# Social-Implicit: Rethinking Trajectory Prediction Evaluation and The Effectiveness of Implicit Maximum Likelihood Estimation

arXiv: https://arxiv.org/abs/2203.03057 · HTML: https://mlsanity.com/paper/2203.03057/

## Key facts

- Cited by 40 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 45 references that are in the map.
- First posted on arXiv 6 Mar 2022.

## Builds on (most cited first, 24 of 24)

- [Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks](https://mlsanity.com/paper/1803.10892/) (2018)
- [MultiPath: Multiple Probabilistic Anchor Trajectory Hypotheses for Behavior Prediction](https://mlsanity.com/paper/1910.05449/) (2019)
- [Learning Lane Graph Representations for Motion Forecasting](https://mlsanity.com/paper/2007.13732/) (2020)
- [AgentFormer: Agent-Aware Transformers for Socio-Temporal Multi-Agent Forecasting](https://mlsanity.com/paper/2103.14023/) (2021)
- [Social-STGCNN: A Social Spatio-Temporal Graph Convolutional Neural Network for Human Trajectory Prediction](https://mlsanity.com/paper/2002.11927/) (2020)
- [DESIRE: Distant Future Prediction in Dynamic Scenes with Interacting Agents](https://mlsanity.com/paper/1704.04394/) (2017)
- [SoPhie: An Attentive GAN for Predicting Paths Compliant to Social and Physical Constraints](https://mlsanity.com/paper/1806.01482/) (2018)
- [Multimodal Trajectory Predictions for Autonomous Driving using Deep Convolutional Networks](https://mlsanity.com/paper/1809.10732/) (2018)
- [Human Motion Trajectory Prediction: A Survey](https://mlsanity.com/paper/1905.06113/) (2019)
- [Social-BiGAT: Multimodal Trajectory Forecasting using Bicycle-GAN and Graph Attention Networks](https://mlsanity.com/paper/1907.03395/) (2019)
- [Convolutional Social Pooling for Vehicle Trajectory Prediction](https://mlsanity.com/paper/1805.06771/) (2018)
- [PRECOG: PREdiction Conditioned On Goals in Visual Multi-Agent Settings](https://mlsanity.com/paper/1905.01296/) (2019)
- [Multiple Futures Prediction](https://mlsanity.com/paper/1911.00997/) (2019)
- [From Goals, Waypoints & Paths To Long Term Human Trajectory Forecasting](https://mlsanity.com/paper/2012.01526/) (2020)
- [MotionNet: Joint Perception and Motion Prediction for Autonomous Driving Based on Bird's Eye View Maps](https://mlsanity.com/paper/2003.06754/) (2020)
- [Social Ways: Learning Multi-Modal Distributions of Pedestrian Trajectories with GANs](https://mlsanity.com/paper/1904.09507/) (2019)
- [GRIP++: Enhanced Graph-based Interaction-aware Trajectory Prediction for Autonomous Driving](https://mlsanity.com/paper/1907.07792/) (2019)
- [Social NCE: Contrastive Learning of Socially-aware Motion Representations](https://mlsanity.com/paper/2012.11717/) (2020)
- [Implicit Maximum Likelihood Estimation](https://mlsanity.com/paper/1809.09087/) (2018)
- [On Exposing the Challenging Long Tail in Future Prediction of Traffic Actors](https://mlsanity.com/paper/2103.12474/) (2021)
- [DiversityGAN: Diversity-Aware Vehicle Motion Prediction via Latent Semantic Sampling](https://mlsanity.com/paper/1911.12736/) (2019)
- [DAG-Net: Double Attentive Graph Neural Network for Trajectory Forecasting](https://mlsanity.com/paper/2005.12661/) (2020)
- [Deep Neural Network Ensembles against Deception: Ensemble Diversity, Accuracy and Robustness](https://mlsanity.com/paper/1908.11091/) (2019)
- [Robust Deep-Learning-Based Road-Prediction for Augmented Reality Navigation Systems](https://mlsanity.com/paper/1605.09533/) (2016)

## Built on by (most cited first, 30 of 40)

- [EigenTrajectory: Low-Rank Descriptors for Multi-Modal Trajectory Forecasting](https://mlsanity.com/paper/2307.09306/) (2023)
- [Fast Inference and Update of Probabilistic Density Estimation on Trajectory Prediction](https://mlsanity.com/paper/2308.08824/) (2023)
- [LG-Traj: LLM Guided Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2403.08032/) (2024)
- [Unified Spatial-Temporal Edge-Enhanced Graph Networks for Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2502.02504/) (2025)
- [Guiding Online Reinforcement Learning with Action-Free Offline Pretraining](https://mlsanity.com/paper/2301.12876/) (2023)
- [Evaluating Pedestrian Trajectory Prediction Methods with Respect to Autonomous Driving](https://mlsanity.com/paper/2308.05194/) (2023)
- [Social Motion Prediction with Cognitive Hierarchies](https://mlsanity.com/paper/2311.04726/) (2023)
- [BP-SGCN: Behavioral Pseudo-Label Informed Sparse Graph Convolution Network for Pedestrian and Heterogeneous Trajectory Prediction](https://mlsanity.com/paper/2502.14676/) (2025)
- [Vision-based Multi-future Trajectory Prediction: A Survey](https://mlsanity.com/paper/2302.10463/) (2023)
- [Best Practices for 2-Body Pose Forecasting](https://mlsanity.com/paper/2304.05758/) (2023)
- [Pedestrian Trajectory Prediction Based on Social Interactions Learning With Random Weights](https://mlsanity.com/paper/2501.07711/) (2025)
- [Risk-Aware Vehicle Trajectory Prediction Under Safety-Critical Scenarios](https://mlsanity.com/paper/2407.13480/) (2024)
- [Staged Contact-Aware Global Human Motion Forecasting](https://mlsanity.com/paper/2309.08947/) (2023)
- [MGF: Mixed Gaussian Flow for Diverse Trajectory Prediction](https://mlsanity.com/paper/2402.12238/) (2024)
- [Uncovering the human motion pattern: Pattern Memory-based Diffusion Model for Trajectory Prediction](https://mlsanity.com/paper/2401.02916/) (2024)
- [Understanding complex crowd dynamics with generative neural simulators](https://mlsanity.com/paper/2412.01491/) (2024)
- [Discovering Intrinsic Spatial-Temporal Logic Rules to Explain Human Actions](https://mlsanity.com/paper/2306.12244/) (2023)
- [Sparse Pedestrian Character Learning for Trajectory Prediction](https://mlsanity.com/paper/2311.15512/) (2023)
- [Testing autonomous vehicles and AI: perspectives and challenges from cybersecurity, transparency, robustness and fairness](https://mlsanity.com/paper/2403.14641/) (2024)
- [Context-aware Multi-task Learning for Pedestrian Intent and Trajectory Prediction](https://mlsanity.com/paper/2407.17162/) (2024)
- [Snapshot: Towards Application-centered Models for Pedestrian Trajectory Prediction in Urban Traffic Environments](https://mlsanity.com/paper/2409.01971/) (2024)
- [Recent Advances in Multi-Agent Human Trajectory Prediction: A Comprehensive Review](https://mlsanity.com/paper/2506.14831/) (2025)
- [Uncertainty-aware Probabilistic 3D Human Motion Forecasting via Invertible Networks](https://mlsanity.com/paper/2507.14694/) (2025)
- [Floating-Body Hydrodynamic Neural Networks](https://mlsanity.com/paper/2509.13783/) (2025)
- [Spatial-Temporal Conditional Random Field for Human Trajectory Prediction](https://mlsanity.com/paper/2311.18198/) (2023)
- [Hyper-STTN: Hypergraph Augmented Spatial-Temporal Transformer Network for Trajectory Prediction](https://mlsanity.com/paper/2401.06344/) (2024)
- [iMotion-LLM: Instruction-Conditioned Trajectory Generation](https://mlsanity.com/paper/2406.06211/) (2024)
- [Pedestrian motion prediction evaluation for urban autonomous driving](https://mlsanity.com/paper/2410.16864/) (2024)
- [An Analysis of Kalman Filter based Object Tracking Methods for Fast-Moving Tiny Objects](https://mlsanity.com/paper/2509.18451/) (2025)
- [Reverberation: Learning the Latencies Before Forecasting Trajectories](https://mlsanity.com/paper/2511.11164/) (2025)

## Abstract (arXiv)

Best-of-N (BoN) Average Displacement Error (ADE)/ Final Displacement Error (FDE) is the most used metric for evaluating trajectory prediction models. Yet, the BoN does not quantify the whole generated samples, resulting in an incomplete view of the model's prediction quality and performance. We propose a new metric, Average Mahalanobis Distance (AMD) to tackle this issue. AMD is a metric that quantifies how close the whole generated samples are to the ground truth. We also introduce the Average Maximum Eigenvalue (AMV) metric that quantifies the overall spread of the predictions. Our metrics are validated empirically by showing that the ADE/FDE is not sensitive to distribution shifts, giving a biased sense of accuracy, unlike the AMD/AMV metrics. We introduce the usage of Implicit Maximum Likelihood Estimation (IMLE) as a replacement for traditional generative models to train our model, Social-Implicit. IMLE training mechanism aligns with AMD/AMV objective of predicting trajectories that are close to the ground truth with a tight spread. Social-Implicit is a memory efficient deep model with only 5.8K parameters that runs in real time of about 580Hz and achieves competitive results. Interactive demo of the problem can be seen at https://www.abduallahmohamed.com/social-implicit-amdamv-adefde-demo . Code is available at https://github.com/abduallahmohamed/Social-Implicit .