KALEIDO: Input-Space Adaptation of a Vision Model for Time-Series Forecasting Through Gated Fold Geometries

Xiangyu Shi; Qinghua Liu; Sam Heshmati; Zubin Abraham

cs.LGOct 3, 2026

KALEIDO: Input-Space Adaptation of a Vision Model for Time-Series Forecasting Through Gated Fold Geometries

Authors: Xiangyu Shi, Qinghua Liu, Sam Heshmati, Zubin Abraham

Organizations: Northwestern University · Ohio State University · Bosch Research North America

Abstract

Time-series foundation models buy zero-shot forecasting with large temporal corpora; a vision model needs none, since a natural image implicitly embeds the patterns a forecaster must model, and an ImageNet-pretrained masked autoencoder forecasts a series by inpainting a rendering of it. A rendered series is not a natural image, however, and closing that gap takes temporal-aware adaptation. We show that the rendering geometry - how the series is folded and drawn - is a controllable, mixable axis for it. Kaleido detects the dominant periods, renders a rule-generated set of fold geometries, combines the inpaintings with a convex per-position gate fit on validation only, and fuses the result with the zero-shot output at one fixed share, with no per-dataset hyperparameter beyond the baseline's published settings. Training only LayerNorm (0.05%), Kaleido lowers MSE by 13% against the published zero-shot baseline on LTSF and, frozen, by 6.6%; on GIFT-Eval it improves the baseline by 7.4% in MASE and 19.3% in CRPS.

Figures & tables

Figure 1: Kaleido overview, left to right. Detected periods generate the arm set: one plane per period, spanning periods per row $m$ and context rows $n$ , for $K$ arms, all inpainted by one shared MAE. The arms are frozen (zero-training tier) or carry their own LayerNorm parameters (trained tier); the anchor, the backbone at the baseline’s default geometry, is never finetuned and never enters any fit. A convex per-position gate fit on validation windows combines the $K$ arms; the anchor bypasses it and fuses in at $\lambda{=}0.75$ .

	Zero-shot					Fine-tuned / supervised
	Kaleido -zs	VisionTS-zs	VisionTS++	Moirai B	Chronos L	Kaleido	VisionTS-fs	DMMV-a	PatchTST
ETTh1	0.384	0.389	0.402	0.434	0.589	0.376	0.395	0.395	0.413
ETTh2	0.330	0.333	0.333	0.346	0.455	0.338	0.336	0.337	0.330
ETTm1	0.349	0.373	0.360	0.382	0.556	0.320	0.338	0.340	0.351
ETTm2	0.256	0.281	0.244	0.272	0.295	0.242	0.261	0.256	0.255
Weather	0.243	0.269	0.222	0.238	0.279	0.222	0.227	0.217	0.225

Table 1: LTSF, multivariate MSE averaged over horizons; the trained column is the mean over 3 seeds (ECL: 1). Groups: no backbone parameter trained on the target dataset (left) versus trained on it (right). Bold : best in group, co-bolded within 0.5%. Per-cell values in App. E .

	TimesFM-2	C-Bolt-B	C-Bolt-S	Kaleido	PatchTST	Chronos-L	Kaleido -zs	iTrans.	VisionTS ⋆	Moirai-B
nMASE	0.758	0.808	0.822	0.832	0.849	0.870	0.879	0.893	0.899	0.901
nCRPS	0.550	0.574	0.577	0.634	0.587	0.647	0.671	0.620	0.786	0.610
leakage	✓	✓	✓	–	–	✓	–	–	–	–

Table 2: GIFT-Eval, the benchmark’s own aggregation (MASE and CRPS normalised by Seasonal-Naive, geometric mean over 97 configurations). Per-configuration values in App. K .

Panel of Figure 2 — Figure 2: Ablations. (a) MSE per dataset at the combination stage, no anchor, zero-training tier; (b) the fusion share, trained-tier MSE over the 24 cells of Table 1 (top) and the zero-training change against the anchor by frequency (bottom); (c) primary period versus all detected periods.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

LTSF (detector v1 = v2, frozen; reference = community seasonality)
dataset	detected	reference
ETTh1	24	24
ETTh2	24	24
ETTm1	96	96
ETTm2	96	96
Weather	144	144

Appendix

Table 3: Every detected period against the reference seasonality of its dataset.

Time Series Forecasting

Time series forecasting predicts future values from ordered observations using statistical, neural, and probabilistic models to support decisions under uncertainty.

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Inherent temporal heterogeneity, such as varying sampling densities and periodic structures, has posed substantial challenges in zero-shot generalization for Time Series Foundation Models (TSFMs). Existing TSFMs predominantly rely on massive parameterization to absorb such heterogeneity, as their static tokenization and positional encoding schemes entangle diverse temporal patterns into a fixed representation space, encouraging memorization rather than adaptation. To address this limitation, we propose Kairos, a flexible and parameter-efficient TSFM dedicated to forecasting tasks, which decouples temporal heterogeneity from model capacity through a novel tokenization perspective. Kairos introduces a dynamic patching tokenizer and a mixture-of-size encoding that adapt observational granularity to local information density, enabling fine-grained temporal abstraction without increasing model width or depth. In addition, we design a multi-granularity positional embedding based on dynamic rotary encodings, which conditions on instance-level spectral features and temporal structure induced by dynamic patching tokenization, allowing robust modeling of diverse temporal dependencies. Trained on a novel Predictability-Stratified Time-Series (PreSTS) corpus, Kairos achieves superior zero-shot performance with substantially fewer parameters on two mainstream benchmarks, GIFT-Eval and Time-Series-Library. The project page is at https://foundation-model-research.github.io/Kairos .

Abstract

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