Steps-to-Go Prediction in FSN

• Steps-to-Go Prediction is a dynamic forecasting approach that computes an optimal number of future steps based on contextual inputs to improve trajectory modeling.
• FSN employs an Adaptive Prediction Module and a Dynamic Decoder to balance overprediction and underprediction, utilizing differentiable Fréchet distance for evaluation.
• Empirical evaluations on datasets like Argoverse and INTERACTION show that FSN reduces prediction errors (ADE and FDE), proving its value in real-world autonomous and robotic applications.

Steps-to-Go Prediction refers to the methodology and algorithms for adaptively forecasting a variable number of future steps in sequential data, rather than employing a predetermined, fixed prediction horizon. This paradigm is increasingly significant in contexts such as autonomous driving, robotics, and intelligent decision-making systems, where the optimal future window for prediction may depend on dynamic environmental and contextual conditions. The FlexiSteps Network (FSN) exemplifies this concept by introducing a mechanism that computes the optimal number of future steps to predict for each instance, thus achieving improved modeling accuracy and adaptability.

1. Principles of Dynamic Step Prediction

Traditional fixed-length trajectory predictors lack the flexibility to adapt their output horizon to situational complexity and uncertainty. FSN overcomes this by integrating a pre-trained Adaptive Prediction Module (APM), which receives encoded representations of agent history, contextual features (e.g., traffic, surrounding agents, HD map data), and environmental signals. During inference, the APM evaluates these inputs and outputs an integer fᵢ, representing the optimal number of steps-to-go for the target agent. Consequently, the downstream Dynamic Decoder (DD) generates a trajectory of length fᵢ that is dynamically matched to the scenario at hand.

This design allows FSN to address the key challenge of balancing overprediction—where excessive steps dilute accuracy—and underprediction—where insufficient forecasting misses critical future dynamics.

2. Model Architecture and Operational Workflow

The FSN pipeline consists of modular components:

• Encoder (φ_enc): Encodes both historical trajectory and contextual cues for each agent, forming latent vector e₍i,k₎.
• Adaptive Prediction Module (φ_step): Trained to determine optimal step count fᵢ given encoded features:

$fᵢ = φ_{\mathrm{step}}(e_{i,k})$

• Dynamic Decoder (φ_DD): Given the adaptive step count fᵢ and latent embedding e₍i,k₎, generates predicted trajectory μ₍i,k₎^fᵢ:

$μ_{i,k}^{(fᵢ)} = φ_{DD}^{(fᵢ)}(e_{i,k}, fᵢ)$

Each decoder branch specializes on different output horizons during training, ensuring robust and accurate prediction regardless of the selected steps-to-go.

3. Scoring Mechanism and Fréchet Distance for Prediction Selection

A principal methodological advance in FSN is the scoring mechanism that evaluates candidate predictions of varying lengths. For each possible output length f, the predicted trajectory μᵢ^f is compared to ground truth gtᵢ^f using a differentiable Fréchet Distance Kernel (FDK):

$$q_i^{(f)} = \frac{\mathrm{FDK}(μ_i^{(f)}, gt_i^{(f)})}{f}$$

The Fréchet distance captures geometric similarity across the entire trajectory, considering both temporal and spatial alignment. Classical Fréchet distance formulations are non-smooth and sensitive to noise. FSN mitigates this via:

• Soft-min and smooth-min approximations to permit gradient-based optimization
• Incorporation of the Huber Loss for robustness to outliers:

$$H(z, δ) = \begin{cases} \frac{1}{2}z^2, & \text{if } |z| \leq δ \ δ(|z| - \frac{1}{2}δ), & \text{otherwise} \end{cases}$$

For each agent, FSN selects the final prediction step via:

$$f_{\mathrm{gt}}^i = \arg\min_{f \in \{5, ..., F\}} q_i^{(f)}$$

Thereby optimizing both geometric fidelity and parsimony.

4. Empirical Evaluation and Benchmarking

FSN was evaluated on Argoverse and INTERACTION datasets, encompassing diverse real-world driving scenarios. Experimental protocols involved comparing FSN against fixed-step methods (e.g., isolated training, intercepted results) and recent dynamic prediction frameworks (FLN, LaKD). Results demonstrate that FSN consistently achieves lower Average Displacement Error (ADE) and Final Displacement Error (FDE) for both short and long prediction horizons. Ablation studies confirm that the dynamic choice of step output (via APM) and the use of the Fréchet scoring mechanism are critical factors contributing to superior performance.

5. Real-World Applications

Adaptively predicting steps-to-go is pivotal for:

• Autonomous Driving: The ability to adjust prediction horizon in real time enables robust and contextually relevant trajectory forecasting, enhancing both safety and efficiency.
• Robotics: Flexible multi-step prediction facilitates obstacle avoidance and dynamic replanning in unstructured environments.
• Intelligent Decision Systems: Systems such as UAV path planning, traffic management, and dynamic resource allocation benefit from variable-horizon forecasting that is responsive to evolving conditions.

A plausible implication is that adaptive step prediction mechanisms, such as those in FSN, will become indispensable for applications requiring real-time decision-making in uncertain or rapidly changing domains.

6. Research Impact and Future Directions

FSN’s plug-and-play architecture (APM and DD) is compatible with a range of trajectory prediction models, inviting future research into further modular integration, online adaptation, and transfer learning techniques. The Fréchet Distance Kernel provides a template for robust, geometry-aware prediction scoring that balances accuracy and horizon length. Subsequent work may seek to augment this metric with additional temporal consistency constraints or hybridize with probabilistic uncertainty measures.

Editor's term: "Dynamic steps-to-go forecasting"—introduced to encapsulate frameworks like FSN that adapt output prediction length via learned context-dependent mechanisms—represents a promising research trajectory likely to influence both theoretical and applied domains in sequential forecasting (Liu et al., 25 Aug 2025).

7. Technical Summary Table

Module	Function	Output
Adaptive Prediction Module (APM)	Computes optimal number of prediction steps	$f_i$
Dynamic Decoder (DD)	Generates variable-length trajectory	$μ_{i,k}^{(f_i)}$
Scoring Mechanism (FDK)	Evaluates geometric accuracy / trade-off	$q_i^{(f)} = \text{FDK}(μ_i^{(f)}, gt_i^{(f)}) / f$

This tabular summary encapsulates FSN's major architectural elements and operational logic.

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Dynamic, context-aware steps-to-go prediction leverages latent feature representations and flexible scoring mechanisms to balance horizon selection and forecast accuracy, as validated on industry-standard datasets. FSN’s approach exemplifies the advances and practical significance of this rapidly evolving research direction.