---
abstract: |
Recent time series modeling faces a sharp divide between numerical generation and semantic understanding, with research showing that generation models often rely on superficial pattern matching, while understanding-oriented models struggle with high-fidelity numerical output. Although unified multimodal models (UMMs) have bridged this gap in vision, their potential for time series remains untapped. We propose , the first vision-centric framework that unifies time series understanding and generation through two key innovations: (1) Fidelity-preserving bidirectional mapping between time series and images (Bi-TSI), which advances Time Series-to-Image (TS2I) and Image-to-Time Series (I2TS) conversions to ensure near-lossless transformations. (2) Understanding-guided generation. We introduce , a novel dataset consists of six understanding tasks rooted in time series analytics that are coupled with two generation tasks. With a calibrated Chain-of-Thought (CoT), is the first to leverage time series understanding as an explicit control signal for high-fidelity generation. Experiments confirm that this unified approach significantly improves semantic understanding and numerical precision, establishing a new frontier for multimodal time series modeling.
bibliography:
- reference.bib
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Introduction
============
Time series are pervasive in modern systems and everyday life, underpinning decision-making across healthcare, transportation, industrial monitoring, and finance [@ShapeX; @TrafficR1; @ITFormer; @BeyondForecasting]. With the advances of time series modeling at scale, recent progress has largely followed two parallel threads: (1) *Generation models*. Led by time series foundation models (TSFMs), this thread prioritizes high-fidelity numerical sequence generation, excelling in tasks such as forecasting [@TimeMoE] and data imputation [@moment] (Figure [1](#fig:intro){reference-type="ref" reference="fig:intro"}b). (2) *Understanding Models*. Influenced by the rise of large language models (LLMs), this thread focuses on temporal reasoning [@TimeOmni-1] by providing explicit, human-readable interpretations of complex dynamics [@ChatTS] (Figure [1](#fig:intro){reference-type="ref" reference="fig:intro"}a). However, a significant divide remains: Generation models often lack explicit structural understanding despite offering representation analysis on signal components [@TimeMixer++], while understanding-oriented models frequently struggle with high-fidelity numerical generation as text-native tokenizers can disrupt numerical continuity (e.g., "123" → "1", "2", "3"). Bridging this gap with a unified model capable of both understanding and generation represents an urgent need for time series processing (Figure [1](#fig:intro){reference-type="ref" reference="fig:intro"}c).
{#fig:intro width="1\\linewidth"}
Likewise, the vision domain has undergone a similar trajectory, with models specialized for visual generation [@GLIDE; @VQ-VAE-2] and those focusing on visual understanding [@clip; @Qwen2VL]. However, recently, the vision community has witnessed advancements in unified multimodal models (UMMs) that excel in both image understanding and generation. A key emerging insight is that robust understanding serves as a foundation for superior generation, since structured semantic guidance improves controllability and fidelity [@UMMs-survey]. Meanwhile, an emerging line of work suggests a similarity between time series and vision modality, as pixel-level variations in natural images can be viewed as sequential signals and exhibit intrinsic commonalities with time series [@VisionTS]. By reframing time series as a visual inpainting problem, visual generative models [@MAE] can achieve impressive time series forecasting [@VisionTS++] and imputation [@FM2I; @Hinge-FM2I] performance even in a training-free manner. Despite their effectiveness, these vision-based approaches largely rely on superficial texture imitation rather than genuine temporal understanding. They lack a mechanism to interpret the underlying signal dynamics from a time series perspective, which includes identifying trend shifts or seasonal dependencies within the visual space. Motivated by these observations, we ask a natural question: *Is it possible to represent time series in the vision modality and thereby internalize time series understanding and generation as native capabilities of UMMs, so that time series performance improves naturally as UMMs continue to advance?*
However, achieving this integration is non-trivial as two fundamental challenges remain: **(1) Fidelity-preserving bidirectional mappings between time series and images are still lacking.** Although VisionTS-style [@VisionTS; @VisionTS++] converters offer a practical interface for vision models, we find that the front-end conversion can already discard numerical information, so the model may not observe the complete series content. Once information is lost at input stage, it cannot be recovered downstream, making high-fidelity generation fundamentally unattainable. **(2) Understanding-guided generation remains underexplored for time series.** While UMMs possess strong semantic capabilities, they are not yet grounded in time series properties such as inherent periodicity and structural changepoints. As a result, they cannot leverage semantics to guide time series generation, preventing the system from achieving the precise and controllable results commonly observed in other multimodal tasks.
To address these challenges, we build around two core design objectives: (1) Fidelity-preserving bidirectional mappings between time series and images and (2) understanding-guided generation (as our primary goal is precise generation, where understanding serves as the necessary control signal, not vice versa). We advance existing converters [@VisionTS] into a fidelity-oriented **Bi**directional **T**ime **S**eries $\Leftrightarrow$ **I**mage mappings (**Bi-TSI**) that avoid information loss at the input stage. Concretely, we introduce robust fidelity normalization (RFN) to stabilize dynamic-range projection and preserve peak geometry under realistic signals, alongside encoding capacity control to prevent implicit downsampling when rendering time series onto a fixed time series image (TS-image) canvas. Building on Bi-TSI, we construct a new dataset by specifying forecasting and imputation as generation tasks and deriving six understanding tasks from the same generation instances, organized into layout-level and signal-level analysis. These tasks encourage UMMs to interpret TS-images from a temporal perspective rather than relying on superficial textures. Finally, we present , the first vision-centric framework that internalizes time series understanding and generation as native capabilities of UMMs. To enable understanding-guided generation, we form a generation Chain-of-Thought (CoT) by organizing the understanding QAs of each generation instance into a calibrated reasoning chain, making temporal understanding an explicit control signal for precise and controllable time series generation. Our contributions lie in three aspects:
**1. New Models.** We present , the first vision-centric framework that unifies time series understanding and generation. integrates: (1) Fidelity-preserving bidirectional Time Series $\Leftrightarrow$ Image mappings to prevent implicit information loss. (2) Generation CoT that organizes instance-level understanding into a calibrated reasoning chain and serves as an explicit control signal for numerical generation tasks like forecasting and imputation.
**2. New Datasets and Testbed.** We introduce , a benchmark comprising two generation tasks and six understanding tasks. The understanding tasks are tailored to the TS-image representation produced by , and are organized into **layout-level** and **signal-level** analyses to encourage temporal interpretation rather than superficial texture.
**3. Comprehensive Evaluation.** Results demonstrate that the understanding tasks effectively teach the base model to interpret TS-images: boosts the base model from near-zero accuracy to near-perfect scores on four understanding tasks (approaching 1.0). On generation, achieves top-tier results on forecasting and reaches state-of-the-art performance on imputation. Moreover, the proposed generation CoT consistently improves generation quality, yielding an average 8.2% gain.
{width="1\\linewidth"}
Related Work
============
**Time Series Generation Models.** In this context, time series generation specifically refers to forecasting and imputation tasks rather than synthetic data generation. Existing models are primarily categorized into two paradigms. **(1) Time series-based models.** Early efforts focused on developing domain-specific architectures which often lacked cross-dataset generalization [@MTGNN; @GraphSTAGE; @TimeMixer++]. With the increasing availability of large-scale datasets, training TSFMs from scratch has become the mainstream approach to achieve superior zero-shot generalization [@moirai; @Chronos; @TimeMoE]. **(2) Image-based models.** Early researchers explored convolutional [@TS2I_1] and patch-based [@FM2I; @Hinge-FM2I] methods to reconstruct time series as images, revealing shared properties between the two modalities. Following the success of general visual generative models, the TS2I paradigm has resurged through models like VisionTS [@VisionTS; @VisionTS++], which demonstrate impressive zero-shot capabilities. However, their reliance on pixel-level pattern matching lacks genuine temporal understanding.
**Time Series Understanding Models.** Time-LLM [@Time-LLM] leverages the generalization capabilities of LLMs for time series, yet its understanding of temporal patterns remains largely implicit. To achieve explicit understanding, existing research has branched into two primary directions. The first involves **time series language models (TSLMs)**, which utilize synthetic datasets to align temporal signals with textual descriptions to ground temporal semantics [@ChatTS; @TimeMQA; @ITFormer; @OpenTSLM]. The second encompasses **time series reasoning models (TSRMs)**, which leverage the R1-paradigm [@DeepSeek-R1] to enhance temporal reasoning [@TimeOmni-1; @STReasoner]. Despite these advancements, both categories are constrained by the text-centric nature of LLMs. Standard vocabularies typically fragment multi-digit numbers into discrete tokens, thereby disrupting numerical continuity and undermining the precision required for high-fidelity generation.
**Unified Multimodal Models.** UMMs have recently emerged in the vision community to integrate understanding and generation within a single framework. These models generally follow either a unified auto-regressive architecture [@Chameleon; @MetaMorph; @Janus; @BLIP3-o; @Emu3.5] or a hybrid paradigm combining auto-regression with diffusion [@JanusFlow; @Bagel; @Qwen-Image]. Currently, the hybrid approach often yields superior results because image understanding prioritizes high-level semantics while generation requires fine-grained pixel details [@UMMs-survey; @Bagel]. Since the time series community lacks universal pre-trained encoders equivalent to ViT [@NaViT] or VAE [@VAE] in vision, recent studies [@TsLLM; @SciTS] attempting unified modeling with auto-regressive LLMs typically rely on shallow MLP layers. However, the effectiveness of such simple layers in projecting time series into the latent space remains unverified. This gap motivates combining TS2I methods with UMMs: by utilizing images as a modality-specific enhancement, we leverage UMMs to achieve a unified framework for temporal understanding and generation.
{width="1\\linewidth"}
Methodology
===========
In this section, we first establish a unified problem formulation for both tasks. We then present , the first vision-centric framework that unifies time series understanding and generation. Finally, we introduce and its construction pipeline, which formalizes both generation and understanding tasks and bridges them by deriving generation CoT directly from understanding QAs.
**Problem Definition.** We formulate unified time series understanding and generation as a conditional *think-then-output* process within UMMs. Unlike in TSRMs [@TimeOmni-1], where CoT mainly serves as a textual explanation, here we treat CoT as a control signal that conditions generation. Given (1) the observed time series input $\mathbf{X}\in\mathbb{R}^{T\times N}$, and (2) an auxiliary context $C$ (e.g., task instructions), the model first generates a CoT $R = (r_1, \dots, r_K)$, and then produces the task target $o$ using $R$ as additional context. Formally, $$p_\theta(R, o \mid \mathbf{X}, C) = p_\theta(R \mid \mathbf{X}, C)
p_\theta(o \mid R, \mathbf{X}, C).$$ To standardize the inference process, we explicitly instruct the model to enclose the CoT $R$ within `` tags across all tasks.
In this paper, we transform time series into the TS-image $I=\mathcal{V}(\mathbf{X})$. For understanding tasks on the TS-image $I$, the output produces a textual answer. For generation tasks (e.g., forecasting or imputation), we formulate the problem as editing the input TS-image: given a source image $I_{\mathrm{src}}$ and a generation instruction $C_{\mathrm{gen}}$, the model outputs an edited image $I_{\mathrm{tgt}}$, which is then decoded back into numerical values.
#### Overall Framework.
As illustrated in Figure [\[fig:1\]](#fig:1){reference-type="ref" reference="fig:1"}, we design to handle both time series understanding and generation tasks. We use Bagel [@Bagel] as the backbone UMM. While our framework is backbone-agnostic, we choose Bagel as it is a widely recognized and lightweight base model that has superior performance among other options. To adapt UMMs to temporal data, we introduce a fidelity-preserving **Bi**directional **T**ime **S**eries $\Leftrightarrow$ **I**mage mappings (**Bi-TSI**), consisting of a TS2I converter and an I2TS converter (Section [3.1](#sec:Bi-TSI){reference-type="ref" reference="sec:Bi-TSI"}). Specifically, the TS2I converter transforms raw time series into a high-fidelity visual representation (TS-image $I$), which is then fed into the backbone model. Within the backbone, the data flow differs by task (the data construction pipeline is described in Section [3.2](#sec:tasks){reference-type="ref" reference="sec:tasks"}): (1) **Understanding tasks**: Given an understanding instruction $C_{\mathrm{und}}$ and the TS-image $I$, the *Understanding Model* first generates an understanding CoT $R$, followed by the final understanding answer $o$. (2) **Generation tasks**: The process follows a "understand-then-generate" paradigm. The model first inputs a generation instruction alongside the TS-image $I_{\mathrm{src}}$ into the *Understanding Model* to derive an generation-oriented CoT $R_{\mathrm{gen}}$. This CoT then serves as a conditional guide, and the TS-image $I_{\mathrm{src}}$ is fed again into the *Generation Module*, which synthesizes the target TS-image $I_{\mathrm{tgt}}$. The output TS-image is converted back to numerical time series $o$ via the I2TS converter.
#### Training Objectives.
We jointly train the *Understanding Model* and the *Generation Module*. For generation tasks, the generation CoT is produced by the understanding model and is therefore supervised by the understanding loss.
**Understanding Loss (Text).** Given a TS-image $I$ and an instruction $C$, we optimize next-token prediction over a text sequence $y$ (understanding: $y=[R;o]$; generation: $y=R_{\mathrm{gen}}$): $$\mathcal{L}_{\mathrm{und}}
= - \sum_{i=1}^{|y|} \log P_{\theta}\!\left(y_i \mid y_{ ` tags, i.e. `` reasoning process here `` answer here
You should first think about the planning process in the mind and then generate the image.\
The planning process is enclosed within ` ` tags, i.e. `` planning process here `` image here
Details of the TS2I and I2TS Process {#app:ts2i_i2ts}
====================================
In this section, we provide a detailed description of the bidirectional mappings between time series and images utilized throughout . Our goal is a fidelity-preserving Time Series $\Leftrightarrow$ Image transformation that is as close to lossless as possible. This requirement is crucial because the TS-image is fed into the UMMs backbone as the model input. If the TS2I conversion discards numerical information, the backbone cannot recover it, and the entire vision-centric pipeline would fail to produce high-fidelity time series outputs. Likewise, the image generated by the backbone must be decoded back to a numerical sequence without losing the information contained in the output image. Therefore, we design TS2I and I2TS as a deterministic round-trip mapping and treat it as near-lossless in practice, with residual errors primarily arising from spatial interpolation and finite numerical precision.
Time Series to Image (TS2I) Converter {#app:ts2i}
-------------------------------------
#### Periodicity-based segmentation.
Given a multivariate time series $\mathbf{X}\in\mathbb{R}^{T\times N}$ with periodicity $f\in\mathbb{Z}^+$, we adopt a periodicity-consistent setting in our experiments, where both the context length and the prediction horizon are integer multiples of $f$. If the available length is not an exact multiple of $f$, we truncate it to the nearest valid length. Consequently, $T$ is divisible by $f$ and the series can be decomposed into $C=T/f$ periodic blocks without padding. Prior to periodic segmentation, $\mathbf{X}$ is normalized using robust fidelity normalization (RFN) in Section [3.1.0.2](#RFN){reference-type="ref" reference="RFN"} to ensure numerically stable and geometry-consistent rendering.
#### Rearrangement into a periodic grid.
For each variable $n$, let $\tilde{\mathbf{x}}^{(n)}\in\mathbb{R}^{T}$ denote the normalized sequence after applying RFN, where $\tilde{(\cdot)}$ indicates values in the normalized space used for image rendering. We fold the normalized sequence $\tilde{\mathbf{x}}^{(n)}$ into a $f\times C$ matrix $\mathbf{S}^{(n)}\in\mathbb{R}^{f\times C}$, where $C=T/f$: $$\mathbf{S}^{(n)}_{i,j}=\tilde{\mathbf{x}}^{(n)}_{jf+i},\qquad i=0,\ldots,f-1,\; j=0,\ldots,C-1.$$ Here, the row index $i$ corresponds to the intra-period position, while the column index $j$ indexes successive periods. This construction maps intra-period structure to vertical locality and inter-period evolution to horizontal progression.
#### Rendering.
Given $\mathbf{S}^{(n)}\in\mathbb{R}^{f\times C}$, the rendering step upsamples the periodic grid into the image coordinate space. Specifically, we allocate each variable a vertical band of height $h=\lfloor H/N \rfloor$ and resize $\mathbf{S}^{(n)}$ to $h\times W_{\mathrm{in}}$, where $W_{\mathrm{in}}$ denotes the width of the unmasked region and the remaining width $W_{\mathrm{out}}=W-W_{\mathrm{in}}$ is masked. For forecasting, the mask occupies the right side so the model completes future periods from left to right; for imputation, masked regions can be placed at arbitrary locations within the TS-image.
#### Supporting multivariate inputs via band stacking and color assignment.
For the multivariate time series input $\mathbf{X}$, TS2I renders each variable into one band and stacks the $N$ bands along the vertical axis to construct the complete TS-image, whose overall resolution is $H\times W$ with the visible context occupying the left width $W_{\mathrm{in}}$. To distinguish different variables within a single image, we follow the setting of VisionTS++ [@VisionTS++] and assign each band a RGB color, while enforcing that adjacent bands do not share the same color. This simple color assignment preserves the band geometry and helps the backbone model separate variable-specific patterns in the visual space.
Image to Time Series (I2TS) Converter {#app:i2ts}
-------------------------------------
#### Recovering the completed region and inverse rearrangement.
Given the output TS-image $\hat{{I}}\in\mathbb{R}^{H\times W}$, I2TS decodes numerical values from the completed region. We first recover each variable band according to its vertical location using the same band height $h=\lfloor H/N \rfloor$ as in TS2I. For variable $n$, we crop its band from $\hat{I}$ and resize the decoded region back to the periodic grid resolution $f\times C$, yielding $\hat{\mathbf{S}}^{(n)}\in\mathbb{R}^{f\times C}$. Finally, we invert the TS2I folding step to obtain the normalized sequence $\hat{\mathbf{x}}^{(n)}\in\mathbb{R}^{T}$: $$\hat{\mathbf{x}}^{(n)}_{j f + i} = \hat{\mathbf{S}}^{(n)}_{i,j},\qquad i=0,\ldots,f-1,\; j=0,\ldots,C-1.$$ Concatenating all variables gives the normalized multivariate sequence $\hat{\mathbf{U}}\in\mathbb{R}^{T\times N}$ for the decoded region.
#### Inverse normalization and value restoration.
I2TS applies the exact inverse of the RFN mapping defined in Equation [\[eq:RFN\_tanh\]](#eq:RFN_tanh){reference-type="ref" reference="eq:RFN_tanh"}. Let $\hat{\mathbf{U}}$ denote the decoded values in the normalized space. We first apply inverse hyperbolic tangent: $$\hat{\mathbf{Z}} = \kappa\,\mathrm{arctanh}\!\left(\hat{\mathbf{U}}\right),$$ where values in $\hat{\mathbf{U}}$ are implicitly clamped within the valid domain $(-1, 1)$ for numerical stability. Finally, we restore the original numerical scale using the per-variable statistics $(\boldsymbol{\mu}, \boldsymbol{\sigma})$ recorded during the encoding stage: $$\hat{\mathbf{X}} = \hat{\mathbf{Z}} \odot \boldsymbol{\sigma} + \boldsymbol{\mu}.$$
In summary, TS2I and I2TS form a deterministic round-trip mapping that is near-lossless in practice. Any residual reconstruction error mainly comes from spatial interpolation introduced in rendering and resizing, rather than from stochasticity in the transformation itself.
Comparison of Different Normalization Strategies {#app:norm_comparison}
================================================
In this section, we provide an intuitive explanation of why existing normalization methods (for example, standard deviation (Std)-based [@VisionTS] and median absolute deviation (MAD)-based normalization [@Chronos2]) fall short and how our robust fidelity normalization (RFN) addresses these issues. We focus on two extreme yet common regimes: signals with extreme outliers and signals with step-like patterns.
Case I: Extreme Outliers {#sub:case_outlier}
------------------------
**Scenario.** Assume a clean informative signal (e.g., a sine wave) contaminated by a single, massive outlier with amplitude $\Delta$. This creates a single abrupt spike in the signal. The standard deviation $\sigma$ is highly sensitive to extreme values. A single massive spike causes $\sigma$ to grow with the outlier size ($\sigma \approx \Delta/\sqrt{T}$). Consequently, for the normal part of the signal $x_t$, the normalized value $\hat{x}_t$ collapses: $$\hat{x}_t \approx \frac{x_t}{\Delta / \sqrt{T}} \xrightarrow{\Delta \to \infty} 0.$$
When applied to TS2I conversion, the informative signal is compressed toward zero. As a result, the outlier is mapped to a single bright pixel in the TS-image, while the underlying temporal patterns collapse into a nearly uniform dark background. The vision backbone consequently focuses almost exclusively on the outlier.
**RFN Solution.** RFN uses the MAD, which ignores the single outlier, keeping the denominator stable. The outlier is smoothly saturated by the bounded $\tanh$ function, preserving the visibility of the main signal.
Case II: Signals with Step-like Patterns {#sub:case_step}
----------------------------------------
**Scenario.** Consider a \`\`step function" or a signal $\mathbf{x}$ that stays constant for a long period. In these flat regions, the value at time $t$ can be expressed as $x_t = c + \eta_t$, where $c$ is a constant and $\eta_t$ represents microscopic noise. For a signal that is constant for more than half of its length, the MAD is mathematically zero. This leads to division by zero, causing the microscopic noise to be amplified to massive magnitudes: $$\hat{x}_t \approx \frac{\eta_t}{0} \to \infty.$$ When applied to TS2I conversion, the normalization artificially amplifies negligible sensor noise into high amplitude pixel level fluctuations. As a result, the TS2I becomes dominated by high contrast artifacts, falsely suggesting violent temporal variability in the input signal.
**RFN Solution.** RFN prevents this collapse by incorporating the standard deviation as a regularizing term. Even if MAD is zero, the standard deviation of a step function remains non-zero, providing a \`\`safety floor\": $$\sigma_{\mathrm{RFN}} = \alpha \cdot \underbrace{\text{MAD}(\mathbf{x})}_{\approx 0} + (1-\alpha)\underbrace{\text{Std}(\mathbf{x})}_{> 0},$$ where $\sigma_{\mathrm{RFN}}$ denotes the robust scaling factor used by RFN. This ensures that the resulting image correctly depicts flat regions with clear transitions.
Table [6](#tab:norm_comparison){reference-type="ref" reference="tab:norm_comparison"} summarizes the behavior of each normalization strategy across representative regimes. RFN is the only method that consistently performs ideal TS2I conversion, remaining effective in both outlier-dominated signals and step-like signals with extended flat regions.
::: {#tab:norm_comparison}
**Regime** **Std-based** **MAD-based** **RFN (Ours)**
----------------- ---------------- --------------------- ----------------
Gaussian signal Ideal Ideal Ideal
Heavy outliers Signal washout Ideal Ideal
Step / flat Ideal Noise amplification Ideal
: Qualitative behavior of different normalization methods under representative challenging regimes. [Ideal]{.underline} indicates faithful visual preservation of the underlying signal structure.
:::
Additional Experimental Results
===============================
The Scoring Criteria for Understanding Tasks {#app: understanding_metrics}
--------------------------------------------
To ensure a rigorous evaluation of the model's ability to interpret TS-images, we design specific scoring metrics for each understanding task. All scores are normalized to the range $[0, 1]$. The detailed criteria are defined as follows:
- **Understanding QA1: Variable Counting.** We utilize exact match (EM). The score is $1$ if the predicted integer representing the number of variables exactly matches the groundtruth, and $0$ otherwise.
- **Understanding QA2: Variable Y-Range.** We evaluate the model's ability to localize variables vertically using the intersection over union (IoU) metric. For each variable, its vertical span is represented as a rectangular region covering the full width of the segment. Let $B_{pred}$ and $B_{gt}$ denote the predicted and groundtruth bounding boxes, respectively. The score is calculated as: $$\text{Score} = \text{IoU}(B_{pred}, B_{gt}) = \frac{\text{Area}(B_{pred} \cap B_{gt})}{\text{Area}(B_{pred} \cup B_{gt})}.$$
- **Understanding QA3: Cycle Bounding Box.** Similarly, we utilize bounding box IoU. The model outputs the specific coordinates $[(x_1, y_1), (x_2, y_2)]$ for a cycle. The score is the IoU between the predicted bounding box $B_{pred}$ and the groundtruth box $B_{gt}$, calculated using the same formula as QA2.
- **Understanding QA4: Mean Comparison.** We utilize EM. The task requires identifying which of two specific cycles has a higher mean value. The score is $1$ if the predicted cycle index exactly matches the groundtruth index (e.g., correctly selecting \`\`Cycle 7\" over \`\`Cycle 9\"), and $0$ otherwise.
- **Understanding QA5: Anomaly Detection.** We utilize weighted accuracy. We parse the output to extract three key count statistics: the total count of anomalous cycles, the count of bright anomalies, and the count of dark anomalies. The final score is the average of the match results for these three components (each contributing $1/3$). For example, if the groundtruth is \`\`2 anomalous cycles (1 bright, 1 dark)" and the model correctly predicts all three counts, the score is $1$; if it correctly predicts the total and bright counts but misses the dark count, the score is $2/3$.
- **Understanding QA6: Trend Analysis.** We utilize a composite score consisting of three equally weighted sub-components ($1/3$ each):
1. **Color Consistency:** We use EM. The score is $1$ if the predicted color channel (e.g., \`\`Blue") exactly matches the groundtruth, and $0$ otherwise.
2. **Localization Accuracy:** We use bounding box IoU between the predicted bounding box and the groundtruth box (between 0 and 1).
3. **Trend Description Quality:** We use BERTScore [@BERTScore] to measure the semantic similarity between the generated textual description and the groundtruth analysis.
The final score is the arithmetic mean of these three sub-scores: $\text{Score} = \frac{1}{3} (\text{EM}_{\text{color}} + \text{IoU}_{\text{bbox}} + \text{BERTScore}_{\text{text}})$.
Results of Understanding Tasks {#app:gemini Performance on Understanding Tasks}
------------------------------
```{=latex}
\renewcommand{\arraystretch}{1}
```
::: {#tab:understanding_result}
---------------------- --------- --------- --------- --------- --------- ---------
(lr)2-4 (lr)5-7 **QA1** **QA2** **QA3** **QA4** **QA5** **QA6**
**Proprietary VLMs**
Gemini2.5-flash 0.540 0.640 0.004 0.535 0 0.342
Gemini2.0-flash 0.230 0.290 0.261 0.279 0 0.220
**Base Model**
Bagel 0 0.502 0.012 0.182 0 0.254
1 1 0.931 1 0.667 0.841
---------------------- --------- --------- --------- --------- --------- ---------
: Performance on Understanding Tasks. The table reports scores for layout-level tasks (QA1--3) and signal-level tasks (QA4--6).
:::
[\[tab:understanding\_result\]]{#tab:understanding_result label="tab:understanding_result"}
Results of Reasoning Tasks {#app:Performance on Reasoning Tasks}
--------------------------
```{=latex}
\renewcommand{\arraystretch}{1}
```
::: {#tab:reasoning_result}
-------------------------- ----------- ----------- ----------------------- -----------
(lr)2-3 (lr)4-4 (lr)5-5 **Task1** **Task2** **Task3$\downarrow$** **Task4**
**LLMs**
Gemini2.5-flash 77.5 25.9 170.78 36.6
Qwen2.5-Instruct-7B 42.8 26.3 24.9
**TSLMs**
Time-MQA-8B [@TimeMQA] 25.1 31.2 \- 11.6
ChatTS [@ChatTS] 39.2 18.6 \- 11.1
ITFormer [@ITFormer] 47.5 14.6 230.04 41.7
Time-R1 [@timer1] 34.0 31.4 160.47 32.2
TimeOmni-1 [@TimeOmni-1]
163.79
-------------------------- ----------- ----------- ----------------------- -----------
: Performance on Reasoning Tasks. The default metric is ACC, except for Task 3 where MAE is used. : the best, : the 2nd best. \`\`--" denotes SR below 10%; not statistically significant.
:::
[\[tab:reasoning\_result\]]{#tab:reasoning_result label="tab:reasoning_result"}
Discussion on Line Plot Representations {#app: discussion of line plot}
---------------------------------------
We exclude line plots due to four practical limitations. (1) Information sparsity. Most pixels correspond to background, while the signal is confined to thin strokes, which limits representational capacity. (2) Variable overlap. In multivariate settings, intersecting curves create ambiguity, making it difficult to uniquely identify and disentangle variables. (3) Misaligned attention. General-purpose vision-language models (VLMs) and UMMs tend to focus on textual labels and legends rather than the fine geometry of thin lines [@CaTSBench]. (4) Decoding complexity. Recovering precise values from rendered curves is an ill-posed inverse problem that is sensitive to stroke width, aliasing, and line overlap, leading to unstable decoding.
Case Study {#app:case_study}
==========
Comprehensive Task Demonstrations of
------------------------------------
In this section, we provide detailed case studies across the six understanding tasks (Tables [\[tab:variable\_counting\_example\]](#tab:variable_counting_example){reference-type="ref" reference="tab:variable_counting_example"} to [\[tab:q6\_trend\_analysis\]](#tab:q6_trend_analysis){reference-type="ref" reference="tab:q6_trend_analysis"}) and two generation tasks (Tables [\[tab:task2\_forecasting\]](#tab:task2_forecasting){reference-type="ref" reference="tab:task2_forecasting"} and [\[tab:task3\_imputation\]](#tab:task3_imputation){reference-type="ref" reference="tab:task3_imputation"}) within the benchmark.
```{=latex}
\newcommand{\usericon}{\raisebox{-0.25ex}{\includegraphics[height=1.3em]{figs/user.png}}}
```
```{=latex}
\newcommand{\modelicon}{\raisebox{-0.25ex}{\includegraphics[height=1.3em]{figs/logo.png}}}
```
```{=latex}
\newcommand{\bagelmodel}{\raisebox{-0.25ex}{\includegraphics[height=1.3em]{figs/bagel.png}}}
```
Comparative Analysis and Failure Cases of the Base Model: Bagel {#app:base_case_bagel}
---------------------------------------------------------------
To further validate the necessity of our time series-specific post-training, we present representative failure cases from our base model, Bagel [@Bagel], on the same generation tasks. Specifically, Table [\[tab:Bagel\_forecasting\]](#tab:Bagel_forecasting){reference-type="ref" reference="tab:Bagel_forecasting"} illustrates a failure in the forecasting task, while Table [\[tab:Bagel\_imputation\]](#tab:Bagel_imputation){reference-type="ref" reference="tab:Bagel_imputation"} demonstrates an unsuccessful case for the imputation task.