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Strategically Diverse Sampling for Self-Training

Alexander Gurung, Esmeralda S. Whitammer, Mirella Lapata

arXiv:2609.31571v1cs.CL

TL;DR

Repeated sampling is central to many LLM methods, but IID self-training tends to favor strategies a model already uses. This paper trains on approaches elicited through GROOT or Verbalized Sampling and finds that strategic sampling outperforms IID across coding and story planning, including when the diverse traces are incorrect.

  • Problem

    IID self-training typically samples responses and filters primarily for correctness, while repeated-sampling methods benefit when responses meaningfully differ in approach.

    Source: §1 · p. 1

  • Method

    The paper trains on strategically diverse data generated by GROOT’s hierarchical paths or Verbalized Sampling’s unstructured approach proposals.

    Source: §1 · p. 2

  • Results

    Strategically sampled training outperforms IID across coding and story planning, and strategically diverse incorrect traces outperform correct IID traces and IID distillation from a 235B teacher.

    Source: §1 · p. 2

  • Takeaways & Limitations

    Strategic diversity can matter more than correctness, sampling budget, or teacher scale for self-training on difficult tasks.

    Source: §1 · pp. 2–3

    Both methods add a generation call per problem or plan list, and this extra cost is excluded from the reported sampling budgets.

    Source: §3 · p. 4

Abstract

from arXiv · show

Many LLM training and inference methods, including RL and test-time scaling, depend on repeated sampling, but benefit only when the responses meaningfully differ. Self-training faces the same challenge: training data is typically constructed by sampling IID responses and filtering primarily for correctness, thereby overrepresenting strategies a model already favours. We investigate strategic diversity, or substantive variation among approaches to a problem, as an alternative principle for constructing self-training data. We generate strategically diverse data with two sampling methods: GROOT, a new method which constructs a hierarchical tree of approaches and samples distinct paths, and Verbalized Sampling (VS), adapted to produce an unstructured set of approaches. Across competitive programming and Next-Chapter Prediction domains, models trained on strategically sampled data outperform IID-trained counterparts on difficult tasks and provide strong initializations for RL and test-time scaling. Most strikingly, self-training on strategically diverse but incorrect traces from Qwen3-4B outperforms IID distillation from a 235B teacher. These results challenge prevailing assumptions about what makes useful self-training data and show that diversity of approaches can matter more than correctness or teacher scale.

1 INTRODUCTION

The paper proposes strategic diversity—substantive variation in approaches—as an alternative to correctness-filtered IID self-training. It introduces two sampling methods and reports gains across coding and story planning, including stronger initializations for downstream methods.

1 INTRODUCTION

  • Repeated-sampling methods benefit from meaningfully different responses, but IID samples often repeat a favored strategy, limiting their value, especially near a model’s capability boundary.Self-training commonly samples outputs and fine-tunes on those that pass a correctness filter.Source: §1 · p. 1
  • GROOT elicits distinct paths through a hierarchical strategy tree, while Verbalized Sampling proposes approaches with estimated probabilities for separate solution generation.Both methods generate strategically diverse self-training data from the model being trained.Source: §1 · pp. 2–3
  • The evaluations span competitive programming and Next-Chapter Prediction, whose approaches involve hierarchical algorithm choices versus interdependent narrative decisions without an obvious hierarchy.Frontier coding problems are those solved in at most two of 64 IID attempts.Source: §1 · p. 2
  • Across coding and story planning, strategically sampled training outperforms IID; strategically diverse incorrect traces also beat correct IID traces and IID distillation from a 235B teacher.Strategically trained models also provide stronger initializations for RL and test-time aggregation.Source: §1 · pp. 2–3

2 RELATED WORK

Prior work addresses reasoning-data construction, post-training diversity collapse, and diversity measurement through several interventions. This paper distinguishes its approach by generating diverse training data from the student and targeting its own conception of reasonable approaches.

2 RELATED WORK

  • Reasoning post-training often samples and filters for correct solutions, including RFT and teacher distillation, but small students do not always benefit from strong-teacher traces.STaR iteratively fine-tunes on successful self-generated rationales; RFT formalizes IID sampling followed by training on correct solutions.Source: §2 · p. 3
  • Unlike related approaches, this work generates data from the student, targets its own conception of the approach space, and samples distinct approaches to difficult tasks.Other cited work uses heuristics, structured hints, conditioned inputs, or inference-time search.Source: §2 · p. 3
  • Post-training can narrow response strategies, reducing reward variation for group-based RL and the diversity available to test-time aggregation.Prior work associates diversity collapse with RL objectives or post-training stages.Source: §2 · p. 3
  • Prior diversity interventions modify RL or SFT objectives, or act at inference time; this work instead targets diversity in warmup training data while keeping those stages fixed.The related work also describes prompting methods that elicit distinct responses and inference-time population evolution.Source: §2 · p. 3
  • Strategic diversity concerns variation in reasonable approaches, unlike surface statistics or measures restricted to variation among correct solutions.The paper evaluates its effect through pass@k on difficult problems, downstream RL, and test-time scaling.Source: §2 · pp. 3–4

3 STRATEGICALLY DIVERSE SAMPLING METHODS

The methods elicit distinct approaches before generating solutions, using either an unstructured list or a hierarchical tree. They separate approach planning from solution execution and add a generation call per problem or plan list.

3 STRATEGICALLY DIVERSE SAMPLING METHODS

  • The methods seek n responses differing in approach while requiring only the model being trained and little data-generation cost; IID sampling and higher temperature may not reliably change underlying strategies.They differ in whether the approach space is unstructured or hierarchically organized.Source: §3 · p. 4
  • Verbalized Sampling proposes approaches with estimated probabilities, then extends each approach into a full answer in a separate call.The model’s enumeration supplies the separation; the probabilities are estimates, not constraints.Source: §3 · p. 4
  • GROOT builds a reasoning tree and selects distinct root-to-leaf paths, making sampled approaches diverge at a decision the model marks as important.The tree is created once during dataset generation; test-time generation remains standard and unstructured.Source: §3 · p. 4
  • The authors hypothesize that method preference depends on domain and downstream objectives: hierarchy may suit coding, while imposed structure may limit exploration and unstructured search may miss decision points.The paper compares the methods empirically.Source: §3 · p. 4
  • Both methods elicit approaches first, then pass each as a hidden instruction alongside the original question to generate a standard reasoning-and-answer response.Responses that explicitly refer to the approach are automatically discarded.Source: §3 · p. 4
  • Both methods add a generation call per problem or plan list, and this cost is excluded from the comparable-size budgets.The diverse datasets are also compared against IID baselines with sampling budgets up to 16× larger.Source: §3 · p. 4

4 EXPERIMENTAL SETUP

Experiments use Qwen3-4B-Instruct, with primary results replicated on Nemotron3 Nano-4B. They cover coding and narrative planning, construct strategic and IID training sets, and evaluate direct performance, test-time scaling, and RL initialization.

4 EXPERIMENTAL SETUP

  • Experiments primarily use Qwen3-4B-Instruct and replicate primary results on Nemotron3 Nano-4B, with data generation, training, and evaluation using the same model within each experiment.The main text reports Qwen results; Nemotron ablations show the same trends.Source: §4 · p. 5

4.1 TASKS AND BENCHMARKS

  • Coding is evaluated on Cobalt and held-out LiveCodeBench and OJBench, with frontier problems defined as solved in at most two of 64 IID attempts.Next-Chapter Prediction evaluates plans for approximately 200-word story chunks by their reduction in true-section perplexity.Source: §4.1 · p. 5

4.2 TRAINING DATA AND FINE-TUNING

  • For code, sampling budgets are 4 and 8, plus high-budget IID-64; under matched budgets against IID, GROOT and VS consistently produce more correct datapoints.Source: §4.2 · p. 5
  • The study also tests higher-temperature sampling and data generated by a stronger Qwen3-235B teacher, and compares SFT, correctness-filtered RFT, and training on incorrect-only ANTI data.Training uses common hyperparameters and reports means over three seeds.Source: §4.2 · pp. 5–6

4.3 EVALUATING TRAINED MODELS

  • Evaluation measures direct pass@k for code and threshold-based coverage for NCP, Recursive Self-Aggregation pass@1, and test-set pass@k after initializing RL from each trained model.RSA refines an initial population of 16 candidates over ten iterations; code RL uses MaxRL and NCP uses GRPO.Source: §4.3 · p. 6

5 RESULTS

Across code and NCP, strategically sampled training outperforms IID baselines even under larger IID budgets, incorrect traces, and teacher-generated data, and yields stronger RL and test-time-scaling starting points.

5 RESULTS

  • On the Cobalt frontier training set, GROOT-4 sampling finds 155 problems versus 42 for IID-4 and 60 for IID-4 at T=1.5; on NCP, GROOT-16 finds plans for 286 sections versus IID’s 156.The paper argues for eliciting distinct approaches rather than simply sampling more.Source: §5 · pp. 6, 7, 9
  • At the 15% bar, VS trained on plans with ≥20% improvement reaches coverage@32 of 4.08%, versus 1.97% for base and 2.08% for IID; the ordering holds across k and thresholds.Increasing budget from 8 to 16 improves VS but leaves GROOT and IID unchanged.Source: Figure 2 · p. 7, §5 · p. 7
  • GROOT-4 and VS-4 reach held-out benchmarks pass@64 of 15.5 and 17.5, versus 5.2 for budget-matched IID-4; even IID-64 reaches only 6.5.Gains concentrate on medium and hard classes, while performance in the most difficult classes remains stable regardless of training.Source: §5 · p. 7
  • Higher-temperature IID improves results but remains below strategic sampling, while further scaling training data has little downstream effect for both IID and strategic methods.Higher temperature can also improve strategic sampling, suggesting temperature and approach-level diversification are complementary.Source: §5 · p. 7
  • Incorrect strategic responses outperform IID-based RFT: ANTI GROOT-4 and VS-4 reach held-out frontier pass@64 of 12.8 and 14.8, versus 7.9 for IID-64 at T=1.5.Correctness filtering still helps within strategic data: RFT reaches 15.5 for GROOT-4 and 17.5 for VS-4, versus 12.8 and 14.8 for ANTI.Source: §5 · pp. 7–8
  • In RSA, strategic models outperform IID in code and NCP; on code, VS-4 rises from pass@1 4.2 to 10.6, while IID-4 rises from 0.9 to 3.8.On NCP, GROOT and VS outperform IID at each quality threshold, and GROOT shows a larger RSA improvement than IID.Source: Table 4 · p. 8, §5 · pp. 8–9, Table 5 · p. 8
  • With a 235B teacher, IID-4 reaches held-out frontier pass@64 of 13.4, below self-trained GROOT-4 at 20.1 and VS-4 at 22.8.Strategic sampling with the teacher improves on teacher IID but remains below student self-training.Source: §5 · p. 8
  • After RL, Cobalt frontier pass@64 is 39.0 for GROOT-4 and 37.8 for VS-4, versus 36.6 for IID-4; on NCP, GROOT coverage@8 is 18.8%, versus 5.5% for VS and 4.8% for IID.GROOT-4 and VS-4 begin at a pass@8 that base-model RL fails to reach over six epochs; IID-4 takes 64 steps to reach their starting pass@8.Source: Figure 2 · p. 7, Table 6 · p. 9, §5 · p. 9

6 CONCLUSION

The paper argues that strategic diversity can improve post-training at difficult tasks, and reports that diverse self-generated sets can outperform larger teacher-generated sets. It leaves inference-time and online-RL induction of strategic diversity for future work.

Conclusion

  • Strategically trained models consistently outperform IID-trained models, including at high sampling temperatures.The paper identifies diversity of reasonable approaches as a driving force in improvement on difficult tasks.Source: §6 · p. 9
  • Larger-teacher data improves each sampling method, but strategic self-generated sets still outperform larger teacher-generated sets.The paper also reports that diverse but incorrect responses can outperform correct IID responses.Source: §6 · pp. 9–10

Future work

  • The authors propose investigating strategic diversity at inference time and optimizing it directly during online RL.Source: §6 · p. 10

A.1 SECOND BASE MODEL: NEMOTRON3-NANO-4B

The Nemotron3-Nano-4B experiments repeat the evaluation using a frontier defined by that model's capabilities. Strategic sampling shows benefits across repeated sampling, RL initialization, data creation, NCP, and use of a larger teacher, though aggregation results vary by benchmark.

Repeated sampling

  • At budget 4, GROOT and VS more than double frontier pass@64 from the base model’s 9.8 to 19.9 and 20.8, while the best IID model reaches 14.9.IID-4 reaches 8.8, slightly below the base model.Source: §A.1 · p. 16

Test-time aggregation

  • The strongest RSA method varies by benchmark: IID-8 leads on Cobalt and OJBench, while VS-4 leads on LiveCodeBench.The model often gains only slightly in pass@1 through aggregation.Source: §A.1 · p. 16

Data creation

  • At matched budgets, GROOT and VS solve more training-frontier code problems than IID: 115 and 137 versus 52 at budget 4, and 197 and 233 versus 97 at budget 8.On NCP, the same ordering appears with smaller margins: at the 20% threshold, VS and GROOT cover 535 and 533 sections versus 472 for IID.Source: §A.1 · pp. 16–17

Reinforcement Learning

  • VS-4 reached validation pass@8 of 40% after 28 RL steps and GROOT-4 after 48, versus 64 steps for IID-4; all trained models converged to the same validation level.After RL, held-out frontier macro pass@64 was 33.6 for VS-4, 33.3 for IID-4, and 31.0 for GROOT-4.Source: §A.1 · p. 16, Figure 3 · p. 17

NCP

  • At k = 16 and the 10% threshold, GROOT and VS reach NCP test-section coverage of 45.3% and 43.6%, versus 37.4% for the base model and 34.6% for IID.Source: §A.1 · p. 17

Larger teacher

  • With a 120B teacher, VS-4 frontier macro pass@64 rises from 20.8 to 27.4 and GROOT-4 from 19.9 to 25.7, while IID-4 rises from 8.8 to 13.8 and remains lower.The teacher change improves every sampling method, but strategic self-training methods remain ahead of IID-4.Source: §A.1 · p. 17

A.2 SAMPLING BUDGET, DATA MIXTURES, AND DATA FILTERS

Increasing the sampling budget has little effect on held-out frontier performance, while strategic datasets outperform much larger IID datasets across data filters. Among the tested filters, RFT performs best for strategic methods.

Sampling budget and mixtures

  • Doubling the sampling budget changes held-out frontier pass@64 by less than two points for every method, and MIX-8 performs comparably to GROOT-8 and VS-8.At budget 4, GROOT and VS datasets contain 220 and 194 examples versus 44 for IID; at budget 8, they contain 419 and 373 versus 83.Source: §A.2 · p. 17

Data filters

  • Across code benchmarks, strategic datasets beat corresponding IID-64 datasets with the same filter; RFT is best within each strategic method, while SFT and ANTI perform nearly identically.The comparison includes multiple budgets and data mixtures.Source: §A.2 · p. 17

A.3 SAMPLING TEMPERATURE

Temperature sweeps find that higher IID sampling temperature initially increases unique frontier problems solved but eventually degrades outputs. For strategic methods, planner temperature has the largest consistent gain, while downstream effects differ between GROOT and VS.

IID temperature

  • IID sampling solves 42 unique frontier problems at T = 0.85, rises to 64 at T = 1.5, then falls to 34 at T = 2.5.The authors select T = 1.5 for IID.Source: §A.3 · p. 18

Strategic-method temperature sweeps

  • Raising planner temperature from T = 0.1 to T = 2.0 increases unique problems solved from 146 to 169 for GROOT and 143 to 162 for VS; every strategic grid cell beats IID at any temperature.Solver temperature helps through T = 1.0, then hurts, with both strategic methods falling to 141 at T = 2.0.Source: §A.3 · pp. 18–19

Downstream performance

  • Higher planner temperature improves GROOT on all three code benchmarks by up to 4.0 frontier Cobalt pass@64 points, while VS gains slightly on Cobalt but performs worse on LiveCodeBench.Source: §A.3 · p. 19

A.4 TEACHER COMPARISON, ALL BENCHMARKS

Teacher traces help IID training but do not consistently help strategically sampled training: Qwen3-4B shows opposite effects at 16k, while held-out comparisons favor strategic methods at 8k. On Nemotron, the larger teacher helps GROOT and VS, yet strategic sampling still outperforms IID.

A.4 TEACHER COMPARISON, ALL BENCHMARKS

  • The Qwen3-235B teacher comparison uses a 16k-token generation limit because Qwen3-235B-A22B-Instruct traces have a high truncation rate.The comparison also includes IID-8 because the two-call planner-solver pipeline costs roughly 1.25× as much per problem as IID sampling.Source: §A.4 · pp. 19–20
  • At 16k, teacher traces raise frontier Macro-Avg pass@64 for IID from 5.8 to 13.4, but lower GROOT from 20.1 to 17.8 and VS from 22.8 to 17.7.The authors conclude that teacher and strategic-sampling gains do not combine for these methods; self-generated traces are a better training signal for GROOT and VS.Source: §A.4 · p. 20
  • On Nemotron, the larger teacher positively affects GROOT and VS, but strategic sampling still outperforms IID; the authors suggest reasoning similarity may explain the teacher effect.Table 12 compares 4B- and 120B-teacher distillation at fixed generation budgets across full and frontier test sets.Source: §A.4 · p. 20, Table 12 · p. 20
  • At 8k, teacher-trained IID reaches frontier pass@64 36.5 versus 30.5 for GROOT-4 on Cobalt, while held-out Macro-Avg is 12.4 for IID versus 17.5 for strategic diversity.The teacher gain concentrates on the in-domain benchmark; strategic diversity remains ahead on held-out benchmarks.Source: §A.4 · p. 21

A.5 RL ABLATIONS

Strategic initializations retain an advantage after RL over the strongest IID initialization, while RL gains differ across strategic methods. IID fine-tuning before RL provides little gain over starting from the base model.

A.5 RL ABLATIONS

  • After RL, Qwen3-4B GROOT, VS, and MIX reach held-out frontier pass@64 of 15.4–18.0, versus 12.3 for the strongest trained IID model and 11.4 from the base model.The strongest IID model is IID-8 at T = 1.5; RL results are from budget-4 RFT models.Source: §A.5 · p. 21
  • RL roughly doubles IID-4 held-out frontier pass@64 from 5.2 to 10.9, while GROOT-4 improves from 15.5 to 18.0 and VS-4 declines from 17.5 to 16.0.The authors report that RL does most of its work on weaker initializations.Source: §A.5 · p. 21
  • VS-initialized RL sometimes concentrates learning on in-distribution problems, with less generalizable reasoning behavior than GROOT-initialized RL.The authors identify the relationship between warmup data and post-RL generalization as a topic for further study.Source: §A.5 · p. 21
  • After RL from SFT or ANTI, SFT GROOT-4 and VS-4 reach held-out frontier pass@64 of 14.4 and 13.2, while IID-4 peaks at 10.8.High-temperature IID starts RL ahead of other IID models, but IID models finish within a few points of one another and below strategic models.Source: §A.5 · p. 21

A.6 PERFORMANCE BY NATIVE DIFFICULTY

Strategic-model gains concentrate in middle difficulty tiers, where the base model is neither already highly capable nor extremely weak. The hardest tiers show little or no change from the base model.

A.6 PERFORMANCE BY NATIVE DIFFICULTY

  • On medium and hard LiveCodeBench problems, GROOT-based models raise base pass@64 from 57.7 to 65.4 and from 20.0 to 28.0, respectively.On medium OJBench problems, GROOT-based models raise pass@64 from 18.5 to 29.3.Source: §A.6 · p. 22
  • On hard OJBench, pass@64 changes only from 2.0% for the base model to 2.4%; easy LiveCodeBench likewise changes little from the base model's 97.7%.The reported gains predominantly occur where base-model pass@1 is neither above 80% nor below 5%.Source: §A.6 · p. 22
  • For test-time scaling, Cobalt-medium coverage is 44.0 for VS-4 and 39.5 for GROOT-4 versus 27.3 for the base model; LiveCodeBench-hard is 15.1 and 14.5 versus 10.9.On the hardest Cobalt tier, all models are comparable to the base model, at 9.1 to 12.8.Source: §A.6 · p. 22

A.7 NCP DETAILS

The NCP experiments compare strategically sampled plans with IID plans using perplexity-improvement thresholds and test-set coverage. Strategic training outperforms IID and the base model across thresholds, while post-RL outcomes vary by initialization.

A.7 NCP DETAILS

  • The dataset contains 7,349 training, 1,147 validation, and 1,457 test sections from 30 books, split by book and divided into roughly 200-word sections.Sections outside 200–420 words and sections containing only chapter headers are excluded; per-section guidance is created using gpt-oss-120B.Source: §A.7 · p. 22
  • GROOT and VS make two planner calls per section, each generating eight approaches, then one solver call per approach; IID makes 16 independent plan calls.Sampling defaults to T = 0.85, and candidates mentioning the hidden approach are dropped (0.4%).Source: §A.7 · p. 22
  • A plan's score is the base model's mean per-token log-likelihood improvement with the plan versus without it, reported as percent perplexity improvement.A candidate clears threshold X when its improvement is at least X%; training retains candidates that clear the selected threshold.Source: §A.7 · pp. 22–23
  • At the 20% training threshold, coverage@32 at the 10% bar is 15.0 for GROOT-16 and 16.6 for VS-16, versus 9.7 for IID-16 and 9.5 for the base model.Across k and thresholds, VS and GROOT are close to each other and clearly above the base model and IID; increasing budget from 8 to 16 helps VS at the 5% bar from 39.8 to 43.1, while GROOT and IID remain within seed noise.Source: §A.7 · p. 23
  • On IID data, RFT, SFT, and ANTI coverage@32 are within 1% of one another at the 10% threshold, while all strategic-data filters remain above the best IID result.RFT keeps candidates above the 20% improvement threshold; SFT samples the same number randomly, and ANTI selects the same number of worst-scoring candidates.Source: §A.7 · p. 23
  • After RL, only GROOT-16 improves on the positive-only threshold metric, from 15.0 to 26.3 at 10%; adding contrastive foil thresholds shows improvement for all models, with GROOT best.Results use one RL seed because RL is costly in this setting; the reward combines high improvement on the target section with low improvement on foil sections.Source: §A.7 · p. 23

A.8 HYPERPARAMETERS

This appendix documents shared experimental settings and prompts for generating, solving, evaluating, and aggregating candidate approaches across coding and next-chapter planning. It illustrates strategic-diversity prompts and plan scoring, including examples where highly scored plans contradict the source scene.

A.8 HYPERPARAMETERS

  • Settings are shared across datasets except for code/NCP sampling budgets and selected training dimensions; Nemotron runs in non-thinking mode because of high truncation.Sampling budgets are 4 per code problem and 16 per NCP section; Nemotron truncation is 41.9% at a 16k-token limit, and code prompts add an explicit step-by-step reasoning instruction.Source: §A.8 · p. 23

A.9 PROMPTS

  • RSA uses the same aggregation prompt across domains, inserting candidate solutions verbatim; when aggregating one candidate, the prompt asks for refinement instead of combination.Outside coding, the problem name and answer format change, while the rest of the prompt remains unchanged.Source: §A.9 · pp. 34–36
  • Code GROOT prompts request a compact decision tree of distinct strategies, then four root-to-leaf approaches that balance strategic coverage with likelihood of success.The prompt asks models to check formulas or feasibility rules against examples and to provide approach summaries rather than code.Source: §A.9 · p. 34
  • Verbalized Sampling requests four randomly sampled approaches with estimated probabilities and full reasoning summaries, which the solver prompt uses as hidden guidance.The solver is instructed to present reasoning and a program as its own work without mentioning the supplied approach.Source: §A.9 · p. 35
  • For NCP, planner trees map fundamentally different plausible story paths, and selected approaches are grounded briefs specifying commitments, evidence, unresolved choices, and what would falsify their reading.The prompt asks for paths grounded in exact phrases from the story information and distinguishes a brief from a finished plan or drafted narration.Source: §A.9 · pp. 36–37
  • The NCP planner prompt requests eight probability-ranked, story-grounded approaches that differ substantively and span plausible alternatives.Each approach must state its commitments, supporting story phrases, unresolved decisions, and evidence that would disconfirm its reading.Source: §A.9 · p. 37
  • The NCP solver receives one approach as a hidden basis, reasons from the story information, then produces an organized 100–300-word plan rather than drafted prose.The prompt requires at least 150 words of written reasoning, including quoted evidence and an alternative, before the plan block; the plan covers ordered events, characters, dialogue, reader information, pace, and register.Source: §A.9 · p. 38

A.10 EXAMPLES

  • The examples section presents one mined problem from each domain; its competitive-programming example asks how many train intervals lie wholly within each queried city interval.The illustrated problem has N cities, M trains, and Q queries.Source: §A.10 · p. 39, COMPETITIVE PROGRAMMING · p. 39

A. Direct query processing with precomputation

  • In the worked example, direct iteration and offline sorting are marked correct, coordinate compression fails, and the binary-search approach is described as invalid.The offline method sorts trains and queries and reports O((M + Q) log M) complexity; coordinate compression is rejected as overcomplex, while binary search does not fit a direct counting task.Source: A. Direct query processing with… · pp. 39–40
  • The cited results are 3 out of 4 correct and 1 out of 4 correct, with no program identified alongside either result in these passages.Source: A. Direct query processing with… · pp. 41–42
  • Another reported attempt returns 0 out of 8 correct.Source: A. Direct query processing with… · p. 42
  • Each plan is scored by how much likelier it makes the gold passage.Source: NEXT-CHAPTER PREDICTION · p. 42
  • A plan scored +13.1% depicts no pinning, although the supplied source scene includes Miles pinning Daphne against the wall.The accompanying approach explicitly rejects emotional intimacy and the interruption, and is described as contradicting the scene’s emotional stakes.Source: NEXT-CHAPTER PREDICTION · pp. 42–44
  • In one reported example, 10 out of 32 plans clear a 10% bar, while in another, 0 out of 32 plans clear a 10% bar.Source: NEXT-CHAPTER PREDICTION · pp. 44–45
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