BaRe-Mem: Bayesian Reliability Memory for Robust and Adaptive Agent Consultation

1 INTRODUCTION

• Task-dependent advisor capabilities and misleading or mutually reinforcing errors make response aggregation alone insufficient for reliable consultation.The central model must estimate the reliability of external evidence for the current question.Source: §1 · p. 1
• Historical memory should turn prior interactions into contextual reliability estimates that regulate external evidence, adapt to changing advisors, and scale over long interactions.The introduction argues reliability should also determine whether to consult, given that collaboration can yield diminishing or negative gains as central-model capability rises.Source: §1 · pp. 1–2
• BaRe-Mem estimates advisor and central-model reliability from verified outcomes, using the estimates to modulate responses and choose between consultation and autonomous reasoning.The paper also applies the mechanism to worker selection in agent teams.Source: §1 · p. 2

2 RELATED WORK

• Text-based memory stores or distills experience into records, reflections, skills, and trajectories, but is constrained by compression fidelity and retrieval noise.The cited approaches include external records and reusable summaries of experience.Source: §2 · p. 2
• Continuous-memory approaches encode experience in persistent latent states, neural memory, generated tokens, or structured competence states updated across interactions.The paper distinguishes this line from text-based memory construction.Source: §2 · p. 2
• Memory steering spans prompt conditioning, parameter adaptation, and internal-state modulation; BaRe-Mem adopts attention modification to apply its reliability estimates to advisor influence.The related work says these estimates can directly modulate each advisor response’s influence.Source: §2 · p. 2

3.1 ORGANISING HISTORICAL RELIABILITY

• The memory represents each candidate using question and answer-content beliefs plus source identity, modeling reliability from both contextual similarity and the candidate response.Verified correctness is modeled with Bayesian linear regression; Kalman-gain updates incorporate new outcomes online using current posterior uncertainty.Source: §3.1 · p. 3
• Without verified evidence, advisors begin with equal reliability; verified correct outcomes raise an estimate, while an incorrect outcome lowers it.The Kalman gain controls update magnitude, and candidates without new evidence remain unchanged.Source: §3.1 · p. 3, Figure 1 · p. 3

3.2 RELIABILITY-GUIDED ATTENTION

• Estimated advisor reliability rescales attention to advisor-response tokens before softmax, leaving the most reliable advisor unchanged and progressively downweighting less reliable ones.This steering uses relative advisor reliability and adds no trainable parameters or training.Source: §3.2 · p. 4

3.3 DECIDING WHETHER TO CONSULT

• Consultation ability interpolates between performance with trustworthy evidence and autonomous ability reduced by unreliable evidence, using the memory’s confidence that trustworthy advice is available.The model compares this estimated consultation ability with autonomous ability on the current question.Source: §3.3 · p. 4
• The current question supplies autonomous ability and the highest advisor reliability, while verified outcomes train estimates of consultation success with reliable evidence and degradation under unreliable evidence.The resulting estimates determine current-question consultation ability.Source: §3.3 · p. 4
• The model selects consultation when its estimated accuracy is at least its autonomous ability; otherwise it reasons autonomously.Consultation is preferred when expected gain from reliable evidence outweighs potential degradation from unreliable evidence.Source: §3.3 · p. 5

4.1 EXPERIMENTAL SETUPS

• The evaluation covers six central models and six advisors across capability-supported and capability-challenging benchmark suites, with questions shuffled within each regime.The supported suite includes GSM8K, APPS, and SQuAD; the challenging suite spans PIQA, MMLU, OpenBookQA, SciQ, BBH, and SuperGLUE.Source: §4.1 · p. 5

4.2 ADAPTIVE CONSULTATION UNDER MISLEADING INFORMATION

• In challenging tasks, Question + Peers and two-round Debate fall below the No consultation baseline once misleading information exceeds 50%.The evaluation varies misleading responses from 0% to 100%; the responses remain fluent and on-topic but are verified incorrect.Source: §4.2 · p. 5
• BaRe-Mem remains above autonomous reasoning across tested misleading-information levels, while reliability-guided consultation without an autonomous option eventually falls below that baseline on challenging tasks.In the capability-challenging regime, consultation ratios fall from 90% to 21% for Qwen3-14B and from 85% to 18% for Phi-4 as misleading information rises from 0% to 100%.Source: Figure 2 · p. 6, §4.2 · p. 6, Table 1 · p. 7

4.3.1 AUTONOMOUS ABILITY ESTIMATION

• Estimated autonomous ability κ tracks changes in empirical autonomous accuracy, and grouped-question accuracy increases monotonically with κ for both analyzed models.The analysis uses Qwen3-14B and Phi-4.Source: §4.3.1 · p. 7, Figure 3 · p. 7

4.3.2 PREDICTED VS. REAL CONSULTATION GAIN

• Real consultation gain increases with predicted gain across misleading-information ratios, and the predicted consultation-versus-autonomy boundary aligns near zero.As misleading information increases, both predicted and real consultation gains shift downward and left, primarily alongside lower estimated consultation ability.Source: Figure 4 · p. 8, §4.3.2 · p. 8

4.3.3 LEARNING FROM SPARSE FEEDBACK

• Both Qwen3-14B and Phi-4 gain over no-feedback performance with less than 1% verified feedback, with performance then largely saturating as feedback increases.The below-1% region corresponds to approximately 170 samples; most eventual gain arrives well before full feedback.Source: Figure 5 · p. 8, §4.3.3 · pp. 8–9

4.4 REAL-WORLD APPLICATION: AGENT TEAM ROUTING

• BaRe-Mem achieves the highest task completion across both lead agents and all verification settings, outperforming random routing and routing by historical success counts.Its advantage persists with no verification, lead-agent verification, and exact dataset verification.Source: Figure 6 · p. 9, §4.4 · p. 9
• With fewer worker calls, BaRe-Mem reaches higher task completion; all routing strategies approach the same ceiling once every worker has been tried.The ceiling is reached when at least one worker can solve the sub-task.Source: Figure 7 · p. 9, §4.4 · p. 10

• BaRe-Mem uses persistent reliability estimates to adaptively determine whom to trust and whether to consult.The authors suggest persistent reliability memory as a practical foundation for robust consultation in long-horizon multi-agent systems.Source: §5 · p. 10

A.1 BAYESIAN REGRESSION POSTERIOR

• The posterior is Gaussian with mean m_n and precision P_n, and its mean uniquely minimizes the corresponding regularized least-squares objective.The derivation expresses the objective as a quadratic and obtains the minimizer by setting its gradient to zero.Source: §A.1 · p. 16

A.2 DERIVING THE KALMAN GAIN

• A data-dependent Kalman gain weights each new prediction residual using current posterior uncertainty and minimizes conditional expected squared estimation error.The gain depends on existing observations and the new input, not the new outcome.Source: §A.2 · pp. 16–17

A.3 EXACT ONLINE UPDATE

• Recursive rank-one updates recover the batch posterior exactly after every verified observation, and BaRe-Mem applies them to its reliability-memory inputs and outcomes.The covariance update avoids recomputing a matrix inverse.Source: §A.3 · pp. 17–18

A.4 ORDER INDEPENDENCE

• For a fixed set of verified observations, BaRe-Mem’s posterior is invariant to the order in which those observations are processed.The memory is therefore insensitive to the arrival order of that evidence.Source: §A.4 · p. 18

A.5 DERIVING THE RELIABILITY ESTIMATE

• BaRe-Mem estimates reliability as the probability that predictive signed correctness is positive, using the posterior mean and uncertainty for each candidate.Before verified evidence, all candidates receive neutral reliability of 1/2.Source: §A.5 · pp. 18–19

A.6 DERIVING THE ESTIMATES OF ρ AND δ

• A two-dimensional Bayesian regression estimates consultation ability when evidence is trustworthy and its shortfall relative to autonomous ability when evidence is unreliable.Intermediate trust levels provide evidence about both parameters.Source: §A.6 · pp. 19–20

A.7 BREAK-EVEN TRUST AND DECISION REGIMES

• When estimated trustworthy consultation ability exceeds autonomous ability and unreliable consultation degrades performance, consultation is preferred above a break-even trust threshold.The threshold rises with greater autonomous ability or unreliable-consultation degradation, and falls when trustworthy evidence is more useful; other parameter regimes can imply always consulting or never consulting.Source: §A.7 · pp. 20–21

A.8 ACCURACY OF ADAPTIVE CONSULTATION SELECTION

• If adaptive selection never chooses the option with lower true accuracy, its expected accuracy is at least that of always consulting or always reasoning autonomously.A wrong-side choice incurs a penalty equal to the true accuracy gap, so errors near ties have little effect on final accuracy.Source: §A.8 · p. 21

B.1 CAPABILITY OF ADVISORS AND CENTRAL MODELS

• Advisor performance varies substantially across tasks, yet the pool often contains a correct answer, making question-specific identification of reliable evidence important.The capability-challenging regime exhibits stronger task-dependent heterogeneity across models and tasks.Source: §B.1 · pp. 21–23

B.2 CONSULTATION GAINS ACROSS CENTRAL MODELS

• 7.2–12.4 accuracy points in the capability-challenging regime and 4.3–13.7 points in the capability-supported regime are BaRe-Mem’s gains across six central models.Figure 8 presents autonomous accuracy, BaRe-Mem’s additional gain, individual advisor accuracy, and the fraction of questions with at least one correct advisor.Source: Figure 8 · p. 23, §B.2 · p. 23

• R1-Distill-Qwen-7B receives the largest advisor attribution and DeepSeek-Coder-V2-Lite the smallest across central models, while attribution shares vary by central model.Figure 9 attributes consulted questions to the advisor with the highest pre-feedback reliability estimate; the shares do not imply exclusive use of one advisor.Source: §B.3 · p. 23, Figure 9 · p. 24
• BaRe-Mem retains autonomous reasoning for every central model instead of forcing consultation on all questions.Figure 9 distinguishes autonomous answers from questions attributed to an advisor.Source: §B.3 · p. 23, Figure 9 · p. 24

B.4 ADVISOR RELIABILITY ESTIMATION

• Across six advisors, higher misleading-information ratios lower both empirical accuracy and reliability estimates from Qwen3-14B and Phi-4.Figures 10–15 show these curves across misleading ratios from 0% to 100%.Source: §B.4 · p. 24, Figure 10 · p. 25, Figure 11 · p. 25
• Reliability estimates decline faster early and then change less as accumulated evidence reduces posterior uncertainty.For a fixed representation, the Kalman gain corrects a fraction v/(1 + v) of the prediction residual.Source: §B.4 · p. 24
• At 100% misleading information, empirical accuracy is nearly 0 while estimates remain around 0.2, exposing a calibration gap.Unit observation noise leaves nonzero predictive probability even when uncertainty about regression parameters vanishes; this is not a universal lower bound.Source: §B.4 · p. 24

B.5 CONSULTATION ROBUSTNESS ACROSS ADDITIONAL CENTRAL MODELS

• At 50% misleading information in the capability-challenging regime, adding reliability memory improves accuracy over Question + Peers by 9.4, 12.6, and 9.1 percentage points for Qwen3-4B, Qwen3-8B, and Qwen3-14B, respectively.The corresponding gains are 11.8 points for Ministral-8B, 7.7 for Qwen2.5-7B, and 19.9 for Phi-4; both methods consult on every question.Source: §B.5 · p. 27
• In the capability-challenging regime, BaRe-Mem stays above autonomous reasoning across tested misleading-information levels for all six models.At 100% misleading information, it exceeds always-consult Advisors + memory by 13.0%–34.6% points and autonomy by 1.5%–2.8% points.Source: §B.5 · p. 27
• In the capability-challenging regime, all six models reduce consultation from 85%–90% without misleading information to 9%–21% at the highest misleading ratio.In the capability-supported regime, Phi-4’s consultation ratio drops only 1%–3% points, while Ministral-8B drops from 84% to 77% and 85% to 71%.Source: §B.5 · p. 27

C.1 AGENT TEAM PIPELINE.

• For worker routing, the lead agent ranks candidates per sub-task, tries the next worker after a rejected report, and updates reliability from verified outcomes.Checking determines whether to retry; after commitment, gold labels update memory for queried workers, while unqueried workers receive no update.Source: §C.1 · p. 31, Figure 22 · p. 32

C.2 TASK SOLVED ACCURACY

• With no retries, BaRe-Mem achieves higher sub-task completion than random or historical-success routing for all six lead models.It improves task completion over random routing by 13.4%–17.8% points across the six models.Source: §C.2 · p. 32
• Under dataset-verifier checking, BaRe-Mem reaches 51.9%–55.0% task completion, exceeding historical-success routing by 1.8%–4.9% points and random routing by 9.1–11.4 points.Sub-task completion exceeds historical-success routing by 1.7%–3.5% points; BaRe-Mem has the highest task and sub-task completion for every lead model.Source: §C.2 · p. 32
• Lead-agent checking improves BaRe-Mem task completion over no checking for five of six models by 1.5%–3.0% points, while dataset-verifier checking improves it over lead-agent checking by 11.6%–14.2% points across all six.For Ministral-8B, lead-agent checking changes task completion from 41.6% to 40.8%, while dataset-verifier checking raises it to 55.0%.Source: §C.2 · pp. 32–33

C.3 AGENT TEAM SWEEP

• Across six lead models, BaRe-Mem achieves higher task and sub-task completion with fewer worker calls, outperforming historical-success routing even with one worker per sub-task.As the budget reaches all seven workers, methods approach the same ceiling because they share the candidate pool; smaller-budget gaps reflect how early a capable worker is selected.Source: Figure 29 · p. 35, §C.3 · p. 36, Figure 30 · p. 36
• Conditioning worker reliability on the current sub-task yields a more informative ranking than a single aggregate past-success rate, with consistent advantages across six lead models.This supports the same instance-specific reliability principle used in advisor consultation.Source: §C.3 · p. 36

C.4 ADAPT SPEED

• Initial-worker accuracy rises quickly early in the 6,404-sub-task stream and remains above historical-success routing, while random routing stays nearly unchanged.The stream is partitioned into eight consecutive blocks of approximately 800 sub-tasks; early verified outcomes have greater influence when posterior uncertainty is high.Source: §C.4 · p. 37, Figure 31 · p. 37