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

• URL: http://arxiv.org/abs/2608.20802v1
• Date: Fri, 21 Aug 2026 07:20:22 GMT
• Title: SPARC: Single-Pass Scaling for Motion Forecasting with Conformal Bayesian Last Layers
• Abstract summary: Single-Pass Adaptive Risk is a structured, calibrated, and efficient uncertainty estimate for human motion forecasters.<n>A deterministic backbone predicts the future mean, and a conjugate Bayesian last layer converts time-domain feature leverage into an analytic horizon-wise scale.<n>It ranks first on NLL and on the combined MPJPE+NLL criterion while retaining competitive point accuracy and efficient calibrated tubes.
• Score: 1.4452289368758382
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Human motion forecasters are increasingly accurate and fast, but reliable deployment requires uncertainty estimates that are structured, calibrated, and efficient. Bayesian and ensemble-based uncertainty estimates often require repeated stochastic inference [15, 26], while conformal calibration alone does not provide an epistemic signal or preserve trajectory covariance structure [14, 50]. We introduce SPARC (Single-Pass Adaptive Risk Calibration), a Bayesian-conformal uncertainty layer for motion forecasting. A deterministic MLP backbone predicts the future mean, and a conjugate Bayesian last layer converts time-domain feature leverage into an analytic horizon-wise epistemic scale $κ_t(x)$. This scale inflates a graph-temporal Gaussian covariance without changing its correlation structure, and split conformal calibration produces 95% marginal prediction tubes with finite-sample validity under exchangeability. The key interface is the structured factorization $κ_t(x)Σ_{\mathrm{str},t}(x)$, which injects feature-space epistemic uncertainty into trajectory densities without Monte Carlo sampling. Across nine dataset-protocol blocks and deterministic, multimodal, and calibration baselines, SPARC ranks first on NLL and on the combined MPJPE+NLL criterion while retaining competitive point accuracy and efficient calibrated tubes. Ranking windows by $κ$ separates high-error cases, making the scale usable as a lightweight risk monitor.

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