There is No "apple" in Timeseries: Rethinking TSFM through the Lens of Invariance

TL;DR

The paper argues that current timeseries foundation models lag behind NLP/CV baselines because timeseries data are not semantically complete on web-scale corpora. It critiques the 'scrape everything' paradigm as effective for text/images but insufficient for time series, since many concepts and dynamics are not captured in TS data. It introduces a Timeseries Invariance Ontology, formalizing invariances as transformations with $T(g \cdot x) = T(x)$ and enumerating classes such as spectral, amplitude, shape, elastic, distributional, and parametric invariances to guide data collection and model design. The authors advocate deliberate dataset curation and synthetic generation to achieve a world-complete representation of temporal dynamics, enabling robust generalisation, reasoning, and emergent behaviour in TSFMs.

Abstract

Timeseries foundation models (TSFMs) have multiplied, yet lightweight supervised baselines and even classical models often match them. We argue this gap stems from the naive importation of NLP or CV pipelines. In language and vision, large web-scale corpora densely capture human concepts i.e. there are countless images and text of apples. In contrast, timeseries data is built to complement the image and text modalities. There are no timeseries dataset that contains the concept apple. As a result, the scrape-everything-online paradigm fails for TS. We posit that progress demands a shift from opportunistic aggregation to principled design: constructing datasets that systematically span the space of invariance that preserve temporal semantics. To this end, we suggest that the ontology of timeseries invariances should be built based on first principles. Only by ensuring representational completeness through invariance coverage can TSFMs achieve the aligned structure necessary for generalisation, reasoning, and truly emergent behaviour.

Figures (2)

• Figure 1: The “scrape everything on the internet” paradigm succeeds in vision and language because web-scale image and text corpora collectively span most of the human-relevant representational space. In contrast, timeseries data occupy a complementary subspace—capturing dynamics, rhythms, and control signals that rarely overlap with such semantic concepts. The slice of reality containing the notion of “apple” huh2024PRH, for example, is densely represented in image and text corpora but absent from timeseries. We picked the "apple" example in direct reference to the first equation in the https://phillipi.github.io/prh/.
• Figure 2: Illustration of invariances in various domains in timeseries. Minor temporal shifts preserve meaning in ECG signals through heart rate variability, yet the same shifts in meteorological data misalign seasonal cycles. Similarly, vertical inversion leaves audio waveforms perceptually unchanged, but in ECG it indicates lead reversal, and in climate data it represents a physically invalid temperature inversion. (Images adapted from publicly available sources.)