# FoSS: Modeling Long Range Dependencies and Multimodal Uncertainty in Trajectory Prediction via Fourier State Space Integration

arXiv: https://arxiv.org/abs/2603.01284 · HTML: https://mlsanity.com/paper/2603.01284/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 34 of its 45 references that are in the map.
- First posted on arXiv 1 Mar 2026.

## Builds on (most cited first, 30 of 34)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Argoverse: 3D Tracking and Forecasting with Rich Maps](https://mlsanity.com/paper/1911.02620/) (2019)
- [Argoverse 2: Next Generation Datasets for Self-Driving Perception and Forecasting](https://mlsanity.com/paper/2301.00493/) (2023)
- [On the Parameterization and Initialization of Diagonal State Space Models](https://mlsanity.com/paper/2206.11893/) (2022)
- [Learning Lane Graph Representations for Motion Forecasting](https://mlsanity.com/paper/2007.13732/) (2020)
- [VideoMamba: State Space Model for Efficient Video Understanding](https://mlsanity.com/paper/2403.06977/) (2024)
- [DenseTNT: End-to-end Trajectory Prediction from Dense Goal Sets](https://mlsanity.com/paper/2108.09640/) (2021)
- [Wayformer: Motion Forecasting via Simple & Efficient Attention Networks](https://mlsanity.com/paper/2207.05844/) (2022)
- [MultiPath++: Efficient Information Fusion and Trajectory Aggregation for Behavior Prediction](https://mlsanity.com/paper/2111.14973/) (2021)
- [Scene Transformer: A unified architecture for predicting multiple agent trajectories](https://mlsanity.com/paper/2106.08417/) (2021)
- [MotionLM: Multi-Agent Motion Forecasting as Language Modeling](https://mlsanity.com/paper/2309.16534/) (2023)
- [GOHOME: Graph-Oriented Heatmap Output for future Motion Estimation](https://mlsanity.com/paper/2109.01827/) (2021)
- [Implicit Latent Variable Model for Scene-Consistent Motion Forecasting](https://mlsanity.com/paper/2007.12036/) (2020)
- [Multimodal Trajectory Prediction Conditioned on Lane-Graph Traversals](https://mlsanity.com/paper/2106.15004/) (2021)
- [HDGT: Heterogeneous Driving Graph Transformer for Multi-Agent Trajectory Prediction via Scene Encoding](https://mlsanity.com/paper/2205.09753/) (2022)
- [Selective Structured State-Spaces for Long-Form Video Understanding](https://mlsanity.com/paper/2303.14526/) (2023)
- [ScePT: Scene-consistent, Policy-based Trajectory Predictions for Planning](https://mlsanity.com/paper/2206.13387/) (2022)
- [GANet: Goal Area Network for Motion Forecasting](https://mlsanity.com/paper/2209.09723/) (2022)
- [View Vertically: A Hierarchical Network for Trajectory Prediction via Fourier Spectrums](https://mlsanity.com/paper/2110.07288/) (2021)
- [HPNet: Dynamic Trajectory Forecasting with Historical Prediction Attention](https://mlsanity.com/paper/2404.06351/) (2024)
- [Spectral Temporal Graph Neural Network for Trajectory Prediction](https://mlsanity.com/paper/2106.02930/) (2021)
- [Real-Time Motion Prediction via Heterogeneous Polyline Transformer with Relative Pose Encoding](https://mlsanity.com/paper/2310.12970/) (2023)
- [FourierMamba: Fourier Learning Integration with State Space Models for Image Deraining](https://mlsanity.com/paper/2405.19450/) (2024)
- [MambaLRP: Explaining Selective State Space Sequence Models](https://mlsanity.com/paper/2406.07592/) (2024)
- [Trust, but Verify: Cross-Modality Fusion for HD Map Change Detection](https://mlsanity.com/paper/2212.07312/) (2022)
- [Convolutional State Space Models for Long-Range Spatiotemporal Modeling](https://mlsanity.com/paper/2310.19694/) (2023)
- [Trajectory Mamba: Efficient Attention-Mamba Forecasting Model Based on Selective SSM](https://mlsanity.com/paper/2503.10898/) (2025)
- [DeMo: Decoupling Motion Forecasting into Directional Intentions and Dynamic States](https://mlsanity.com/paper/2410.05982/) (2024)
- [Multi-Head State Space Model for Speech Recognition](https://mlsanity.com/paper/2305.12498/) (2023)
- [What Do You See in Vehicle? Comprehensive Vision Solution for In-Vehicle Gaze Estimation](https://mlsanity.com/paper/2403.15664/) (2024)

## Abstract (arXiv)

Accurate trajectory prediction is vital for safe autonomous driving, yet existing approaches struggle to balance modeling power and computational efficiency. Attention-based architectures incur quadratic complexity with increasing agents, while recurrent models struggle to capture long-range dependencies and fine-grained local dynamics. Building upon this, we present FoSS, a dual-branch framework that unifies frequency-domain reasoning with linear-time sequence modeling. The frequency-domain branch performs a discrete Fourier transform to decompose trajectories into amplitude components encoding global intent and phase components capturing local variations, followed by a progressive helix reordering module that preserves spectral order; two selective state-space submodules, Coarse2Fine-SSM and SpecEvolve-SSM, refine spectral features with O(N) complexity. In parallel, a time-domain dynamic selective SSM reconstructs self-attention behavior in linear time to retain long-range temporal context. A cross-attention layer fuses temporal and spectral representations, while learnable queries generate multiple candidate trajectories, and a weighted fusion head expresses motion uncertainty. Experiments on Argoverse 1 and Argoverse 2 benchmarks demonstrate that FoSS achieves state-of-the-art accuracy while reducing computation by 22.5% and parameters by over 40%. Comprehensive ablations confirm the necessity of each component.