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

arXiv: https://arxiv.org/abs/2608.20802 · HTML: https://mlsanity.com/paper/2608.20802/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 65 references that are in the map.
- First posted on arXiv 21 Aug 2026.

## Builds on (most cited first, 30 of 37)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift](https://mlsanity.com/paper/1906.02530/) (2019)
- [AMASS: Archive of Motion Capture as Surface Shapes](https://mlsanity.com/paper/1904.03278/) (2019)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [On human motion prediction using recurrent neural networks](https://mlsanity.com/paper/1705.02445/) (2017)
- [Robust Motion In-betweening](https://mlsanity.com/paper/2102.04942/) (2021)
- [DLow: Diversifying Latent Flows for Diverse Human Motion Prediction](https://mlsanity.com/paper/2003.08386/) (2020)
- [Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling](https://mlsanity.com/paper/1802.09127/) (2018)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [MSR-GCN: Multi-Scale Residual Graph Convolution Networks for Human Motion Prediction](https://mlsanity.com/paper/2108.07152/) (2021)
- [Back to MLP: A Simple Baseline for Human Motion Prediction](https://mlsanity.com/paper/2207.01567/) (2022)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [BeLFusion: Latent Diffusion for Behavior-Driven Human Motion Prediction](https://mlsanity.com/paper/2211.14304/) (2022)
- [HumanMAC: Masked Motion Completion for Human Motion Prediction](https://mlsanity.com/paper/2302.03665/) (2023)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [Generating Smooth Pose Sequences for Diverse Human Motion Prediction](https://mlsanity.com/paper/2108.08422/) (2021)
- [Conformal Bayesian Computation](https://mlsanity.com/paper/2106.06137/) (2021)
- [Conformal Prediction Bands for Multivariate Functional Data](https://mlsanity.com/paper/2106.01792/) (2021)
- [Pose Forecasting in Industrial Human-Robot Collaboration](https://mlsanity.com/paper/2208.07308/) (2022)
- [CoMusion: Towards Consistent Stochastic Human Motion Prediction via Motion Diffusion](https://mlsanity.com/paper/2305.12554/) (2023)
- [Auxiliary Tasks Benefit 3D Skeleton-based Human Motion Prediction](https://mlsanity.com/paper/2308.08942/) (2023)
- [TransFusion: A Practical and Effective Transformer-based Diffusion Model for 3D Human Motion Prediction](https://mlsanity.com/paper/2307.16106/) (2023)
- [Learning Semantic Latent Directions for Accurate and Controllable Human Motion Prediction](https://mlsanity.com/paper/2407.11494/) (2024)
- [Nonisotropic Gaussian Diffusion for Realistic 3D Human Motion Prediction](https://mlsanity.com/paper/2501.06035/) (2025)
- [Conformal Structured Prediction](https://mlsanity.com/paper/2410.06296/) (2024)

## Abstract (arXiv)

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 kappat(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 kappat(x)Sigmastr,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 kappa separates high-error cases, making the scale usable as a lightweight risk monitor.