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Provenance-Aware Belief Updating in Human-AI Feedback Loops

Tianyi Huang, Eric Liu, Jay Chong, Emily Yin, Wanqi Zhao

arXiv:2610.13008v1cs.AI

TL;DR

Repeated reports can make one observation appear to be independent corroboration, and sparse transcript-level supervision does not directly enforce cross-transcript update relations. LQET combines sparse Bayesian supervision with relational constraints; on a controlled binary benchmark, it reduces update error and long-relay drift across two backbones.

  • Problem

    With explicit multi-hop report provenance, the question is whether models preserve predictions for relays yet apply the same reliability-conditioned update when new evidence arrives after different relay histories.

    Source: §1 · p. 1

  • Method

    LQET combines sparse soft-target supervision with invariance, new-evidence update-consistency, and presentation-order constraints across transcripts.

    Source: §1 · p. 2

  • Results

    LQET lowers new-evidence update RMSE by 41.25% on Qwen and 44.45% on Phi, and depth-8 relay drift by 91.36% and 89.38%, respectively, versus task-only.

    Source: §5.1 · p. 5

  • Takeaways & Limitations

    The results support treating evidence provenance as a structure for learning which context changes warrant changes in belief.

    Source: §8 · p. 8

    The controlled binary, supplied-provenance setting does not establish transfer to larger models, naturalistic tasks, or incomplete or unreliable provenance.

    Source: §7 · p. 8

Abstract

from arXiv · show

In repeated human-AI interaction, a single observation can be quoted, summarized, and returned to a model as multiple reports, making repetition look like independent corroboration. We study whether language models can use supplied report lineage to update according to evidence provenance rather than report count. We introduce Latent Quotient Evidence Training (LQET), a relational objective that combines sparse Bayesian supervision with constraints that encourage stable predictions when reports add no new evidence and consistent updates to the same new evidence across relay histories. On a controlled binary benchmark, LQET reduces new-evidence update RMSE by 41-44% and log-odds drift after eight relay steps by 89-91% relative to task-only training across Qwen3-4B and Phi-4-mini, with three paired training seeds per backbone. The gains extend to a closed-loop simulation in which model confidence controls how many relayed reports re-enter the model's context in later rounds. By grounding belief updates in supplied provenance, LQET offers a route toward dynamic human-AI systems in which influence follows new evidence, not the number of times the same evidence returns.

1 Introduction

Repeated reports can make one observation appear corroborated, while appropriate updating depends on whether reports add evidence. The paper formalizes provenance-aware updating and introduces LQET to train consistent belief changes across relay histories.

1 Introduction

  • Sparse pointwise supervision assigns targets to individual transcript views but does not directly enforce relations across transcripts that differ only in relay history or new evidence.The desired behavior is unchanged predictions for relays and consistent changes when new evidence arrives.Source: §1 · p. 1
  • LQET combines sparse soft-target supervision with invariance, new-evidence update-consistency, and presentation-order constraints.Its aim is to translate visible lineage into consistent belief updates rather than infer unobserved report dependencies.Source: §1 · p. 2
  • Across two language-model backbones, paired training seeds, and controlled distribution shifts, LQET improves new-evidence update accuracy and stability across long relay histories.The introduction reports consistent gains without giving metric values.Source: §1 · p. 2
  • A confidence-dependent feedback simulation tests how model confidence affects the number of inherited reports returned as later input.This connects provenance-aware updating to repeated human-AI interaction.Source: §1 · p. 2

2 Evidence provenance and Bayesian targets

The section defines evidence by distinct query-relevant roots, not by the number of reports. Under the specified source-reliability model, equivalent root sets share a Bayesian target.

2 Evidence provenance and Bayesian targets

  • Each source has a Beta reliability prior updated by its visible correct and incorrect calibration counts.The prior parameters are αs = cs + 1 and βs = ws + 1.Source: §2 · p. 2
  • Distinct roots are conditionally independent given the answer and source reliabilities, while roots from one source become dependent after reliability is marginalized.Reports and query-irrelevant roots add no information about the answer once relevant observations and calibration records are conditioned on.Source: §2 · pp. 2–3
  • Transcripts are provenance-equivalent when they contain the same set of distinct query-relevant evidence roots, with repeated descendants removed by set union.The equivalence classes form the quotient used by the method.Source: §2 · p. 3
  • The Bayesian target is the posterior probability obtained by applying the sigmoid to the difference between the positive- and negative-answer log targets.The log targets combine the prior with source reliability marginalized over calibration records.Source: §2 · p. 3
  • Relays leave the target unchanged, while new roots can change it according to source, reported outcome, and the other roots from that source.With prior and calibration fixed, the target depends on root sets through source-by-outcome counts under the exchangeable source model.Source: §2 · p. 3
  • The 14-view matched families cross relay history with new evidence; composition views separately add two roots from distinct sources and reverse their presentation order.Matched controls hold author and displayed outcome fixed while varying whether a report relays an observation or introduces a new one.Source: §2 · p. 3

3 Latent Quotient Evidence Training

LQET trains a forced-choice YES-NO score to approximate Bayesian targets while satisfying relations across matched transcript views. The objective combines sparse pointwise supervision with relational losses.

3 Latent Quotient Evidence Training

  • The model score is the difference between YES and NO next-token logits, converted to a forced-choice YES probability rather than a full-vocabulary response probability.The tokenizer maps YES and NO to distinct single tokens at the assistant boundary.Source: §3 · p. 3
  • Seven views receive pointwise soft targets, while views such as h11 and c11 receive supervision only through relational losses.The task-only baseline uses seven pointwise-supervised views.Source: §3 · p. 4
  • The relational objective includes four provenance-invariance residuals and three new-evidence update residuals, with target differences relying on three mutually distinct sources.Updates from multiple roots sharing a source need not be additive.Source: §3 · p. 4
  • An order penalty compares c11 with its reversed presentation, and LQET uses 13 training views versus seven for task-only under matched families and optimizer-update counts.The passage also states that each loss component is averaged separately before weighting.Source: §3 · p. 4

4 Experimental design

The experiments compare LQET and task-only training on matched prompts, multiple distribution shifts, and recursive relay histories. Primary endpoints and a paired bootstrap support a prespecified conjunctive decision criterion.

4 Experimental design

  • Training uses Qwen3-4B-Instruct-2507 and Phi-4-mini-instruct with three paired seeds, 4,000 training families, and 500 updates per run.The same fixed optimizer settings were transferred to Phi without validation-set hyperparameter search, and final checkpoints were evaluated.Source: §4 · p. 4
  • Each run is tested on 400 IID families, 800 controlled-shift OOD families, and 200 recursive-relay families at depths 1, 2, 4, and 8.The OOD set covers five factor groups, including longer histories, provenance graphs, templates, and prior or calibration supports.Source: §4 · p. 5
  • Primary endpoints pool update RMSE and supervised-view KL over 800 OOD families, while depth-8 relay drift measures score change after eight generated relays.Backbone-level estimates average the three seed-level estimates, with the RMSE square root taken within each seed.Source: §4 · p. 5
  • The prespecified criterion requires lower update RMSE and depth-8 drift in every seed with pooled upper bounds below zero, plus supervised-view KL within a +0.02-nat margin.Inference uses 10,000 paired crossed seed-by-family bootstrap replicates and analyzes each backbone separately.Source: §4 · p. 5

5 Results

Across two backbones, LQET improves new-evidence updating and relay stability while keeping supervised-view KL within the stated non-inferiority margin. The results also show selective invariance, reduced feedback amplification in simulation, and a distinct contribution from presentation-order consistency.

5.1 Controlled results across backbones

  • Across relay depths, LQET mean drift stays below 0.14, and update RMSE is lower on every controlled shift.Supervised-view KL is lower or essentially unchanged on four shifts, but rises on the held-out prior-and-calibration shift, the only shift changing both numerical supports.Source: §5.1 · p. 5, Figure 2 · p. 6
  • New-evidence update RMSE falls 41.25% on Qwen and 44.45% on Phi, while depth-8 relay drift falls 91.36% and 89.38%, respectively.Both improvements hold in every training seed; pooled supervised-view KL changes by +0.00228 on Qwen and +0.00120 on Phi, with upper bounds below the +0.02-nat margin.Source: §5.1 · p. 5, Table 1 · p. 6

5.2 Selective invariance, not uniform update suppression

  • Copy-versus-new RMSE drops from 1.0145 to 0.4383 on Qwen and from 0.9818 to 0.4630 on Phi, while new-evidence update errors remain near task-only.The matched comparison holds report author and displayed outcome fixed while varying supplied provenance; LQET is less sensitive to declared relays while retaining responses to declared new observations.Source: §5.2 · p. 6, Figure 3 · p. 7

5.3 Closed-loop feedback dynamics

  • All three closed-loop metrics improve in every backbone-seed pair, with mean reductions of 64.6–76.9% on Qwen and 79.1–90.9% on Phi.In the simulation, confidence influences how many inherited reports return; lower sensitivity to inherited reports also reduces feedback amplification.Source: §5.3 · p. 7

5.4 What each relation contributes

  • Full LQET lowers the order-sensitivity gap from 0.0426 to 0.0359 compared with no-order, showing the order term's clearest contribution is presentation-order robustness.Full LQET also lowers update RMSE from 0.4105 to 0.4058 and supervised-view KL from 0.0239 to 0.0232; update-consistency supervision with composition views accounts for most of the compositional gain.Source: §5.4 · p. 7

6 Related work

Related work studies probabilistic updating, repetition effects, feedback, and evidence provenance from several perspectives. This paper distinguishes its focus on explicit report lineage and supplied dependencies from approaches that infer or retrieve them.

Belief updating and predictive consistency

  • Prior work examines probabilistic updating from demonstrations [19], evidence reliability [13], sequential belief trajectories, and martingale consistency [8] [14].This work instead asks whether supplied dependence changes the evidential force of otherwise matched reports.Source: §6 · p. 7

Repetition bias and dependent social learning

  • Repetition studies report source-preference changes [22], paraphrase effects and presentation-order sensitivity, while graph-based methods address data incest when topology and a probabilistic model are available.LQET extends repetition invariance to explicit multi-hop lineage, reliability-conditioned targets, new-root updates across relay histories, composition, and presentation order.Source: §6 · pp. 7–8

Feedback loops and evidence propagation

  • Prior work examines how model outputs enter later contexts [18] [23] and traces evidence propagation through later messages [25].The paper's simulation isolates score-dependent return of inherited reports and provenance-sensitive updating.Source: §6 · p. 8

Provenance, aggregation, and dependence discovery

  • Unlike evidence aggregation or dependence-discovery approaches [28], LQET assumes parent-report links are supplied and learns consistent updates from them.The paper distinguishes report-lineage updating from retrieving evidence or discovering hidden dependence.Source: §6 · p. 8

7 Scope and limitations

The evaluation supports conclusions within a controlled binary setting with supplied parent links and a specified source-reliability model. Transfer, measurement, and training-protocol boundaries qualify the reported gains.

Scope and limitations

  • The study evaluates controlled binary updating with supplied parent links and a specified source-reliability model; transfer to larger models, naturalistic tasks, or incomplete or unreliable provenance remains for further study.The forced-choice YES-NO score measures binary preference; free-form probability estimation and downstream decision quality require separate evaluation.Source: §7 · p. 8
  • Training comparisons differ in transcript-view exposure, so reported gains characterize the complete training protocol.Under held-out prior and calibration supports, lower update RMSE accompanies higher supervised-view KL, leaving numerical generalization as a remaining challenge.Source: §7 · p. 8
  • The feedback simulation uses a prescribed trust rule; human-participant studies are needed to assess how this mechanism operates in practical human-AI interaction.Source: §7 · p. 8

8 Conclusion

LQET treats evidence accounting as relational learning over provenance-aware reports, pairing stability under relays with consistent updates when genuinely new evidence arrives.

8 Conclusion

  • LQET connects predictions across matched transcripts through provenance invariance and new-evidence update consistency, while matched controls distinguish stability from indiscriminate update suppression.A confidence-dependent feedback simulation shows reduced amplification when model predictions shape future inputs.Source: §8 · p. 8

A.1 Beta–Bernoulli derivation

  • The Bayesian target uses distinct roots once: same-source roots become dependent after reliability is marginalized, while matched-new and counter controls vary provenance and outcome polarity separately.Integrating source reliability yields posterior log-odds; the log beta-function terms cancel between the two values of Y.Source: §A.1 · p. 11

A.2 Report provenance and validity

  • A provenance-equivalence class contains transcripts with the same set of relevant roots; equal source-by-outcome counts suffice for equal targets but do not define class membership.Each root has one introducing report, and relays must link to a parent carrying that root.Source: §A.2 · pp. 11–12

B Matched transcript views

  • The benchmark has 14 matched views, with LQET trained on 13 because c00 duplicates h00; Table 2 distinguishes pointwise targets from relational loss terms.The primary task-only and LQET runs are evaluated on all 14 views in the static IID and controlled-shift sets.Source: B Matched transcript views · p. 12, Table 2 · p. 12

C.2 Optimization configuration

  • Optimization settings were fixed before the multi-seed Qwen runs and transferred unchanged to Phi, without validation-based hyperparameter search or checkpoint selection.Validation results served only as run diagnostics.Source: §C.2 · p. 13

C.3 Generator supports and prompt format

  • Generator prompts expose parent links and whether reports introduce independent observations or relay earlier ones; each controlled shift changes only its named factor group.The generator samples source reliability from Beta(c+1, w+1) and uses separate SHA-256-derived streams for evidence, calibration, domain, graph, and surface choices.Source: §C.3 · pp. 13–14, Table 5 · p. 13

C.4 Static and recursive-relay evaluation sets

Evaluation spans static IID and controlled-shift families plus recursive relay chains, with comparisons using paired seed-by-family resampling.

C.4 Static and recursive-relay evaluation sets

  • Static evaluation uses 400 IID families and five 160-family controlled shifts, while recursive-relay evaluation follows 200 families through depth eight.The recursive snapshots are nested, and each new-root probe is evaluated on a separate branch.Source: §C.4 · p. 14

C.5 Endpoint definitions and bootstrap

  • New-evidence update RMSE uses three oriented update edges over 800 pooled controlled-shift families, while depth-eight drift compares base and eight-relay scores.Endpoints are averaged across three seeds; 10,000 paired crossed bootstrap replicates resample seeds and shared family rosters.Source: §C.5 · pp. 14–15

D.1 Every training seed

  • Table 6 reports per-seed primary endpoint effects as LQET minus task-only, computed from unrounded estimates, with lower values better.The supplied caption identifies the table's scope and comparison direction.Source: Table 6 · p. 16

D.2 IID test results

Across controlled shifts, LQET improves new-evidence updates, though the hardest prior-and-calibration shift has a small supervised-view KL increase. Further checks examine benchmark targets, provenance selectivity, and confidence-linked feedback.

D.2 IID test results

  • The IID evaluation reports results on 400 independent test families, with point estimates averaged across three paired training seeds.Source: Table 7 · p. 16

D.3 Controlled-shift decomposition

  • Update RMSE falls from 0.9817 to 0.8694 on Qwen (11.4%) and from 1.0439 to 0.9005 on Phi (13.7%), while supervised-view KL rises approximately 0.013 nats on each.The prior-and-calibration shift requires generalization to held-out numerical supports for both the class prior and source-calibration records.Source: §D.3 · p. 17

D.4 Recursive-relay depth trajectory

  • Table 9 reports mean absolute pre-update log-odds drift over three seeds across recursive-relay depths.Source: Table 9 · p. 17

E.1 Bayesian-target recovery from rendered prompts

  • The rendered-prompt calculator processed 16,800 views, with maximum absolute difference below 5 × 10−15 from exact Bayesian log-odds.This confirms the Bayesian target is uniquely determined by the rendered prompt in this benchmark.Source: §E.1 · p. 17

E.2 Matched copy-versus-new-root controls

  • Matched-copy and matched-new controls hold author and displayed outcome fixed; results argue models use supplied provenance rather than author/outcome alone or uniform suppression of log-odds changes.Source: §E.2 · p. 18

F Closed-loop feedback details

  • LQET reduces the mean cumulative number of simulated human relays from 5.4349 to 4.4557 on Qwen and from 5.0469 to 4.3438 on Phi; relay count depends on score-derived confidence.Source: F Closed-loop feedback details · p. 19

G Component analysis

The component analysis compares full LQET with variants that remove or alter objective components, finding distinct effects on update accuracy, order sensitivity, and relay drift.

G Component analysis

  • Full LQET and No-order use identical forward computation and 13 training views, while Pair-invariance uses 11; No-order sets the order-loss weight to zero.Source: G Component analysis · p. 19
  • No-order reduces update RMSE by 0.1755 and the order-sensitivity gap by 0.0759 versus Pair-invariance; composition edges account for most update improvement, but do not isolate the loss term.Figure 4 presents the single-seed component trade-off and edgewise update RMSE.Source: Figure 4 · p. 20, G Component analysis · p. 20
  • The order term most clearly improves the order-sensitivity gap and modestly improves update RMSE and supervised-view KL, while No-order has lower depth-8 drift for this seed.Source: G Component analysis · p. 20
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