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Who to Trust in Multi-Robot Systems: Joint Robot and Object Hypothesis Trust Inference via Neural-Symbolic Cross-Validation

Ruiyang Wang, Hao-Lun Hsu, Haocheng Meng, Songqiao Xie, Miroslav Pajic

arXiv:2610.14530v1cs.ROcs.AI

TL;DR

Reliable multi-robot cooperation requires judging both information sources and their reported hypotheses, while existing methods may rely on prior trust, side channels, or hand-designed consistency rules. NeST-Bayes learns relational evidence for joint trust inference and accumulates it in Bayesian trust beliefs. Across evaluated conditions, it generally achieves the highest precision and leads in recall among trust-based methods.

  • Problem

    Trust inference must assess both reporting robots and their hypotheses under partial observability and adversarial interference, while existing methods rely on prior trust, side channels, or hand-designed evidence rules.

    Source: §I · p. 1

  • Method

    NeST-Bayes uses typed relations in ego-centric heterogeneous graphs to infer robot and object-hypothesis evidence, then accumulates scores through Bayesian updates of Beta-distributed trust beliefs.

    Source: §I · p. 1

  • Results

    Across noisy sensing, adversarial reporting, and occlusion-rich simulations, NeST-Bayes generally achieves the highest precision and leads in recall among trust-based methods.

    Source: §I · p. 1, E. High Fidelity Simulations · p. 7, C. Generalization with Optimized… · p. 7

  • Takeaways & Limitations

    Comparisons with Naïve Bayesian indicate benefits from learned relational reasoning for precision and recall, including under occlusion-rich conditions.

    Source: §VI · p. 7

Abstract

from arXiv · show

Multi-robot systems (MRS) offer significant advantages over single-robot platforms by enabling information sharing and coordination for different tasks in complex environments. However, reliable cooperation critically depends on inferring trust over both information sources and their reported hypotheses, particularly under partial observability and potential adversarial interference. Existing approaches frequently depend on pre-established trust relationships or side-channel information, which may not be available or reliable in realistic MRS deployments. This work introduces NeST-Bayes, a neural-symbolic framework that jointly infers robot and hypothesis trust using only inter-robot observation consistency, without requiring preassigned robot trust, reputation information, or side-channel identity signals. NeST-Bayes infers instantaneous trust evidence scores for robots and object hypotheses by reasoning over ego-centric relational graphs constructed from cross-robot observation consistency. These evidence scores are accumulated over time through Bayesian updates of Beta-distributed trust beliefs to maintain temporally consistent trust estimates. Extensive evaluations show that NeST-Bayes achieves the highest mean object precision and robot recall across all benchmark settings, and the highest robot precision and object recall in most settings, compared to trust-based methods. Under aggressive optimized attacks, it achieves 98.8\% robot precision with 93.8\% recall and 98.3\% object precision with 95.4\% recall. In an occlusion-rich Webots warehouse, it maintains 92.5\% robot precision with 92.0\% recall and 97.3\% object precision with 85.0\% recall. These results demonstrate joint improvements in the reliability and coverage of retained information.

I. INTRODUCTION

Multi-robot cooperation depends on assessing both the robots sharing information and the hypotheses they report, especially under partial observability and adversarial interference. NeST-Bayes learns relational evidence for joint trust inference and evaluates it across sensing and adversarial conditions.

A. MRS Vulnerabilities

  • Partial observability, sensing uncertainty, restricted fields of view, and adversarial reports make trust in both reporting robots and their hypotheses central to information aggregation.False identities and Byzantine behavior can distort objectives or corrupt distributed estimation.Source: §I · p. 1, A. MRS Vulnerabilities · p. 2

B. Trust in MRS

  • Existing approaches rely on prior trust, hand-designed behavior models, or side channels, while consistency-based methods still use hand-designed rules to map relations to trust evidence.The stated gap is learning how typed consistency and contradiction relations combine to infer robot and object-hypothesis trust.Source: §I · p. 1

I. INTRODUCTION

  • NeST-Bayes jointly estimates robot and object-hypothesis trust from cross-robot consistency using ego-centric heterogeneous graphs and Bayesian updates of Beta-distributed beliefs.Typed agreement and contradiction edges are encoded using geometric and field-of-view checks; graph attention produces evidence scores accumulated as fractional pseudo-counts.Source: §I · p. 1
  • Across noisy sensing, adversarial reporting, and occlusion-rich simulations, NeST-Bayes generally achieves the highest precision and leads in recall among trust-based methods.The framework requires no preassigned robot trust or side-channel identity signals; ablations report recall gains from relational propagation while maintaining high precision.Source: §I · p. 1

C. Neural-Symbolic AI

The paper situates trust inference among neural-symbolic and relational reasoning approaches, then formulates local sensing and track reports under noisy observations and limited communication.

C. Neural-Symbolic AI

  • NeST-Bayes uses ego-centric heterogeneous graphs for typed robot and object-hypothesis relations, rather than Neural Logic Machines’ explicit predicate operators.The paper describes relation-aware graph networks as a sparse substrate for heterogeneous message passing.Source: C. Neural-Symbolic AI · p. 2

A. Noisy Sensing and Local Information

  • Each robot’s nominal detector can miss visible objects or produce persistent sensor artifacts, with noisy position measurements for detections.True-positive detections are retained with probability 1 − λ^s_FN,i; nominal sensor false positives occur at rate λ^s_FP,i.Source: A. Noisy Sensing and Local Information · p. 2
  • Robots communicate with neighbors within a communication range and broadcast local tracks consisting of an object identifier and estimated position.Track labels come from the perception and association front end, may contain association errors, and are assumed matchable across reports.Source: A. Noisy Sensing and Local Information · p. 2

B. Reporting Policies

The reporting-policy setup distinguishes legitimate robots from adversaries that manipulate detector reports while keeping their broadcast states authentic. Adversarial false hypotheses may persist and be shared across multiple robots.

B. Reporting Policies

  • Adversaries receive outputs from the same sensing model but manipulate reported hypotheses, while their broadcast states remain authentic.The text notes that authentic states may be verifiable through inter-robot localization.Source: B. Reporting Policies · p. 2
  • Persistent adversarial false hypotheses have identifiers disjoint from ground-truth objects and can be mutually supported by multiple adversarial robots.These hypotheses may be visible to adversarial robots and included among their false-positive track observations.Source: B. Reporting Policies · p. 2
  • Under the normal adversarial policy, robots randomly suppress nominal detections and inject visible persistent false hypotheses.The supplied description identifies an optimized policy that selects reports, without specifying its full selection objective here.Source: B. Reporting Policies · p. 3
  • The optimized policy uses report-selection variables and weighs promoting adversarial false hypotheses against suppressing nominal hypotheses, subject to a per-step manipulation limit.The manipulation budget is described as a stealthiness constraint.Source: B. Reporting Policies · p. 3

C. Trust Inference Objective

The objective is to identify legitimate robots and credible object hypotheses despite sensor artifacts and adversarial false hypotheses. Trust scores are inferred from cross-robot consistency without prior trust, reputation, or inference-time ground-truth labels.

C. Trust Inference Objective

  • The trust module estimates a robot score, while each robot maintains trust scores for its local tracks.The supplied formulation assigns these scores values in [0, 1].Source: C. Trust Inference Objective · p. 3
  • Robot and track trust scores are inferred from cross-robot observation consistency without prior trust, reputation, or ground-truth labels at inference time.Source: C. Trust Inference Objective · p. 3
  • For evaluation, local tracks are grouped into fused hypotheses and a credible object set is defined.The supplied passages state that credibility is computed for each fused hypothesis, but do not provide its full definition.Source: C. Trust Inference Objective · p. 3
  • The objective is identifying legitimate robots and credible object hypotheses despite natural sensor artifacts and adversarial false hypotheses.Source: C. Trust Inference Objective · p. 3

IV. NEST-BAYES: NEURAL-SYMBOLIC TRUST WITH BAYESIAN EVIDENCE ACCUMULATION

NeST-Bayes builds an ego-centric graph for each robot from its own and neighboring reports, encoding cross-robot consistency as directed relations for joint robot and track trust reasoning.

IV. NEST-BAYES: NEURAL-SYMBOLIC TRUST WITH BAYESIAN EVIDENCE ACCUMULATION

  • The centralized Trust Aggregation Module builds each robot’s graph from its own and neighboring reports, then returns validated track evidence for onboard beliefs.Robot evidence is accumulated in a system-wide registry; the authors leave a fully decentralized deployment to future work.Source: §IV · p. 3, 1) Ego-Centric Graph Construction · p. 3

1) Ego-Centric Graph Construction:

2) Neural-Symbolic Reasoning:

NeST-Bayes turns symbolic relations in each ego-centric graph into instantaneous trust evidence through learned, typed relational reasoning.

2) Neural-Symbolic Reasoning:

  • Each node’s symbolic profile is an unordered bag of triplets encoding endpoint node types and an 8-bit one-hot relation type.A permutation-invariant pooling step produces a 128-dimensional initial embedding for robot and track nodes.Source: 2) Neural-Symbolic Reasoning · pp. 4–5
  • Three relation-specific Hetero GAT layers with four attention heads propagate evidence from local consistency relations to broader multi-hop consensus.Head outputs and incoming relation representations are mean-aggregated; residual connections follow the second and third layers.Source: 2) Neural-Symbolic Reasoning · p. 5
  • Type-specific MLP heads with sigmoid activation convert final node embeddings into scalar evidence scores between 0 and 1.These scores are instantaneous evidence for robots and object hypotheses, later accumulated through Beta updates.Source: 2) Neural-Symbolic Reasoning · pp. 4–5

3) Validity Filtering:

The validity filter retains only ego-robot and local-track scores supported by cross-robot graph connections.

3) Validity Filtering:

  • An ego robot is valid for a robot-trust update only when it has an incident edge involving a neighboring robot.Source: 3) Validity Filtering · p. 5
  • A local track is valid only when its fused node connects to both the ego robot and at least one neighboring robot.Source: 3) Validity Filtering · p. 5
  • Only the valid ego-robot score and local-track scores are retained; robot trust is updated system-wide and track evidence is mapped back onboard by persistent identifier.Source: 3) Validity Filtering · p. 5

B. Bayesian Temporal Evidence Accumulation

NeST-Bayes accumulates valid instantaneous evidence in Beta trust beliefs, preserving neutral priors when cross-robot evidence is unavailable.

B. Bayesian Temporal Evidence Accumulation

  • Each node’s trustworthiness is represented by a Beta belief whose parameters accumulate positive and negative evidence.Robot beliefs are held in a system-wide registry, while each robot maintains beliefs for its local tracks.Source: B. Bayesian Temporal Evidence… · p. 5
  • New robots and tracks start from the symmetric prior (1, 1), a neutral trust score of 0.5, and retain it when they receive no valid cross-robot evidence.Source: B. Bayesian Temporal Evidence… · p. 5
  • Valid neural evidence scores update Beta parameters as fractional pseudo-counts, while invalid nodes leave those parameters unchanged.Source: B. Bayesian Temporal Evidence… · p. 5
  • Final robot and track trust scores are Beta expectations after repeated validated updates over the horizon, rather than single-snapshot estimates.Source: B. Bayesian Temporal Evidence… · p. 5

V. EVALUATIONS

Evaluation trains and validates NeST-Bayes in a controlled 2D environment with sampled sensing noise and adversarial policies, using ego-centric graphs extracted from simulated scenarios.

V. EVALUATIONS

  • Robots and objects move from random starts to goals for 100 steps in a 100×100 environment, with 2|R| objects and |R| sampled from 5 to 20.Robots have an occlusion-free π/3 field of view, 50-unit sensing range, and 80-unit communication range.Source: §V · p. 5
  • Training and testing independently sample each robot’s nominal sensor false-positive and false-negative rates from 0.01 to 0.05.Training samples adversarial ratios from 0.1 to 0.3; nominal false-negative suppression probability for normal adversaries is sampled from 0.1 to 0.3.Source: §V · p. 5
  • From 10,000 scenarios, the study extracts 71,940 valid ego-centric graphs and partitions them 80/20 by scenario into training and validation sets.The scenarios are split evenly between normal and optimized aggressive policies.Source: §V · p. 5
  • Supervision labels legitimate robots and real hypotheses as positive; a factor of 5 balances the single ego-robot label against multiple track labels.The Beta updates add no learned parameters.Source: §V · p. 5

A. Baselines and Evaluation Metrics

NeST-Bayes is evaluated against trust baselines under normal and optimized adversarial reporting. It leads on key robot and object precision and recall measures, including under aggressive attacks.

A. Baselines and Evaluation Metrics

  • No Trust indiscriminately trusts robots; Naïve Bayesian applies fixed evidence rules to the same symbolic relations, while MATE uses hand-designed aggregation rules.Trust accumulates over 100 time steps, final classifications use ψ = 0.5, and precision and recall are reported separately for robots and objects.Source: A. Baselines and Evaluation Metrics · pp. 5–6

C. Generalization with Optimized Adversaries

  • Under aggressive attacks, NeST-Bayes reaches 98.8% robot precision, 93.8% robot recall, 98.3% object precision, and 95.4% object recall, leading trust-based methods in both recalls.Robot precision rises 12.3 percentage points from conservative to aggressive attacks, compared with 7.7 points for Naïve Bayesian.Source: Table II · p. 6, C. Generalization with Optimized… · pp. 6–7

B. Generalization with Normal Adversaries

  • Across three normal-adversary settings, NeST-Bayes has the highest mean robot precision and recall and object precision among trust-based methods.The study also reports it leads in precision and recall for both entity types overall in this comparison.Source: B. Generalization with Normal… · p. 6

C. Generalization with Optimized Adversaries

  • Under conservative attacks, robot precision remains near the 85.1% No Trust baseline across trust methods, while NeST-Bayes reaches 97.0% object precision and 94.4% object recall.Its object precision is highest among trust-based methods; the policy selectively injects neighbor-supported false hypotheses and suppresses detections lacking corroboration, producing few observable inconsistencies.Source: C. Generalization with Optimized… · p. 6
  • Table III reports component ablations over 100 comprehensive scenarios, with results given as mean ± standard deviation.Source: Table III · p. 7
  • With adversarial ratio 0.4–0.5, NeST-Bayes leads all four metrics: 89.1% robot precision, 85.9% robot recall, 93.3% object precision, and 86.5% object recall.Compared with Naïve Bayesian, robot precision and recall improve by 15.3 and 36.6 percentage points, respectively.Source: C. Generalization with Optimized… · p. 7

D. Ablation Studies

Across benchmarks, NeST-Bayes leads in object precision and robot recall, and Webots results show strong performance under occlusion. Ablations distinguish contributions from relational propagation and symbolic initialization; the conclusion points to active verification as future work.

D. Ablation Studies

  • 97.2% robot precision, 95.5% robot recall, 99.0% object precision, and 94.8% object recall for the full model; ablations support contributions from relational propagation, typed relations, and symbolic initialization.Removing the Hetero GAT lowers robot recall from 95.5% to 75.4% and object recall from 94.8% to 89.3%; typed relations improve robot precision and recall by 10.4 and 16.8 percentage points, and object precision by 12.0 points. Replacing triplet initialization lowers robot precision from 97.2% to 95.8% and recall from 95.5% to 91.3%.Source: D. Ablation Studies · p. 7

E. High Fidelity Simulations

  • 92.5% robot precision with 92.0% recall, and 97.3% object precision with 85.0% recall; NeST-Bayes leads trust-based methods in Webots despite sparse cross-robot validation.The evaluation uses 100 scenarios and transfers without retraining in an occlusion-rich warehouse.Source: Table IV · p. 7, E. High Fidelity Simulations · p. 7, Figure 3 · p. 7

VI. DISCUSSION AND CONCLUSION

  • Across benchmarks, NeST-Bayes has the highest mean object precision and robot recall, and leads in robot precision and object recall in most settings among trust-based methods.Source: §VI · p. 7
  • Future work will explore trust-aware active verification by directing robots to obtain additional viewpoints or revisit uncertain detections under sparse cross-robot evidence.Source: §VI · p. 8
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