README.md

---
title: SPARC
colorFrom: green
colorTo: blue
sdk: static
app_file: index.html
pinned: false
short_description: Single-pass structured motion uncertainty
tags:
  - human-motion-forecasting
  - uncertainty-quantification
  - conformal-prediction
  - bayesian-last-layer
---

# SPARC

**Single-Pass Scaling for Motion Forecasting with Conformal Bayesian Last Layers**

Sakif Hossain*, Julian Teusch*, Jörg P. Müller · TU Clausthal · ECCV 2026 Spotlight

*Equal contribution.

**Paper: https://arxiv.org/abs/2608.20802**

Project: https://julianteusch.github.io/projects/sparc/

**Code: [SPARC-UQ on GitHub](https://github.com/julianteusch/sparc-uq)**

The Apache-2.0-licensed repository provides a reusable scaling and conformal
calibration core for existing point estimators. It is an initial integration
library, not the full paper benchmark implementation or a checkpoint release.

## Python Package and Visual Notebook

**[SPARC-UQ v0.1.0](https://github.com/julianteusch/sparc-uq/releases/tag/v0.1.0)**
is an initial alpha Python package, distributed as a GitHub wheel and source
archive. PyPI publication is pending. Installation instructions are in the
[repository README](https://github.com/julianteusch/sparc-uq#install-and-run).

The **[executed notebook](https://github.com/julianteusch/sparc-uq/blob/main/notebooks/01_forecasts_and_diagnostics.ipynb)**
contains six visualizations: forecast intervals, held-out coverage and width,
feature support, covariance/correlation, signed leverage contributions, and
kappa versus prediction error. The example is synthetic, not a reproduction of
the paper's benchmark results.

Optional **[Matplotlib helpers and diagnostics](https://github.com/julianteusch/sparc-uq/blob/main/docs/visualization.md)**
can be reused with your own predictions. Feature-leverage contributions explain
the computed scale in a chosen feature basis, not causal importance or SHAP values.

## About This Space

An illustrated explanation of SPARC, not live model inference. The animations
are deterministic schematics, not experimental predictions or coverage tests.
This Space does not distribute model checkpoints or process uploaded motion data.

SPARC retains a deterministic motion forecast, adds analytic Bayesian last-layer
scaling to a graph-temporal covariance, and calibrates marginal prediction
intervals using held-out residual scores. Inference uses one network forward
pass plus analytic calculations, rather than repeated stochastic passes.

The scalar conjugate core preserves covariance correlations. The full recipe
also includes temporal stabilization and CP-specific joint scaling; see the
paper for the complete method and evaluation protocol.

## Scope

- Conformal validity is marginal for the induced score distribution under
  exchangeability, not simultaneous coverage of an entire future trajectory.
- Coordinate pooling targets the reported mean marginal coverage metric.
- The feature-dependent scale is not a universal out-of-distribution detector.
- The reported empirical risk diagnostic is not a safety guarantee.
- No claim of a generative multimodal forecast or validated robot deployment.

## Results

Across nine dataset/protocol blocks, SPARC's mean ranks are 1.00 for NLL,
2.69 for combined MPJPE + NLL, 2.50 for calibrated interval width, and 4.39 for
MPJPE. Lower is better. These are ranks, not raw errors or percentage gains;
point accuracy is competitive rather than uniformly best.

## Citation

```bibtex
@misc{hossain2026sparc,
  title = {{SPARC}: Single-Pass Scaling for Motion Forecasting with Conformal Bayesian Last Layers},
  author = {Hossain, Sakif and Teusch, Julian and M{\"u}ller, J{\"o}rg P.},
  year = {2026},
  eprint = {2608.20802},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.20802}
}
```

## Files

Vanilla HTML, CSS and JavaScript; no backend, analytics, external fonts or build
step. The figures and silent MP4 animations come from the authors' SPARC
communication and presentation materials. No training data or private speaker
notes are included. The project website remains the primary resource page.