Rethinking Training & Inference for Forecasting: Linking Winner-Take-All back to GMMs
Authors: Qiyuan Wu, Katie Z Luo, Bharath Hariharan, Wei-Lun Chao, Mark Campbell
Organizations: Cornell University · Stanford University · Boston University
Abstract
Trajectory forecasting for autonomous driving has advanced rapidly, yet representative models often produce uninformative posteriors over forecast modes, causing problems for mode pruning. We trace this to a modeling-training mismatch: forecasters are typically modeled as conditional Gaussian mixture models (GMMs) but trained with a winner-take-all (WTA) loss that assigns each sample to its nearest mode. We argue that this K-means-like hard assignment (one-hot), while preventing mode collapse, is the source of uninformative mode probabilities: it over-segments the trajectory space, ignores relatedness among nearby modes, and yields assignment instability under small perturbations. Guided by this lens, we introduce two post-hoc treatments: (1) test-time posterior-weighted merging that aggregates nearby candidate trajectories; and (2) a one-step expectation-maximization (EM) update that replaces hard labels with soft responsibilities, sharing probability mass across neighboring modes. Across several WTA-trained architectures, these lightweight steps produce more informative, faithfully ranked mode posteriors and strengthen final forecasts on popular displacement metrics -- without retraining. Our analysis unifies recent design choices through a GMM-vs-K-means perspective and offers principled, practical corrections that better align training objectives with inference.
Accurate trajectory forecasting of surrounding traffic participants is a core capability for autonomous driving, enabling vehicles to anticipate behavior and plan safe maneuvers. We observe that current state-of-the-art forecasting models on Argoverse 2 and the Waymo Open Motion Dataset tailor their training objectives to the different benchmark metrics. Because these metrics encourage conflicting behavior, we propose a paradigm change for trajectory forecasting: training models with metric-agnostic probabilistic objectives and treating metric optimization as a downstream task applied to the predictive distribution. Concretely, we introduce Trajectory Distribution Evaluation (TraDiE) policies, metric-specific policies that map a predictive distribution to the set of K trajectories and confidences required by trajectory forecasting metrics. We evaluate this framework by introducing DONUT-NLL, which adapts the training objective of the state-of-the-art trajectory forecasting model DONUT to directly optimize the predictive distribution. Using our policies, DONUT-NLL achieves state-of-the-art results on all metrics of the Waymo motion prediction benchmark.
Multi-agent motion prediction is essential for automated vehicles to understand the intentions of surrounding vehicles. However, previous prediction-based and anchor-based methods have limitations in mode diversity and prediction accuracy, respectively. These limitations may cause inadequate safety assessments and behavioral deviations in automated vehicles. To address this issue, a mode-world weighted regression loss is proposed to bridge the gap between these features. Specifically, this approach mitigates mode collapse while simultaneously improving world ranking and top-1 confidence. Furthermore, the proposed iterative decoder improves prediction accuracy by recurrently and segmentally generating trajectories. Experimental results show the proposed method ranks first in the Argoverse 2 multi-agent motion forecasting benchmark against other methods.
Multimodal motion forecasting is inherently under-supervised: each training scene provides only one realized future, yet multiple plausible futures exist. This sparse supervision often leads to mode collapse (redundant hypotheses and insufficient mode coverage) and unreliable confidence ranking when predicting a small set of trajectories. We propose Mode-as-Sequence, a unified decoding framework that translates an unordered mode set into an ordered mode sequence and explicitly models mode-to-mode dependency. Under this framework, we develop two complementary instantiations. ModeSeq performs recurrent mode decoding, where each mode is generated conditioned on the previously generated modes, encouraging diverse, non-redundant hypotheses with calibrated confidence ordering. To remove the mode-by-mode autoregressive bottleneck, we further propose Parallel ModeSeq, which preserves the same causal dependency using masked mode-to-mode self-attention while decoding all modes in a single forward pass, enabling efficient large-K inference and scalable joint-scene prediction. To learn representative modes and calibrated confidence under sparse labels, we introduce Early-Match-Take-All (EMTA) and its joint-scene extension MA-EMTA, together with a lightweight ranking regularizer that reduces confidence inversions. Extensive experiments on large-scale benchmarks demonstrate consistent improvements in both ranking-oriented metrics and best-of-K accuracy across datasets, horizons, and object types. In the Waymo Open Dataset challenges, ModeSeq achieves 1st place in the 2024 LiDAR-free motion prediction track, and Parallel ModeSeq achieves 1st place in the 2025 Interaction Prediction Challenge, validating the effectiveness of Mode-as-Sequence for both accuracy and efficiency.