Rethinking Training & Inference for Forecasting: Linking Winner-Take-All back to GMMs

2026-06-24

AI Summary

This work addresses the issue in trajectory prediction where Winner-Take-All (WTA) training yields uninformative posterior probabilities over modes, hindering effective mode pruning. The study identifies hard assignment in WTA as the root cause of mode oversplitting and instability, and unifies existing approaches under a Gaussian Mixture Model (GMM) framework. To rectify mode probabilities without retraining, the authors propose two lightweight post-processing strategies: test-time posterior-weighted fusion and a single-step EM-based soft responsibility update. Evaluated across multiple WTA-based architectures, these methods significantly enhance the informativeness of posterior probabilities, improve mode ranking accuracy, and boost overall prediction performance.

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.

Problem

• trajectory forecasting
• Gaussian mixture models
• winner-take-all
• mode collapse
• posterior probability

Innovation

• Winner-Take-All
• Gaussian Mixture Models
• Expectation-Maximization
• Trajectory Forecasting
• Posterior Calibration