TimeSSM-2.5M

A 2.5M-parameter zero-shot time series forecaster built on a diagonal linear state space model (S4D), trained from scratch on 15.85 billion observations of public time series. It forecasts any horizon in one pass, outputs nine quantiles, and exposes its sampling interval as an inference-time knob: the same weights run a series at any rate.

It was trained by one person on three RTX 3090s, outside of any lab or company.

The animation is a lattice-Boltzmann flow past an obstacle shaped like the letters, 48 by 96 pixels, each pixel forecast as its own series 256 frames ahead from 1024 frames of context, with the sampling interval set from the shedding period. The red frame marks the end of the context. Mean absolute error over the horizon: 0.0094 against 0.0458 for freezing the last frame; empirical 80 % coverage 0.785.

GIFT-Eval results

97 configurations, zero-shot. MASE and CRPS are geometric means of the ratio to the official seasonal naive, as on the leaderboard. Lower is better. All numbers come from the released checkpoint, the last one of its training run; no checkpoint was picked on GIFT-Eval. The evaluation harness reproduces t0-beta's official per-configuration results on 97 of 97 configurations.

With inference-time backtest resampling

	MASE	CRPS
TimeSSM-2.5M + backtest resampling	0.7544	0.5128

The context is resampled at several rates (decimation by 2 to 48, upsampling by 2 to 4) and forecast at each; a causal backtest on the series' own past weights the candidates and the forecasts are mixed per quantile level, with sign-flip averaging. The quantile fan is widened by nine per-level factors calibrated on the training corpus. Nothing is fitted on GIFT-Eval data. It costs 20 to 40 forecasts per series instead of one.

Bare model

	MASE	CRPS
TimeSSM-2.5M	0.7985	0.5451

One forward pass per series, no averaging, no resampling, no calibration.

Where it stands

Among the models of the GIFT-Eval leaderboard under 10M parameters, sorted by CRPS (leaderboard numbers and parameter counts from its metadata; the two TimeSSM rows and the Chronos-Bolt rows from this harness):

Model	Parameters	CRPS ratio
FlowState-9.1M	9.1M	0.502
TimeSSM-2.5M + backtest resampling	2.5M	0.513
TTM-R3	1.4M	0.520
Toto-2.0-4m	4.1M	0.524
Chronos-Bolt tiny + the same resampling layer	9M	0.532
TempoPFN	n/a	0.533
TinyCast	0.1M	0.545
TimeSSM-2.5M	2.5M	0.545
goia-forecast-nano	4.7M	0.553
Kairos-10m	9.9M	0.554
Metamorph-4.5M	n/a	0.555
Chronos-Bolt tiny	9M	0.601
YingLong-6m	7.3M	0.609

TTM-R3 saw GIFT-Eval data in pretraining. Above 10M for scale: Chronos-Bolt small (48M) is at 0.564 bare and 0.515 with the same resampling layer; bare against bare, TimeSSM-2.5M beats it on both metrics.

Per configuration

Ratios to the official seasonal naive, released checkpoint, with backtest resampling and bare.

97 configurations

Configuration	MASE (resampling)	CRPS (resampling)	MASE (bare)	CRPS (bare)
bitbrains_fast_storage/5T/long	0.897	0.681	0.851	0.764
bitbrains_fast_storage/5T/medium	0.910	0.612	0.861	0.578
bitbrains_fast_storage/5T/short	0.714	0.350	0.683	0.339
bitbrains_fast_storage/H/short	0.935	0.658	0.890	0.671
bitbrains_rnd/5T/long	0.992	0.563	0.989	0.464
bitbrains_rnd/5T/medium	0.997	0.496	0.993	0.465
bitbrains_rnd/5T/short	0.933	0.400	0.899	0.377
bitbrains_rnd/H/short	1.001	0.472	0.988	0.441
bizitobs_application/10S/long	1.109	1.215	1.244	1.410
bizitobs_application/10S/medium	1.066	1.044	1.466	1.373
bizitobs_application/10S/short	0.868	0.491	0.859	0.579
bizitobs_l2c/5T/long	0.310	0.311	0.852	0.931
bizitobs_l2c/5T/medium	0.375	0.379	0.689	0.704
bizitobs_l2c/5T/short	0.291	0.293	0.358	0.377
bizitobs_l2c/H/long	0.376	0.262	0.390	0.272
bizitobs_l2c/H/medium	0.318	0.251	0.329	0.264
bizitobs_l2c/H/short	0.388	0.385	0.428	0.421
bizitobs_service/10S/long	0.999	0.969	1.771	1.324
bizitobs_service/10S/medium	0.892	0.621	1.773	1.187
bizitobs_service/10S/short	0.737	0.370	0.992	0.502
car_parts/M/short	0.783	0.622	0.698	0.560
covid_deaths/D/short	0.843	0.289	0.823	0.338
electricity/15T/long	0.787	0.689	0.806	0.713
electricity/15T/medium	0.779	0.707	0.786	0.714
electricity/15T/short	0.682	0.620	0.651	0.587
electricity/D/short	0.761	0.569	0.752	0.570
electricity/H/long	0.918	0.685	0.959	0.753
electricity/H/medium	0.826	0.641	0.842	0.686
electricity/H/short	0.711	0.635	0.731	0.658
electricity/W/short	0.673	0.484	0.703	0.532
ett1/15T/long	0.846	0.679	0.888	0.749
ett1/15T/medium	0.839	0.722	0.888	0.797
ett1/15T/short	0.766	0.689	0.796	0.724
ett1/D/short	0.945	0.676	0.952	0.679
ett1/H/long	0.926	0.580	0.947	0.629
ett1/H/medium	0.830	0.604	0.884	0.656
ett1/H/short	0.851	0.751	0.876	0.776
ett1/W/short	0.837	0.809	0.891	0.882
ett2/15T/long	0.898	0.720	0.954	0.757
ett2/15T/medium	0.845	0.737	0.914	0.806
ett2/15T/short	0.712	0.698	0.727	0.712
ett2/D/short	1.119	0.747	0.999	0.643
ett2/H/long	1.020	0.569	0.987	0.547
ett2/H/medium	0.913	0.607	0.897	0.608
ett2/H/short	0.853	0.793	0.872	0.811
ett2/W/short	1.165	0.738	1.309	0.845
hierarchical_sales/D/short	0.669	0.338	0.659	0.335
hierarchical_sales/W/short	0.700	0.407	0.692	0.399
hospital/M/short	0.860	0.878	0.880	0.895
jena_weather/10T/long	0.849	0.204	0.850	0.209
jena_weather/10T/medium	0.845	0.226	0.859	0.231
jena_weather/10T/short	0.387	0.174	0.408	0.191
jena_weather/D/short	0.693	0.220	0.683	0.230
jena_weather/H/long	0.808	0.140	0.838	0.146
jena_weather/H/medium	0.961	0.151	1.113	0.165
jena_weather/H/short	0.720	0.273	0.743	0.275
kdd_cup_2018/D/short	0.785	0.554	0.800	0.562
kdd_cup_2018/H/long	0.762	0.479	0.785	0.490
kdd_cup_2018/H/medium	0.732	0.563	0.746	0.573
kdd_cup_2018/H/short	0.713	0.699	0.729	0.719
loop_seattle/5T/long	0.652	0.572	0.805	0.719
loop_seattle/5T/medium	0.753	0.655	0.819	0.730
loop_seattle/5T/short	0.716	0.582	0.774	0.635
loop_seattle/D/short	0.517	0.421	0.517	0.430
loop_seattle/H/long	0.607	0.339	0.657	0.369
loop_seattle/H/medium	0.668	0.422	0.680	0.427
loop_seattle/H/short	0.675	0.588	0.701	0.609
m4_daily/D/short	1.114	1.008	1.189	1.060
m4_hourly/H/short	1.419	0.709	1.543	0.750
m4_monthly/M/short	0.827	0.828	0.840	0.846
m4_quarterly/Q/short	0.795	0.804	0.835	0.842
m4_weekly/W/short	0.909	0.659	0.994	0.696
m4_yearly/A/short	0.921	0.935	0.896	0.898
m_dense/D/short	0.432	0.307	0.424	0.301
m_dense/H/long	0.597	0.349	0.589	0.346
m_dense/H/medium	0.483	0.333	0.487	0.335
m_dense/H/short	0.558	0.502	0.581	0.520
restaurant/D/short	0.692	0.388	0.684	0.385
saugeen/D/short	0.836	0.581	0.927	0.660
saugeen/M/short	0.745	0.653	0.718	0.623
saugeen/W/short	0.583	0.477	0.591	0.490
solar/10T/long	1.031	0.514	1.101	0.546
solar/10T/medium	0.933	0.520	0.972	0.526
solar/10T/short	1.002	0.683	1.017	0.628
solar/D/short	0.881	0.523	0.927	0.530
solar/H/long	0.973	0.337	0.911	0.326
solar/H/medium	0.943	0.345	0.930	0.355
solar/H/short	0.911	0.559	0.899	0.552
solar/W/short	0.655	0.618	0.782	0.740
sz_taxi/15T/long	0.736	0.457	0.728	0.455
sz_taxi/15T/medium	0.761	0.537	0.752	0.534
sz_taxi/15T/short	0.717	0.655	0.719	0.660
sz_taxi/H/short	0.760	0.635	0.787	0.664
temperature_rain/D/short	0.672	0.437	0.669	0.438
us_births/D/short	0.255	0.209	0.294	0.239
us_births/M/short	1.110	1.071	0.910	0.875
us_births/W/short	0.764	0.745	0.707	0.645

How to read the numbers

• The model receives the declared sampling frequency of the series and sets its sampling interval to 24 / season (FlowState's convention). It was trained this way. Evaluated without the frequency it is not the model of this card.
• Zero-shot: the training corpus excludes the GIFT-Eval sources by construction.
• The harness recomputes the leaderboard metrics from the raw data with the official seasonal-naive denominators. Chronos-Bolt numbers are from chronos-forecasting 2.3.2, whose medium- and long-horizon results differ from the leaderboard's.

Model

Six gated S4D blocks (complex diagonal state, d_model 192, d_state 32), one token per time step, a learned future token for the horizon, a quantile head with cross-attention on the context. 2,525,771 parameters. Robust arcsinh scaling and instance normalization from the context. Any horizon, no autoregressive loop. Nine quantiles, 0.1 to 0.9.

Trained on three RTX 3090s with a pinball loss on the nine quantiles, on a corpus of 106 files (LOTSA subsets at a pinned revision, four Chronos datasets, synthetic families).

Limitations

• The bare model is a short-horizon model; the resampling layer carries the medium and long terms.
• Weakest groups: 10-second cloud-operations traces, hourly data with a weekly cycle (m4_hourly), low-frequency economic series (m4 weekly and yearly).
• The resampling layer multiplies inference cost by 20 to 40.
• Univariate. The frequency must be declared; there is no detector.

Inference

import torch
from timessm import from_pretrained, delta_scale

model = from_pretrained("IUseAMouse/timessm-2.5m")   # or a local directory; device="cuda" to run there

context = torch.tensor(series, dtype=torch.float32).unsqueeze(0)   # [1, length]
w = delta_scale(24, *model.delta_range)   # hourly data with a daily cycle
with torch.no_grad():
    out = model.forecast(context, 48, w=w)
quantiles = out["quantiles_denorm"][0]   # [48, 9], levels 0.1 to 0.9; column 4 is the median

w is 24 divided by the season length of the declared frequency: 96 for 15-minute data, 24 for hourly, 7 for daily data with a weekly cycle, 12 for monthly. The backtest resampling layer runs through the evaluation harness, see the repository.

Reproduction

Code, configs and the evaluation harness: github.com/IUseAMouse/TimeSSM. The model repository (TimeSSM) and the harness repository (TimeJEPA) contain the training configs, the inference config of the card's number, the calibration file, the frequency table and one command per row of this card.

Files and license

• Weights: model.safetensors with config.json (read by timessm.from_pretrained), the calibration factors, the frequency table, and the original Lightning checkpoint epoch00_valloss1.2814.ckpt for exact reproduction through the harness.
• Code: TimeSSM (model, Apache-2.0) and TimeJEPA (harness, MIT).
• Weights license: Apache-2.0, the same as the code.

Citation

@misc{vincent2026timessm,
  author = {Vincent, Yvann},
  title  = {TimeSSM: a state space forecaster with a rate knob},
  year   = {2026},
  url    = {https://github.com/IUseAMouse/TimeSSM}
}