Twice Upon a Time: Complementary Representations for Time-Series Reasoning

Hedi Zisling; Liran Nochumsohn; Ilan Naiman; Mihir Parmar; Omri Azencot

cs.LGOct 15, 2026

Twice Upon a Time: Complementary Representations for Time-Series Reasoning

Authors: Hedi Zisling, Liran Nochumsohn, Ilan Naiman, Mihir Parmar, Omri Azencot

Organizations: Ben-Gurion University · Google

Abstract

Time Series Language Models (TSLMs) enable language-based understanding and reasoning over temporal data, yet a fundamental question remains: what information should their time-series representations preserve, and what variation should they factor out? Existing TSLMs typically expose the language model to a single representation, imposing a fixed inductive bias across downstream tasks. We instead introduce complementary representations as a design principle for time-series reasoning. Our model combines two visual views: line plots preserve absolute measurements and the observed coordinate frame, while normalized delay embeddings factor out positive amplitude rescaling and offsets while exposing temporal structure. Dedicated visual encoders integrate both views into a shared language model through visual tokens and multi-level feature fusion. Evaluation-time interventions verify that the two views exhibit distinct invariance profiles, while single-view ablations show that their combination is particularly beneficial beyond basic perception, with the large gains in prediction and reasoning. Built on Qwen3-VL-8B, our dual-view model improves overall TSRBench accuracy from 44.5% with line plots alone to 53.2%, substantially exceeding the strongest evaluated dedicated TSLM baseline at 36.7%. It further achieves 89.9% accuracy on TSExam and 86.8% numerical accuracy on multivariate ChatTS alignment. Together, these results demonstrate that complementary representations provide an effective design principle for general-purpose TSLMs, enabling models to exploit temporal structure without sacrificing access to the original measurement frame.

Figures & tables

Panel of Figure 1 — Figure 1: Cross-benchmark accuracy (%). ChatTS-A and ChatTS-B report categorical (Cat.) and numerical (Num.) alignment on the univariate and multivariate datasets, respectively. Bold marks the best result in each panel, excluding GPT-5 (T+V), shown in gray, which is a large proprietary model included as a reference rather than a size-matched comparison.

	Model	TS Representation	Normalization	Scale Information	Representation Views	Task Scope
Forecast.	PromptCast ( Xue and Salim, 2023 )	Text	None	In representation	Single	Forecasting
	LLMTime ( Gruver et al., 2023 )	Text	Per-series rescaling	Not provided	Single	Forecasting
	Time-LLM ( Jin et al., 2024 )	Reprogrammed patches	Per-series	Not provided	Single	Forecasting
TSLMs	TimeOmni-1 ( Guan et al., 2026 )	Text	None	In representation	Single	QA & reasoning
	ChatTS ( Xie et al., 2025 )	1D patches	Per-series	Auxiliary metadata	Single	QA & reasoning
	OpenTSLM ( Langer et al., 2026 )	1D patches	Per-series	Auxiliary metadata	Single	QA & reasoning

Table 1: Comparison of time-series representations in existing TSLMs. The methods differ in how the time series is represented, whether the primary representation is normalized, and how absolute measurement-scale information is provided to the language model. Forecasting-oriented LLM methods are included for completeness; unlike TSLMs, they target numerical forecasting rather than general question answering and reasoning.

Figure 2: Overview of the Dual-View TSLM. Each visual span is wrapped by vision_start and vision_end . Stage I trains the DINOv3 LoRA and the merger. Stage II trains the LM LoRA. The Qwen vision encoder, the text embedding, and the LLM backbone stay frozen.

Stage	Source	Origin	Rows	Supervision
I	CaTS-Bench	Real ( Zhou et al., 2026 )	15,995	Caption
I	ChatTS-style captions	Synthetic ( Xie et al., 2025 )	32,000	Caption
I	Structural captions	Synthetic, in-house	7,701	Caption
II	ChatTS ift	Synthetic ( Xie et al., 2025 )	6,373	Free-form QA
II	ChatTS sft	Synthetic ( Xie et al., 2025 )	44,802	Free-form QA
II	TSExam perception	Synthetic, in-house	20,640	MCQ

Table 2: Training-data composition. Rows denote distinct examples available to the corresponding training stage. Stage I sources are sampled with equal probability; Stage II uses a balanced mixture described in the text.

		Perception				Reasoning							Prediction		Decision
	Model	PR	NU	AD	CA	ER	CD	AR	TR	NR	DR	IR	TSF	EP	QuaDM	QuanDM	Overall
General	GPT-5 (V)	83.6	72.4	69.8	73.5	34.6	37.0	81.3	68.1	64.0	48.0	57.0	38.8	71.9	26.9	30.0	52.4
	GPT-5 (T+V)	84.9	72.4	61.2	70.8	38.9	50.3	93.3	68.8	72.0	44.0	58.0	37.8	78.1	31.9	34.3	55.6
	Qwen3-VL-8B (V)	54.7	57.5	62.8	65.5	24.3	31.7	52.0	23.1	33.2	19.2	29.0	51.7	30.6	36.1	29.0	38.9
TSLMs	ChatTS-14B	50.7	50.6	46.5	55.8	21.7	34.3	51.3	24.4	30.5	23.6	25.0	19.2	52.2	29.3	27.7	33.5
	TS-Reasoner-7B	53.1	56.3	48.1	50.4	28.9	24.3	57.3	26.9	37.2	23.6	24.0	31.7	55.0	32.8	21.7	36.4

Table 3: TSRBench accuracy (%) across all 15 tasks. Rows are grouped into general-purpose models, dedicated TSLMs, and representation ablations. In the Overall column, bold and underline mark the best and second-best results, respectively. Gray rows denote large proprietary models included as reference points rather than size-matched comparisons and are excluded from this ranking. Full task descriptions and results are provided in Appendix C .

Model	Clean	$\times 0.1$	$\times 10$	$+5\sigma$	$-5\sigma$	$z$ -score	20 dB	10 dB	0 dB	Smooth	256	2048
		Affine					Noise / Smoothing				Sampling
Plot only	52.7	58.2	49.6	48.9	49.2	47.5	50.6	47.4	43.2	50.1	51.6	52.9
Delay only	44.7	43.4	44.9	44.9	44.1	44.3	42.3	38.3	35.3	40.7	45.1	42.8
Ours	66.5	63.4	64.8	62.9	65.0	60.7	65.4	62.4	56.6	60.7	64.8	66.8

Table 4: Evaluation-time interventions on scale- and sampling-invariant TSRBench subsets (2,020 items; excludes NR, DR, IR, TSF, and decision tasks). Each entry reports accuracy (%).

Appendix figures & tables16 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 3 — Figure 3: Dual-view visual representations of a time-series variate. (a) The line plot retains the original measurement frame and axis values. (b) The normalized delay map arranges overlapping windows as columns, so recurring structure appears as diagonal stripes.

Symbol	Description	Value
$\rho$	Window length as a fraction of series length	$0.6$
$\ell_{\min}$	Minimum window length	$48$
$\ell_{\max}$	Maximum window length	$192$
$W$	Number of windows (map width)	$256$
$H$	Resampled window length (map height)	$256$

Appendix

Table 5: Hyperparameters of the normalized delay-embedding view.

	TSExam	ChatTS-A		ChatTS-B		ChatTS	TSRBench
Model	Overall	Cat.	Num.	Cat.	Num.	Reason.	Overall
Delay only	0.749	0.782	0.290	0.806	0.308	0.596	0.405
Plot only	0.899	0.861	0.781	0.895	0.864	0.613	0.452
Delay+Delay	0.790	0.858	0.424	0.848	0.348	0.604	0.426
Plot+Plot	0.865	0.873	0.805	0.877	0.859	0.586	0.448
Ours	0.899	0.864	0.805	0.893	0.868	0.615	0.532

Appendix

Table 6: Cross-benchmark representation ablations. ChatTS-A and ChatTS-B report categorical (Cat.) and numerical (Num.) alignment accuracy. ChatTS Reason. reports average accuracy across the four reasoning evaluations. TSRBench reports overall accuracy. Plot+Plot and Delay+Delay feed the same representation to both towers while matching the architecture and visual-token budget of our model.

Model	Perception	Reasoning	Prediction	Decision	Overall
Delay only	63.7	36.5	39.4	27.6	40.5
Plot only	87.4	35.8	38.0	36.4	45.2
Delay+Delay	71.6	37.0	41.7	27.4	42.6
Plot+Plot	85.3	36.3	40.3	30.7	44.8
Ours	86.4	40.1	61.7	37.6	53.2

Appendix

Table 7: TSRBench category-level accuracy (%) for the representation ablations. Overall accuracy is computed using the benchmark’s complete task-level evaluation.

Model	Induct.	Deduct.	Causal	MCQ2	Average
Delay only	0.403	0.605	0.857	0.520	0.596
Plot only	0.441	0.548	0.851	0.610	0.613
Ours	0.479	0.535	0.826	0.620	0.615

Appendix

Table 8: ChatTS reasoning accuracy for the single-view and dual-view models on inductive, deductive, and causal reasoning and two-series multiple-choice questions (MCQ2). Inductive reasoning is scored with the RAGAS pipeline; Average reports the mean over the four tasks.

		Plot only		Ours		Delay only
Intervention Type	Transformation	Acc.	$\Delta$ vs. Clean	Acc.	$\Delta$ vs. Clean	Acc.	$\Delta$ vs. Clean
Baseline	Clean	0.452	—	0.532	—	0.405	—
Affine Invariance	Scale $\times 0.1$	0.467	$+1.5$	0.496	$-3.6$	0.407	$\mathbf{+0.2}$
	Scale $\times 10$	0.439	$-1.4$	0.522	$-1.0$	0.411	$\mathbf{+0.6}$
	Offset $+5\sigma$	0.431	$-2.1$	0.511	$-2.2$	0.397	$\mathbf{-0.8}$
	Offset $-5\sigma$	0.430	$-2.2$	0.520	$-1.3$	0.400	$\mathbf{-0.6}$

Appendix

Table 9: Evaluation-time affine and dynamical interventions across the full TSRBench benchmark (all 15 tasks, including forecasting). For each model, we report clean accuracy and the percentage-point change (

\Delta

) relative to clean performance. Daggers (

\dagger

) mark non-invariance interventions for which gold targets legitimately change. Bold values indicate the smallest absolute shift (

|\Delta|

) in each row.

Secondary Representation	Only	+ Plot
STFT ( $z$ -normalized)	0.739	0.889
STFT (raw)	0.745	0.894
Delay	0.737	0.893

Appendix

Table 10: Controlled TSExam comparison of alternative secondary representations. “Only” evaluates the secondary representation without the line-plot stream, whereas “+ Plot” combines it with the line plot.

		STFT ( $z$ -normalized)		STFT (raw)		Delay
Intervention Type	Transformation	Acc.	$\Delta$ vs. Clean	Acc.	$\Delta$ vs. Clean	Acc.	$\Delta$ vs. Clean
Baseline	Clean	0.739	—	0.745	—	0.737	—
Affine Invariance	Scale $\times 0.1$	0.725	$-1.3$	0.727	$-1.9$	0.733	$\mathbf{-0.4}$
	Scale $\times 10$	0.728	$-1.1$	0.727	$-1.9$	0.731	$\mathbf{-0.7}$
	Offset $+5\sigma$	0.728	$-1.1$	0.634	$-11.1$	0.732	$\mathbf{-0.5}$
	Offset $-5\sigma$	0.729	$-0.9$	0.649	$-9.7$	0.731	$\mathbf{-0.7}$

Appendix

Table 11: Evaluation-time affine and dynamical interventions on TSExam (

N=746

) for the single-representation models. For each model, we report clean accuracy and the percentage-point change (

\Delta

) relative to clean performance. Daggers (

\dagger

) mark non-invariance interventions for which gold targets legitimately change. Bold values indicate the smallest absolute shift (

|\Delta|

) in each row.

Model	TSExam	Cat.	Num.	Cat.	Num.	Reason.	TSRBench
		ChatTS-A		ChatTS-B
Plot + STFT	0.890	0.859	0.809	0.894	0.871	0.628	0.467
Plot + Delay (Ours)	0.899	0.864	0.805	0.893	0.868	0.615	0.532

Appendix

Table 12: Full-training comparison between the proposed delay-based dual-view model and an alternative model using STFT as the secondary representation. ChatTS-A and ChatTS-B report categorical (Cat.) and numerical (Num.) alignment accuracy; Reason. reports the ChatTS reasoning average.

Textual Time Series as Input
	Perception					Reasoning								Prediction			Decision
Model	Perc.	PR	NU	AD	CA	Reas.	ER	CD	AR	TR	NR	DR	IR	Pred.	TSF	EP	Dec.	QualDM	QuantDM	Overall
DeepSeek-V3.2	63.9	67.7	56.3	57.4	64.6	35.6	32.0	35.7	70.7	19.4	27.3	47.6	24.0	33.4	26.5	47.2	30.8	33.1	28.3	39.1
GPT-OSS-120B	64.6	66.8	56.3	59.8	69.0	38.5	39.1	26.3	58.7	31.3	48.5	28.0	40.0	40.6	31.1	59.7	32.4	33.7	31.0	42.0
Qwen3-235B-A22B	63.8	66.0	56.3	59.7	67.3	40.9	22.6	34.7	86.7	28.1	44.8	49.2	39.0	35.6	29.0	48.9	32.5	34.8	30.0	42.2
GPT-5-mini	68.7	72.2	59.8	63.6	69.9	47.5	45.1	27.7	62.7	39.4	65.2	41.3	50.0	38.3	23.5	67.8	33.0	35.5	30.3	46.6

Appendix

Table 13: TSRBench accuracy (%) by input modality. Bold columns (Perc., Reas., Pred., Dec.) are item-weighted category averages over their sub-tasks. Gray rows denote reference models (proprietary or open-weight models larger than 72B parameters).

Dataset	Model	Trend		Season		Noise		Local		Corr.	Clus.	Overall
		Cate.	Num.	Cate.	Num.	Cate.	Num.	Cate.	Num.	Cate.	Cate.	Cate.	Num.
A	GPT-4o (T)	0.585	0.882	0.811	0.768	0.905	0.153	0.379	0.256	0.476	0.333	0.542	0.371
	GPT-4o (V)	0.659	0.613	0.811	0.559	0.810	0.248	0.537	0.414	0.476	0.480	0.609	0.436
	GPT-5 (T)	0.512	0.887	0.973	0.000	0.905	0.350	0.905	0.741	0.881	0.485	0.797	0.724
	GPT-5 (V)	0.732	0.646	0.973	0.000	0.762	0.394	0.874	0.725	0.857	0.600	0.810	0.670
	GPT-5 (T+V)	0.585	0.905	0.973	0.000	0.905	0.423	0.863	0.735	0.857	0.558	0.801	0.731

Appendix

Table 14: ChatTS alignment benchmark on univariate (Dataset A) and multivariate (Dataset B) series. Gray rows denote reference models. Corr. and Clus. are the correlation and clustering sub-tasks (categorical only). Bold values mark the best result per column within each dataset, excluding reference models.

Model	Induct.	Deduct.	Causal	MCQ2	Average
GPT-4o (T)	0.336	0.628	0.685	0.510	0.540
GPT-4o (V)	0.322	0.605	0.652	0.490	0.517
GPT-5 (T)	0.277	0.581	0.663	0.730	0.563
GPT-5 (V)	0.382	0.674	0.707	0.675	0.610
GPT-5 (T+V)	0.315	0.605	0.717	0.760	0.599
Qwen3-VL-8B (V)	0.197	0.558	0.685	0.480	0.480

Appendix

Table 15: ChatTS reasoning evaluation (Dataset A). Inductive reasoning is free-form Q&A scored with the RAGAS pipeline; the other tasks are multiple-choice or true/false accuracy. MCQ2 samples 100 questions from the two-series set. Gray rows denote reference models. Bold values mark the best result per column, excluding reference models.

Model	Overall	Anomaly	Causality	Noise	Pattern	Similarity
GPT-4o (T)	0.586	0.491	0.458	0.667	0.594	0.667
GPT-4o (V)	0.736	0.583	0.611	0.786	0.787	0.758
GPT-5 (T)	0.724	0.704	0.556	0.679	0.782	0.700
GPT-5 (V)	0.784	0.648	0.431	0.750	0.906	0.775
GPT-5 (T+V)	0.808	0.731	0.417	0.738	0.931	0.792
Qwen3-VL-8B (V)	0.618	0.546	0.514	0.643	0.630	0.692

Appendix

Table 16: TSExam accuracy across the 746 questions, by category. Gray rows denote reference models. Bold values mark the best result per column, excluding reference models.

Stage	Source	Raw Examples	Effective Draws / Epoch	Supervision
I	CaTS	15,995	$\sim$ 18,565	Caption / description
I	ChatTS-style captions	32,000	$\sim$ 18,565	Caption / description
I	Structural captions	7,701	$\sim$ 18,565	Caption / description
	Stage I total	55,696	55,696
II	ChatTS IFT	6,373	$\sim$ 23,938	Instruction following
II	ChatTS SFT	44,802	$\sim$ 23,938	Instruction following

Appendix

Table 17: Training-data composition. Raw examples denote the number of available examples before sampling, whereas effective draws denote the approximate number presented in one training epoch. Stage-I sources are sampled with equal source probability. In Stage II, the reasoning and numerical corpora retain their natural sizes, while the remaining sampling budget is divided approximately equally among the three instruction/multiple-choice sources.

Family	Tmpl.	Items	Share	Underlying Generation / Governing Process	Channels	Options	Output
NR	8	16,874	16.9%	Eight physical formulas: traffic flow, cooling load, growing degree days, seismic S–P distance, reaction kinetics, Penman–Monteith evapotranspiration, intersection delay, and wind power.	2–4	4	Rationale + Letter
EP	1	15,225	15.2%	Five-channel synthetic weather traces in which rainfall events are triggered by a latent humidity surge and barometric-pressure drop; two informative and three nuisance channels.	5	2	Rationale + Letter
ER	2	14,802	14.8%	Parameterized light curves spanning five variable-star classes and tri-axial accelerometer segments spanning six physical-activity classes.	1 / 3	5 / 6	Option Letter
CD	1	12,687	12.7%	Random five-node directed acyclic graphs simulating sensor networks across heterogeneous ranges; the task is to identify the generating adjacency structure.	5	4	Option Letter
TSF	1	12,500	12.5%	Histories containing trend, seasonality, and autoregressive structure; the task is to select the appropriate continuation trajectory among generated alternatives.	4	4	Option Letter
DR	3	10,573	10.6%	Propagation of dynamical processes including AR(1), geometric growth, and continuous Lorenz-attractor state trajectories.	4	4	Option Letter

Appendix

Table 18: Taxonomy of the reasoning corpus (100,000 examples across 25 templates). Shares are computed over the complete reasoning corpus. Where a family mixes sources, Channels and Options are listed per source in the order of the description.

Subcategory	Tmpl.	Items	Share	Target Statistic	Channels	Options	Output
Statistical retrieval	10	5,500	50.0%	Maximum, minimum, mean, median, first and third quartile, standard deviation, variance, first value, and last value.	1	—	Scalar
Signal properties	5	2,750	25.0%	Range, interquartile range, mean absolute value, lag-1 autocorrelation, and number of zero crossings.	1	—	Scalar
Step dynamics	5	2,750	25.0%	Mean absolute first difference, largest one-step jump, best-fit slope, first-half minus second-half mean, and energy.	1	—	Scalar

Appendix

Table 19: Taxonomy of the numerical corpus (11,000 examples across 20 templates). Shares are computed over the complete numerical corpus.

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Lapras: Latent Reasoning for Time Series Language Models

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Time Series Language Models (TSLMs) offer a promising path toward time series understanding by reasoning over temporal signals and producing natural language answers and explanations. A common approach is Chain-of-Thought (CoT), which generates step-by-step rationales linking relevant signal patterns to final answers. Although these models learn from reference CoT traces during post-training, generating faithful descriptions of input time series at inference remains challenging. Expressing high-dimensional, continuous temporal representations in discrete language tokens may cause the model to neglect task-relevant patterns or describe them inaccurately. Because later reasoning steps build on these descriptions, early errors propagate, leading to incorrect answers with plausible explanations that are inconsistent with the input signal. We propose Lapras (Latent Post-trained Reasoning Across Series), a post-training framework that equips TSLMs with latent reasoning. A model trained with Lapras reasons through a sequence of continuous thoughts in the joint time series-language space, producing text only for the final answer. It learns this through teacher-student self-distillation, where a teacher trained on CoT reference traces reasons explicitly through text. The student aligns its hidden states with the teacher's at the answer stage, transferring the teacher's reasoning ability into its latent computation. We evaluate Lapras across four TSLM backbones on five time series question answering benchmarks. Lapras improves average F1 by up to 10.79% over explicit CoT while generating 23.9x fewer tokens. Lapras's continuous thoughts can also be decoded into readable reasoning traces via standard language decoding, preserving textual explanations. Together, these results highlight Lapras as a promising post-training paradigm for efficient, effective, and interpretable TSLM reasoning.

Abstract

Time Series Language Modeling

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