SPARC | Structured Motion Uncertainty

Structure, scale, calibration.

Illustration, not live inference

SPARC schematic. Structured covariance models related motion errors. Analytic feature-dependent scaling preserves correlations in the scalar conjugate core. Held-out calibration supplies marginal prediction intervals under exchangeable scores. — Scalar conjugate core. The full deployment recipe adds temporal stabilization and CP-specific joint scaling.

One network forward pass + analytic calculations. No repeated stochastic inference loop.

Keep the forecast

Start with a trained deterministic motion predictor. Retain its mean forecast and fit a structured covariance to the residuals.

Adapt the scale

The Bayesian last-layer factor κ_t(x) depends on training-feature leverage. It rescales uncertainty, but is not a universal OOD detector.

Calibrate separately

Use held-out scores to calibrate marginal intervals. Feature statistics and network parameters stay fixed during this step.

Reported results

Nine dataset/protocol blocks. Mean ranks, lower is better. Point accuracy is competitive, not uniformly best.

SPARC mean ranks from the paper
Metric	Mean rank
NLL	1.00
MPJPE + NLL	2.69
Calibrated interval width W95(CP)	2.50
MPJPE	4.39

What the guarantee does not say

Validity is marginal for the induced score distribution under exchangeability. Coordinate pooling targets the reported mean marginal coverage metric. This is not simultaneous coverage of an entire trajectory, a guarantee under arbitrary distribution shift, or evidence of safe robot deployment.

This Space contains explanatory media only. It does not run a checkpoint, accept motion uploads or generate new predictions.

Cite SPARC

@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}
}