AdaSports-Traj: Adaptive Sports Trajectory Model

• AdaSports-Traj is an adaptive multi-agent trajectory framework that addresses intra- and inter-domain discrepancies using role- and domain-aware mechanisms.
• It integrates a CVAE backbone with a Role- and Domain-Aware Adapter and hierarchical contrastive learning to effectively model heterogeneous sports data.
• Empirical evaluations on Basketball-U, Football-U, and Soccer-U demonstrate significant prediction improvements compared to traditional methods like UniTraj.

AdaSports-Traj is an adaptive framework for multi-agent trajectory modeling in sports, explicitly designed to address both intra-domain and inter-domain distributional discrepancies that arise from heterogeneous agent roles (such as players versus balls) and varying sports domains (e.g., basketball, football, soccer). By introducing a Role- and Domain-Aware Adapter in conjunction with a hierarchical contrastive learning paradigm, AdaSports-Traj achieves robust performance in both unified and cross-domain trajectory prediction scenarios, as demonstrated empirically on Basketball-U, Football-U, and Soccer-U datasets (Xu et al., 19 Sep 2025).

1. Model Architecture and Adapter Design

At its core, AdaSports-Traj employs a Conditional Variational Autoencoder (CVAE) backbone, following the unified trajectory modeling conventions of UniTraj (Xu & Fu ’25). The model processes masked multi-agent trajectories $X \in \mathbb{R}^{N \times T \times D}$ (with mask $M \in \{0, 1\}^{N \times T}$). Its encoder $q_\phi(z^{\leq T} | x^{\leq T})$ and prior $p_\theta(z^t | x^{<t}, z^{<t})$ model the latent states as Gaussian distributions, while the decoder reconstructs both visible and missing portions of input trajectories. The training maximizes the evidence lower bound (ELBO), as formalized by:

$$\mathrm{ELBO}(\theta, \phi) = \mathbb{E}_{q_\phi(z|x)} \left[ \sum_{t=1}^T \log p_\theta(x^t | z^{\leq t}, x^{<t}) - \mathrm{KL}(q_\phi(z^t | x^{\leq t}, z^{<t}) \| p_\theta(z^t | x^{<t}, z^{<t})) \right]$$

A key innovation is the Role- and Domain-Aware Adapter (RDA), which modulates the encoder’s latent features $z$ based on agent role ($r \in \{\text{Player}, \text{Ball}\}$) and sports domain ($$d \in \{\text{Basketball}, \text{Football}, \text{Soccer}\}$$):

• Embeddings: $$e_\mathrm{role} = \mathrm{Emb}_\mathrm{role}(r),\ e_\mathrm{domain} = \mathrm{Emb}_\mathrm{domain}(d)$$, both of dimension $\mathbb{R}^h$.
• Cross-Attention: Using $e_\mathrm{role} + e_\mathrm{domain}$ as query and $z$ as key/value:

$$z_\mathrm{cond} = \mathrm{CrossAttention}(e_\mathrm{role} + e_\mathrm{domain},\ z, z)$$

• Token-wise Gating: Per-token gating weight $$\alpha_\mathrm{gate} = \sigma(\mathrm{MLP}([z, z_\mathrm{cond}]))$$ determines the interpolation:

$$z_\mathrm{adapted} = \alpha_\mathrm{gate} \odot z_\mathrm{cond} + (1 - \alpha_\mathrm{gate}) \odot z$$

This lightweight, plug-and-play adapter setup requires minimal additional computational overhead and is fully differentiable, supporting end-to-end learning through the primary modeling and contrastive losses.

2. Hierarchical Contrastive Learning

AdaSports-Traj introduces a hierarchical contrastive objective to separately supervise role-sensitive and domain-aware latent representations, thereby encouraging their disentanglement.

• Projection Heads: Starting from $z_\mathrm{adapted}$, the model produces two L²-normalized projections:

$$z_\mathrm{role} = \mathrm{MLP}_\mathrm{role}(z_\mathrm{adapted}),\qquad z_\mathrm{domain} = \mathrm{MLP}_\mathrm{domain}(z_\mathrm{adapted})$$

• InfoNCE Contrastive Losses: For a given batch, role-positive pairs share the same agent type, domain-positive pairs share the same sport, and all other batch members serve as negatives:

$$\begin{align*} \mathcal{L}_\mathrm{role} &= -\frac{1}{|P_\mathrm{role}|} \sum_{(i, j) \in P_\mathrm{role}} \log \frac{\exp(\mathrm{sim}(z^i_\mathrm{role}, z^j_\mathrm{role})/\tau_c)} {\sum_{k\neq i} \exp(\mathrm{sim}(z^i_\mathrm{role}, z^k_\mathrm{role})/\tau_c)} \ \mathcal{L}_\mathrm{domain} &= -\frac{1}{|P_\mathrm{domain}|} \sum_{(i, j) \in P_\mathrm{domain}} \log \frac{\exp(\mathrm{sim}(z^i_\mathrm{domain}, z^j_\mathrm{domain})/\tau_c)} {\sum_{k\neq i} \exp(\mathrm{sim}(z^i_\mathrm{domain}, z^k_\mathrm{domain})/\tau_c)} \end{align*}$$

• Combined Hierarchical Loss:

$$\mathcal{L}_\mathrm{hier} = \mathcal{L}_\mathrm{role} + \lambda_c\,\mathcal{L}_\mathrm{domain}$$

Projecting into orthogonal subspaces eliminates optimization conflict between agent role and domain supervision. Empirical ablations confirm that variants lacking this separation (e.g., shared-feature projection) yield significantly inferior results.

3. Training Objectives and Implementation

The complete loss function of AdaSports-Traj augments the CVAE objectives with the hierarchical contrastive term and a Winner-Take-All (WTA) sampling loss to promote diversity:

• Reconstruction and Regularization:

$$\mathcal{L}_\mathrm{elbo} = \|\hat X_m - X_m\|^2 + \lambda_1\,\mathrm{KL}(\mathcal{N}(\mu_q, \mathrm{diag}(\sigma_q^2))\| \mathcal{N}(0, I))$$

$\mathcal{L}_\mathrm{rec} = \|\hat X_v - X_v\|^2$

$$\mathcal{L}_\mathrm{wta} = \min_{k\in\{1..K\}}\|\hat Y^{(k)} - Y\|^2$$

• Final Training Loss:

$$\mathcal{L} = \mathcal{L}_\mathrm{elbo} + \lambda_2\,\mathcal{L}_\mathrm{rec} + \lambda_3\,\mathcal{L}_\mathrm{wta} + \lambda_4\,\mathcal{L}_\mathrm{hier}$$

Training employs Adam (β₁=0.9, β₂=0.999), an initial learning rate of 0.001 decayed by 0.9 every 20 epochs, and batch size 128. Mixed-domain batches in unified-to-single (U2S) settings permit simultaneous domain and role contrastive supervision, while single-to-single (S2S) batches enable only role-based losses. The hardware consists of an NVIDIA A6000 GPU and PyTorch implementation.

4. Experimental Evaluation

Datasets

Experiments use three unified multi-agent trajectory datasets:

Dataset	Agents (N)	Train/Test Size
Basketball-U	11 (5+5+1)	93,490 / 11,543
Football-U	23 (22+1)	10,762 / 2,624
Soccer-U	23 (22+1)	9,882 / 2,448

Metrics

• minADE₍₂₀₎: Minimum Averaged Displacement Error over 20 samples (lower is better)
• OOB: Fraction of predicted points outside field boundaries
• Step: Mean stepwise trajectory displacement (closeness to ground truth)
• Path-L: Total agent path length
• Path-D: Net start-to-end agent displacement

Results

AdaSports-Traj consistently outperforms UniTraj across all settings. Example: In S2S, Basketball-U minADE₍₂₀₎ drops from 4.77 (UniTraj) to 4.21; similarly, unified-to-single (U2S) settings show clear improvement (Basketball-U minADE₍₂₀₎: 11.12 → 8.74). Detailed ablations reveal:

• Combining RDA and HC yields the best outcome (S2S: 4.21/3.04/91.52 versus RDA or HC alone).
• Token-wise gating in the adapter surpasses feature-wise or no gating configurations.
• Role-only and domain-only contrastive variants underperform relative to hierarchical contrastive learning.

5. Analysis, Visualization, and Limitations

t-SNE analysis of learned projections shows distinct clustering for the three sports domains in $z_\mathrm{domain}$ and clear separation between Ball and Player roles in $z_\mathrm{role}$. Qualitative rollout visualizations indicate improved plausible completion and forecast trajectories, especially under heavy observation masking, with fewer out-of-bounds outputs compared to UniTraj.

A principal limitation is that AdaSports-Traj relies on pre-defined role and domain annotations during training, which precludes unsupervised deployment across novel agent types or sports. Future research directions include unsupervised or weakly-supervised discovery of role/domain labels and extending the adapter mechanism to generative backbones beyond CVAEs, such as diffusion models, and to real-time online adaptation contexts.

6. Context and Significance

AdaSports-Traj directly addresses the structured heterogeneity and distributional shift challenges characteristic of multi-agent sports trajectory prediction. By introducing a modular and lightweight plug-in for latent space adaptation and validating the necessity of disentangled, orthogonal subspace supervision, it establishes a new methodological baseline for cross-domain, multirole trajectory forecasting. Empirical results on Basketball-U, Football-U, and Soccer-U demonstrate domain-agnostic improvements. This framework represents a substantial step toward unified, adaptable models for structured multi-agent systems in sports and potentially other domains requiring explicit role and context awareness (Xu et al., 19 Sep 2025).