite questions do not have gold CoT annotations, we use a rejection\-fine\-tuning procedure\. Specifically, for each prompt, we sample 32 responses from theTimeThink\(SFT\) checkpoint and retain the responses that receive a maximum reward under the same verifiable reward used for GRPO\. The resulting data are then used for additional SFT fine\-tuning, providing a controlled comparison with RL\. As shown in[Table5](https://arxiv.org/html/2609.13457#A1.T5), RL achieves the best performance on most metrics, suggesting that RL provides benefits beyond additional fine\-tuning on reward\-filtered responses\.

Table 5:Additional SFT vs\. RL from the sameTimeThink\(SFT\) checkpoint, both using 10K additional training samples\.
### A\.3Clustering Task

Clustering includes two synchronization criteria:*trend*, based on matching or opposite trend\-segment patterns, and*local fluctuation*, based on events near a target position\. Both criteria appear during SFT phase\.[Table6](https://arxiv.org/html/2609.13457#A1.T6)shows thatTimeThink\(SFT\) already learns this task well, improving average F1 over ChatTS by 25\.5 points\. RLVR adds only a small gain of 1\.1 points\. This is consistent with our training design: when a task family is well covered by supervised reasoning traces, most of the improvement comes from SFT, while RLVR has a smaller effect\.

Table 6:Clustering by synchronization criterion \(F1 metric\)\.
### A\.4Numerical Task

During RL optimization, numerical tasks \(position and magnitude\) are scored with a proximity reward rather than exact match, so predictions receive partial credit when they are close to the ground truth\.[Table7](https://arxiv.org/html/2609.13457#A1.T7)reports relative accuracy for each task\.TimeThink\(RL\) is the strongest model in every category\. It outperforms the best text\-only baseline by 23\.1 points on position, 17\.1 points on count, and 5\.9 points on magnitude\. Within the same TS\-native models, RLVR also gives consistent gains overTimeThink\(SFT\), improving position, count, and magnitude by 14\.9, 17\.2, and 10\.7 points, respectively\. We hypothesize that CoT supervision encourages step\-wise but verbose responses, which are more error\-prone on numerical tasks and RL corrects this\.

Table 7:Numeric\-task relative accuracy;ΔRLVR\\Delta\_\{\\mathrm\{RLVR\}\}is the RL gain over SFT\.
### A\.5Descriptive Task

We present the cross\-architecture comparison in terms of description performance scored by LLM in[Table8](https://arxiv.org/html/2609.13457#A1.T8)\. It demonstrates thatTimeThink\(RL\) exhibits superiority in describing the timeseries data\.

Table 8:Free\-form descriptive task, judge score\.
### A\.6Full Results on SenTSR\-Bench

We present the complete results of SenTSR\-Bench in[Table9](https://arxiv.org/html/2609.13457#A1.T9)which showsTimeThink\(RL\), despite being trained only on synthetic data, almost matches the performance of TimeOmni\-1 in average performance\.

Table 9:Full SenTSR\-Bench accuracy\. Columns are theWhat Happened,How HappenedandSuggested Fixsplits\.
### A\.7Full Results on MCQ2

We present the complete results of MCQ2 benchmark in[Table10](https://arxiv.org/html/2609.13457#A1.T10)which showsTimeThink\(RL\) outperforms all baselines except TimeOmni\-1\.

Table 10:Full MCQ2 evaluation\.
### A\.8Reward Design Case Studies

Proximity\-based vs\. exact\-match reward\.Two periodicity tasks in our benchmark enable a comparison\. Both require the model to output a single scalar derived from a timeseries: either the period of the series or the number of complete cycles within a given window\. We assign a proximity reward to the former and an exact\-match reward to the latter\. Empirically, RL training yields a gain of only\+8\.4\+8\.4pp on the exact\-match task, compared to\+18\.4\+18\.4pp on the proximity\-rewarded counterpart, suggesting the advantage of proximity\-based rewards for numerical tasks\.

Is rewarding composite QAs enough?We study this in a setting where the atomic primitive receives only indirect supervision\.TimeThink\(SFT\) supervises trend\-segment enumeration of the form\[\(’increase’, start, end\), \(’decrease’, start, end\), …\]\. DuringTimeThink\(RL\), we restrict reward on this atom to count\-based QAs over the segment list\. The drift is sharp on OOD composites that require precise trend\-segment positions:TimeThink\(RL\) underperformsTimeThink\(SFT\) by18\.918\.9pp oncross trend convergence\(comparing trend agreement across temporal halves\) and by13\.413\.4pp ontrend reversal\(detecting whether the dominant trend reverses at the largest change point\)\. Both compositions decompose through the same primitive whose positional structure was never directly rewarded under our count\-only RL signal\. Atomic primitives should therefore be rewarded directly; otherwise the policy degrades on them, and the OOD composites built on them suffer most\.

## Appendix BQualitative Example

[Figure6](https://arxiv.org/html/2609.13457#A2.F6)compares the responses of ChatTS,TimeThink\(SFT\) andTimeThink\(RL\) on the same question\.

![Refer to caption](https://arxiv.org/html/2609.13457v1/response_figure.png)Figure 6:Comparison of responses from ChatTS,TimeThink\(SFT\) andTimeThink\(RL\) on the same question\.
## Appendix CLLM\-as\-Judge Prompt Templates

All free\-form and structured\-verdict evaluations are graded byQwen2\.5\-72B\-Instruct\-GPTQ\-Int4served via vLLM with greedy decoding\. The judge is invoked through one of four prompt templates selected by the task family of each evaluation sample\. We reproduce each template verbatim below; placeholder fields \(e\.g\.\{question\},\{pred\}\) are filled with sample\-specific content at inference time\. Outputs are parsed as JSON\.

##### Free\-form judge\.

Used for the descriptive task and for the TSEvol’s inductive tasks\. Returns a single graded score for explanation quality\.

You are an expert time\-series analyst evaluator\. Your task is to rate the quality of a generated explanation compared to a ground truth explanation\. Question: \{question\} Ground Truth: \{gt\} Prediction: \{pred\} Critique the prediction based on physical significance and accuracy\. Finally, provide a score from 0\.0 to 1\.0\. Output ONLY the JSON object\. Do not include any introductory text, markdown headers, or explanations outside of the JSON block: \{ "reasoning": "your critique here", "score": 0\.85 \}

##### Multiple\-choice judge\.

Used for MCQ2, SenTSR\-Bench\. The judge first identifies which option the model committed to, then sets a binaryverdict\_matchand a separate explanation\-quality score\.

You are grading a multiple\-choice answer\. Question: \{question\} Options: \{options\_block\} Correct answer: \{correct\_letter\}\) \{correct\_option\} Model response: \{pred\} Task: 1\. Identify which option \(A/B/C/D\) the model ultimately picked\. Acceptable forms: \-\- Starts with the letter \(e\.g\. "A\) \.\.\.", "Answer: B", "The answer is C"\)\. \-\- Paraphrases or quotes the option text without the letter — match by content\. \-\- Rambles or revises — use the final committed choice \(the answer it ends on\)\. \-\- Does NOT commit to any option→\\rightarrowpicked\_letter==null\. 2\. Set verdict\_match==1\.0 iff picked\_letter=⁣===correct\_letter, else 0\.0\. If picked\_letter is null, verdict\_match==0\.0\. 3\. Rate reasoning quality in score \(0\.0\-\-1\.0\) INDEPENDENT of correctness — how clear, grounded in the time series, and well\-structured the justification is\. Output ONLY the JSON object\. No preface, no markdown: \{ "picked\_letter": "A", "verdict\_match": 1\.0, "reasoning": "brief justification for the grading", "score": 0\.85 \}

##### Structured\-verdict judge\.

Used for our compositional task families \(segment\-family, list\-and\-set tasks, and numerical\-verdict compositions\)\. Returns four signals: a binaryverdict\_match, a gradedcorrectness\_score\(Kendall’s tau intuition for ordered lists, Jaccard intuition for sets\), an overall explanationscore, and anextracted\_numberfor numeric\-verdict tasks \(e\.g\., proportions stated as “3 of 7” are auto\-converted to0\.430\.43\)\.

You are an expert time\-series analyst evaluator\. Your task is to evaluate a model’s response to a structured time\-series question\. Question: \{question\} Expected Answer: \{expected\_verdict\} Ground Truth Response: \{gt\} Model Response: \{pred\} Evaluate FOUR things: 1\.verdict\_match: Does the model’s response convey the same answer/verdict as the expected answer? Use 1\.0 for correct, 0\.0 for incorrect\. Be lenient with formatting \-\- ‘‘yes’’, ‘‘Yes\.’’, and ‘‘Yes, because…’’ all match an expected verdict of ‘‘yes’’\. For numeric verdicts, allow small rounding differences\. 2\.correctness\_score: A graded measure of ANSWER CORRECTNESS only \-\- ignore explanation quality, depth, or verbosity\. Range 0\.0\-\-1\.0: \-\- 1\.0==fully matches the expected answer \(any acceptable phrasing\) \-\- 0\.7\-\-0\.9==mostly correct with a small/specific error \(one swap in a 6\-list, a partially\-overlapping set\) \-\- 0\.4\-\-0\.6==roughly half right \(half a list correct, right order of magnitude but off\) \-\- 0\.1\-\-0\.3==mostly wrong but some element is recognizable \-\- 0\.0==wrong, or no answer For ordered lists, use Kendall’s tau intuition \(more swaps→\\rightarrowlower score\)\. For sets, use Jaccard intuition \(\|\|intersection\|/\|\|/\|union\|\|\)\. 3\.score: Overall explanation quality \(reasoning, accuracy, completeness\) from 0\.0 to 1\.0\. Diagnostic; can differ from correctness\_score \(a terse\-but\-correct answer can have low score and high correctness\_score\)\. 4\.extracted\_number: If the Expected Answer is numeric, identify the final numeric verdict the model is asserting \-\- the number it CLAIMS as its answer, not an intermediate calculation\. For ratios in words \(‘‘3 of 7’’\), compute to 2 decimal places \(≈0\.43\\approx 0\.43\)\. Output as a JSON number; null if no clear numeric verdict\. Output ONLY the JSON object: \{ "reasoning": "your critique here", "verdict\_match": 1\.0, "correctness\_score": 0\.85, "score": 0\.85, "extracted\_number": 0\.52 \}

##### Description\-extraction judge\.

For the descriptive task we additionally extract a structured representation of the model’s free\-form description \(trend, seasonality, noise, local events, physical explanation\), allowing per\-axis precision and recall against the ground\-truth structured fields\. This complements the free\-form judge above; the per\-axis F1 contributes to thedescription\_overallcolumn reported in our descriptive\-task table\.

Extract structured time series description data from the following text\. IMPORTANT: Read the ENTIRE response holistically before extracting\. Do NOT do raw keyword extraction\. Instead, logically reason about the content: \-\- If ‘‘spike’’ is mentioned in one sentence and ‘‘followed by increase’’ in another, understand them as related context\. \-\- Synthesize scattered descriptions into coherent structured fields\. Only fill in perspectives that are actually discussed in the text\. Leave others as null\. Fortrend: identify the overall type \(increasing/decreasing/steady/multiple\), start value, end value, amplitude, and any segments\. Forseasonality/periodicity: identify whether periodicity exists, its type, period length, and amplitude\. Fornoise: identify the noise level category \(smooth or noisy\) and the noise strength value \(ratio of signal amplitude\)\. Forlocal characteristics: identify each local event with its type \(spike, dip, shake, sudden increase/decrease, etc\.\), approximate position, amplitude, and any explanation of physical meaning specific to that event\. Forphysical explanation: extract any text that explains the physical meaning or significance of the time series characteristics\. Return a valid JSON object matching the output schema\.

## Appendix DQA Types

### D\.1Atomic QA

Atomic QA exercises a single primitive operatorf∈ℱatomf\\in\\mathcal\{F\}\_\{\\mathrm\{atom\}\}extracting one fact directly from the timeseries\. We instantiate\|ℱatom\|=9\|\\mathcal\{F\}\_\{\\mathrm\{atom\}\}\|=9primitives across 14 single\-metric question variants\.

- •Mean:*“What mean value does metricX take?”*
- •Mean:*“What is the average value of metricX from positionaatobb?”*
- •Mean\(per chunk\):*“What are the means of consecutive 16\-point chunks of metricX from indexaatobb?”*
- •Std:*“What is the spread of metricX measured by standard deviation?”*
- •Std:*“What is the standard deviation of metricX over\[a,b\]\[a,b\]?”*
- •Percentile:*“Report the 50thpercentile value for metricX\.”*
- •ExtVal:*“What is the largest value of metricX?”*
- •ExtVal:*“What is the minimum value of metricX?”*
- •ExtPos:*“Where is the highest value in metricX?”*
- •ExtPos:*“At which index does metricX attain its minimum?”*
- •EventEnum:*“Enumerate the local events in metricX, including type, position, amplitude\.”*
- •SegEnum:*“Describe the segments of the trend in metricX over time\.”*
- •Period:*“Describe the periodic behavior of metricX\.”*
- •TrendClassify:*“What is the overall trend direction of metricX \(increase, decrease, or keep steady\)?”*

### D\.2Sub\-skills

Sub\-skillsℱop\\mathcal\{F\}\_\{\\mathrm\{op\}\}act on the outputs of atoms \(or earlier sub\-skills\), not on the raw series\. We instantiate\|ℱop\|=9\|\\mathcal\{F\}\_\{\\mathrm\{op\}\}\|=9\.

- •Count: cardinality of a \(possibly filtered\) list\.
- •Sum: sum over a list of weighted scalars \(used for total durations, mode counts, weighted means\)\.
- •Filter: subset of a list matching a predicate\.
- •Locate: find the structure \(segment / chunk / half / quarter / interval\) containing a given index, or the bin a derived value falls in\.
- •Compare: binary inequality between two scalars or labels\.
- •Threshold:x\>cx\>cfor a constantcc\.
- •Argmax/Argmin: select the element with the largest/smallest key\.
- •Rank: total order over a list by a key\.
- •Arith: scalar arithmetic over reals:\+,−,×,÷,\|⋅\|\+,\-,\\times,\\div,\|\\cdot\|\.

### D\.3Comp\-D compositions \(36\)

- •Mean/Stdon two metrics \+Compare:*“Is metricB’s mean higher than metricA’s?”*
- •Mean/Stdon each metric \+Argmax:*“Identify the metric with the largest standard deviation\.”*
- •TrendClassifyon each metric \+Filter:*“Which metrics show an increase trend?”*
- •Mean/TrendClassifyon each metric \+Count:*“Count the metrics whose mean exceedsτ\\tau\.”*
- •TrendClassifyon two metrics \+Compare:*“Is the overall trend of metricA the same as metricB?”*
- •EventEnum→Locate\\textsc\{EventEnum\}\\to\\textsc\{Locate\}\(within tolerance\)→Threshold\(\>0\)\\to\\textsc\{Threshold\}\(\{\>\}0\)\.*“Does metricX have a noticeable event around pointppwithin toleranceτ\\tau?”*
- •Period\(andCountfor cycle count\)\.*“Compute the estimated period for metricX\.”*
- •SegEnum→Argmax\\textsc\{SegEnum\}\\to\\textsc\{Argmax\}\(largest level shift\) and/orCount\.*“How many times does metricX change its dominant trend?”*
- •Mean/Std/Percentile\\textsc\{Mean\}/\\textsc\{Std\}/\\textsc\{Percentile\}on sub\-intervals \+Arith/Compare\.*“How does the std of metricX change from the first half to the second half?”*
- •multi\-condition compound:Mean×2\+Arith\+Threshold\\textsc\{Mean\}\{\\times\}2\+\\textsc\{Arith\}\+\\textsc\{Threshold\}\.*“If a ‘significant upward shift’ is when \(mean\(Q3\)\-mean\(Q1\)\)/range \> 15%, does metricX qualify?”*
- •SegEnum→Filter\\textsc\{SegEnum\}\\to\\textsc\{Filter\}\(intersect\[a,b\]\[a,b\]\)→Sum\\to\\textsc\{Sum\}per type→Argmax\\to\\textsc\{Argmax\}\.*“Between pointsaaandbbin metricX, which trend behavior dominates?”*
- •EventEnum→\{Filter,Count,Argmax\}\\textsc\{EventEnum\}\\to\\\{\\textsc\{Filter\},\\textsc\{Count\},\\textsc\{Argmax\}\\\}\.*“What is the shortest local event in metricX in terms of duration?”*
- •SegEnum→\{Filter,Count,Argmax\}\\textsc\{SegEnum\}\\to\\\{\\textsc\{Filter\},\\textsc\{Count\},\\textsc\{Argmax\}\\\}\.*“How many trend segments show an increase in metricX?”*
- •SegEnum→\\textsc\{SegEnum\}\\toadjacent\-pair extraction→\{Filter/Count,Argmax\}\\to\\\{\\textsc\{Filter\}/\\textsc\{Count\},\\textsc\{Argmax\}\\\}\.*“Which adjacent segment pair pattern is most common in metricX?”*
- •EventEnum,SegEnum→Filter/Locate→\{Count,Argmax\}\\textsc\{EventEnum\},\\textsc\{SegEnum\}\\to\\textsc\{Filter\}/\\textsc\{Locate\}\\to\\\{\\textsc\{Count\},\\textsc\{Argmax\}\\\}\.*“Count the local events in metricX that fall within decrease segments\.”*
- •EventEnum→Locate\\textsc\{EventEnum\}\\to\\textsc\{Locate\}\(first/last/gap\)\.*“Where does the last local event appear in metricX?”*
- •SegEnum→Filter\\textsc\{SegEnum\}\\to\\textsc\{Filter\}per type→Sum\\to\\textsc\{Sum\}\+Compare\.*“In metricX, which has a longer total duration: increase or decrease?”*
- •TrendClassifyon two metrics over aligned windows \+ similarity check\.*“Evaluate the trend similarity between metricA and metricB; transitions within 2 timesteps are aligned\.”*
- •TrendClassifyon two metrics \+ opposite\-trend predicate\.*“Determine whether metricA and metricB exhibit opposite trend behavior\.”*
- •TrendClassify/EventEnumon each metric \+ similarity to anchor \+Filter\.*“Identify metrics whose local behavior near pointppresembles metricAnchor\.”*
- •TrendClassifyon each metric \+ opposite\-anchorFilter\.*“Find metrics that move opposite to metricAnchor\.”*
- •atom on each metric \+\{Filter,Argmax\}\\\{\\textsc\{Filter\},\\textsc\{Argmax\}\\\}\.*“Which metric has the highest standard deviation?”*
- •atom on two metrics \+Arith\(ratio/difference\) \+Threshold\.*“An ‘instability gap’ occurs when std\(metricA\) is at leastr×r\\timesstd\(metricB\); does it occur?”*
- •anticorrelation predicate∧\\wedgenoise\-strength threshold\.*“An ‘anticorrelated high\-noise state’ is when metricA and metricB are anti\-correlated AND noise of metricB exceedsτ\\tau; does it hold?”*
- •TrendClassifyon metricA \+ conditionalTrendClassifyon metricB over the same windows\.*“When metricA is increasing, what does metricB’s trend look like?”*
- •Mean×2→Compare\\textsc\{Mean\}\{\\times\}2\\to\\textsc\{Compare\}\.*“Does the first\-half mean of metricX exceed the second\-half mean?”*
- •Std×2→Compare\\textsc\{Std\}\{\\times\}2\\to\\textsc\{Compare\}\.*“Is the std of the second half of metricX higher than the first?”*
- •EventEnum,SegEnum→Locate/Filter→Threshold\(\>0\)\\textsc\{EventEnum\},\\textsc\{SegEnum\}\\to\\textsc\{Locate\}/\\textsc\{Filter\}\\to\\textsc\{Threshold\}\(\{\>\}0\)\.*“Does any local event of metricX fall in an increase segment?”*
- •ExtPos,SegEnum→Locate→Compare\\textsc\{ExtPos\},\\textsc\{SegEnum\}\\to\\textsc\{Locate\}\\to\\textsc\{Compare\}on type\.*“Does the global max of metricX fall within a decrease segment?”*
- •EventEnum,Std→Argmax→Arith\(×k\)→Threshold\\textsc\{EventEnum\},\\textsc\{Std\}\\to\\textsc\{Argmax\}\\to\\textsc\{Arith\}\(\{\\times\}k\)\\to\\textsc\{Threshold\}\.*“Is the seasonal amplitude of metricX greater thank​σk\\sigma?”*
- •EventEnum→Filter→Count\\textsc\{EventEnum\}\\to\\textsc\{Filter\}\\to\\textsc\{Count\}\.*“How many decrease events are there in metricX?”*
- •SegEnum→Argmax\\textsc\{SegEnum\}\\to\\textsc\{Argmax\}\(duration\)→\\toextract type\.*“Is the longest segment in metricX an increase, decrease, or steady segment?”*
- •SegEnum→Filter→Sum→Arith\(÷total\)\\textsc\{SegEnum\}\\to\\textsc\{Filter\}\\to\\textsc\{Sum\}\\to\\textsc\{Arith\}\(\{\\div\}\\,\\text\{total\}\)\.*“What share of metricX is decreasing?”*
- •Std×2→Arith​\(÷\)→Threshold\\textsc\{Std\}\{\\times\}2\\to\\textsc\{Arith\}\(\{\\div\}\)\\to\\textsc\{Threshold\}\.*“Does metricA have a std at leastr×r\\timesthat of metricB?”*
- •Mean×N→Rank\\textsc\{Mean\}\{\\times\}N\\to\\textsc\{Rank\}\.*“Rank the metrics by mean from highest to lowest\.”*
- •TrendClassify×N→Filter/Count\\textsc\{TrendClassify\}\{\\times\}N\\to\\textsc\{Filter\}/\\textsc\{Count\}per type→Argmax→Arith\(÷N\)\\to\\textsc\{Argmax\}\\to\\textsc\{Arith\}\(\{\\div\}\\,N\)\.*“How dominant is the most common trend? Report the mode share\.”*

### D\.4Comp\-R compositions \(32\)

- •EventEnum→Count\\textsc\{EventEnum\}\\to\\textsc\{Count\}\.*“How many spikes, dips, or sudden changes are in metricX?”*
- •SegEnum→Count\\textsc\{SegEnum\}\\to\\textsc\{Count\}\.*“How many distinct trend segments does metricX have?”*
- •SegEnum→Locate\\textsc\{SegEnum\}\\to\\textsc\{Locate\}\(by index\)→\\toduration\.*“How many points are in the segment of metricX containing indexpp?”*
- •SegEnum→Locate→\\textsc\{SegEnum\}\\to\\textsc\{Locate\}\\totype\.*“What is happening in metricX at indexpp?”*
- •SegEnum,Mean×2→Locate×2→Compare\\textsc\{SegEnum\},\\textsc\{Mean\}\{\\times\}2\\to\\textsc\{Locate\}\{\\times\}2\\to\\textsc\{Compare\}\.*“Is the mean of the segment at indexppgreater than atqq?”*
- •SegEnum→Argmax\\textsc\{SegEnum\}\\to\\textsc\{Argmax\}\(duration\)\.*“What is the duration of the longest trend segment in metricX?”*
- •SegEnum→Filter/Count\\textsc\{SegEnum\}\\to\\textsc\{Filter\}/\\textsc\{Count\}per type→Argmax\\to\\textsc\{Argmax\}\.*“What is the dominant trend type by segment count in metricX?”*
- •EventEnum→Argmax→\\textsc\{EventEnum\}\\to\\textsc\{Argmax\}\\totype\.*“Find the local event of metricX with the largest amplitude; report its type\.”*
- •EventEnum→Locate\\textsc\{EventEnum\}\\to\\textsc\{Locate\}\(nearest\)→\\totype\.*“What is the nearest event type to positionppin metricX?”*
- •ExtPos,EventEnum→Locate\\textsc\{ExtPos\},\\textsc\{EventEnum\}\\to\\textsc\{Locate\}\(window\)→Threshold\(\>0\)\\to\\textsc\{Threshold\}\(\{\>\}0\)\.*“Does a local event of metricX occur near its global max or min?”*
- •ExtPos×2→Locate→Compare\\textsc\{ExtPos\}\{\\times\}2\\to\\textsc\{Locate\}\\to\\textsc\{Compare\}\.*“Are the global max and min of metricX in the same half?”*
- •ExtPos→Locate\\textsc\{ExtPos\}\\to\\textsc\{Locate\}\(half\)\.*“Does the global max of metricX occur before the midpoint?”*
- •ExtVal×2→Arith​\(−\)\\textsc\{ExtVal\}\{\\times\}2\\to\\textsc\{Arith\}\(\{\-\}\)\.*“What is the spread of metricX \(max minus min\)?”*
- •ExtVal×2,Std→Arith​\(−,÷\)\\textsc\{ExtVal\}\{\\times\}2,\\textsc\{Std\}\\to\\textsc\{Arith\}\(\{\-\},\{\\div\}\)\.*“What is the normalized range of metricX?”*
- •EventEnum,ExtVal×2→Argmax→Arith→Threshold\\textsc\{EventEnum\},\\textsc\{ExtVal\}\{\\times\}2\\to\\textsc\{Argmax\}\\to\\textsc\{Arith\}\\to\\textsc\{Threshold\}\.*“Does the peak event amplitude of metricX exceed half the value range?”*
- •Mean×2→Arith\(\|−\|\)\\textsc\{Mean\}\{\\times\}2\\to\\textsc\{Arith\}\(\|\{\-\}\|\)\.*“Compute\|mean⁡\(first half\)−mean⁡\(second half\)\|\|\\mathrm\{mean\}\(\\text\{first half\}\)\{\-\}\\mathrm\{mean\}\(\\text\{second half\}\)\|\.”*
- •Mean×2\\textsc\{Mean\}\{\\times\}2\(thirds\)→Arith\(\|−\|\)→Threshold\\to\\textsc\{Arith\}\(\|\{\-\}\|\)\\to\\textsc\{Threshold\}\.*“Is there a mean shift greater thanτ\\taubetween the first and last thirds of metricX?”*
- •Mean×2\\textsc\{Mean\}\{\\times\}2\(Q1,Q4Q\_\{1\},Q\_\{4\}\)→Arith\(\|−\|\)→Threshold\(<τ\)\\to\\textsc\{Arith\}\(\|\{\-\}\|\)\\to\\textsc\{Threshold\}\(\{<\}\\tau\)\.*“Is\|mean⁡\(Q1\)−mean⁡\(Q4\)\|<τ\|\\mathrm\{mean\}\(Q\_\{1\}\)\{\-\}\\mathrm\{mean\}\(Q\_\{4\}\)\|<\\taufor metricX?”*
- •Mean,Mean\\textsc\{Mean\},\\textsc\{Mean\}over chunks→Filter\\to\\textsc\{Filter\}\(withinτ\\tau\)→Compare\\to\\textsc\{Compare\}to\|L\|\|L\|\.*“Are all 16\-point chunk means of metricX withinτ\\tauof the global mean?”*
- •Percentile\(50\),Mean→Arith\(\|−\|\)→Threshold\\textsc\{Percentile\}\(50\),\\textsc\{Mean\}\\to\\textsc\{Arith\}\(\|\{\-\}\|\)\\to\\textsc\{Threshold\}\.*“Is metricX’s median withinτ\\tauof its mean?”*
- •Mean×2→Compare\\textsc\{Mean\}\{\\times\}2\\to\\textsc\{Compare\}\.*“Is the mean of metricX on\[a1,b1\]\[a\_\{1\},b\_\{1\}\]greater than on\[a2,b2\]\[a\_\{2\},b\_\{2\}\]?”*
- •Period→Count\\textsc\{Period\}\\to\\textsc\{Count\}\.*“Count the approximate number of complete cycles in metricX\.”*
- •Period\.*“Estimate the period of metricX in time steps\.”*
- •Period→Threshold\\textsc\{Period\}\\to\\textsc\{Threshold\}\.*“Does metricX contain a periodic component?”*
- •TrendClassify×N→Filter/Count\\textsc\{TrendClassify\}\{\\times\}N\\to\\textsc\{Filter\}/\\textsc\{Count\}per type→Argmax\\to\\textsc\{Argmax\}\.*“Which trend pattern is most common across the metrics?”*
- •TrendClassify×N→\\textsc\{TrendClassify\}\{\\times\}N\\todistinct count\.*“Into how many groups do the metrics cluster by trend?”*
- •TrendClassify×N→Filter/Count\\textsc\{TrendClassify\}\{\\times\}N\\to\\textsc\{Filter\}/\\textsc\{Count\}per type→Argmax\\to\\textsc\{Argmax\}\.*“What is the dominant trend cluster?”*
- •EventEnum×2→Locate\\textsc\{EventEnum\}\{\\times\}2\\to\\textsc\{Locate\}\(withinww\)→Threshold\(\>0\)\\to\\textsc\{Threshold\}\(\{\>\}0\)\.*“Do metricA and metricB have temporally close events?”*
- •Period×2→Compare\\textsc\{Period\}\{\\times\}2\\to\\textsc\{Compare\}\.*“Does metricA oscillate faster than metricB?”*
- •Mean×N,Std×N→Argmax×2→Compare\\textsc\{Mean\}\{\\times\}N,\\textsc\{Std\}\{\\times\}N\\to\\textsc\{Argmax\}\{\\times\}2\\to\\textsc\{Compare\}\(equal\)\.*“Is the metric with the highest mean also the one with the highest std?”*
- •TrendClassify×N,Mean/Std×N→Filter→Argmax\\textsc\{TrendClassify\}\{\\times\}N,\\textsc\{Mean\}/\\textsc\{Std\}\{\\times\}N\\to\\textsc\{Filter\}\\to\\textsc\{Argmax\}\.*“Among metrics with an increase trend, which has the largest range?”*
- •Mean×2×N→Compare\\textsc\{Mean\}\{\\times\}2\{\\times\}N\\to\\textsc\{Compare\}per metric→Filter\+Count\\to\\textsc\{Filter\}\+\\textsc\{Count\}\.*“How many metrics show an upward shift in mean between halves?”*

### D\.5OOD compositions \(34\)

- •ExtPos×2→Compare\\textsc\{ExtPos\}\{\\times\}2\\to\\textsc\{Compare\}\.*“Is the index of the global max before the index of the global min?”*
- •Mean×4,ExtPos→Argmax→Locate→Compare\\textsc\{Mean\}\{\\times\}4,\\textsc\{ExtPos\}\\to\\textsc\{Argmax\}\\to\\textsc\{Locate\}\\to\\textsc\{Compare\}\.*“Does the global max fall in the quarter with the highest mean?”*
- •Mean×4→Rank\\textsc\{Mean\}\{\\times\}4\\to\\textsc\{Rank\}\.*“Do the quarter means of metricX strictly increase \(or decrease\)?”*
- •Meanover chunks→Argmax\\to\\textsc\{Argmax\}\.*“Find the 16\-point chunk with the largest mean and report its index\.”*
- •Meanover chunks,Mean→Filter→Count→Arith\(÷\|L\|\)\\textsc\{Mean\}\\to\\textsc\{Filter\}\\to\\textsc\{Count\}\\to\\textsc\{Arith\}\(\{\\div\}\\,\|L\|\)\.*“What fraction of 16\-point chunks have a mean above the global mean?”*
- •Std,ExtVal×2→Arith→Threshold\\textsc\{Std\},\\textsc\{ExtVal\}\{\\times\}2\\to\\textsc\{Arith\}\\to\\textsc\{Threshold\}\.*“Is the standard deviation greater than13\\tfrac\{1\}\{3\}of the range?”*
- •Mean×4→Arith\(\|−\|\)×2→Threshold×2→∧\\textsc\{Mean\}\{\\times\}4\\to\\textsc\{Arith\}\(\|\{\-\}\|\)\{\\times\}2\\to\\textsc\{Threshold\}\{\\times\}2\\to\\wedge\.*“Does metricX exhibit symmetric recovery \(Q1≈Q4Q\_\{1\}\{\\approx\}Q\_\{4\}andQ2≈Q3Q\_\{2\}\{\\approx\}Q\_\{3\}\)?”*
- •Period,Mean\\textsc\{Period\},\\textsc\{Mean\}per cycle→TrendClassify\\to\\textsc\{TrendClassify\}on cycle\-mean list\.*“Do the cycle\-level means show an increasing or decreasing trend?”*
- •EventEnum,SegEnum,Std→Argmax→Locate→Threshold\\textsc\{EventEnum\},\\textsc\{SegEnum\},\\textsc\{Std\}\\to\\textsc\{Argmax\}\\to\\textsc\{Locate\}\\to\\textsc\{Threshold\}\.*“Does the largest event amplitude exceed the std of its containing segment?”*
- •EventEnum,Std→Argmax→Arith\(×k\)→Threshold\\textsc\{EventEnum\},\\textsc\{Std\}\\to\\textsc\{Argmax\}\\to\\textsc\{Arith\}\(\{\\times\}k\)\\to\\textsc\{Threshold\}\.*“Does the largest event amplitude exceedk​σk\\sigma?”*
- •EventEnum,ExtVal×2→Argmax→Arith→Threshold\\textsc\{EventEnum\},\\textsc\{ExtVal\}\{\\times\}2\\to\\textsc\{Argmax\}\\to\\textsc\{Arith\}\\to\\textsc\{Threshold\}\.*“Does the largest event amplitude exceed half the value range?”*
- •EventEnum,SegEnum→Filter→Count/Sum→Arith​\(÷\)→Argmax/Argmin\\textsc\{EventEnum\},\\textsc\{SegEnum\}\\to\\textsc\{Filter\}\\to\\textsc\{Count\}/\\textsc\{Sum\}\\to\\textsc\{Arith\}\(\{\\div\}\)\\to\\textsc\{Argmax\}/\\textsc\{Argmin\}\.*“Which trend type has the lowest density of local events?”*
- •EventEnum,SegEnum→Filter→Count,Sum→Arith​\(÷\)\\textsc\{EventEnum\},\\textsc\{SegEnum\}\\to\\textsc\{Filter\}\\to\\textsc\{Count\},\\textsc\{Sum\}\\to\\textsc\{Arith\}\(\{\\div\}\)\.*“What is the event density in increase segments?”*
- •SegEnum,EventEnum→Argmax→Filter→Argmax\\textsc\{SegEnum\},\\textsc\{EventEnum\}\\to\\textsc\{Argmax\}\\to\\textsc\{Filter\}\\to\\textsc\{Argmax\}\.*“What is the largest event amplitude in the longest trend segment?”*
- •SegEnum,ExtPos→Argmax→Locate\\textsc\{SegEnum\},\\textsc\{ExtPos\}\\to\\textsc\{Argmax\}\\to\\textsc\{Locate\}\.*“Does the global max fall inside the longest trend segment?”*
- •SegEnum→Sum\\textsc\{SegEnum\}\\to\\textsc\{Sum\}\(weighted\)→Arith\(÷total\)\\to\\textsc\{Arith\}\(\{\\div\}\\,\\text\{total\}\)\.*“Compute the duration\-weighted mean across trend segments\.”*
- •SegEnum→Argmax→Filter\\textsc\{SegEnum\}\\to\\textsc\{Argmax\}\\to\\textsc\{Filter\}\(same type\)→Sum→Arith​\(÷\)\\to\\textsc\{Sum\}\\to\\textsc\{Arith\}\(\{\\div\}\)\.*“What fraction of metricX is covered by the trend type of the longest segment?”*
- •SegEnum→Filter→Mean\\textsc\{SegEnum\}\\to\\textsc\{Filter\}\\to\\textsc\{Mean\}on union\.*“Compute the mean of metricX restricted to increase segments\.”*
- •SegEnum→Filter→Sum→Arith\(÷count\)\\textsc\{SegEnum\}\\to\\textsc\{Filter\}\\to\\textsc\{Sum\}\\to\\textsc\{Arith\}\(\{\\div\}\\,\\text\{count\}\)\.*“What is the average of segment means for all increase segments?”*
- •SegEnum,Mean→Filter→Threshold→Count\\textsc\{SegEnum\},\\textsc\{Mean\}\\to\\textsc\{Filter\}\\to\\textsc\{Threshold\}\\to\\textsc\{Count\}\.*“Count increase segments whose mean exceeds the global mean\.”*
- •SegEnum→Locate\\textsc\{SegEnum\}\\to\\textsc\{Locate\}\(first/last\)→Compare\\to\\textsc\{Compare\}\.*“Is the mean of the first segment greater than the last segment?”*
- •SegEnum,Mean→Filter→Compare​\(∀\)\\textsc\{SegEnum\},\\textsc\{Mean\}\\to\\textsc\{Filter\}\\to\\textsc\{Compare\}\\ \(\\forall\)\.*“Do all increase segments have above\-average means?”*
- •SegEnum→Argmax\\textsc\{SegEnum\}\\to\\textsc\{Argmax\}\(level shift\)→Compare\\to\\textsc\{Compare\}on types\.*“Does the dominant trend reverse after the largest change point?”*
- •SegEnum→\\textsc\{SegEnum\}\\topalindrome via pairwiseCompare\.*“Is the trend pattern of metricX palindromic?”*
- •TrendClassify×N→\\textsc\{TrendClassify\}\{\\times\}N\\topairwiseCompare→Count\\textsc\{Compare\}\\to\\textsc\{Count\}\.*“How many pairs of metrics share the same overall trend direction?”*
- •TrendClassify×N\\textsc\{TrendClassify\}\{\\times\}Nover halves→Count→Compare\\to\\textsc\{Count\}\\to\\textsc\{Compare\}\.*“Do the metrics become more aligned in trend in the second half than the first?”*
- •ExtPos×N→\\textsc\{ExtPos\}\{\\times\}N\\topairwiseLocatewithin window\.*“Do metricA and metricB have their maxima at similar positions?”*
- •ExtVal×2×N→Compare\\textsc\{ExtVal\}\{\\times\}2\{\\times\}N\\to\\textsc\{Compare\}on interval ends\.*“Is there any overlap between the value ranges of two metrics?”*
- •Mean×2×N→Compare\\textsc\{Mean\}\{\\times\}2\{\\times\}N\\to\\textsc\{Compare\}per metric→Count\\to\\textsc\{Count\}\.*“How many metrics show an upward shift in mean between halves?”*
- •TrendClassify×N→Filter/Count∃\\textsc\{TrendClassify\}\{\\times\}N\\to\\textsc\{Filter\}/\\textsc\{Count\}\\ \\exists\.*“Is any metric in its own unique trend cluster?”*
- •TrendClassify×3→Compare×2→∧\\textsc\{TrendClassify\}\{\\times\}3\\to\\textsc\{Compare\}\{\\times\}2\\to\\wedge\.*“If A’s trend matches B’s and B’s matches C’s, does A’s match C’s?”*
- •TrendClassify×N→\\textsc\{TrendClassify\}\{\\times\}N\\topairwise opposite check→Count\\to\\textsc\{Count\}\.*“Count the anti\-correlated pairs among the metrics\.”*
- •Mean×N,TrendClassify→Filter\\textsc\{Mean\}\{\\times\}N,\\textsc\{TrendClassify\}\\to\\textsc\{Filter\}\(upper half\)→Filter/Count\\to\\textsc\{Filter\}/\\textsc\{Count\}per type→Argmax\\to\\textsc\{Argmax\}\.*“Among metrics in the upper\-half mean group, identify the dominant trend type\.”*
- •EventEnum×2→Locate\\textsc\{EventEnum\}\{\\times\}2\\to\\textsc\{Locate\}\(precedence withinww\)\.*“Does an event in metricA precede an event in metricB withinwwtimesteps?”*

## Appendix ECompositional Performance Breakdown

[Tables11](https://arxiv.org/html/2609.13457#A5.T11),[12](https://arxiv.org/html/2609.13457#A5.T12)and[13](https://arxiv.org/html/2609.13457#A5.T13)give the per\-composition breakdown behind[Figure2](https://arxiv.org/html/2609.13457#S5.F2), for the Comp\-D, Comp\-R and OOD splits respectively\. For each composition we report the score ofTimeThink\(SFT\) andTimeThink\(RL\) on its constituent atoms \(atomic gainΔa\\Delta\_\{a\}\) and on the composition itself \(composition gainΔc\\Delta\_\{c\}\)\.

Table 11:Compositional reasoning in Comp\-D QAs\. Composition gainsΔc\\Delta\_\{c\}are small on average because SFT CoT supervision already teaches the decomposition\.Table 12:Compositional reasoning in Comp\-R QAs\. LargeΔc\\Delta\_\{c\}values reflect compositional skills RL acquires without any CoT supervision, since the composition itself was never demonstrated during SFT\.Table 13:Compositional reasoning in OOD composite QAs\. Compositions are held out at every training phase;Δc\\Delta\_\{c\}measures how much of the procedure RL learns transfers to unseen composition shapes\.