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Destination Support Restoration for Finite-Set Multimodal Trajectory Prediction

Fengrui Liu, Jiajun Peng, Duo Peng, Feng Liu

arXiv:2609.25942v1cs.ROcs.AI

TL;DR

A fixed-size trajectory set can underrepresent or lose plausible destinations, limiting which futures downstream decision making can consider. DSR repairs that allocation using candidate evidence while preserving the host and set size. It reduces MIF weighted ADE and FDE on the Edinburgh protocol and improves both metrics in paired integrations with five other predictors.

  • Problem

    A fixed hypothesis budget can concentrate on dominant destinations and omit plausible alternatives, even while observations remain compatible with them.

    Source: §I · pp. 1–2

  • Method

    DSR uses a temporary mode-stratified candidate bank to derive integer target counts, protects active support, and reallocates surplus hypotheses without changing the host or set size.

    Source: §I · p. 2

  • Results

    13.36% and 13.30%: DSR reduces MIF weighted ADE and FDE on the complete 3,719-trajectory Edinburgh protocol, and paired integrations improve both metrics for CLiFF, PPT, causal GDTS, Social Informer, and PECNet.

    Source: §I · p. 2

  • Takeaways & Limitations

    Finite-set support allocation can serve as a prediction-side control layer between prediction and downstream decision making without increasing the maintained set size.

    Source: §V · p. 7

    DSR’s effectiveness depends on meaningful mode definitions and compatible candidate generation; evaluation is limited to pedestrian trajectory prediction with fixed repair hyperparameters, and closed-loop robot experiments remain future work.

    Source: §V · p. 7

Abstract

from arXiv · show

Robots operating around pedestrians often reason over a finite set of predicted human futures. Repeated online updates can concentrate this limited prediction budget on dominant destinations and leave plausible alternatives underrepresented or absent, removing those alternatives from the finite representation available to downstream decision making. We introduce Destination Support Restoration (DSR), a causal post-selection operator that repairs destination support without retraining the host predictor or increasing the maintained set size. At a repair step, DSR evaluates a temporary destination-stratified candidate bank from the observed prefix, converts candidate evidence into integer target counts, protects representatives of active modes, and reallocates redundant surplus hypotheses to deficient modes. The maintained and returned sets retain exactly $N$ hypotheses, and DSR replaces at most $\lceilρN\rceil$ entries. Protected representatives preserve current categorical support; lineage-aware particle filters also preserve surviving resampling ancestors. Each replacement reduces the allocation mismatch to the evidence-driven target by one. On the complete 3,719-trajectory Edinburgh protocol over three seeds, DSR reduces MIF weighted ADE and FDE by 13.36% and 13.30% at $N=64$. Paired integrations with CLiFF, PPT, causal GDTS, Social Informer, and PECNet improve both metrics in every evaluated pair. These results show that finite-set support allocation is a useful prediction-side control point when a fixed hypothesis set serves as the interface to downstream systems.

I. INTRODUCTION

A fixed-size prediction set can lose or underrepresent plausible destinations, limiting the alternatives available to downstream decision making. DSR repairs that allocation online while preserving the set size and host predictor.

I. INTRODUCTION

  • A finite set can omit plausible futures, leaving downstream decision making unable to consider those alternatives even when observations remain compatible with them.Repeated propagation, weighting, and resampling can concentrate hypotheses on dominant destinations and remove low-mass categorical destinations.Source: §I · p. 1
  • Support-allocation mismatch includes both complete mode extinction and underrepresentation of a plausible destination within the fixed hypothesis budget.The goal is to restore missing support and reallocate redundant slots before extinction, without enlarging the output set.Source: §I · p. 2
  • DSR uses a temporary mode-stratified candidate bank to set integer targets, protects active-mode representatives, and reallocates only surplus hypotheses, replacing at most ⌈ρN⌉ entries.The host predictor and maintained and returned set sizes remain unchanged.Source: §I · p. 2
  • Lineage-aware filters protect the first offspring of each distinct resampling ancestor, while predictors without ancestry protect one representative of every active mode.The repair rule is integrated with MIF particles, CLiFF through GoalBridge, and other predictors through mode adapters.Source: §I · p. 2
  • 13.36% and 13.30%: DSR reduces MIF weighted ADE and FDE on the complete 3,719-trajectory Edinburgh protocol, with 64 hypotheses maintained and returned.Paired integrations also reduce both metrics for CLiFF, PPT, causal GDTS, Social Informer, and PECNet.Source: §I · p. 2
  • The paper evaluates the repair principle across a destination-particle filter, a flow-map bridge, and learned finite-set predictors, with cross-scene, component, support-event, sensitivity, and runtime analyses.These analyses examine where gains arise and the additional computation required.Source: §I · p. 2

A. Multimodal and Goal-Conditioned Trajectory Prediction

Multimodal and goal-conditioned predictors generate or structure possible trajectories in different ways. DSR instead operates on the finite set exposed by a host, while recursive hosts retain their own update and decoding operations.

A. Multimodal and Goal-Conditioned Trajectory Prediction

  • PECNet, Y-Net, PPT, and GDTS structure forecasts around destinations or goals, while Social Informer represents stochastic motion using interaction modeling and adaptive variance.The approaches use endpoint conditioning, goal-and-waypoint decomposition, destination pretext tasks, goal-guided diffusion, or an Informer-based predictor, respectively.Source: A. Multimodal and Goal-Conditioned… · p. 2
  • DSR acts after a host exposes modes and conditional candidates, reallocating the maintained and returned hypotheses without changing the host generator.This distinguishes DSR’s allocation role from methods that learn or sample a conditional trajectory distribution.Source: A. Multimodal and Goal-Conditioned… · p. 2

B. Recursive Intention and Long-Horizon Prediction

  • Recursive predictors update latent motion intent as observations arrive; MIF-WLSTM combines a mutable intention filter over predefined destination regions with a Warp LSTM decoder.Its mutation mechanism can introduce random replacements, but the described passage ends before specifying the full contrast with DSR.Source: B. Recursive Intention and… · p. 2
  • CLiFF exposes no particle ancestry, so GoalBridge keeps its generated paths outside the DSR particle state and uses the repaired distribution to reweight the original proposals.Lineage-aware filters use ancestry-based protection; other predictors use host-defined modes and protected representatives.Source: B. Recursive Intention and… · p. 3
  • Propagation, observation processing, resampling or hypothesis generation, and trajectory decoding remain host operations; DSR intervenes only in finite allocation between those stages.The pipeline checks effective sample size and, when ESS < ηN, returns N equally weighted hypotheses to the host after repair.Source: B. Recursive Intention and… · p. 3, Figure 2 · p. 3

C. Particle Rejuvenation, Resampling, and Diverse Hypothesis Selection

Existing particle-rejuvenation and diverse-sampling methods address related but distinct problems. DSR instead treats semantic mode counts in an instantiated finite set as a resource to repair between host operations.

C. Particle Rejuvenation, Resampling, and Diverse Hypothesis Selection

  • Resample–move methods apply Markov transitions, KLD sampling adapts particle count, and other resampling methods redistribute particle mass or reduce impoverishment.Auxiliary particle filters use look-ahead information, while entropy-regularized optimal-transport resampling differentiably redistributes mass.Source: C. Particle Rejuvenation, Resampling,… · p. 3
  • DSR leaves host propagation, likelihood updates, the ESS criterion, and resampling unchanged, then reallocates bounded surplus slots toward evidence-supported deficits in the finite set.It is a controlled repair of the finite representation, not an invariant Markov transition or an unbiased posterior correction.Source: C. Particle Rejuvenation, Resampling,… · p. 3
  • Diverse sampling constructs a new output set from a fixed observation window, whereas DSR reallocates categorical counts within an already instantiated finite support state.The former controls where a generator places hypotheses; DSR controls their semantic allocation in the maintained set.Source: C. Particle Rejuvenation, Resampling,… · p. 3

III. METHOD

A. Finite Sets Expose Allocation Error

  • DSR requires mode-conditioned candidates, a causal compatibility energy, and a protected set; ancestry-based hosts protect a surviving ancestor’s first offspring, while other hosts protect an active-mode representative.The latter guarantees categorical support preservation but makes no ancestry claim.Source: A. Finite Sets Expose Allocation Error · p. 4

B. Candidate Evidence Defines Target Counts

DSR turns evidence from a temporary, mode-stratified candidate bank into integer target counts, then restricts repair to plausible underrepresented modes and eligible donors.

B. Candidate Evidence Defines Target Counts

  • A temporary candidate bank is stratified across modes and discarded after the allocation decision unless a candidate enters the maintained set.For each mode, candidate evidence is computed from its candidates using compatibility energy and converted to a softmax allocation score.Source: B. Candidate Evidence Defines Target… · p. 4
  • The evidence score q_g represents support for allocating finite set slots to mode g, not a calibrated destination posterior.The real-valued allocation Nq is converted into integer target counts using largest-remainder rounding.Source: B. Candidate Evidence Defines Target… · p. 4
  • Only plausible underrepresented modes are eligible for repair, and donation is restricted to an eligible donor set with a maximum repair ratio ρ.The supplied passage identifies the donor eligibility and cap but does not state their detailed formulas.Source: B. Candidate Evidence Defines Target… · p. 4

C. Surplus Donation Preserves Support

DSR releases only unprotected hypotheses from target-surplus modes and assigns replacement slots to deficient modes. Energy orders both donor removal and candidate insertion.

C. Surplus Donation Preserves Support

D. Repair Contracts the Allocation Error

DSR preserves active categorical support while bounding intervention size, and each replacement moves the finite allocation one step toward its evidence-driven target. Lineage-aware filters additionally preserve surviving resampling ancestors.

D. Repair Contracts the Allocation Error

  • DSR modifies at most ⌈ρN⌉ hypotheses and preserves active categorical support when the protected set includes a representative of every active mode.In lineage-aware filters, protecting the first offspring of each distinct resampling ancestor also preserves an unchanged offspring of every surviving ancestor.Source: D. Repair Contracts the Allocation Error · p. 4
  • Each replacement moves one slot from a target-surplus mode to a target-deficient mode.The resulting intervention moves the finite categorical allocation exactly R steps toward its evidence-driven target.Source: D. Repair Contracts the Allocation Error · p. 4
  • The shared allocation operator supports MIF particles, CLiFF through GoalBridge, and mode adapters for PPT, GDTS, Social Informer, and PECNet.Each host supplies its candidate generator and compatibility energy.Source: D. Repair Contracts the Allocation Error · p. 4

A. Experimental Setup

The evaluation uses an online Edinburgh protocol and paired, three-seed comparisons of each host with and without DSR. It reports weighted displacement errors and a host-specific probabilistic score.

1) Dataset and Online Protocol:

  • The Edinburgh test split contains 3,719 trajectories, evaluated online at 10 Hz across 34 destination regions with 20-position prediction and correction windows.Each run produces 86,404 online updates; prediction starts after a 10-position warm-up and advances every two positions.Source: 1) Dataset and Online Protocol · p. 4
  • Every method is reported as a three-seed mean, with each host compared against the same configuration with and without DSR.Comparative conclusions are supported by paired statistical analysis.Source: 1) Dataset and Online Protocol · p. 5
  • MIF uses N = 64 particles; CLiFF returns K = 64 proposals, while PPT, GDTS, Social Informer, and PECNet use support-safe adapters.CLiFF connects to the repaired destination state through GoalBridge.Source: 1) Dataset and Online Protocol · p. 5

2) Metrics:

  • The evaluation reports weighted ADE and FDE, plus NLL as a secondary score compared only within each host.NLL uses each host’s postintegration output distribution, and lower displacement error need not imply lower NLL.Source: 2) Metrics · p. 5

B. DSR Improves Paired Hosts

Paired host comparisons show lower displacement errors with DSR on Edinburgh and broadly across five ETH/UCY scenes. The evaluation distinguishes DSR’s contribution from host-specific changes such as CLiFF’s GoalBridge.

1) DSR Improves the Lineage-Aware Host:

  • 13.36% and 13.30%: MIF wADE and wFDE reductions, respectively, with N = 64 maintained and returned particles.The paired values change from 0.6594 to 0.5713 for wADE and from 1.2420 to 1.0768 for wFDE; the repaired N = 64 model also outperforms the N = 340 reference.Source: 1) DSR Improves the Lineage-Aware Host · pp. 5–6

2) Complete DSR Transfers Across Hosts:

  • PPT, causal GDTS, and Social Informer reduce both displacement metrics; PECNet has the largest displacement reductions, while its NLL increases.PPT reductions are 8.30% and 8.49%; causal GDTS reductions are 7.36% and 6.95%; Social Informer reductions are 8.85% and 8.36%. PECNet reduces wADE by 24.55% and wFDE by 27.27%, while NLL rises from 1.8110 to 2.3484.Source: 2) Complete DSR Transfers Across Hosts · p. 6
  • For CLiFF, the strict DSR comparison is GoalBridge versus GoalBridge+DSR, with wADE/wFDE reductions of 1.03%/1.36%.The larger difference from original CLiFF is not attributed entirely to DSR because GoalBridge also modifies proposal weights.Source: 2) Complete DSR Transfers Across Hosts · p. 6

C. Cross-Scene Generalization

  • Across five ETH/UCY scenes, DSR lowers wFDE in all 15 host–scene pairs and lowers mean wADE in 14.PPT’s wADE on ZARA1 changes from 2.2856 to 2.2858; its mean wFDE reduction is 5.16%.Source: C. Cross-Scene Generalization · p. 6

D. Ablation of DSR Components

The ablation identifies repair and its design choices as contributors to performance, while support-event analyses show repair gains across active-mode strata and persisting displacement improvements.

D. Ablation of DSR Components

  • Disabling repair increases wADE/wFDE by 21.46%/21.35% versus Full DSR, the largest ablation deterioration; random donor and candidate selection also worsen performance.Removing lineage protection together with surplus-only donation degrades performance to 0.58088/1.09413; random donor and candidate selection yield 4.42%/2.11% and 2.17%/2.04% degradations, respectively.Source: D. Ablation of DSR Components · p. 6, Table III · p. 6

E. Displacement Gains Persist After Support Repair

  • The event analysis tracks immediate revival, historical recovery, and pre-extinction support increase; Random Reset matches DSR’s trigger and replacement count but selects uniformly.True destinations label the support events post hoc; DSR receives no future labels, and paired bootstrap clusters are seed–trajectory pairs.Source: E. Displacement Gains Persist After… · pp. 6–7
  • DSR raises each support-repair rate by at least 19.07 percentage points over Random Reset and reduces wADE in every active-mode bucket.The wADE reductions are 13.69% with 1–2 active modes, 16.47% with 3–4, and 4.96% with at least five.Source: E. Displacement Gains Persist After… · p. 7, Table IV · p. 7
  • Nonzero repairs occur on 21.63% of updates and average 6.737 replaced hypotheses; after immediate revival, DSR-minus-host wADE remains negative through +10 updates.The reported differences are −0.0784 at +1, −0.1056 at +5, and −0.1257 at +10 updates.Source: E. Displacement Gains Persist After… · p. 7

F. Sensitivity to Repair Capacity and Support Threshold

Sensitivity tests show that repair capacity and candidate budget affect errors and runtime, while DSR improves accuracy on three hosts at additional, model-dependent runtime cost. The authors frame it as a prediction-side control layer, with evaluation scope and dependencies that bound its use.

F. Sensitivity to Repair Capacity and Support Threshold

  • For MIF, increasing ρ from 0.10 to 0.20 and C from 68 to 272 further reduces wADE, wFDE, and NLL, with higher runtime and candidate-scoring cost.Disabling repair raises wADE, wFDE, and NLL by 21.5%, 21.4%, and 64.2%; τ ∈[0, 0.01] leaves results nearly unchanged, while τ = 0.02 raises wADE and wFDE by about 0.2%. The defaults balance intervention size and cost rather than maximizing offline accuracy.Source: F. Sensitivity to Repair Capacity and… · p. 7

G. Accuracy–Runtime Trade-off

  • DSR reduces MIF wADE/wFDE by 13.36%/13.30% as runtime rises 15.25%; CLiFF+GoalBridge improves 1.03%/1.36% with an 8.24% runtime increase.For PECNet, runtime rises from 0.90 ms to 6.13 ms per step while wADE/wFDE decrease by 24.55%/27.27%.Source: G. Accuracy–Runtime Trade-off · p. 7

V. DISCUSSION AND CONCLUSION

  • DSR is a prediction-side intervention, not a complete planning solution, and depends on meaningful mode definitions and compatible candidate generation.The evaluation is limited to pedestrian trajectory prediction with fixed repair hyperparameters; closed-loop robot experiments are left for future work.Source: §V · p. 7
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