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Event-Inference Reliability for Physical AI over Wireless Networks

Anup Mishra, Petar Popovski

arXiv:2608.30663v1eess.SP

TL;DR

Wireless-enabled physical AI needs reliability measures that reflect whether available cues are timely and informative enough for event inference. The paper develops a context-conditioned EIR framework linking cue informativeness, availability, and temporal admissibility to residual uncertainty, event-error limits, and event-aware wireless design. An indoor multiclass activity-inference study demonstrates how usefulness horizons and cue-reliability allocation characterize EIR and event-inference coverage.

  • Problem

    Reliable data delivery does not determine whether the decision node has sufficiently timely and informative evidence to infer a physical event.

  • Method

    The paper defines context-conditioned EIER and EIR from uncertainty before and after TWI-admitted cue incorporation, distinguishes Bayes and decoder-specific error, and derives an entropy-based error bound.

  • Results

    Event-aware allocation reaches matched Bayes event-error targets with shorter usefulness horizons than link-level allocation, especially when context is more degraded.

  • Takeaways & Limitations

    EIR supports wireless design through cue prioritisation, inferentially informed reliability allocation, and event-inference coverage characterization.

Abstract

from arXiv · show

Wireless-enabled physical artificial intelligence (physical AI) systems call for a shift from reliable data delivery to reliable inference of physical events. The relevant question is not only whether packets arrive, but whether the set of cues available at the decision node, i.e., the evidence, is sufficiently timely and informative to support reliable inference about the event. Accordingly, this paper develops a framework in which event-inference reliability (EIR) is determined jointly by cue informativeness, cue availability, and temporal admissibility. The latter is determined by the downstream task requirement and represented through the usefulness horizon. We define event-inference error ratio (EIER) as the normalised residual event uncertainty after incorporating admitted cues, and EIR as the corresponding normalised uncertainty reduction, both conditioned on decision-node context. We further distinguish the evidence-limited Bayes benchmark from operational performance of a particular inference engine and derive an entropy-based lower bound on the minimum achievable event error from the same decision-node information. The framework then enables an event-aware wireless design interface for cue prioritisation, cue-reliability allocation, and event-inference coverage characterisation. A multiclass indoor activity-inference study combining empirical cue likelihoods with wireless delivery instantiates the framework and demonstrates how it characterises EIR under finite usefulness horizons.

I. INTRODUCTION

Wireless-enabled physical AI requires reliability measures focused on whether timely, informative cues support event inference, not merely whether data are delivered. The paper connects cue properties, temporal admissibility, event uncertainty, and wireless design through EIR.

  • Motivation: Wireless delivery determines which distributed sensory cues reach the decision node, when they arrive, and whether they remain useful for inference.This makes the wireless system part of the evidence interface rather than only a data pipe.
  • Motivation: TWI conditions determine temporal admissibility through event-relative simultaneity, causality, and usefulness, while wireless delivery determines cue availability.The usefulness horizon is anchored to the event reference time and is task-dependent.
  • Contribution: The paper develops EIR by combining cue informativeness, availability, and temporal admissibility to quantify uncertainty resolved about a specific event.EIER is the residual context-conditioned uncertainty fraction, while EIR is the complementary fraction resolved by admitted cues.
  • Related Work: Existing approaches address availability, temporal admissibility, or evidence fusion separately; the paper introduces an event-level measure connecting these layers to wireless design.The framework distinguishes delivery-based cue-reliability allocation from event-aware allocation that accounts for inferential contribution.
  • Contribution: The framework distinguishes evidence-limited Bayes performance from decoder-specific performance and derives an entropy-based lower bound on achievable event error.This separates uncertainty supported by admitted evidence from additional loss caused by an implemented inference engine.

II. SYSTEM MODEL

The system model represents event inference at a decision node using context, multimodal cues, wireless delivery, and TWI-based admission. It separates prior uncertainty, cue-generation statistics, and the evidence actually available for updating event beliefs.

  • System Model: A base station infers a task-relevant physical event from prior context and multimodal cues generated by distributed sensing.Cue delivery and end-to-end timing determine which generated cues become available and admissible.
  • Temporal Reference: The event reference time t anchors the event-belief update, while the usefulness horizon ∆ specifies when arriving cues remain admissible.The horizon is task-dependent and can be short in high-mobility settings.
  • Context and Prior: The context C_t forms the prior before current cues are incorporated and may include belief history, world-model state, geometry, task information, or operating mode.Current cues are excluded from C_t so their incremental contribution can be evaluated.
  • Context and Prior: The context-conditioned entropy measures event uncertainty before evidence is incorporated, either for a realised context or averaged across contexts.When no explicit context is modeled, the prior and entropy reduce to their unconditional forms.
  • Cue Generation and Informativeness: Multimodal cue statistics capture sensing noise, partial observability, modality-specific degradation, spatial configuration, and dependence across modalities.These event-conditioned distributions determine cue informativeness, whereas delivery and TWI admission determine whether that information enters the evidence.

C. TWI Admissibility of Delivered Cues

Temporal admissibility determines whether delivered cues remain usable for event inference. The usefulness horizon is defined by downstream task validity and translated into delivery conditions for individual cues.

  • Temporal admissibility: Usefulness is governed by simultaneity, causality, and a task-level usefulness horizon ∆, with simultaneity and causality enforced upstream here.The horizon can be combined with additional admission constraints without changing the model structure.
  • Cue admission: A cue contributes only when its delivery path succeeds and its event-relative delay satisfies the usefulness condition.The delay may include propagation, sensing, local computation or compression, and wireless communication.
  • Usefulness horizon: The usefulness horizon ∆ reflects the temporal validity of the multimodal cue set for the downstream task, not a link-level communication requirement.It can be translated into packet-level deadlines after accounting for sensing, computation, propagation, and communication delays.
  • Cue admission: For each modality, r_m(∆) is the probability that delivery and usefulness requirements are jointly satisfied.This probability incorporates delivery failure and the conditional CDF of event-relative delay.
  • Decision-node evidence: The admitted cue set contains only cues successfully delivered and temporally admissible by t+∆; absent cues are represented by ⊥.Cue metadata such as timestamps, confidence scores, and uncertainty estimates may be included in the decision-node representation.

E. Event-Belief Update and Decoding

The decision node combines context with cues admitted under delivery and usefulness constraints to form posterior event beliefs. The framework separates uncertainty supported by available information from the behavior of an approximate inference engine.

  • Event-belief update: The perception stack combines decision-node context with admitted evidence to form the posterior belief over event classes.The posterior is induced by the underlying joint distribution of event, context, and admitted evidence.
  • Inference engine: An implemented engine may use the exact posterior or an approximate Bayesian, learned, or world-model-based mechanism, with dependence on ∆ through the admitted cue set.Different usefulness horizons can therefore produce different evidence inputs to inference.
  • Decoding: The hard event estimate is obtained using maximum a posteriori (MAP) decoding.
  • Information versus implementation: The framework distinguishes information-supported uncertainty and minimum error from operational decisions produced by the implemented engine.When q_θ=p and the posterior is used exactly, the distinction collapses to the Bayes-optimal case.
  • Information measures: EIER measures the residual fraction of context-conditioned event uncertainty, while EIR measures the fraction resolved by admitted evidence.These normalized quantities require H(E_t | C_t)>0; when context already determines the event, the case is treated as resolved by context.
  • Information measures: EIR increases when admitted evidence resolves a larger fraction of uncertainty, depending on both cue admission and cue informativeness.

B. Evidence-Limited Event Error

The evidence-limited event error is the best achievable error from the available context and admitted evidence, independent of any particular implementation. Residual entropy and operational approximation represent distinct sources of performance limitation.

  • Evidence-limited benchmark: The Bayes-optimal error is the minimum average event error achievable by any decision rule using the available context and admitted evidence.It is an implementation-independent benchmark induced by the decision-node information law.
  • Entropy and error: Residual entropy and Bayes error capture different posterior properties, so EIER does not uniquely determine the minimum event error or order evidence configurations identically.Residual entropy nevertheless constrains the minimum achievable event error through an entropy-based bound.
  • Decoder-specific error: An implemented engine can incur additional performance loss when its approximate posterior differs from the underlying posterior.If q_θ matches the posterior and MAP decoding is used, the inequality becomes equality and no decoder-specific gap remains.
  • Evaluation: Operational event error can be estimated on an independent labelled evaluation set using indicator-based averaging.
  • Interpretation: The framework separates ambiguity caused by available evidence from loss introduced by model mismatch, finite training data, or computational constraints.EIER and EIR provide the complementary uncertainty-based characterization of residual and resolved uncertainty.

IV. EVENT-INFERENCE LIMITS AND WIRELESS DESIGN

The framework connects residual event uncertainty to evidence-limited decision performance and wireless control. Wireless design affects performance by shaping which cues are admitted within the usefulness horizon.

  • Event-inference limits: The paper derives an entropy-based lower bound on minimum achievable event error from residual event uncertainty.The connection applies to the same context and admitted evidence used to define EIER.
  • Event-inference limits: Fano’s inequality applies to every decision rule based on decision-node information and therefore also constrains the Bayes-optimal rule.
  • Event-inference limits: When residual entropy is sufficiently large, it imposes a strictly positive lower bound on evidence-limited event error.Reducing EIER relaxes this constraint, although the exact Bayes error remains determined by the full posterior distribution.
  • Wireless design: Wireless design shapes admitted evidence and residual event uncertainty by determining which cues become available within the prescribed usefulness horizon.

B. Event-Aware Wireless Design

Event-aware wireless design evaluates and controls wireless policies through the quality of the admitted evidence and resulting event inference. The framework supports cue prioritisation, resource-aware reliability optimisation, and usefulness-horizon coverage analysis.

  • Control interface: Wireless controls shape which cues become available at the decision node and include scheduling, retransmission, resource allocation, path selection, compression, and access priority.These controls also include cue-reliability allocation under a prescribed usefulness horizon.
  • Control interface: EIER measures posterior uncertainty, whereas Bayes event error measures the largest posterior probability, allowing objectives to target belief quality or decision accuracy.The two criteria capture complementary properties of the event belief.
  • Optimisation formulations: Feasible wireless policies can minimise an event-level criterion under temporal, resource, and operating constraints or minimise wireless-resource cost subject to an event-reliability requirement.The formulations provide an interface for driving wireless control by event-inference quality.
  • Design specialisations: Cue prioritisation accounts for how timely cue admission affects event-decision performance rather than relying on link-level delivery characteristics alone.This is presented as a specialisation using Bayes event error as the event-level criterion.
  • Design specialisations: Event-inference coverage is a network capability measure giving the shortest task-imposed usefulness horizon for which feasible wireless design supports the required event-error level.Across operating conditions, it provides a temporal measure of event-inference coverage.
  • Indoor instantiation: The indoor instantiation combines distributed activity cues, wireless delivery, TWI admission, empirical cue likelihoods, and posterior evaluation at the base station.The activity-inference and wireless evidence-admission layers use OPPORTUNITY and Wi3R-based data sources, respectively.

A. Activity State and Cue Observation Model

The activity model represents each inference instance by a finite activity event and a context-conditioned prior, while distributed sources produce discrete activity-class cues. Wireless delivery, readiness, and TWI admission determine which cues enter the posterior update.

  • Activity state: Each labelled activity window defines an inference instance with an activity event drawn from a finite activity alphabet.The activity taxonomy determines the number of classes and the distinctions relevant to the application.
  • Activity state: The decision node forms a context-conditioned prior from information available before the current cue set is admitted.This prior represents belief over activity classes before the current event-belief update.
  • Cue observations: Distributed sensor streams are grouped into cue sources, transformed into source-specific representations, and classified into activity-class observations over the common event alphabet.The final estimate is formed only after combining admitted cues with the context prior.
  • Cue observations: Each source’s empirical likelihood matrix captures which activity classes it distinguishes well and which it tends to confuse.The six-source indoor topology is illustrated through multimodal cue generation and delivery to the base station.
  • Cue fusion: Multimodal fusion assumes conditional independence of cue observations given the activity event, with joint likelihoods allowed for statistically dependent cues.The prior and likelihood terms determine the subsequent posterior, entropy, and event-error calculations.
  • Timing and admission: Cue readiness includes sensing, feature construction, and encoding, with computation/readiness quantised to the frame duration and fixed classifier time deducted from the usefulness budget.Physical event-propagation delays are negligible relative to cue formation and wireless delivery in the indoor setting.
  • Timing and admission: Grant-free wireless delivery uses ACK/NACK feedback and bounded retransmission attempts, producing cue admission when successful delivery occurs within the usefulness horizon.The admission subset is random and determines which cue-likelihood factors enter the posterior.
  • Timing and admission: Admission probabilities and admitted-subset distributions depend on operating conditions, wireless controls, packet-error behavior, and end-to-end delay distributions.Under the stated assumption, admission is independent of the activity event and cue realisations conditioned on operating condition and control.

C. Bayesian Activity Inference and Residual Uncertainty

Bayesian activity inference combines context with the likelihoods of admitted cues to produce a posterior belief over events. Averaging posterior and prior entropies yields residual uncertainty and EIR-related measures, while posterior maxima determine evidence-limited Bayes error.

  • Posterior inference: For each admitted cue subset and realisation, the base station combines the context prior with admitted-cue likelihoods to form the posterior event belief.The admission model determines which likelihood factors enter the update.
  • Posterior inference: With no admitted cues, the likelihood is one and the posterior reduces to the context prior.This establishes the prior-only case for the inference chain.
  • Residual uncertainty: Expected posterior entropy is conditioned on the admitted subset and then averaged over random cue admission to obtain residual uncertainty.The corresponding uncertainty before current cues are incorporated is represented by the prior entropy.
  • Event error: The same posterior determines expected Bayes event error for each admitted subset, which is then averaged over cue admission.This produces the evidence-limited event-error measure.
  • Evaluation measures: The empirical EIER and EIR average residual and prior entropies over labelled instances, while empirical evidence-limited event error averages the corresponding Bayes errors.The posterior is the Bayes posterior under the empirical activity model and therefore defines a model-based evidence-limited benchmark.

D. Inference and Evaluation Setup

The evaluation uses subject-based activity data, coarsened activity classes, six classified cue sources, and a virtual indoor wireless overlay. Context uncertainty and wireless delivery are varied through prescribed model parameters and replayed realisations.

  • Activity data: Subjects S1–S3 estimate transitions and train cue classifiers, while S4 estimates cue-likelihood matrices and evaluates TWI-gated inference.Activity windows contain 60 consecutive samples and use the majority coarsened activity label.
  • Context model: The context prior propagates the preceding activity state through a transition matrix while assigning confusion probability ν to imperfect context knowledge.The study considers ν = 0.15 and ν = 0.40 for relatively reliable and degraded recent-context information.
  • Wireless model: Table I presents cue-source-specific wireless evaluation parameters used by the activity-inference and delivery models.These parameters include source-specific readiness and retransmission settings.
  • Cue model: Six cue sources—wearable, object1, object2, object3, ambient1, and ambient2—use window-level mean and standard-deviation features with one-versus-all multiclass logistic classifiers.The compact representations contain 32, 16, and 8 components for wearable, object-oriented, and ambient sources, respectively.
  • Wireless model: The wireless layer uses Wi3R received-power records in a virtual indoor overlay with 1000 wireless realisations and source-specific placement, readiness, and retransmission parameters.OPPORTUNITY and Wi3R are not co-recorded, so cue-source identities are assigned independently of wireless link quality.
  • Wireless model: Wireless delivery uses 10 ms frames, 133-byte packets, a −100 dBm receiver noise floor, and an IEEE 802.15.4-like packet-error model with residual link-margin perturbation.The packet length accounts for compact source representations and protocol overhead.

E. EIR and Event Error versus Usefulness Horizon

The usefulness horizon governs which cues arrive in time for inference: increasing it generally improves EIR and reduces Bayes event error, with gains eventually saturating. Residual gaps can reflect unrecovered wireless packet drops, while the entropy-based bound characterizes an evidence-limited performance limit rather than achieved Bayes error.

  • Increasing the usefulness horizon ∆ raises timely cue availability, reducing residual event uncertainty and Bayes event error until gains progressively saturate.The largest changes occur where cue-readiness and retransmission-delay probability mass is concentrated.
  • A more informative previous-activity context changes the value of admitted cues, while both EIR and Bayes event error approach their full-cue benchmarks as ∆ increases.Smaller ν provides more informative context; larger ν leaves more uncertainty for incoming cues to resolve.
  • Unrecovered packet drops remain a source of gap from full-cue performance that extending the usefulness horizon cannot eliminate.
  • The entropy-based lower bound depends on residual entropy and K, whereas Bayes event error depends on the full posterior distribution.Thus, the bound is an information-theoretic limit on evidence-limited performance, not a prediction of achieved Bayes error.

F. Event-Aware Cue Prioritisation

Event-aware wireless control evaluates cues by their contribution to event inference rather than delivery timeliness alone. Under prioritisation and reliability-allocation constraints, it can reduce Bayes error or attain matched error targets with shorter usefulness horizons, especially when context is less informative.

  • Event-Aware Cue Prioritisation: With Mp = 3, event-aware prioritisation reduces Bayes event error relative to link-level prioritisation across the distance–∆plane.The largest gains occur when several cues may arrive but the priority constraint forces a subset choice.
  • Event-Aware Cue Prioritisation: The prioritisation gain depends on context noise: reliable previous-activity context changes the distance–∆pattern, while degraded context leaves more cues useful.
  • Event-Aware Cue Prioritisation: For intermediate priority budgets, event-aware prioritisation achieves lower Bayes event error; the two rules coincide when no subset-selection choice remains.The rules coincide when no source or all sources are prioritised.
  • Event-Inference Coverage under a Cue-Reliability Budget: Event-aware reliability allocation reaches the same Bayes event-error target with a shorter usefulness horizon than link-level allocation.It does so by directing reliability toward cues with greater inferential value; the gain is larger when ν = 0.40.
  • Event-Inference Coverage under a Cue-Reliability Budget: As ϵnet increases, the minimum required horizon decreases because greater aggregate cue unavailability is permitted.
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