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REVIEW 6 major objections 6 minor 104 references

LLM-First Search: Self-Guided Exploration of the Solution Space

T0 review · 6 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read LLM-First Search replaces the fixed exploration constant of MCTS with a single model-made "continue or jump" decision, and claims this wins more hard Countdown and Sudoku games while spending fewer tokens.

desk verdict LFS is a plausible new LLM-guided backtracking variant, but Algorithm 1 isn't executable as written and the reported wins are statistically fragile. read the letter →

arxiv 2506.05213 v1 pith:BIS6STTA submitted 2025-06-05 cs.AI cs.CL

Nathan Herr , Tim Rocktäschel , Roberta Raileanu This is my paper
classification cs.AIcs.CL
keywords LLM-FirstSearchself-guidedtest-timecomputesearch-basedreasoningMonteCarloTreeexploration-exploitationtrade-offCountdownSudoku
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to show that a search procedure can be driven entirely by the LLM's own judgment instead of by a hand-tuned strategy. In LLM-First Search (LFS), the model scores the actions available at the current state, commits to the best one, and at each step answers one yes/no question: keep going or jump to the highest-scoring unexplored alternative. The authors argue this removes the exploration constant that MCTS needs tuned per task and model, and the beam width that limits ToT-BFS. On Countdown and Sudoku, they report LFS matching or beating ToT-BFS, BestFS, and MCTS on the hardest instances while using fewer tokens, and that the advantage grows with model strength and compute budget. A reader should care because it points to a simpler, more adaptive way to spend test-time compute, with no per-task calibration.

What carries the argument

The load-bearing mechanism is a two-prompt loop. At a state, an evaluate prompt asks the LLM to score every legal next action; the best action is taken and all others are pushed onto a priority queue ordered by those scores. Then an explore prompt asks the LLM for a single boolean: continue from the current state, or pop the highest-value alternative from the queue and switch to it. This single binary decision replaces the exploration constant $C$ in PUCT, the beam width in ToT-BFS, and the greedy queue rule in BestFS, and is meant to let the same prompt work across tasks and models.

What would settle it

Solve a fixed set of Countdown diff=7 games, log every explore decision, and after each run determine by exhaustive search whether the abandoned path actually contained a solution within the remaining token budget; if LFS's explore decisions agree with that oracle no more than chance, yet LFS still wins, then the win rate is not explained by self-guided backtracking and the central mechanism is not doing the claimed work.

Watch

Extended reading notes

Core claim

The central claim is that an LLM can internalise the search strategy itself: it can both evaluate its options and decide when to abandon the current reasoning path, and this is enough to outperform fixed search algorithms. Concretely, LFS achieves 47.37% on Countdown diff=7 with GPT-4o versus 32.63% for the best tuned MCTS, and 78.95% with o3-mini versus 41.05%; on 6x6 Sudoku with GPT-4o it is the only method to solve any game, and with o3-mini it reaches 25.26% versus 4.21% for MCTS. The paper reads these results as evidence that self-guided exploration scales better with task difficulty, model strength, and token budget, and that the need for hand-tuned search hyperparameters can be removed.

Load-bearing premise

The whole method rests on one binary judgment: the model must be able to tell, from its own internal estimate, when the current path is hopeless and when another branch is worth jumping to, without any task-specific tuning; an overconfident model never backtracks and an underconfident model thrashes.

Editorial extensions

If this is right

  • On harder Countdown instances the gap widens: at diff=7 LFS beats MCTS by 14.74 points with GPT-4o and by 37.9 points with o3-mini.
  • On 6x6 Sudoku with GPT-4o LFS is the only method with nonzero win rate, and with o3-mini it reaches 25.26% versus 4.21% for MCTS.
  • LFS has the highest Area Under Performance Profile for both win rate and win-rate-per-token on both models, meaning the advantage holds in aggregate rather than on a single cherry-picked setting.
  • Because LFS needs no search hyperparameters, switching tasks, difficulty levels, or base models requires no re-tuning, unlike MCTS whose best $C$ changed across tasks.
  • LFS builds smaller or equal-sized search trees than MCTS on Countdown and Sudoku, consistent with a more targeted exploration strategy.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: if LFS's advantage comes from the explore decision, then measuring that decision against an oracle (was the abandoned path actually unsolvable within budget?) would directly test the mechanism; the paper reports only end-task win rates.
  • Beyond the paper: LFS's requirement to revert to prior states limits it to reversible environments; applying it to irreversible settings would need a memory of visited states or a bounded rollback budget.
  • Beyond the paper: the same binary explore prompt could be layered onto MCTS as an adaptive halting rule for simulations, potentially removing the need to retune $C$ while retaining MCTS's statistical backups.
  • Beyond the paper: on tasks where model self-evaluation is miscalibrated, one could add a cheap external check, such as one-step lookahead, to veto explore decisions; the paper does not test this.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

6 major / 6 minor

Summary. The paper proposes LLM-First Search (LFS), a search method in which a single LLM both decides whether to continue along the current solution path or pop an alternative from a priority queue, and evaluates the value of available actions at the current state. The method is presented as removing the need for hand-tuned exploration hyperparameters such as MCTS's C constant, and is evaluated on Countdown and Sudoku against ToT-BFS, BestFS, and MCTS using GPT-4o and o3-mini. The reported results show that LFS matches or exceeds the baselines on most tasks, uses fewer tokens on several tasks, and scales better with model strength and compute budget. The authors also report Area Under Performance Profile (AUP) scores, cumulative wins as a function of token budget, and tree-size comparisons.

Significance. If the central claims hold, LFS is a meaningful contribution to inference-time LLM reasoning: it replaces an explicit exploration constant with an LLM-driven exploration decision, and the reported efficiency gains are practically relevant. The paper includes several strengths: the code is publicly available, the comparison spans two complementary benchmarks and two model families, token usage is reported alongside accuracy, and the AUP methodology is appropriate for aggregating heterogeneous tasks. The main results are plausible and the experimental design is mostly standard. However, the significance is currently limited by three issues: the algorithm as written in the manuscript is not executable, several evaluation choices weaken the statistical and comparative claims, and the central 'no handcrafted heuristics' assertion is contradicted by the task-specific prompts in Appendix E. These issues are fixable and do not, in my view, invalidate the underlying idea, but they must be addressed before the claims can be accepted.

major comments (6)
  1. [§4, Algorithm 1] Algorithm 1 is internally inconsistent. Lines 5 and 14 add raw actions to the priority queue Q (for example, Q := Q ∪ {a ∈ A0 | a ≠ a*_0}), but line 10 pops a state-action pair: (s'_t, A'_t) ← pop(Q). Since Q never stores states or (state, action) pairs, the algorithm cannot be executed as written. The accompanying text also says the method 'pops the highest-value node', which does not match the queue contents. Additionally, line 15 contains typos: 'st'' should be 'st' and 'a*_t''' should be 'a*_t'. The public code may resolve this, but the manuscript must specify the actual data structure (for example, storing successor states along with their values, or storing (state, action, value) tuples and applying the transition function on pop). Without this, the reported empirical results cannot be attributed to the described method.
  2. [§5.1, Table 1 and Appendix F] The MCTS exploration constant C is selected on the same test tasks that are used in the final comparison. The hyperparameter sweep in Table 1 evaluates C ∈ {0.5, 1.0, 2.5} on Countdown variants and Sudoku 4x4 with GPT-4o, and C = 0.5 is then adopted for all main results, including Sudoku 4x4 where the sweep shows a very large gap (100% vs 2.2% for C = 1.0). This is a form of test-set selection that gives MCTS an advantage and risks overfitting the baseline to the specific tasks. The paper should either select C on a held-out validation set, report all C values in the main table, or otherwise justify that the sweep does not materially affect the conclusions.
  3. [§5.3.1] The evaluation protocol is underspecified and the statistical treatment is questionable. The paper states that each game is run n = 5 times at temperature t = 0.0, but greedy decoding at temperature 0.0 is deterministic, so the five runs are not independent samples; the reported Wilson confidence intervals therefore overstate the effective sample size. The number of games per difficulty level is never stated, so the percentages in Table 2 and the confidence intervals in Appendix G cannot be interpreted without knowing the denominators. The authors should report the number of games per task, justify why temperature 0.0 is used despite the stated goal of measuring stochastic variation, and either use a nonzero sampling temperature or treat the results as deterministic and omit the Wilson intervals.
  4. [§5.1, §6.1, Table 2] ToT-BFS is absent from all o3-mini comparisons, despite the paper's claim that all methods are evaluated with two models. Table 2 shows no ToT-BFS row for o3-mini on any task, and the text only mentions that 'TOT-BFS-O3MINI is not tested' in the Countdown diff=3 discussion. This missing baseline affects the o3-mini AUP scores and weakens the 'scales better with a stronger model' claim, which is only made relative to MCTS and BestFS. The authors should either run ToT-BFS with o3-mini or explicitly state in the main text that this baseline is missing and discuss how it affects the comparison.
  5. [Table 3 and Appendix G.1] The AUP numbers are inconsistent between the main text and the appendix. For example, the BestFS GPT-4o WinRate AUP is 5.98 in Table 3 but 6.204 in Figure 9; the MCTS (C=0.5) GPT-4o EfficiencyScore AUP is 3.68 in Table 3 but 3.544 in Figure 10. Table 1 reports MCTS (C=0.5) WinRate AUP 7.20 and EfficiencyScore 7.16, while Figures 3 and 4 report 7.200 and 7.157, respectively. These discrepancies may be due to different subsets of tasks or minor rounding, but the paper does not explain them. Because AUP is a headline aggregate metric, the values must be reproducible from a single, clearly defined computation.
  6. [§1, §4, Appendix E] The paper repeatedly claims that LFS removes the need for 'handcrafted heuristics' and 'task-specific adaptation', but the prompts in Appendix E contain substantial task-specific, handcrafted guidance. For Countdown, the exploration prompt instructs the model that 'Creating small, flexible numbers (1-10) can be valuable' and lists four detailed scoring criteria; for Sudoku, it instructs the model to look for 'naked singles or hidden singles' and to consider 'how actions might create naked singles or hidden singles in other cells'. These are exactly the kind of handcrafted heuristics that the abstract and introduction say are eliminated. The authors should either qualify the claim (e.g., 'no hand-tuned numerical exploration parameters') or demonstrate that the same generic prompt works across both tasks without task-specific content.
minor comments (6)
  1. [§5.3.1] The sentence 'Due to the stochastic nature of language model generation' is at odds with the use of temperature 0.0; please clarify whether the API introduces nondeterminism despite the temperature setting.
  2. [§6.1] The text refers to 'Figure 22' for cumulative Sudoku wins, but the figure numbering in the appendix places these panels as part of a larger Figure 22; please verify all cross-references.
  3. [Appendix H] The caption of Figure 32 calls LFS 'Limited-Depth Forward Search', but the method is 'LLM-First Search'; please correct the acronym expansion.
  4. [§5.2.2] The Sudoku notation is inconsistent: the main text uses 'ℓ × w' grids with '2 × 3' subgrids for the 6x6 case, while Appendix C uses 'l × l' and '2 × 2' subgrids for the 4x4 case; please unify the notation.
  5. [Table 2] The row labels 'TOT-BFS-GPT4 O' and 'MCTS (C=0.5)' contain formatting irregularities (extra spaces and inconsistent capitalization); please standardize the method names throughout.
  6. [Appendix G] Several figure captions contain typos, such as 'furtehr' in the main text and inconsistent use of 'WinRate' vs 'Win Rate'; a careful proofread is recommended.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: LFS has no fitted parameters and its results are not forced by construction.

full rationale

The paper's central claim is an empirical comparison of LFS against ToT-BFS, BestFS, and MCTS. LFS has no fitted parameters; its only inputs are the LLM and the fixed prompts. The reported WinRates are measurements, not quantities derived from the method's definition, so there is no self-definitional reduction. The MCTS baseline's exploration constant is selected by a sweep over the same tasks used in the final comparison (Appendix F), which is a test-set tuning concern for the baseline, but it cannot force LFS's results and is not a prediction by the paper. The LFS prompts embed task-specific heuristics ('small flexible numbers 1-10 are valuable', 'Only choose to explore if you are certain'), which contradicts the paper's 'no handcrafted heuristics' framing, but this is an internal-consistency issue rather than a circular derivation. Algorithm 1 is internally inconsistent (Q stores actions while pop(Q) returns states), making the method non-reproducible from the manuscript; again, this is a correctness defect, not circularity. No self-citations are load-bearing, and no uniqueness theorem or ansatz is imported from the authors' prior work. Accordingly, no step reduces by construction to its inputs.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

LFS itself introduces no numeric free parameters: the only degrees of freedom are the prompt texts. The analysis includes one fitted quantity, the MCTS exploration constant C=0.5, which is selected via a sweep over the same tasks used in the final comparison. The prompt heuristics (e.g., valuing small numbers in Countdown) are handcrafted per task, which functions as a form of task-specific tuning even though no number is fitted.

free parameters (1)
  • MCTS exploration constant C = 0.5
    The MCTS baseline is evaluated with C=0.5 selected via a hyperparameter sweep on the same Countdown and Sudoku tasks used in the final comparison (Appendix F, Figures 3-8). The sweep was run only with GPT-4o; the same C is then applied to o3-mini, which may disadvantage MCTS if the optimal C changes with model.
assumptions (3)
  • domain assumption LLM-provided scalar value estimates are reliable enough to guide both action selection and exploration decisions across tasks of different search depth and branching factor.
    The LFS algorithm treats argmax over LLM operation scores as the best action and treats the LLM's binary explore decision as a correct signal to backtrack. No calibration or verification of these estimates is provided (Section 4).
  • domain assumption Running the same game five times at temperature 0.0 yields statistically independent samples of model behavior.
    Section 5.3.1 states n=5 runs at temperature t=0.0 and uses Wilson intervals; if temperature-0 decoding is deterministic or near-deterministic, the runs are not independent and the intervals understate uncertainty.
  • domain assumption Countdown and Sudoku are representative benchmarks for drawing conclusions about general LLM search scalability.
    Section 5.2 justifies this with scalability and complementarity, but only two tasks are used; the conclusions (1)-(4) in the abstract are intended to be general.

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Cite this review

Pith. "Pith review of LLM-First Search: Self-Guided Exploration of the Solution Space." pith.science (2026). https://pith.science/paper/BIS6STTA

@misc{pith2026250605213,
  author       = {Pith},
  title        = {Pith review of: LLM-First Search: Self-Guided Exploration of the Solution Space},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BIS6STTA}},
  note         = {Machine review of arXiv:2506.05213}
}
read the original abstract

Large Language Models (LLMs) have demonstrated remarkable improvements in reasoning and planning through increased test-time compute, often by framing problem-solving as a search process. While methods like Monte Carlo Tree Search (MCTS) have proven effective in some domains, their reliance on fixed exploration hyperparameters limits their adaptability across tasks of varying difficulty, rendering them impractical or expensive in certain settings. In this paper, we propose \textbf{LLM-First Search (LFS)}, a novel \textit{LLM Self-Guided Search} method that removes the need for pre-defined search strategies by empowering the LLM to autonomously control the search process via self-guided exploration. Rather than relying on external heuristics or hardcoded policies, the LLM evaluates whether to pursue the current search path or explore alternative branches based on its internal scoring mechanisms. This enables more flexible and context-sensitive reasoning without requiring manual tuning or task-specific adaptation. We evaluate LFS on Countdown and Sudoku against three classic widely-used search algorithms, Tree-of-Thoughts' Breadth First Search (ToT-BFS), Best First Search (BestFS), and MCTS, each of which have been used to achieve SotA results on a range of challenging reasoning tasks. We found that LFS (1) performs better on more challenging tasks without additional tuning, (2) is more computationally efficient compared to the other methods, especially when powered by a stronger model, (3) scales better with stronger models, due to its LLM-First design, and (4) scales better with increased compute budget. Our code is publicly available at \href{https://github.com/NathanHerr/LLM-First-Search}{LLM-First-Search}.

Figures

Figures reproduced from arXiv: 2506.05213 by the authors.

Figure 1
Figure 1. Illustrative comparison of search strategies. This figure visualises how different methods expand the search tree during reasoning. Tree of Thought Breadth-First Search (TOT-BFS) risks prematurely discarding promising paths due to rigid filtering criteria. Best-First Search (BESTFS) tends to over-exploit high-scoring nodes based on early estimations, potentially overlooking better long-term solutions. Monte Carlo Tr… view at source ↗
Figure 2
Figure 2. Cumulative Wins with increasing Token Usage, for all Countdown games, for (a) GPT-4o [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Performance profiles of MCTS across different exploration constants ( [PITH_FULL_IMAGE:figures/full_fig_p031_3.png] view at source ↗
Figures from the paper (29 more)
Figure 4
Figure 4. Figure 4: Performance profiles of MCTS across different exploration constants ( [PITH_FULL_IMAGE:figures/full_fig_p031_4.png]
Figure 5
Figure 5. Figure 5: WinRate and token usage for MCTS on the Countdown task (difficulty 3) using GPT [PITH_FULL_IMAGE:figures/full_fig_p032_5.png]
Figure 6
Figure 6. Figure 6: WinRate and token usage for MCTS on the Countdown task (difficulty 5) using GPT-4o. [PITH_FULL_IMAGE:figures/full_fig_p032_6.png]
Figure 7
Figure 7. Figure 7: WinRate and token usage for MCTS on the Countdown task (difficulty 7) using GPT-4o. [PITH_FULL_IMAGE:figures/full_fig_p033_7.png]
Figure 8
Figure 8. Figure 8: WinRate and token usage for MCTS on the Sudoku (4 [PITH_FULL_IMAGE:figures/full_fig_p033_8.png]
Figure 9
Figure 9. Figure 9: Performance profiles (WinRate) across all variants of Countdown and Sudoku tasks for [PITH_FULL_IMAGE:figures/full_fig_p034_9.png]
Figure 10
Figure 10. Figure 10: Performance profiles (WinRate per Token Ratio) across all variants of Countdown and [PITH_FULL_IMAGE:figures/full_fig_p034_10.png]
Figure 11
Figure 11. Figure 11: Performance profiles (WinRate) across all variants of Countdown and Sudoku tasks for [PITH_FULL_IMAGE:figures/full_fig_p035_11.png]
Figure 12
Figure 12. Figure 12: Performance profiles (WinRate per Token Ratio) across all variants of Countdown and [PITH_FULL_IMAGE:figures/full_fig_p035_12.png]
Figure 13
Figure 13. Figure 13: WinRate and token usage for different methods (ToT-BFS, BestFS, MCTS, and LFS) on [PITH_FULL_IMAGE:figures/full_fig_p036_13.png]
Figure 14
Figure 14. Figure 14: WinRate and token usage for different methods (ToT-BFS, BestFS, MCTS, and LFS) on [PITH_FULL_IMAGE:figures/full_fig_p037_14.png]
Figure 15
Figure 15. Figure 15: WinRate and Token Usage for different methods (ToT-BFS, BestFS, MCTS, and LFS) on [PITH_FULL_IMAGE:figures/full_fig_p038_15.png]
Figure 16
Figure 16. Figure 16: WinRate and Token Usage for different methods (BestFS, MCTS, and LFS) on the [PITH_FULL_IMAGE:figures/full_fig_p039_16.png]
Figure 17
Figure 17. Figure 17: WinRate and Token Usage for different methods (BestFS, MCTS, and LFS) on the [PITH_FULL_IMAGE:figures/full_fig_p040_17.png]
Figure 18
Figure 18. Figure 18: WinRate and Token Usage on the Sudoku 4×4 task using GPT-4o. (a) WinRate; (b) Token Usage. Results are shown for ToT-BFS, BestFS, MCTS, and LFS. MCTS marginally outperforms LFS in both WinRate and token efficiency, while ToT-BFS and BestFS lag significantly behind. Va…
Figure 19
Figure 19. Figure 19: WinRate and Token Usage on the Sudoku 6 × 6 task using GPT-4o. (a) WinRate; (b) Token Usage. Results are shown for ToT-BFS, MCTS, and LFS. All methods fail to solve any instances, except LFS, which successfully solves a single game. Despite the overall difficulty. Val…
Figure 20
Figure 20. Figure 20: WinRate and Token Usage on the Sudoku 4 × 4 task using o3-mini. (a) WinRate; (b) Token Usage. Results are shown for BestFS, MCTS, and LFS. Unlike the GPT-4o setting, LFS now outperforms MCTS in both WinRate and token efficiency, highlighting that our method scales mor…
Figure 21
Figure 21. Figure 21: WinRate and Token Usage on the Sudoku 6 × 6 task using o3-mini. (a) WinRate; (b) Token Usage. Results are shown for BestFS, MCTS, and LFS. The trend from the 4 × 4 variant continues, with LFS significantly outperforming MCTS in both accuracy and token efficiency. This…
Figure 22
Figure 22. Figure 22: Cumulative wins across varying token budgets for Countdown and Sudoku games using [PITH_FULL_IMAGE:figures/full_fig_p045_22.png]
Figure 23
Figure 23. Figure 23: Average tree size for Countdown (difficulty 3) using GPT-4o. [PITH_FULL_IMAGE:figures/full_fig_p046_23.png]
Figure 24
Figure 24. Figure 24: Average tree size for Countdown (difficulty 5) using GPT-4o. [PITH_FULL_IMAGE:figures/full_fig_p046_24.png]
Figure 25
Figure 25. Figure 25: Average tree size for Countdown (difficulty 7) using GPT-4o. [PITH_FULL_IMAGE:figures/full_fig_p046_25.png]
Figure 26
Figure 26. Figure 26: Average tree size for Countdown (difficulty 5) using o3-mini. [PITH_FULL_IMAGE:figures/full_fig_p047_26.png]
Figure 27
Figure 27. Figure 27: Average tree size for Countdown (difficulty 7) using o3-mini. [PITH_FULL_IMAGE:figures/full_fig_p047_27.png]
Figure 28
Figure 28. Figure 28: Average tree size for Sudoku (2 × 2) using GPT-4o. 47 [PITH_FULL_IMAGE:figures/full_fig_p047_28.png]
Figure 29
Figure 29. Figure 29: Average tree size for Sudoku (2 × 3) using GPT-4o. BESTFS MCTS(c=0.5) LFS Methods 0 50 100 150 200 Tree Size *167* [154, 180] *103* [101, 106] *97* [96, 99] Tree Size for Sudoku (width=2, height=2) Model: o3-mini BESTFS MCTS(c=0.5) LFS [PITH_FULL_IMAGE:figures/full_f…
Figure 30
Figure 30. Figure 30: Average tree size for Sudoku (2 × 2) using o3-mini. BESTFS MCTS(c=0.5) LFS Methods 0 500 1000 1500 2000 2500 Tree Size *1,978* [1,943, 2,012] *801* [779, 824] *487* [467, 506] Tree Size for Sudoku (width=2, height=3) Model: o3-mini BESTFS MCTS(c=0.5) LFS [PITH_FULL_I…
Figure 31
Figure 31. Figure 31: Average tree size for Sudoku (2 × 3) using o3-mini. 48 [PITH_FULL_IMAGE:figures/full_fig_p048_31.png]
Figure 32
Figure 32. Figure 32: Example search trees generated for a Countdown game (difficulty = 7) using (a) Monte [PITH_FULL_IMAGE:figures/full_fig_p049_32.png]

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.