Sequential decomposition and attribution for trajectory forecasting

December 23, 2025·
Yonghui Liu
Yonghui Liu
,
Inhi Kim
DOI
The SDA protocol: inputs are split into Past, Current, and Prior streams, combined through controlled gating, then fed to the forecasting model and evaluator to attribute each stream’s contribution.
Abstract
Trajectory forecasting is fundamental to intelligent mobility systems. A prevailing assumption is that longer historical inputs consistently help, which has motivated the design of models with extended observation windows. Yet empirical results often show diminishing returns, higher computational cost, and increased sensitivity to noise. Despite extensive architectural innovation, there is still no unified framework for systematically attributing forecasting performance to different temporal inputs. Rather than introducing a new forecasting model, we present the Sequential Decomposition and Attribution (SDA) protocol, a model-agnostic evaluation paradigm that decomposes inputs into Past (historical trajectory), Current (present state), and Prior (i.e., destination or goal, when available) and quantifies their standalone utility, marginal contributions, and interactions through controlled input gating. Instantiated on trajectory forecasting on two real-world datasets (Porto taxi and ETH pedestrian) with two representative backbones (LSTM and Transformer), SDA shows that accuracy gains from history saturate with short sequences, the most recent state alone is highly informative at short horizons, and reliable priors yield substantial improvements with greater value at longer horizons. Interaction analyses further reveal conditional complementarity among sources. These findings highlight the importance of input-aware designs that prioritize efficient use of the latest state and goal-conditioning over indiscriminate history accumulation. While demonstrated on trajectories, SDA offers a general lens for sequential information attribution.
Type
Publication
Knowledge-Based Systems
publications

Trajectory forecasting models keep getting longer input windows on the assumption that more history means better predictions. In practice that assumption often breaks down: accuracy gains taper off quickly, extra history adds compute cost, and longer windows pull in more noise. SDA is not another forecasting model — it is an evaluation protocol for measuring why a model performs the way it does.

SDA splits any trajectory forecasting input into three interpretable streams and gates them on/off in controlled combinations to measure each one’s standalone value, its marginal contribution on top of the others, and how the streams interact:

  • Past — the historical trajectory before the current step
  • Current — the most recent observed state
  • Prior — an optional destination or goal, when available

Running this protocol on two real-world datasets (Porto taxi, ETH pedestrian) with both an LSTM and a Transformer backbone gives a consistent picture:

History-length ablation on the Porto taxi dataset: absolute error (ADE, left) and improvement over the no-history baseline (Δ%, right) for LSTM (top) and Transformer (bottom) backbones, across prediction horizons H. Accuracy gains saturate around L*≈6 (LSTM) and L*≈8 (Transformer) — feeding in more history beyond that yields almost no further improvement.
Accuracy sensitivity to history length L, across horizons H and both backbones.

  • Accuracy gains from history saturate after a short window (L*≈6–8 steps) regardless of backbone or prediction horizon.
  • The Current state alone is already highly informative at short horizons.
  • A reliable Prior (goal/destination) gives a bigger boost than piling on more history, especially at longer horizons.
  • Past, Current, and Prior show conditional complementarity — their combined value is not simply additive.

The takeaway for model design: prioritize making good use of the latest state and any available goal information, rather than defaulting to ever-longer observation windows.

Trajectory Modeling Spatiotemporal AI Intelligent Transportation Systems
Yonghui Liu
Authors
Yonghui Liu
PhD candidate
My research spans spatiotemporal AI, generative modeling, and representation learning. My published work covers trajectory reconstruction, motion prediction analysis, and road-network representations. I am currently developing research systems for controllable traffic simulation and adaptive sensing, with applications in autonomous driving and urban mobility.