提出单次推理的运动预测不确定性估计方法，兼顾准确性与效率。
SPARC: Single-Pass Scaling for Motion Forecasting with Conformal Bayesian Last Layers
- 用确定性主干+共轭贝叶斯层，直接生成分时域的不确定性尺度
- 在9个数据集上同时优化了负对数似然与轨迹误差，且无需重复采样
- 可作轻量风险监测器，识别高错误场景，适合实际部署
人类运动预测模型日益精确快速，但可靠部署需结构化、校准且高效的不确定性估计。传统贝叶斯或集成方法常需重复随机推理，而仅靠符合校准无法提供认知不确定性或保持轨迹协方差结构。我们提出SPARC（单次自适应风险校准），一种用于运动预测的贝叶斯-符合不确定性层。确定性MLP主干预测未来均值，共轭贝叶斯末层将时域特征权重转化为解析式分时域认知尺度κ_t(x)。该尺度在不改变相关结构的前提下放大图-时序高斯协方差，结合分段符合校准，在交换性假设下实现有限样本有效的95%边际预测管。关键接口为结构化分解κ_t(x)Σ_str,t(x)，将特征空间认知不确定性注入轨迹分布，无需蒙特卡洛采样。在九个数据集-协议组合及确定性、多模态和校准基线中，SPARC在负对数似然（NLL）与综合MPJPE+NLL指标上均排名第一，同时保持竞争性点预测精度和高效校准区间。按κ排序的窗口可区分高误差情况，使尺度可用作轻量风险监控器。
原文摘要 · Abstract (English)
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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