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Socialality Anchors: Towards Group-bounded Trajectory Prediction

Ziqian Zou, Conghao Wong, Qinmu Peng, Xinge You

arXiv:2609.36852v1cs.CV

TL;DR

Trajectory prediction needs to account for group affiliations, but existing grouping approaches may use fixed rules and miss agent-specific, context-adaptive, temporally coherent boundaries. Socialality learns grouping cues from past observations and short-term previews, and the authors report consistent benchmark gains alongside interpretable, stable anchor patterns.

  • Problem

    Existing group modeling may rely on fixed thresholds and observed relative positions, leaving agent-specific, context-adaptive, temporally coherent grouping rules unaddressed.

    Source: §1 · pp. 2, 4

  • Method

    Socialality learns distance- and speed-based anchors from historical observations and short-term trajectory previews, then uses group priors in group-wise perception.

    Source: §1 · pp. 4–5

  • Results

    The authors report consistent improvements over strong baselines and coherent, scene-consistent anchor structures aligned with recognizable motion modes.

    Source: §5 · p. 40

  • Takeaways & Limitations

    Qualitative analyses and anchor-distribution studies support the interpretability and stability of the learned socialality anchors.

    Source: §5 · p. 40

    The authors note that group priors may be less evident in vehicle-dominated scenes, limiting potential generalization to vehicle trajectory prediction datasets.

    Source: §5 · p. 40

Abstract

from arXiv · show

Trajectory prediction is a key component for understanding human behavior patterns in dynamic scenes. Researchers have devoted substantial efforts to modeling social interactions, especially group-wise interactions, since group membership often reflects shared intention, coordinated motion, and stable mutual adaptation, thus providing a persistent and semantically meaningful social prior for forecasting. However, existing group modeling methods may rely on a fixed threshold and infer groups mainly from agents' relative positions within the observation window, overlooking the fact that grouping rules should be agent-specific, temporally coherent, and context-adaptive across diverse personalities, culturalities, and evolving interaction contexts. Inspired by human social perception that alternates between interpersonal distance in boundary-sensitive situations and relative speed consistency in dynamic interactions, we propose Socialality, a human-inspired trajectory prediction framework with interpretable Socialality anchors and an extended grouping window for stable, context-aware grouping inference. Concretely, Socialality introduces a duo-scalar-controlled grouping kernel Socialality that jointly leverages historical observations and short-term future trajectory previews to learn agent-specific grouping rules, and employs a group-wise perception mechanism to model in-group and out-of-group interactions in an intuitive and explainable manner. Furthermore, we conduct extensive experiments on standard benchmarks to demonstrate the performance gains of Socialality, and provide qualitative analyses and statistical studies of anchor distributions to verify the interpretability and stability of the proposed Socialality anchors.

1 Introduction

Crowded-scene prediction benefits from explicit group affiliations, but existing approaches often miss the agent-specific, context-adaptive, and temporally coherent nature of social boundaries. Socialality learns these boundaries from behavioral cues to provide group priors for trajectory prediction.

1 Introduction

  • Group affiliation provides an interaction prior, yet many methods flatten distinctions between in-group companions and pedestrians from other groups.Group members may jointly adjust speed and direction around obstacles; social boundaries specify which neighbors count as group members.Source: §1 · pp. 2–3
  • Social boundaries should be agent-specific, context-adaptive, and temporally coherent across observation and anticipation.Boundaries can vary with agent preferences and interaction context, and should reflect continuous motion rather than isolated observations.Source: §1 · pp. 3–4
  • Graph-based methods may encode group structure implicitly, while explicit grouping methods can rely on subjective annotations or fixed thresholds.GPCC uses a manually set rule and historical motion cues, overlooking agent-specific boundaries and short-term future tendencies.Source: §1 · pp. 3–4
  • Socialality anchors learn which distance and speed cues explain each agent’s group affiliation, using observations and short-term trajectory previews.The extended grouping window adds anticipation to the original observation-only kernel to capture motion tendency over time.Source: §1 · pp. 4–5
  • The model combines an anchors-controlled grouping kernel with group-wise perception, and evaluates performance and anchor interpretability on standard benchmarks.The authors also analyze anchor distributions to assess their interpretability and stability.Source: §1 · p. 5

2 Related Works

Prior trajectory-prediction work spans learned interaction models and group-aware approaches, but group boundaries are often implicit or unstable. Socialality builds on human-inspired perception with explicit, learnable social boundaries for group-aware reasoning.

2.1 Trajectory Prediction and Social Interactions

  • RNNs and LSTMs modeled temporal dependencies and social context, while graph and Transformer methods enable flexible interaction aggregation.Social-LSTM introduced social pooling; later work explored interpretable interaction cues, including angle-based representations, numeric tokens, and spectrum-level co-vibration.Source: §2.1 · p. 6

2.2 Group Modeling Methods in Trajectory Prediction

  • Graph-based group methods infer collective relations through proximity or latent dependencies, but can leave group boundaries implicit and unstable over time.Local observations and instantaneous interaction graphs may make inferred structures sensitive to short-term motion fluctuations.Source: §2.2 · pp. 6–7

2.3 Human-inspired Methods in Trajectory Prediction

  • Human-inspired prediction uses selective perception and visual attention, while explicit, temporally coherent social boundaries remain an open modeling need.Socialality adds learnable anchors to GPCC’s perception mechanism to capture diverse grouping preferences and establish group-bounded priors.Source: §2.3 · pp. 7–8

3 Method

The method develops Socialality for trajectory prediction by replacing fixed-distance grouping with an extended-window, agent-specific kernel and group-wise perception, then fusing social and self representations. It uses a Transformer with MSN’s multi-style trajectory generation module and is trained end to end with a weighted sum of basic ℓ2 and preview losses.

3.1 Problem Formulation

  • The method formulates prediction as forecasting each agent’s future trajectory from the observed trajectories of all considered agents.The trajectories are uniformly sampled at fixed temporal intervals.Source: §3.1 · pp. 8–9

3.2.1 The Long-Term Distance Kernel

  • The original long-term distance kernel assigns group membership using a fixed threshold on summed distances across the observation window, treating consistently close pedestrians as socially affiliated.The distance summation provides lightweight grouping and reduces sensitivity to isolated interaction periods such as temporary collision avoidance.Source: §3.2.1 · p. 10

3.2.2 The Socialality Kernel

  • Two learnable socialality anchors adapt grouping to each target agent: one controls acceptable social distance and the other speed mismatch over an extended grouping window.Short-term trajectory previews supply temporal cues around the current time; the preview network is trained using trajectories from the observation window, without adding supervision to subsequent modeling.Source: §3.2.2 · pp. 11–13

3.3 Perception Mechanism

  • The perception mechanism encodes in-group and out-of-group interactions differently, combining self and group trajectory representations with region-aware cues for surrounding agents.It organizes out-of-group neighbors by field-of-view region and weakens directional and velocity cues for agents behind the target, retaining distance cues.Source: §3.3 · pp. 13, 15, 16

3.4 The Socialality Trajectory Prediction Model

  • Three learnable coefficients derived from the socialality anchors rescale representations before concatenation, replacing GPCC ’s simple concatenation of social and self cues.The paper motivates this change by noting that equal contributions may bias optimization toward a dominant representation.Source: §3.4 · p. 16
  • A Transformer encodes the final representation and decodes with the target agent’s linearly fitted trajectory before MSN’s generation module produces future trajectories.The decoder attends to the encoder outputs, and the generation module receives the resulting feature embedding.Source: §3.4 · p. 16

3.5 Training

  • Socialality is trained end to end, including the short-term future prediction network, using a weighted sum of basic ℓ2 loss Lo and preview loss Lp.The basic ℓ2 loss is described as similar to that of the original GPCC Model.Source: §3.5 · p. 17

4 Experiments

The experiments evaluate Socialality on ETH-UCY and SDD, use ablations and interventions to examine its grouping and preview components and how grouping priors shape predictions, and qualitatively assess trajectories and group assignments. They also analyze learned anchors as agent-specific, behaviorally meaningful grouping preferences, including their low-dimensional structure, recurrence across independent training runs, and polar organization.

4.1.1 Datasets

  • ETH-UCY uses leave-one-out evaluation, while SDD videos are split 60%/20%/20% into training, validation, and test sets; both use 8 observed and 12 predicted steps at 0.4-second intervals.Both datasets use four history and four future steps for the short-term prediction subnetwork.Source: §4.1.1 · p. 17

4.1.2 Metrics

  • Performance is evaluated using best-of-20 minimum ADE/FDE, averaged over agents; ETH-UCY reports meters and SDD reports pixels, with lower values indicating better predictions.The metric notation is minADEKf/minFDEKf, with Kf usually set to 20.Source: §4.1.2 · pp. 17–18, §4.2 · p. 19

4.2 Comparisons to State-of-the-Art Methods

  • On SDD, Socialality achieves 6.28/10.12 ADE/FDE, versus 6.39/10.17 for GPCC, and reduces ADE by over 34% versus GroupNet+PECNet and 40% versus GP-Graph-STGCNN.On ETH-UCY, it reduces average ADE by approximately 41% versus GP-Graph-STGCNN and GP-Graph-PECNet; it also outperforms LGTRAJ and EigenTrajectory+HighGraph. The GPCC backbone is unchanged; the static distance kernel is replaced by the Socialality kernel.Source: Table 2 · p. 18, §4.2 · pp. 18–19, Table 3 · p. 19

4.1.3 Implementation Details

  • Training uses an NVIDIA GeForce RTX 3090, Adam with learning rate 0.0002, batch size 1000, and up to 200 epochs.Most subnetworks use dimension 32; preview-loss ratio β=0.4 and perception FOV is 180°.Source: §4.1.3 · p. 18

4.3 Ablation Analyses

  • On eth, grouping variations a2 and a0 improve ADE/FDE by 50.2%/63.6% over ungrouped a1, while a0 gains up to 40% ADE across datasets.Against the long-term-distance-kernel variation a2, full Socialality gains up to 4.1% ADE on eth and 4.5% FDE on univ. These variants share the same backbone and network capacity.Source: §4.3 · p. 20
  • The full model performs best or near-best on almost all subsets; reviews and previews improve over a current-only window, and combining them with current-time cues performs best overall.On hotel, full-model ADE/FDE changes from 0.115/0.180 in a1 to 0.102/0.156; on univ it changes from 0.248/0.460 in current-only a6 to 0.240/0.428. Preview-only a8 also slightly outperforms reviews-plus-current a7 on most subsets, suggesting grouping evidence can be direction-sensitive.Source: §4.3 · pp. 21–22
  • On hotel, preview-loss weight β=0.2 is not reported as best overall, while β=0.6 is best on eth and β=0.2 is best on univ; simple preview predictors remain competitive.Without preview supervision (β=0), univ ADE/FDE is 3.3%/2.8% worse than a0; β=1.0 worsens hotel ADE/FDE by 7.8%/9.6%. Linear prediction on eth gives 0.236/0.372, 1.3%/0.8% worse than full Socialality; MLP is 1.7%/1.1% worse. The network’s purpose is to provide preview cues, not depend on a specific architecture.Source: §4.3 · pp. 23–24

4.4.1 Overall Model Predictions

  • Qualitative examples show more plausible, scene-consistent predictions than GPCC, including greater stability for weak-motion agents and more varied SDD trajectory modes.Grouping visualizations show Socialality can include group members missed by a static threshold, including in larger V-shaped groups, while excluding a nearby passerby; manual-neighbor interventions vary relative position and motion to examine group assignment under controlled contexts.Source: §4.4.1 · p. 25, Figure 5 · p. 25, §4.4.2 · pp. 26–27

4.4.2 Discussions of Groupings

  • Socialality adapts group membership to local context, rejecting brief passers and including sustained co-walkers while allowing agents to join, leave, or remain outside groups.Unlike GPCC’s fixed proximity criterion, Socialality also accounts for motion consistency and target speed, including tighter distance preferences for slower pedestrians.Source: §4.4.2 · p. 28
  • The learned grouping strategy a0 performs best on all five subsets; rg=0 is worse by about 7.4% and 8.0%, while rg=1 worsens average ADE/FDE by 24.1% and 25.8% versus a0.The rg=1 setting also worsens average ADE/FDE by 15.5% and 16.6% versus rg=0, indicating that forcing every neighbor into one group is especially harmful.Source: §4.4.2 · p. 29, Table 8 · p. 29
  • Conditioned predictions vary with grouping priors: removing group members can concentrate or diversify predictions, while forcing a group member can create a new trajectory branch.For an originally solitary target, rg=0 leaves predictions nearly unchanged, but rg=1 creates a branch toward the forcibly assigned neighbor.Source: Figure 8 · p. 30, §4.4.2 · p. 31
  • Combining historical observations with short-term future previews recovers stable groups that retention-only or protention-only windows miss, supporting temporally coherent membership.Mixed windows recover both a two-agent pair and all members of a five-agent V-shaped group; past proximity alone can miss members, while predictions alone are unstable.Source: §4.4.2 · pp. 31–32, Figure 9 · p. 32

4.4.3 Discussions of Socialality Anchors

  • Socialality anchors encode agent-specific grouping preferences rather than group labels: same-group agents tend to have nearby anchors, but nearby anchors do not guarantee shared membership.Manual-neighbor examples further show anchor distance reflecting similarity in grouping preferences, with sustained companions closer to the target than unrelated neighbors.Source: §4.4.3 · pp. 33–34
  • Anchor distributions form dataset- and scene-dependent wings, with richer multi-wing patterns indicating more varied grouping and interaction styles.ETH-UCY scenes tend toward one or two dominant wings, whereas SDD examples show richer structures; the two anchors jointly regulate distance tolerance and speed flexibility.Source: §4.4.3 · pp. 34–35, Figure 11 · p. 35
  • Anchor regions correspond to distinct motion behaviors, and their distribution lies near a low-dimensional manifold in R2 rather than requiring additional anchors.The zara1 V-shape separates left-moving, right-moving, and near-stationary targets, with speed-related ordering within wings; correlation results are bounded away from 0 and 1.Source: §4.4.3 · pp. 35–38, Table 9 · p. 38
  • The learned anchors occupy a descriptive “1.5D” regime: angular direction concentrates while radial magnitude varies more freely, relating the representation to distance and speed.“1.5D” is descriptive, not a formal fractal or Hausdorff dimension.Source: §4.4.3 · p. 38
  • Across independent runs, anchor distributions retain dataset-specific structure despite variation in fine-grained appearance, supporting the Socialality kernel’s stability.Examples include V-like patterns on zara1, compact distributions on hotel, and bent shapes on zara2; the anchors use no explicit geometric supervision.Source: §4.4.3 · pp. 38–39, Figure 14 · p. 39
  • Learned anchors compactly represent agent-specific, context-adaptive preferences for social distance and in-group common speed.The structured anchor distributions support the interpretability of this parameterization.Source: §4.4.3 · p. 39

5 Conclusion and Limitations

Socialality extends GPCC with a kernel that uses two learnable anchors to set agent-specific, temporally coherent, context-adaptive social boundaries for grouping before interaction modeling. The conclusion reports benchmark gains and interpretable, stable anchor patterns, while noting a possible limitation for vehicle trajectory prediction.

5 Conclusion and Limitations

  • Socialality uses two learnable anchors to jointly regulate acceptable social distance and speed flexibility over an extended grouping window.The resulting group affiliations serve as priors for the subsequent interaction-perception mechanism.Source: §5 · pp. 39–40
  • The model shows consistent improvements over strong baselines, and qualitative analyses report coherent, scene-consistent anchor structures aligned with different motion modes.The authors describe these analyses as evidence of anchor interpretability, stability, and practical effectiveness.Source: §5 · p. 40
  • The two anchors correspond to distance and speed factors that may relate to human spatial social activities and inspire further behavior research.The authors frame this relationship as a possibility, not a demonstrated causal account.Source: §5 · p. 40
  • The current two-stage grouping-before-interaction design may have less evident group-prior impact in vehicle-centered scenes, limiting generalization to vehicle datasets.The authors identify a more universal human-inspired prior for complex scenes as future work.Source: §5 · p. 40

Appendix A Nomenclature Table

  • Appendix A provides a nomenclature table to help readers interpret the methodology’s key variables.The table is labeled as a nomenclature of key variables in the proposed methodology.Source: Appendix A · p. 48, Table A1 · p. 48

B.1 Ego Loss Ratio

The ego loss ratio β influences inferred group size by affecting the stability of ego predictions used in grouping. The analysis supports β = 0.4 as a trade-off across subsets, with stronger effects in interaction-heavy scenes.

B.1 Ego Loss Ratio

  • At low β, weak supervision leaves ego predictions noisy, encouraging conservative and inconsistent membership decisions that hinder larger coherent groups.Agent-specific ego rehearsals serve as short-term previews for temporary extension.Source: §B.1 · pp. 49–50
  • Around β = 0.4, stabilized ego predictions support more confident and consistent group expansion; larger ratios can sharply shrink inferred groups on univ.The average number of group members is plotted against β for each scene.Source: Figure B1 · p. 49, §B.1 · p. 50
  • Subsets differ in sensitivity: zara1 and univ peak near 0.4, while hotel, zara2, and hyang0 vary more mildly.The authors characterize β = 0.4 as a trade-off that supports interactive scenes without noticeable degradation on weaker-interaction subsets.Source: §B.1 · p. 50

B.2 Short-term Prediction Intervention

Short-term prediction interventions test how altered neighbor previews affect grouping and final prediction performance. The appendix also describes an adaptive-FOV variant that adds a learned field-of-view angle to the model.

B.2 Short-term Prediction Intervention

  • The interventions perturb forecasted neighbor previews with Gaussian noise, trajectory swapping, or trajectory flipping before combining them with observed reviews for the Socialality kernel.The intervention parameters control noise magnitude or the proportion of neighbors whose previews are exchanged or mirrored.Source: §B.2 · pp. 50–51
  • Intervention examples show noisy previews fluctuating and swapping reducing in-group members, with complete swapping reducing them to zero.The figure presents examples for different intervention parameters and methods.Source: §B.2 · p. 51, Figure B2 · p. 52
  • Swapping 20% of neighbors’ previews (r_s = 0.2) lowers group consistency to 41.61%, while σ = 0.1 noise yields 0.43%/0.06% ADE/FDE degradation.Structural swapping and flipping cause larger performance drops than noise injection; swapping or flipping all previews can produce drops approaching 50%.Source: Table B2 · p. 52, §B.2 · p. 53

C.1 The Adaptive FOV Variant

  • The adaptive-FOV variant uses a lightweight embedding network to encode surrounding players’ relative directions as a normalized FOV angle.The appendix describes evaluation on ETH-UCY, SDD, and NBA datasets.Source: §C.1 · pp. 53–54

C.2 Evaluation with NBA Dataset

On NBA, the evaluated methods show promising results against state-of-the-art methods, and Socialality+team achieves the best performance. The adaptive-FOV variant also outperforms vanilla Socialality on NBA, while its effects on pedestrian benchmarks are marginal or mixed.

C.2 Evaluation with NBA Dataset

  • On ETH-UCY and SDD, adaptive FOV brings only marginal or mixed changes; on SDD it underperforms vanilla Socialality by 0.74%/0.69% ADE/FDE.The reported comparisons are summarized in Table C3.Source: Table C3 · p. 54, §C.2 · p. 54
  • For NBA, team ownership labels from dataset metadata define teammates as in-group and opponents and the ball as out-of-group.This operational group mask differs from street-scene grouping based on motion cues.Source: §C.2 · p. 55
  • Socialality+team achieves the best prediction performance among the four tested methods on NBA, and all four are reported as promising versus state-of-the-art methods.Table C4 reports ADE/FDE in meters using best-of-20; lower values indicate better performance.Source: Table C4 · p. 55, §C.2 · p. 55
  • On NBA, Socialality+adaptive FOV performs better than Socialality, while Socialality+team’s best result supports using group priors before interaction modeling.The authors interpret the adaptive-FOV comparison as indicating that fixed FOV limits performance on NBA.Source: §C.2 · p. 55

C.3 Distributions of FOV

Adaptive FOV angles differ across the reported datasets, with the NBA scene showing the widest average angle. The distributions indicate that Socialality adjusts perception range to scene motion without physical hard-coding.

C.3 Distributions of FOV

  • 149.5° for zara1, 230.2° for univ, and 286.9° for NBA are the reported average FOV angles.Fig. C3 visualizes FOV-angle distributions across datasets.Source: §C.3 · p. 56, Figure C3 · p. 56
  • For NBA, most FOV-angle samples fall between 280° and 295°.Source: §C.3 · p. 56
  • The authors report that perception range adapts to scene-specific motion distributions without physical hard-coding.Source: §C.3 · p. 56

D.1 Design of sa-map Variant

The sa-map variant incorporates environmental context by treating map-derived virtual agents like social agents, grouping and processing them alongside real agents. Hand-labeled segmentation maps provide the virtual-agent locations and walkability cues.

D.1 Design of sa-map Variant

  • The sa-map variant groups map-derived virtual agents as in-group or out-of-group agents and fuses their interaction features with social features for trajectory prediction.The virtual agents represent environmental constraints and are processed by the same perception mechanism as neighboring agents.Source: §D.1 · pp. 56–57
  • Segmentation maps are hand-labeled at pixel level for walkability; ETH-UCY uses two labels, while SDD grass regions receive an intermediate value.The authors describe SDD scenes as larger and environmentally more complex than ETH-UCY scenes.Source: §D.1 · p. 57
  • Segmentation-map pixel coordinates become stationary virtual-agent positions with zero velocity, and the sa-map variant adds mixed-agent trajectories to the base model's real-agent inputs.The mixed trajectories are extended through the short-term prediction network.Source: §D.1 · p. 58
  • Stride s controls virtual-agent density: s = 5 reduces a maximum 100 × 100 grid to 20 × 20 agents.Source: §D.1 · p. 58

D.2 Quantitative Analyses

The sa-map variant's results vary with virtual-agent pooling stride, and the authors report that s = 5 gives the best overall balance and outperforms base Socialality across most datasets. The variant adds 3.2% more parameters.

D.2 Quantitative Analyses

  • With s = 5, sa-map achieves the overall best balance and outperforms baseline Socialality across most datasets.The authors attribute the gain to incorporating environmental context into the grouping mechanism.Source: §D.2 · p. 59
  • The sa-map variant has 3.2% more parameters than the original Socialality.Source: §D.2 · p. 59
  • Prediction performance varies with pooling stride s, which controls virtual-agent density.The authors select s = 5 for the qualitative comparisons in Fig. D6 and Fig. D8 because it gives the best prediction performance.Source: §D.2 · p. 59

D.3 Qualitative Analyses

Qualitative analyses show that map context shapes predictions and grouping decisions, while anchor distributions also change in the sa-map variant. With s = 5, the model uses virtual agents as group priors and produces predictions that better align with environmental conditions.

D.3 Qualitative Analyses

  • The sa-map variant predicts trajectories more aligned with walkable regions and map restrictions, while base Socialality can produce more diverse distributions.The comparison also shows cases where the variants' prediction distributions are similar, suggesting environmental constraints are applied selectively.Source: §D.3 · p. 60
  • Base Socialality shows a more inclusive grouping preference than sa-map in examples where it includes approaching agents that sa-map excludes.Both models can provide the same group priors in other examples.Source: §D.3 · p. 61
  • With s = 1, sa-map can exclude virtual agents or group many of them, whereas s = 5 uses fewer virtual agents in the illustrated non-walkable-region case.The authors describe maxpooling as necessary because excessive virtual-agent density can lead to too many virtual agents being considered.Source: §D.3 · p. 62
  • Both base Socialality and sa-map with s = 5 show a distinct V-shaped anchor distribution, but sa-map's distribution is more scattered and shifted.Many sa-map anchors fall in the middle of the V shape, with large speed tolerance τb and evenly distributed distance tolerance τa.Source: §D.3 · pp. 62–63, Figure D9 · p. 62
  • The authors interpret sa-map's larger τb values as reflecting a need to include stationary virtual agents as in-group agents.They report that anchor distributions adapt to represent agents' grouping preferences.Source: §D.3 · p. 63

E.1 Definition of Higher-degree Group Members

The section defines higher-degree group members by recursively extending a target agent’s first-degree group through its members’ own groups. It then describes using these expanded sets to distinguish in-group agents by degree.

E.1 Definition of Higher-degree Group Members

  • Each first-degree group member’s own first-degree group contributes to the target’s second-degree group set.The section extends this recursive construction to third-degree and higher-degree sets.Source: §E.1 · p. 63
  • Considering up to q-degree group members means including the corresponding group sets through degree q.The section applies different interaction modeling strategies to in-group and out-of-group agents, and expands the in-group set to include higher-degree members.Source: §E.1 · pp. 63–64
  • The target itself is its zero-degree group set, while the first-degree set contains its in-group neighbors.The section illustrates the relation with a chain in which C becomes A’s second-degree member through B.Source: §E.1 · p. 63

E.2 Different Degree Group Members Feature Energy

Expanding the in-group set from first- to second-degree members increases in-group feature energy, while further expansion has marginal gains. Feature sensitivity is concentrated differently across zara1 and SDD.

E.2 Different Degree Group Members Feature Energy

  • +28.1% in #1zara1 and +32.8% in #1sdd: expanding from first- to second-degree members increases in-group feature energy across models.In #1zara1, the increase rises only from +28.1% to +29.8% when expanding to third-degree members.Source: §E.2 · pp. 64–65, Table E6 · p. 65

E.3 Different Degree Group Members Feature Sensitivity

  • In zara1, most runs allocate a major share of feature energy to first-degree members, whereas SDD assigns higher energy sensitivity to higher-degree members.Despite the increased in-group feature energy at second degree, sensitivity does not increase accordingly from first to second degree in zara1; allocation varies across scenes and distributions.Source: §E.3 · pp. 65–66, Table E7 · p. 65

Appendix F Prediction Backbone Verifications

Socialality’s group-conditioned representations perform comparably across three alternative prediction backbones on ETH-UCY. The sa-re variant exceeds the base model in ADE/FDE on eth, univ, and zara2.

Appendix F Prediction Backbone Verifications

  • Socialality obtains group priors, derives a social-interaction representation, and passes that representation to a trajectory prediction backbone.The backbone evaluation tests whether prediction performance is maintained across different interaction-modeling architectures.Source: Appendix F · p. 66
  • The variants replace MSN’s social-interaction modules with group-conditioned representations, using Transformer, E-V2-Net, or Resonance as prediction backbones.The base sa-MSN model uses MSN as its backbone; sa-tran removes MSN-related components.Source: Appendix F · p. 66
  • sa-re outperforms the base model in ADE/FDE on eth, univ, and zara2, while all three variants perform comparably to base Socialality on ETH-UCY.sa-tran remains competitive on zara1 despite removing MSN-related modules and reducing parameter count.Source: Table F8 · p. 66, Appendix F · p. 67

Appendix G Dataset Analyses

ETH-UCY subsets differ in pairwise and nearest-neighbor distance distributions, including scenes recorded at the same location. The reported variation supports the need for grouping boundaries that adapt to scene and crowd density.

Appendix G Dataset Analyses

  • 1.184 m in hotel versus 0.632 m in univ: median nearest-neighbor distance is almost twice as large in hotel.Univ has the largest pairwise median distance but the smallest nearest-neighbor median distance, consistent with agents forming small groups across a large scene.Source: Table G10 · p. 67, Appendix G · p. 68
  • Pairwise distance distributions for zara1 and zara2 are similar, but their nearest-neighbor distance distributions differ substantially.The figure presents both pairwise and nearest-neighbor distance distributions across ETH-UCY subsets.Source: Appendix G · p. 68, Figure G11 · p. 68
  • A fixed 1.0 m grouping threshold would be too strict in hotel and could classify many out-of-group neighbors as in-group in dense univ.The passage uses the scene-specific distance statistics to motivate context-adaptive and agent-specific grouping boundaries.Source: Appendix G · pp. 68–69
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