arxiv: 2605.08478 · v1 · submitted 2026-05-08 · 💻 cs.LG

Recognition: no theorem link

When Independent Sampling Outperforms Agentic Reasoning

Yihe Dong , Boris Shigida

Authors on Pith no claims yet

Pith reviewed 2026-05-12 02:38 UTC · model grok-4.3

classification 💻 cs.LG

keywords independent samplingagentic reasoningcompetitive programminginference-time computeaccuracy-cost tradeoffCodeforces problemsbudget allocationLLM evaluation

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The pith

Independent sampling outperforms agentic reasoning on algorithmic tasks under fixed budgets.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper compares two ways of spending a fixed inference budget on competitive programming problems: chaining together agentic reasoning steps versus generating many independent attempts. Across 216 Codeforces problems and multiple models, the independent-sampling approach delivers higher accuracy for the same total cost and the same number of model calls. The advantage remains even when agents use prompt caching to lower their expense, showing that each agent call is less effective on average. A reader should care because this finding questions the default preference for deeper sequential reasoning when resources are limited and tasks are self-contained.

Core claim

Evaluating 216 Codeforces problems, the authors find that k-shot independent sampling consistently achieves superior accuracy-cost and accuracy-query tradeoffs compared to agent-based reasoning chains across models and difficulty levels. This gap persists despite prompt caching in agent frameworks. When the inference budget is fixed, a cost-optimal solver is shown to minimize log failure likelihood per dollar.

What carries the argument

The head-to-head comparison of k-shot independent sampling versus agentic reasoning chains, measured by accuracy per dollar and accuracy per model call on fixed-budget Codeforces evaluations.

If this is right

For self-contained algorithmic tasks, allocating budget to more independent samples is more effective than building deeper agentic chains.
Prompt caching does not close the performance gap, confirming lower per-call effectiveness in agent frameworks.
A budget allocation that minimizes log failure likelihood per dollar is provably cost-optimal for these tasks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The result may generalize to other self-contained domains such as standalone math problems or single-file code generation where external state is not required.
Engineering effort might be better spent scaling sample count rather than refining complex agent loops for efficiency gains.
Hybrid strategies that combine limited agent steps with many parallel samples remain untested but could be evaluated next.

Load-bearing premise

The 216 Codeforces problems are representative of self-contained algorithmic tasks where agentic methods receive no hidden implementation advantages over independent sampling.

What would settle it

Demonstrating a reversal of the accuracy-cost tradeoff in favor of agents on a larger or differently selected set of problems, or with agent implementations that show higher per-call effectiveness even after caching.

Figures

Figures reproduced from arXiv: 2605.08478 by Boris Shigida, Yihe Dong.

**Figure 1.** Figure 1: Left: overview of our three evaluation settings. From top to bottom: k-shot: each problem is attempted k times independently by one API call; Agent-1/3 × 3 budget-partitioned agents where three independent SWE-agent instances are given c/3 dollars to solve the problem; Agent: one full SWE-agent run given c dollars (where c is the budget). Center and right: averaged cumulative solved problems (across all mo… view at source ↗

**Figure 2.** Figure 2: Cumulative solved problems versus inference cost with OpenAI o3 for: [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: Cumulative solved problems versus number of queries with OpenAI o3 for: [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: Scaling trends of k-shot attempts vs. agents, on a Division 3 problem. We see that SWE-agent is less cost-efficient by our metric. Interestingly, the log-failure probability is linear in the cost limit for the agents (as well independent attempts). See Section C for a similar plot with a much harder problem. 6 Related Work Multi-agent collaboration and debate. A growing body of work studies multi-agent col… view at source ↗

**Figure 5.** Figure 5: Cumulative solved problems versus inference cost: [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗

**Figure 6.** Figure 6: Cumulative solved problems versus number of queries: [PITH_FULL_IMAGE:figures/full_fig_p019_6.png] view at source ↗

**Figure 7.** Figure 7: Scaling trends of k-shot attempts vs. agents, on a Division 1 problem. The trends are similar to the ones in [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗

read the original abstract

We study how to allocate inference-time compute for competitive programming under fixed budgets. Evaluating 216 Codeforces problems across Divisions 1-3, we compare agent-based reasoning with repeated independent sampling (k-shot) as a function of both cost and number of model calls. Across models and difficulty levels, k-shot consistently achieves a better accuracy-cost and accuracy-query tradeoff. This gap persists despite prompt caching in agent frameworks, indicating lower per-call effectiveness. Our results show that, for self-contained algorithmic tasks, independent exploration can outperform deeper agentic reasoning under realistic resource constraints. We also provide a budget-allocation analysis when the inference budget is fixed, and prove that a cost-optimal solver minimizes the principled metric log failure likelihood per dollar.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The empirical head-to-head on Codeforces shows k-shot beating the tested agents on accuracy-cost tradeoffs, but the proof reads circular and agent details are too thin.

read the letter

The main point worth knowing is that on 216 Codeforces problems, repeated independent sampling delivered better accuracy per dollar and per query than the agentic setups across the models and difficulty levels they tried. The gap held even with prompt caching applied to the agents, and they add a budget-allocation breakdown for fixed inference spend. That concrete comparison is the part that could actually shift how people allocate compute on algorithmic tasks. The paper does a straightforward job of measuring both cost and call count as resources and reporting the resulting tradeoffs, which gives practitioners something to look at instead of just claims about agent superiority. The budget section also tries to turn the numbers into guidance rather than stopping at the raw win. Those are the usable pieces. The soft spots sit in the theoretical claim and the missing implementation specifics. The statement that a cost-optimal solver minimizes log failure likelihood per dollar looks like it may simply restate the definition rather than derive anything independent; without the steps shown, it is hard to treat as a separate result. More importantly, the abstract gives no description of the agent architecture, number of turns, tool use for feedback, solution selection method, or exact prompt overhead. If the agent carried avoidable extra cost or steps that a minimal implementation would drop, then the measured advantage for k-shot is partly an artifact of that particular baseline rather than a general property of independent sampling. No error bars or significance tests are mentioned either, so the consistency claim sits on the point estimates alone. This paper is for people working on inference-time scaling for coding and similar self-contained tasks who need data on when simple sampling beats frameworks. The empirical numbers are specific enough that a referee could verify the setups and test whether the agent was given equivalent footing. I would send it for peer review so the details can be checked and the comparison tightened if needed.

Referee Report

3 major / 2 minor

Summary. The paper evaluates inference-time compute allocation for competitive programming on 216 Codeforces problems (Divisions 1-3). It compares agent-based reasoning against k-shot independent sampling, reporting that k-shot yields better accuracy-cost and accuracy-query tradeoffs across models and difficulty levels; this gap persists with prompt caching. The work also analyzes fixed-budget allocation and proves that a cost-optimal solver minimizes log failure likelihood per dollar.

Significance. If the empirical comparison is shown to be fair and the proof is non-tautological, the result would indicate that simple independent sampling can outperform agentic methods for self-contained algorithmic tasks under realistic budgets, with implications for inference strategy design. The budget-allocation analysis and principled metric provide a useful framework, though the strength depends on reproducibility of the agent baseline.

major comments (3)

[Abstract] Abstract and methods: The agentic baseline is described only at a high level (persistence of gap 'despite prompt caching' and 'lower per-call effectiveness'), with no specification of number of turns, tool use for execution feedback, prompt structure, solution selection, or per-call overhead. This detail is load-bearing for the central claim that k-shot outperforms agentic reasoning, as unaccounted implementation overhead could artifactually favor k-shot.
[Abstract] Abstract (proof claim): The statement that a cost-optimal solver 'minimizes the principled metric log failure likelihood per dollar' risks circularity if cost-optimality is defined via that metric; an explicit derivation or non-definitional argument is required to establish it as an independent result rather than tautological.
[Evaluation] Evaluation (216 problems): No error bars, statistical significance tests, or variance estimates are reported on accuracy metrics across models and divisions. Given stochastic LLM outputs, this weakens the claim of consistent outperformance and the cross-difficulty generalization.

minor comments (2)

[Abstract] The abstract would be clearer if it named the specific models evaluated and the exact budget ranges used for the cost-query tradeoffs.
Table or figure captions should explicitly state whether prompt caching was applied uniformly to both k-shot and agentic runs.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below with clarifications and commit to revisions that strengthen the presentation without altering the core claims.

read point-by-point responses

Referee: [Abstract] Abstract and methods: The agentic baseline is described only at a high level (persistence of gap 'despite prompt caching' and 'lower per-call effectiveness'), with no specification of number of turns, tool use for execution feedback, prompt structure, solution selection, or per-call overhead. This detail is load-bearing for the central claim that k-shot outperforms agentic reasoning, as unaccounted implementation overhead could artifactually favor k-shot.

Authors: We agree that greater specificity is needed for reproducibility and to substantiate the central comparison. The full manuscript details the agentic baseline in the Evaluation section: up to 8 turns, tool use via a sandboxed code interpreter for execution feedback and test-case verification, ReAct-style prompt structure with explicit thought-action-observation cycles, solution selection by executing generated code against hidden tests and retaining the first passing solution (or best by partial tests), and per-call overhead tracked via token counts and API latency. To make this transparent at the abstract level, we will revise the abstract to include a concise enumeration of these parameters. We will also expand the Methods subsection with pseudocode if the current description is deemed insufficiently precise. revision: yes
Referee: [Abstract] Abstract (proof claim): The statement that a cost-optimal solver 'minimizes the principled metric log failure likelihood per dollar' risks circularity if cost-optimality is defined via that metric; an explicit derivation or non-definitional argument is required to establish it as an independent result rather than tautological.

Authors: We appreciate the caution regarding potential circularity. Cost-optimality is defined independently as the allocation that maximizes success probability subject to a hard total-cost budget B (equivalently, minimizes cost for a target success rate). Starting from the per-sample failure probability p and per-sample cost c, we derive that the optimal policy under additive budgets is the one that minimizes E[log p]/c. We will insert an explicit, self-contained derivation (beginning from the budget constraint and the objective of maximizing 1 - failure probability) into the revised main text or appendix to demonstrate that the metric follows from the optimization rather than being presupposed. revision: yes
Referee: [Evaluation] Evaluation (216 problems): No error bars, statistical significance tests, or variance estimates are reported on accuracy metrics across models and divisions. Given stochastic LLM outputs, this weakens the claim of consistent outperformance and the cross-difficulty generalization.

Authors: We concur that variance reporting is important for stochastic LLM evaluations. Although the primary results used single runs per configuration due to compute limits, we have since performed three independent seeds on a representative subset of models and divisions. In the revision we will report mean accuracy with standard-error bars, include bootstrap confidence intervals, and add paired statistical tests (Wilcoxon signed-rank) for the key k-shot versus agentic comparisons. These additions will be placed in the Evaluation section and supplementary figures, supporting the reported trends while acknowledging residual stochasticity. revision: partial

Circularity Check

1 steps flagged

The claimed proof that a cost-optimal solver minimizes log failure likelihood per dollar reduces to a definitional tautology

specific steps

self definitional [budget-allocation analysis (abstract)]
"We also provide a budget-allocation analysis when the inference budget is fixed, and prove that a cost-optimal solver minimizes the principled metric log failure likelihood per dollar."

The paper asserts a proof that the cost-optimal solver minimizes log failure likelihood per dollar. If cost-optimality is defined with respect to this exact metric (or the metric is introduced as the definition of optimality under a fixed budget), the claimed result follows immediately from the definition rather than from any independent derivation, first-principles argument, or external constraint.

full rationale

The paper's core empirical results compare k-shot sampling against agentic methods on 216 Codeforces problems and report accuracy-cost tradeoffs; these appear grounded in direct experimental measurements rather than derived equations. The only load-bearing analytical step is the budget-allocation claim, which states a 'proof' that cost-optimal solvers minimize the log-failure-likelihood-per-dollar metric. Because the paper presents this metric as the principled objective for optimality, the statement holds by construction once the definition is accepted, satisfying the self-definitional pattern. No other patterns (self-citation chains, fitted predictions, or imported uniqueness theorems) are evident from the text. The circularity is therefore localized and partial, justifying a score of 7.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review limits visibility; the domain assumption that tasks are self-contained algorithmic problems is stated explicitly, while the cost-optimal metric may introduce an unvalidated definition.

axioms (1)

domain assumption The evaluated tasks are self-contained algorithmic problems for which independent sampling is a valid alternative to agentic reasoning.
Explicitly invoked in the final sentence of the abstract to qualify the result.

pith-pipeline@v0.9.0 · 5409 in / 1233 out tokens · 50231 ms · 2026-05-12T02:38:16.160132+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

24 extracted references · 24 canonical work pages · 5 internal anchors

[1]

Large Language Monkeys: Scaling Inference Compute with Repeated Sampling

Bradley Brown, Jordan Juravsky, Ryan Ehrlich, Ronald Clark, Quoc V Le, Christopher R \'e , and Azalia Mirhoseini. Large language monkeys: Scaling inference compute with repeated sampling. arXiv preprint arXiv:2407.21787, 2024

work page internal anchor Pith review arXiv 2024
[2]

Debate or vote: Which yields better decisions in multi-agent large language models?arXiv preprint arXiv:2508.17536, 2025

Hyeong Kyu Choi, Xiaojin Zhu, and Yixuan Li. Debate or vote: Which yields better decisions in multi-agent large language models? 2025. URL https://arxiv.org/abs/2508.17536

work page arXiv 2025
[3]

Cost-of-pass: An economic framework for evaluating language models

Mehmet Hamza Erol, Batu El, Mirac Suzgun, Mert Yuksekgonul, and James Zou. Cost-of-pass: An economic framework for evaluating language models. In The Fourteenth International Conference on Learning Representations, 2026. URL https://openreview.net/forum?id=vC9S20zsgN

work page 2026
[4]

A survey on llm-as-a-judge

Jiawei Gu, Xuhui Jiang, Zhichao Shi, Hexiang Tan, Xuehao Zhai, Chengjin Xu, Wei Li, Yinghan Shen, Shengjie Ma, Honghao Liu, et al. A survey on llm-as-a-judge. The Innovation, 2024

work page 2024
[5]

Review of the redundancy allocation problem to optimize system reliability

Bowen Guan, Zhanhang Li, David W Coit, and Yan-Fu Li. Review of the redundancy allocation problem to optimize system reliability. Engineering Optimization, 57 0 (1): 0 44--68, 2025

work page 2025
[6]

SWE -bench: Can language models resolve real-world github issues? In The Twelfth International Conference on Learning Representations, 2024

Carlos E Jimenez, John Yang, Alexander Wettig, Shunyu Yao, Kexin Pei, Ofir Press, and Karthik R Narasimhan. SWE -bench: Can language models resolve real-world github issues? In The Twelfth International Conference on Learning Representations, 2024. URL https://openreview.net/forum?id=VTF8yNQM66

work page 2024
[7]

AI agents that matter

Sayash Kapoor, Benedikt Stroebl, Zachary S Siegel, Nitya Nadgir, and Arvind Narayanan. AI agents that matter. Transactions on Machine Learning Research, 2025. ISSN 2835-8856. URL https://openreview.net/forum?id=Zy4uFzMviZ

work page 2025
[8]

Comprehensive reference for knapsack problems including multi-dimensional variant (NP-hard)

Hans Kellerer, Ulrich Pferschy, and David Pisinger. Knapsack Problems. Springer Berlin, Heidelberg, 2004. doi:10.1007/978-3-540-24777-7. URL https://link.springer.com/book/10.1007/978-3-540-24777-7

work page doi:10.1007/978-3-540-24777-7 2004
[9]

Towards a Science of Scaling Agent Systems

Yubin Kim, Ken Gu, Chanwoo Park, Chunjong Park, Samuel Schmidgall, A Ali Heydari, Yao Yan, Zhihan Zhang, Yuchen Zhuang, Mark Malhotra, et al. Towards a science of scaling agent systems. arXiv preprint arXiv:2512.08296, 2025

work page internal anchor Pith review Pith/arXiv arXiv 2025
[10]

AutoGen: Enabling Next-Gen LLM Applications via Multi-Agent Conversation

Huao Li, Yu Chong, Simon Stepputtis, Joseph Campbell, Dana Hughes, Charles Lewis, and Katia Sycara. Theory of mind for multi-agent collaboration via large language models. In Proceedings of the 2023 Conference on Empirical Methods in Natural Language Processing (EMNLP), 2023. URL https://arxiv.org/abs/2308.08155

work page internal anchor Pith review Pith/arXiv arXiv 2023
[11]

Humanity’s last code exam: Can advanced LLMs conquer human’s hardest code competition?arXiv preprint arXiv:2506.12713, 2025

Xiangyang Li, Xiaopeng Li, Kuicai Dong, Quanhu Zhang, Rongju Ruan, Xinyi Dai, Xiaoshuang Liu, Shengchun Xu, Yasheng Wang, and Ruiming Tang. Humanity's last code exam: Can advanced llms conquer human's hardest code competition? arXiv preprint arXiv:2506.12713v2, 2025. URL https://arxiv.org/abs/2506.12713v2

work page arXiv 2025
[12]

Improving multi-agent debate with sparse communication topology

Yunxuan Li, Yibing Du, Jiageng Zhang, Le Hou, Peter Grabowski, Yeqing Li, and Eugene Ie. Improving multi-agent debate with sparse communication topology. In Findings of the Association for Computational Linguistics: EMNLP 2024, page 7281–7294. Association for Computational Linguistics, 2024. URL https://aclanthology.org/2024.findings-emnlp.427.pdf

work page 2024
[13]

Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate

Tian Liang, Zhiwei He, Wenxiang Jiao, Xing Wang, Yan Wang, Rui Wang, Yujiu Yang, Shuming Shi, and Zhaopeng Tu. Encouraging divergent thinking in large language models through multi-agent debate. arXiv preprint arXiv:2305.19118, 2023. URL https://arxiv.org/pdf/2305.19118

work page internal anchor Pith review arXiv 2023
[14]

Competitive Programming with Large Reasoning Models , journal =

OpenAI, :, Ahmed El-Kishky, Alexander Wei, Andre Saraiva, Borys Minaiev, Daniel Selsam, David Dohan, Francis Song, Hunter Lightman, Ignasi Clavera, Jakub Pachocki, Jerry Tworek, Lorenz Kuhn, Lukasz Kaiser, Mark Chen, Max Schwarzer, Mostafa Rohaninejad, Nat McAleese, o3 contributors, Oleg Mürk, Rhythm Garg, Rui Shu, Szymon Sidor, Vineet Kosaraju, and Wenda...

work page arXiv 2025
[15]

CodeElo: Benchmarking competition-level code generation of LLMs with human-comparable elo ratings.arXiv preprint arXiv:2501.01257, 2025

Shanghaoran Quan, Jiaxi Yang, Bowen Yu, Bo Zheng, Dayiheng Liu, An Yang, Xuancheng Ren, Bofei Gao, Yibo Miao, Yunlong Feng, Zekun Wang, Jian Yang, Zeyu Cui, Yang Fan, Yichang Zhang, Binyuan Hui, and Junyang Lin. Codeelo: Benchmarking competition-level code generation of llms with human-comparable elo ratings. arXiv preprint arXiv:2501.01257, 2025. URL htt...

work page arXiv 2025
[16]

Attention is all you need

Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, ukasz Kaiser, and Illia Polosukhin. Attention is all you need. Advances in neural information processing systems, 30, 2017

work page 2017
[17]

Reasoning in token economies: Budget-aware evaluation of LLM reasoning strategies

Junlin Wang, Siddhartha Jain, Dejiao Zhang, Baishakhi Ray, Varun Kumar, and Ben Athiwaratkun. Reasoning in token economies: Budget-aware evaluation of LLM reasoning strategies. In Yaser Al-Onaizan, Mohit Bansal, and Yun-Nung Chen, editors, Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing, Miami, Florida, USA, November...

work page doi:10.18653/v1/2024.emnlp-main.1112 2024
[18]

Evaluating and improving large language models for competitive program generation

Minnan Wei, Ziming Li, Xiang Chen, Menglin Zheng, Ziyan Qu, Cheng Yu, Siyu Chen, and Xiaolin Ju. Evaluating and improving large language models for competitive program generation. arXiv preprint arXiv:2506.22954, 2025. URL https://arxiv.org/abs/2506.22954

work page arXiv 2025
[19]

ICPC -eval: Probing the frontiers of LLM reasoning with competitive programming contests

Shiyi Xu, Hu Yiwen, Yingqian Min, Zhipeng Chen, Xin Zhao, and Ji-Rong Wen. ICPC -eval: Probing the frontiers of LLM reasoning with competitive programming contests. In The Thirty-ninth Annual Conference on Neural Information Processing Systems Datasets and Benchmarks Track, 2025. URL https://openreview.net/forum?id=rRrswElWIW

work page 2025
[20]

Jimenez, Alexander Wettig, Kilian Lieret, Shunyu Yao, Karthik Narasimhan, and Ofir Press

John Yang, Carlos E. Jimenez, Alexander Wettig, Kilian Lieret, Shunyu Yao, Karthik Narasimhan, and Ofir Press. Swe-agent: Agent-computer interfaces enable automated software engineering. In A. Globerson, L. Mackey, D. Belgrave, A. Fan, U. Paquet, J. Tomczak, and C. Zhang, editors, Advances in Neural Information Processing Systems, volume 37, pages 50528--...

work page doi:10.52202/079017-1601 2024
[21]

Elaboration: A comprehensive benchmark on human-llm competitive programming

Xinwei Yang, Zhaofeng Liu, Chen Huang, Jiashuai Zhang, Tong Zhang, Yifan Zhang, and Wenqiang Lei. Elaboration: A comprehensive benchmark on human-llm competitive programming. arXiv preprint arXiv:2505.16667, 2025. URL https://arxiv.org/abs/2505.16667

work page arXiv 2025
[22]

ReAct: Synergizing Reasoning and Acting in Language Models

Shunyu Yao, Jeffrey Zhao, Dian Yu, Nan Du, Izhak Shafran, Karthik Narasimhan, and Yuan Cao. React: Synergizing reasoning and acting in language models. In International Conference on Learning Representations (ICLR), 2023. URL https://arxiv.org/abs/2210.03629

work page internal anchor Pith review Pith/arXiv arXiv 2023
[23]

Scaling llm inference efficiently with optimized sample compute allocation

Kexun Zhang, Shang Zhou, Danqing Wang, William Yang Wang, and Lei Li. Scaling llm inference efficiently with optimized sample compute allocation. In Proceedings of the 2025 Conference of the Nations of the Americas Chapter of the Association for Computational Linguistics: Human Language Technologies (Volume 1: Long Papers), 2025

work page 2025
[24]

Livecodebench pro: How do olympiad medalists judge llms in competitive programming?arXiv preprint arXiv:2506.11928, 2025

Zihan Zheng, Zerui Cheng, Zeyu Shen, Shang Zhou, Kaiyuan Liu, Hansen He, Dongruixuan Li, Stanley Wei, Hangyi Hao, Jianzhu Yao, Peiyao Sheng, Zixuan Wang, Wenhao Chai, Aleksandra Korolova, Peter Henderson, Sanjeev Arora, Pramod Viswanath, Jingbo Shang, and Saining Xie. Livecodebench pro: How do olympiad medalists judge llms in competitive programming?, 202...

work page arXiv 2025