Retaining Repair Hypotheses for Cost-Aware Execution

• Prior work addresses evidence-based model learning, plan-constrained repair, and executable-world-model search; this study focuses on finite compatible repairs at the execution boundary.Source: §1 · p. 2
• The interface retains compatible programs, weights their guard predictions, and uses their disagreement to choose a route, buy a diagnostic, or take a backup.Source: §1 · p. 2
• A half-AI, half-uniform mixture has lower aggregate independent-task cost than either the point-repair or uniform endpoint, but its paired interval excludes zero only versus point repair.Source: §1 · p. 2
• Value-directed probes help when information is inexpensive, but access charges shrink their benefit and can erase it on isolated tasks.Source: §1 · p. 2
• Under AI-weighted beliefs, workload-valued selection costs less in aggregate than random selection; under uniform beliefs, information gain is cheaper, and uniform normal learning beats AI-weighted workload-valued selection.Source: §1 · p. 3

• Each synthetic device has two sequential stages that accept or reject bit-vector contexts, with stage B running only after stage A succeeds and a known-cost backup available.Source: §2 · p. 4
• Candidate guards start from a shared erroneous guard and use a small Boolean grammar; equivalent expressions are represented by truth-table behavior, and observations remove incompatible candidates.Source: §2 · p. 4
• The controller treats hidden guards as model parameters, while diagnostics and execution both yield observations; it approximates planning with separate stage beliefs and one-step diagnostic scoring, without an optimality guarantee.Source: §2 · p. 4
• The synthetic context identifiers encode four Boolean settings without assigning them physical sensor meanings.Source: §2 · p. 4

3.1 Hypothesis representation

• Each stage retains compatible behaviors with normalized weights; uniform beliefs assign equal weight, while AI- or MDL-weighted beliefs allocate half to a selected repair and half uniformly.The half-mass allocation is made once at initialization; observations eliminate incompatible candidates and renormalize the remaining weights.Source: §3.1 · pp. 4–5

3.2 Choosing an execution route

• The controller minimizes expected route-plus-fallback cost across menu routes and immediate backup; because backup guarantees completion, first-route success—not completion—is reported as a success measure.Task cost uses action costs and a backup cost of 8.Source: §3.2 · p. 5

3.3 Purchasing a diagnostic observation

• Tests are selected by posterior-dependent expected task-cost value net of test cost, then update beliefs; the access-aware variant charges reset and stage-B setup.Independent probes take at most two tests, while repeated-workload selection sums expected reductions across remaining menus and shares a four-test budget.Source: §3.3 · p. 5

3.4 Decision relevance and stopping

• Stopping targets decision value, not full model identification: if one route is optimal in every test branch, a positive-cost test has negative net value.The criterion is myopic and does not fully account for information later acquired through ordinary execution.Source: §3.4 · p. 6

3.5 A recorded decision

• For device 5, menu 7, an accepted stage-B test switches backup to route (5,11), costing 4.25 total versus AI-point backup 8 and uniform no-test 3.25.The recorded case uses direct stage-B access; its total is not comparable to access-aware costs.Source: §3.5 · p. 6

• The small-grammar cohort has 24 two-stage devices, 64 menus per device, and 1,536 task decisions treated as repeated measurements; route menus use contexts held out from initial observations.Six common observations precede decisions, and four possible routes are available per menu.Source: §4 · pp. 6–7
• Matched controls compare a generated point repair with its AI-weighted mixture, test uniform and MDL weighting, and replace flat query prices with reset and setup charges.The point repair and AI-weighted mixture share the generated repair and observations.Source: §4 · p. 7
• Every repeated-work arm learns from ordinary execution outcomes, while diagnostic arms add tests; selector comparisons use a common four-test cap.The repeated-workload study runs the same devices and menus in sequence.Source: §4 · p. 7
• The larger-grammar study uses 12 eight-variable DNF guards and 384 menu decisions, comparing single repairs with syntax-counted candidate predictions; its table reports execution cost only.Its prediction histories use six initial observations and four additional tests per guard, with 64 held-out contexts per world.Source: §4 · pp. 7–8
• Reported costs measure abstract action expenditure, excluding common data-acquisition and model-generation latency; exploratory intervals are conditional on the saved cohort and paired by device.The device is the aggregation unit, and task menus are correlated within devices.Source: §4 · p. 8

5.1 Repair uncertainty and test cost

• At test cost 0.25, AI-weighted testing lowers total cost from 9,029.75 to 8,322.5 (7.83%); at cost 4, both policies buy no tests.The AI-weighted policy improves totals on 18 of 24 devices and worsens them on six.Source: §5.1 · p. 8, Table 2 · p. 8, Figure 3 · p. 9

5.2 Access-charged diagnosis in repeated workloads

• With access charges, isolated-task testing does not lower cost: uniform VOI costs 9,278 versus 9,263.75 without diagnosis, and the AI-weighted policy buys no tests.In repeated work, workload-valued selection lowers AI-weighted total cost by 431 (5.07%), from 8,500.25 to 8,069.25.Source: §5.2 · p. 9, Figure 3 · p. 9, Table 4 · p. 10
• Uniform normal learning costs 109.75 (1.36%) less than AI-weighted workload-valued selection; adding workload tests under uniform beliefs raises cost despite more first-route successes.The aggregate difference first becomes nonpositive after 20 jobs per device and remains so through job 64.Source: §5.2 · pp. 9–10, Figure 3 · p. 9, Table 4 · p. 10

5.3 Device-level heterogeneity and execution events

• Aggregate savings mask device-level variation: workload-valued selection improves 11 devices, worsens 13, and has a median cost difference of +4.375.Nine initially incorrect guards are refuted only with diagnostics, eight on devices where costs improve.Source: §5.3 · p. 10, Figure 4 · p. 11

5.4 Candidate retention in a larger grammar

• On the same AI-selected history, the full belief predicts 599 of 768 outcomes correctly versus 568 for an AI repair, and lowers execution cost from 3,106.25 to 3,054.625.The six-device paired interval includes zero, and the comparison does not isolate weighting from candidate retention.Source: Table 5 · p. 11, §5.4 · p. 11

5.5 Gap to the full-information oracle

• The full-information oracle is an unpaid evaluation bound; AI-weighted workload selection closes 45.01% of its baseline gap, while uniform normal learning leaves a 416.75-unit gap.For the larger grammar, the full-belief cost reduction is 17.375 units, or 3.71% of the oracle gap.Source: §5.5 · pp. 11–12

5.6 Matched-budget diagnostic selection

• Under the AI-weighted belief, workload-valued selection costs 8,069.25 versus 8,346.97 for mean random selection (3.33% less); its advantage over EIG is uncertain.The workload-minus-random interval excludes zero, while the workload-minus-EIG interval includes zero.Source: Table 6 · p. 12, §5.6 · p. 12
• Under uniform beliefs, EIG costs 7,920.5 versus 7,977.75 for workload-valued selection; uniform normal learning costs 39 less than EIG, with an interval including zero.Workload-valued selection also costs 57.25 more than EIG, with a paired interval above zero.Source: §5.6 · p. 13, Figure 5 · p. 13

6 Related work

• Model-repair work spans learning from traces, minimal edits that satisfy plan constraints, and language-model repair evaluated by model recovery and test-plan validity.The present work instead evaluates task costs while multiple repairs remain compatible.Source: §6 · pp. 13–14
• Bayesian exploration propagates uncertainty into action values, while this interface conditions finite executable guard repairs and evaluates available tests by downstream decision cost.Expected information gain is one common experimental-design utility; workload-valued selection uses expected task cost.Source: §6 · p. 14
• Executable-world-model methods learn through acting, but their program-search populations differ from this paper’s weighted execution-time belief over compatible repairs.The bounded guard grammar enables complete candidate conditioning and controlled point-repair versus belief-based comparisons.Source: §6 · p. 14
• Diagnosis and hypothesis-identification methods seek explanations, equivalence classes, or distinguishing queries, whereas this interface uses remaining uncertainty in route, test, and backup choices.Troubleshooting work also uses expected-cost reasoning with observations, repairs, and fallback.Source: §6 · p. 14
• Belief-state planning and BAMCP account for information gained through action, while this workload heuristic scores diagnostics against remaining menus without forecasting subsequent passive learning.LLM-SMC-S maintains weighted language-model hypotheses and selects experiments by information gain; this implementation enumerates finite guards and accounts for task and access costs.Source: §6 · pp. 14–15

7 Discussion

• Diagnostic value shrinks when reset and setup must be purchased; under repeated work, uniform beliefs fall back less, observe more, and refute more initially incorrect AI guards.These event summaries locate policy differences but do not identify the causal contribution of each event type.Source: §7 · p. 15
• The cheaper diagnostic selector changes with belief weighting, making belief concentration a candidate cue—not a validated switching rule—for choosing task-cost versus information-gain scoring.Selection and weighting should be assessed together against a controller already learning from execution.Source: §7 · p. 15
• Quantitative findings concern deterministic finite guards, known task menus and costs, and complete candidate support within the chosen grammar.Applying the interface requires executable candidates, observation likelihoods, and known action costs; reported costs exclude initial acquisition and model inference.Source: §7 · p. 15

8 Reproducibility

• The three archived generation batches identify provider model gpt-6-astra with high reasoning effort, but the model snapshot and decoding settings are unavailable.Prompts, observation packets, output schemas, hashes, and metadata accompany the fixed generated outputs in the arXiv ancillary files.Source: §8 · p. 15
• The ancillary archive includes the parser, planner, belief-update and test-selection functions, saved tasks and repairs, and scripts or event checks for reported analyses.Replay coverage includes principal small-grammar comparisons and the MDL cheap-test arm; other analyses use saved decisions, predictions, histories, and scripts.Source: §8 · p. 15

9 Conclusion

• 7.83 percent; inexpensive tests reduce the AI-weighted policy’s cost on the 24-device cohort.Access-charged workload-valued selection reduces its baseline by 5.07 percent and costs 3.33 percent less than matched-budget random testing under the same belief; its 1.79 percent advantage over EIG is sensitive to two devices.Source: §9 · p. 16
• Under uniform beliefs, EIG is cheaper than workload-valued selection, while uniform normal learning without tests costs less than every AI-weighted arm.In the larger grammar, the full syntax-counted belief predicts 599 versus 568 of 768 held-out outcomes correctly, but its lower aggregate execution cost has an interval including zero.Source: §9 · p. 16
• The authors report that AI assistants helped implement analysis code and draft and edit the manuscript, while they defined and verified the research and conclusions.The authors state that they take full responsibility for the content.Source: §9 · p. 16