tso-foundation-v14

TSO Foundation Model — v14

Time is geometry. The Time-Series Operator (TSO) is a foundation model that learns the shape of dynamical systems instead of token-chunking numbers. Pretraining uses four self-supervised pretexts — reconstruction, Koopman-linear dynamics, scale covariance (a renormalization leg), and the arrow of time — on 40 series across 8 domains (electricity grids, meteorology, ECG, finance, epidemiology, economics, solar physics, chaotic systems). Transfer to a never-seen series is a closed-form Koopman fit on the frozen latent: zero gradient steps.

Results (v14, latent 256 / hidden 768,

25,000 iters, Kaggle CPU (8-core))

The frozen operator rediscovers the ~11-year Schwabe solar cycle from a scale-space scan of its fitted Koopman eigenvalues on the held-out sunspot series — a purely structural, unsupervised discovery.

Zero-shot usage

import torch
from model import FoundationOperator, zero_shot_forecast

model = FoundationOperator(latent_dim=256, hidden=768)
model.load_state_dict(torch.load("foundation_model.pt", map_location="cpu"))

series = [...]  # your 1-D series (any domain, any sampling rate)
res = zero_shot_forecast(model, series)
print(res["skill_pct"], res["corr"])   # skill vs persistence on the test split

No training on your data is needed: the Koopman operator is fitted in closed form on the frozen latent (ridge-regularized), then rolled out with an envelope projection that keeps the trajectory on the observed attractor.

Architecture

1. Takens embeddings — raw series → delay-embedding (per-series tau).
2. Scale space — fine + coarsened (renormalized) embeddings; the scale_map forces scale covariance, so periods like the solar cycle reappear as clean eigenmodes at coarse scales.
3. Koopman lift — a deep encoder flattens the nonlinear attractor into a latent where dynamics are approximately linear (K).
4. Arrow of time — a conv head classifies forward vs reversed windows.

Honest limitations

• Spike / near-unit-root series (Dogecoin, covid-india) still defeat any closed-form probe; persistence is unbeatable there.
• The frozen linear probe plateaus: pretraining past pretext saturation (≈25k iters at this width) does not buy transfer — capacity and corpus breadth are the levers.
• Pretext losses pay off only above ~15k iterations.

Reproduce

Training protocol: merged kaggle_kernel_tso kernel: balanced 192-series dynamics battery + 40 real series, Koopman pretext dyn_w=2.5, 25k iters. Full study + manuscript: output/study/paper/main.pdf in the source repo.

Citation

@misc{tso-v14,
  title={Time is geometry: an operator foundation model that learns the shape of dynamical systems},
  author={{TSO} Project},
  year={2026}
}