---
license: apache-2.0
pipeline_tag: time-series-forecasting
library_name: fracast
paper: https://arxiv.org/abs/2609.32209
doi: 10.48550/arXiv.2609.32209
tags:
- fracast
- fracast-0
- time-series-foundation-model
- time-series-forecasting
- foundation-models
- pretrained-models
- pretrained
- time-series
- timeseries
- forecasting
- probabilistic-forecasting
- pytorch
- cpu
- safetensors
- quantization
- w8
- gift-eval
- fev-bench
- time-benchmark
- boom
- github
- mimo-2-6-pro
- deepseek-v4-1-flash
- xiaomi-mimo
- deepseek
- arxiv
- arxiv:2609.32209
- model-compression
- browser-inference
datasets:
- Salesforce/GiftEvalPretrain
- Salesforce/lotsa_data
- autogluon/chronos_datasets
- Datadog/BOOM
- autogluon/fev_datasets
model-index:
- name: Fracast-0
  results:
  - task:
      type: time-series-forecasting
      name: Time Series Forecasting
    dataset:
      type: gift-eval
      name: GIFT-Eval pretrained protocol
    metrics:
    - type: normalized_mase
      value: 0.807133
      name: Overall Normalized MASE
    - type: normalized_mwql
      value: 0.563008
      name: Overall Normalized MWQL
    - type: normalized_mase
      value: 0.769573
      name: Short Normalized MASE
    - type: normalized_mwql
      value: 0.568038
      name: Short Normalized MWQL
    - type: normalized_mase
      value: 0.842959
      name: Medium Normalized MASE
    - type: normalized_mwql
      value: 0.557024
      name: Medium Normalized MWQL
    - type: normalized_mase
      value: 0.875558
      name: Long Normalized MASE
    - type: normalized_mwql
      value: 0.555953
      name: Long Normalized MWQL
    source:
      name: Official GIFT-Eval results
      url: https://github.com/SalesforceAIResearch/gift-eval/tree/main/results/Fracast-0
  - task:
      type: time-series-forecasting
      name: Time Series Forecasting
    dataset:
      type: time-benchmark
      name: TIME 98-task evaluation
    metrics:
    - type: normalized_mase
      value: 0.767965
      name: Overall Normalized MASE
    - type: normalized_crps
      value: 0.649192
      name: Overall Normalized CRPS
    - type: rank
      value: 24
      name: Overall MASE rank of 29
    - type: rank
      value: 24
      name: Overall CRPS rank of 29
    source:
      name: TIME official leaderboard
      url: https://huggingface.co/spaces/Real-TSF/TIME-leaderboard
  - task:
      type: time-series-forecasting
      name: Time Series Forecasting
    dataset:
      type: fev-bench
      name: FEV-Bench in-corpus protocol
    metrics:
    - type: rank
      value: 17
      name: SQL rank of 30 (raw)
    - type: rank
      value: 16
      name: SQL rank of 30 (controlled)
    - type: rank
      value: 20
      name: MASE rank of 30 (raw)
    - type: rank
      value: 16
      name: MASE rank of 30 (controlled)
    source:
      name: FEV-Bench official leaderboard
      url: https://huggingface.co/spaces/autogluon/fev-bench
  - task:
      type: time-series-forecasting
      name: Time Series Forecasting
    dataset:
      type: boom
      name: BOOM in-corpus protocol
    metrics:
    - type: scaled_mase
      value: 0.723
      name: Scaled MASE
    - type: scaled_crps
      value: 0.434
      name: Scaled CRPS
    - type: rank
      value: 11.808
      name: Mean per-dataset rank of 24
    source:
      name: BOOM official leaderboard
      url: https://huggingface.co/spaces/Datadog/BOOM
---

# Fracast-0

**Fracast-0 is an 85K-parameter pretrained Time Series Foundation Model, small enough to load directly in a web page.**

The technical report is available at
[arXiv:2609.32209](https://arxiv.org/abs/2609.32209). Source code and
reproducible pretraining recipes are available in the
[GitHub repository](https://github.com/ztxtech/fracast-0).

<div align="center">
  <em>"We built this solely to explore whether model compression can be pushed to an even more extreme state. We spent 15 days on this exploration. Although the work is not perfect, it is at least usable, so we are releasing it. Fracast-0 is the published version, and future versions will only get better."</em>
  <br /><br />
  <strong>Tianxiang Zhan</strong>
</div>

Fracast-0 is a compact pretrained model for probabilistic time-series forecasting. It uses a 2,048-point context, predicts 48 future points, and emits quantiles from 0.1 through 0.9.

The release has 85,001 parameters. The FP32 checkpoint is 344,412 bytes; the W8 checkpoint is 113,228 bytes.

## Python Quick Start

Install the Python package in one command:

```bash
python -m pip install fracast
```

The package embeds both checkpoints, so this loads without network access:

```python
import numpy as np
from fracast import FracastModel

model = FracastModel.from_pretrained(device="cpu")

# Input: [time]. Output: [horizon, quantile].
context = np.sin(np.arange(240) / 7.0)
forecast = model.forecast(context)
assert forecast.shape == (48, 9)

# The native head predicts 48 steps; longer horizons roll median blocks.
long_forecast = model.forecast(context, horizon=144)
assert long_forecast.shape == (144, 9)

# Input: [variables, time]. Output: [variables, horizon, quantile].
multivariate = np.stack([context, context * 0.5 + 2.0])
forecast = model.forecast(multivariate)
long_multivariate = model.forecast(multivariate, horizon=144)
assert forecast.shape == (2, 48, 9)
assert long_multivariate.shape == (2, 144, 9)
```

Pass `weights="fp32"` for the bundled full-precision checkpoint. The first
argument can also be a local directory or a Hugging Face repository id such as
`"ztxtech/fracast-0"` when remote loading is preferred. The W8 file stores
symmetric per-output-channel INT8 weights with FP32 scales and residual
tensors, then dequantizes them for inference.

## Inference Contract

- Input shapes: `[T]`, `[1, T]`, or `[V, T]`.
- Output shapes: `[H, 9]`, `[1, H, 9]`, or `[V, H, 9]`; `H` defaults to 48.
- Maximum context: 2,048 observations; longer input keeps the latest 2,048.
- Minimum context: 8 finite observations per channel.
- Missing values: use `NaN`; the runtime masks them.
- Quantile order: `[0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]`.
- Multivariate input is forecast channel-independently. The model does not use cross-variable interactions or future covariates.
- Quantile crossings are not post-processed away.

The [browser Playground](https://huggingface.co/spaces/ztxtech/fracast-0-demo) loads the W8 checkpoint into page memory and releases it when the page is closed.

## GIFT-Eval Benchmark

Fracast-0 was evaluated on all 97 GIFT-Eval configurations with the official
aggregation protocol. The result is labeled `pretrained`: the complete
pretraining recipe includes datasets from families present in the GIFT-Eval
test corpus.

| Protocol split | Configurations | Normalized MASE | Normalized MWQL |
| --- | ---: | ---: | ---: |
| Short | 55 | 0.769573 | 0.568038 |
| Medium | 21 | 0.842959 | 0.557024 |
| Long | 21 | 0.875558 | 0.555953 |
| **Overall** | **97** | **0.807133** | **0.563008** |

The official aggregate first divides each configuration by the matching
`Seasonal_Naive` result and then takes the geometric mean over all 97
configurations. The leaderboard result uses the FP32 release checkpoint. The
shipped W8 form dequantizes weights before inference and is not an
integer-only kernel. The official results are public in the
[GIFT-Eval `results/Fracast-0` directory](https://github.com/SalesforceAIResearch/gift-eval/tree/main/results/Fracast-0).
The compact summary is in
[`benchmark/gift_eval/`](benchmark/gift_eval).

## TIME Benchmark

Fracast-0 completed all 98 TIME tasks in a local Apple MPS run with batch size
512 and the FP32 release checkpoint. The normalized scores use seasonal-naive
normalization by `(dataset_id, horizon)` and a geometric mean over MASE and
CRPS.

| Scope | MASE norm | CRPS norm | MASE rank | CRPS rank |
| --- | ---: | ---: | ---: | ---: |
| Short | 0.701284 | 0.586018 | 25 / 29 | 24 / 29 |
| Medium | 0.855065 | 0.736344 | 25 / 29 | 24 / 29 |
| Long | 0.833422 | 0.708427 | 24 / 29 | 20 / 29 |
| **Overall** | **0.767965** | **0.649192** | **24 / 29** | **24 / 29** |

The ranking table is the official 29-model
[TIME leaderboard](https://huggingface.co/spaces/Real-TSF/TIME-leaderboard),
and the raw 98-task outputs are in
[`Real-TSF/TIME-Output`](https://huggingface.co/datasets/Real-TSF/TIME-Output).
The compact scores in this archive come from the archived raw outputs and the
official table; no separate recomputation is recorded for them.

Of the 98 tasks, 47 use the released 48-step head with median-quantile
feedback for longer horizons. This rollout path is disclosed in every raw
task configuration and is not a strict official-protocol claim. The compact
analysis and reproducibility scripts are archived in the
[GitHub TIME archive](https://github.com/ztxtech/fracast-0/tree/main/script/time_benchmark)
and the public tables are also stored here under
[`benchmark/time_benchmark/`](benchmark/time_benchmark).

In the parameter-count analysis, Fracast-0 has 85,001 parameters and lies on
both the parameter-MASE and parameter-CRPS Pareto fronts. Its dominator lists
are empty for both metrics. The smallest better-performing comparator is
Toto-2.0-4m with 4,144,456 parameters, MASE 0.691002, and CRPS 0.582490.
OmniScient uses a conservative Chronos-2 base lower bound, and
PatchTST-FM-Extended uses the public R1 count from the same default
architecture.

## FEV-Bench

Fracast-0 also completed the official local 100-task FEV-Bench run with Apple
MPS, batch size 512, FP32 computation, and the `w8` checkpoint. The full
adapter, pinned analysis code, raw result, and ranking tables are archived in
the [GitHub repository](https://github.com/ztxtech/fracast-0/tree/main/script/fev_bench).
The raw CSV is also stored here as
[`benchmark/fev_bench/fracast-0.csv`](benchmark/fev_bench/fracast-0.csv).

| Metric | Raw rank | Leakage-controlled rank |
| --- | ---: | ---: |
| SQL | 17 / 30 | 16 / 30 |
| MASE | 20 / 30 | 16 / 30 |
| WQL | 17 / 30 | 16 / 30 |
| WAPE | 20 / 30 | 17 / 30 |

The raw SQL win rate is 44.44% with a 35.72% skill score. All 100 tasks
completed without a task failure. Fracast-0 was pretrained on every
`autogluon/fev_datasets` configuration in the benchmark, so the official
leakage-controlled aggregate replaces Fracast-0 errors with Chronos-Bolt. This
is an in-corpus result and must not be read as an independent zero-shot score.
The protocol and comparison table are in the
[FEV-Bench leaderboard](https://huggingface.co/spaces/autogluon/fev-bench) and
the [FEV-Bench repository](https://github.com/autogluon/fev).

572 of 235,039 sequence windows (0.243%) had fewer than eight finite
observations after official task slicing. The adapter repeats the most recent
finite value for those windows; it does not use labels to change forecasts.

## BOOM Benchmark

Fracast-0 completed all 7,413 BOOM dataset-term configurations and all
623,602 forecasts with the FP32 checkpoint and no task failures. In the
official 24-model comparison, it obtains scaled MASE `0.723`, scaled CRPS
`0.434`, and mean per-dataset rank `11.808`. The corresponding ordinal
positions are `12 / 24` by MASE and `11 / 24` by CRPS.

`Datadog/BOOM` is also part of the complete Fracast-0 pretraining recipe, so
this result is in-corpus and must not be presented as zero-shot. The official
protocol and comparison table are in the
[BOOM leaderboard](https://huggingface.co/spaces/Datadog/BOOM). The raw
per-configuration result, manifest, and comparator leaderboard are archived in
the [GitHub repository](https://github.com/ztxtech/fracast-0/tree/main/script/boom_bench).

## Scenario Highlights

These slices use per-configuration or per-task error ratios against Seasonal
Naive. Lower is better, and TIME ranks use the official 29-model table.

- **GIFT-Eval, Sales:** All four short-horizon Sales configurations improve on
  Seasonal Naive in normalized MASE and normalized MWQL. The geometric means
  are 0.693 and 0.422, and Fracast-0 leads TinyCast on both metrics in every
  configuration.
- **GIFT-Eval, Cloud operations:** Across the three hourly `bizitobs_l2c`
  short, medium, and long slices, normalized MASE is 0.430 and normalized MWQL
  is 0.353.
- **TIME, Solar forecasting:** `Australia_Solar/H` ranks 4th to 6th of 29 by
  MASE and 7th to 13th by CRPS over short, medium, and long horizons.
- **TIME, Manufacturing:** On `Smart_Manufacturing/H`, medium and long
  horizons rank 8th of 29 by MASE, while CRPS ranks range from 8th to 10th
  across all three horizons.
These are scenario slices, not separate aggregate rankings. The benchmark
disclosures above still apply.

## Files

| File | Size | SHA-256 |
|---|---:|---|
| `model.safetensors` | 344,412 B | `0d678f123f3d1f91c5065cca2b5d40eccc469360afc2381b27290486011ded2c` |
| `model.int8.safetensors` | 113,228 B | `77beb5e5f17cf77525c4c1813fdaacfba586ac0b9d6f67a7ad4355de25b05544` |
| `config.json` | 1,338 B | `1d7d2cf831f51ae2c5c9bf4cb4d8d4a49ec0085d6d55010814a1aae2a777a5dc` |
| `w8_manifest.json` | 4,944 B | `7ade15dcc72aa6d597f398c85d73333d93ee16ebb5128810110723e3f25704ee` |
| `benchmark/gift_eval/all_results.csv` | 24,537 B | `09118b804e0f20895991d9ce993bb60be8ef6f80fe5c35bb88820bbe4dc30c3b` |
| `benchmark/gift_eval/config.json` | 343 B | `94a7b09e963336c8251664830796088b36cc60ea0d017b52ae89562523f8da8e` |
| `benchmark/gift_eval/protocol_summary.csv` | 172 B | `71722d8473999f3fe2edf66272725e06e757973fd18c86a0cb1818327f73a57d` |
| `benchmark/gift_eval/run-manifest.json` | 2,174 B | `5c4328710b4fa0b03821fcbfd79174408ee5bd405a98af407aa6d548f7379abd` |
| `benchmark/fev_bench/fracast-0.csv` | 68,587 B | `9dda82627d03966a279b4118a140d3b293c495c508c1037e05b536326e193ab2` |
| `benchmark/fev_bench/fracast_ranks.csv` | 743 B | `272a3270e4074f50ac40aea7fdc4d28664bed83bf99aa8e807964e2f4b9c9487` |
| `benchmark/fev_bench/run-manifest.json` | 3,460 B | `5281dc1ff441732f6390254a495c00145d4d9b0a1ca1b6ab59196e5a42030176` |
| `benchmark/time_benchmark/Fracast-0_TIME_tasks.csv` | 8,491 B | `1b493d95de44df4bda87f82e0dbb7707a7fbf8b1ca7c57f762769367b5fea31e` |
| `benchmark/time_benchmark/TIME_horizon_leaderboard.csv` | 6,522 B | `13faabfcb15acbc53a3d548efa9ab35c5a3338bfaedee10a814d0fc85970b1ff` |
| `benchmark/time_benchmark/TIME_overall_leaderboard.csv` | 1,561 B | `778fd266be0639b042ae9d6ebe9019479f60d6dcee79f1b68ada8a3e72d809ee` |
| `benchmark/time_benchmark/TIME_pareto.csv` | 2,885 B | `8c33c9f3fc0bc592103653d40f10fdd79600eb83b7b563cdff049660b875b44e` |
| `benchmark/time_benchmark/TIME_pareto_summary.json` | 2,831 B | `f3b91a0641149683056526db2b0d1b366bfaf554e6c1ea701a2d687681426afb` |
| `benchmark/time_benchmark/run-manifest.json` | 3,457 B | `fad7d60261f41193aeb34233735185de76104770a0c2907909eb306c2255b1d5` |
| `benchmark/boom_bench/all_results.csv` | 2,025,022 B | `bc303c1ec2501938193b580b218de324009db997be1c46b4727676e281efc2f6` |
| `benchmark/boom_bench/run-manifest.json` | 1,442 B | `385d44d779021eaf3bd8103259599ab1028bddb2361d1fc27e9fa917aa793128` |
| `benchmark/boom_bench/leaderboard.csv` | 1,335 B | `6156f9d10fa76bfcbd006fec85c2f41cd6198151c3ca22871cae744187175958` |

## Training Data

Fracast-0 was trained on five pinned public datasets plus the four official
TinyCast synthetic shards. The five source datasets are immutable snapshots in
`script/data/download_public_data.py`:

| Key | Hugging Face dataset | Pinned revision | Approx. size |
|---|---|---|---:|
| `pretrain` | [`Salesforce/GiftEvalPretrain`](https://huggingface.co/datasets/Salesforce/GiftEvalPretrain) | `6830b624de7ed2b3d3e5b85bb6959d81dcc5d874` | 908.1 GiB |
| `lotsa` | [`Salesforce/lotsa_data`](https://huggingface.co/datasets/Salesforce/lotsa_data) | `8191fd29eb5cf906ec55effca44d8059888b615d` | 861.2 GiB |
| `chronos` | [`autogluon/chronos_datasets`](https://huggingface.co/datasets/autogluon/chronos_datasets) | `eeecad0b82a8c237e212ce6f8d1abecb513e2cec` | 833.3 GiB |
| `boom` | [`Datadog/BOOM`](https://huggingface.co/datasets/Datadog/BOOM) | `69325b544c45ff0d6c43c7a99c49a6601a01725b` | 2.6 GiB |
| `fev` | [`autogluon/fev_datasets`](https://huggingface.co/datasets/autogluon/fev_datasets) | `f71c0fff4cf81283a2c43e7f3a73aa4f9826aef8` | 0.6 GiB |

The five sources total about 2.6 TiB before conversion. They are converted
independently into the fast-corpus layout; the TinyCast synthetic shards are
built from the official four-shard recipe and converted into the same layout.

The corpus scan covered 69,614,455 series and about 549.85 billion points across 3,234 datasets; the training split used 62,653,010 series. The checkpoint is from step 45,776 with an effective batch of 4,096 windows, approximately 187.5 million training windows.

Because several corpus roots can overlap GIFT-Eval families, results are labeled **pretrained**, not zero-shot.

## Limitations

- Fracast-0 is univariate and channel-independent; it does not model cross-variable dependence.
- The native head predicts 48 steps at a time. Longer horizons append median
  predictions and re-normalize each 2,048-point context before the next block.
- The GIFT-Eval result is labeled `pretrained` with test-data leakage because
  the pretraining recipe includes GIFT-Eval-family datasets.
- The FEV-Bench pretraining corpus overlaps every benchmark dataset, so its
  official leakage-controlled result is not an independent zero-shot score.
- 47 of 98 TIME tasks use median-quantile rollout beyond the native
  48-step head; the compact scores come from the archived raw outputs and the
  official 29-model table, with no separate recomputation recorded for them.
- The W8 export is not an integer-only kernel.
- This release is distributed under the Apache-2.0 license.

## Acknowledgements

Fracast-0 depends on the teams behind the benchmark, compact baseline, and
public pretraining corpora:

- [GIFT-Eval](https://github.com/SalesforceAIResearch/gift-eval) provides the
  97-configuration evaluation protocol used for the public result.
- [FEV-Bench](https://github.com/autogluon/fev) provides the 100-dataset
  evaluation protocol and leaderboard submission format.
- [TIME](https://github.com/zqiao11/TIME) provides the 98-task evaluation
  workflow, output format, and leaderboard submission protocol.
- [TinyCast](https://github.com/raws-labs/tinycast) provides the compact design
  baseline and the Apache-2.0 components recorded in the source repository.
- [Salesforce/GiftEvalPretrain](https://huggingface.co/datasets/Salesforce/GiftEvalPretrain),
  [Salesforce/lotsa_data](https://huggingface.co/datasets/Salesforce/lotsa_data),
  [autogluon/chronos_datasets](https://huggingface.co/datasets/autogluon/chronos_datasets),
  [Datadog/BOOM](https://huggingface.co/datasets/Datadog/BOOM), and
  [autogluon/fev_datasets](https://huggingface.co/datasets/autogluon/fev_datasets)
  provide the public training data.
- The TinyCast team also publishes the synthetic pretraining shards used by the
  recipe.

## Development support

The implementation, debugging, and release work used paid API access to
**Xiaomi MiMo 2.6 Pro** and **DeepSeek V4.1 Flash**. Both were effective for
this project and are recommended.

## Supporters / sponsors

There are no sponsors yet. Continued maintenance still needs API credits and
server resources. Feedback and support are welcome through:

- [zhantianxianguestc@hotmail.com](mailto:zhantianxianguestc@hotmail.com)

## Citation

```bibtex
@article{zhan2026fracast0fractalweightsharing,
  title={Fracast-0: Fractal Weight Sharing for a Time Series Foundation Model with Only 85K Parameters},
  author={Tianxiang Zhan and Huanyao Zhang and Yuanpeng He},
  year={2026},
  journal={arXiv preprint arXiv:2609.32209},
  eprint={2609.32209},
  archivePrefix={arXiv},
  primaryClass={cs.AI},
  doi={10.48550/arXiv.2609.32209},
  url={https://arxiv.org/abs/2609.32209}
}
```