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REVIEW 4 major objections 6 minor 2 cited by

Rethinking the Illusion of Thinking

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper argues that Towers of Hanoi failures in large reasoning models persist around eight disks even under stepwise and agentic prompting, while River Crossing failures dissolve once tests are limited to solvable configurations.

desk verdict Useful empirical follow-up on the Apple reasoning debate, but the central 'not output length' claim is undercut by an unreported p and no same-model single-pass control. read the letter →

arxiv 2507.01231 v1 pith:IPZSK3TX submitted 2025-07-01 cs.AI

Iñaki Dellibarda Varela , Pablo Romero-Sorozabal , Eduardo Rocon , Manuel Cebrian This is my paper
classification cs.AI
keywords largereasoningmodelsTowersofHanoiRiverCrossingstepwisepromptingagenticdialoguelong-horizonplanningoutputwindowsolvability
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 attempts to resolve a public dispute over whether large reasoning models have a genuine planning deficit or are merely capped by their output windows. It replicates the two most contested puzzles from the original study and introduces two ablations: stepwise prompting, which asks for only small chunks of moves at a time, and agentic dialogue between two models. The paper reports that Towers of Hanoi success still collapses around eight disks under both ablations, which it reads as evidence that the failure tracks structural complexity rather than output length. For River Crossing, it finds that restricting the tests to mathematically solvable configurations turns the previously catastrophic results into near-routine success, even with more than a hundred agent pairs. A sympathetic reader would take away that reasoning performance in these models is configuration-dependent, not a single scalable capacity.

What carries the argument

The load-bearing object is the decomposition protocol: the stepwise strategy splits a full solution into substages and asks the model for the next $p$ legal moves from the current state, and the agentic strategy runs two models in alternating dialogue with shared memory, each proposing the next $p$ moves. These two protocols are meant to break the output-length constraint while keeping the underlying puzzle intact. On the River Crossing side, the machinery is a formal solvability filter: an instance is solvable only if $k \geq 4$ (all $N$) or $k \leq 3$ with $N \leq 2k-1$, and the paper restricts all tests to instances passing that filter. The third recurring tool is per-request token usage, treated as a proxy for perceived difficulty: tokens per substage rise with difficulty while the task is still believed solvable, then drop when the model abandons.

What would settle it

Run the stepwise protocol with exactly one move per request ($p=1$) on the same model family and record per-request token counts for $N=8,9,10$; if success improves materially or per-request outputs approach the model's output ceiling, the structural-complexity claim fails. Adding a single-pass baseline on the same model would also tell whether the comparison to the original study is really apples-to-apples.

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Extended reading notes

Core claim

The central discovery the paper argues for is that the Towers of Hanoi cliff is not mainly an output-window artifact. Using the same family of reasoning model, it tests both a stepwise protocol and a two-agent dialogue protocol; in both, success rates fall sharply once the puzzle reaches roughly $N=8$ disks, with per-request token use peaking just before failure and dropping once the model appears to give up. Since each request in these protocols asks for only a fixed number $p$ of moves, the paper concludes that the limiting factor is the structural complexity of the configuration, not the length of the generated answer. The companion result is that River Crossing, previously the weakest task, becomes one of the strongest once the evaluation is restricted to solvable instances satisfying $k \geq 4$ or $N \leq 2k-1$: configurations with up to $N=100$ agent pairs are solved reliably, while the hardest case is the intermediate boundary configuration $(N=5, k=3)$. The paper frames LRMs as stochastic, reinforcement-learning-tuned search processes whose failures and successes depend on the shape of the solution space rather than on problem size.

Load-bearing premise

The load-bearing assumption is that splitting the task into requests of $p$ moves removes the output-length constraint; the paper never states $p$, and if per-request outputs still approach the maximum window at $N=8$, the claim that the failure is structural rather than length-driven is not yet established.

Editorial extensions

If this is right

  • Stepwise prompting does not resurrect long-horizon planning in current reasoning models; the structural cliff around eight disks persists.
  • River Crossing performance in earlier studies cannot be read as a reasoning failure because the tested instances were largely unsolvable; solvable large instances are handled reliably.
  • Task difficulty for these models is not monotone in problem size; intermediate configurations with narrow solution spaces can be harder than much larger ones.
  • Token consumption is a signal of perceived solvability, not of actual competence: agentic systems keep spending tokens while looping without reaching a solution.
  • Benchmark conclusions about reasoning ability need to separate structural impossibility from model failure.

Reading between the lines

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

  • A direct test the paper leaves open is the same model in a single pass versus stepwise with $p=1$; if one-move steps restore Hanoi performance, the structural-complexity reading would need revision.
  • The phase-transition idea at $(N=5,k=3)$ suggests a testable prediction: formal counting of viable solution paths should correlate with token spikes and failure rates better than $N$ or $k$ alone.
  • If the structural account is correct, scaling output windows or context length will not fix long-horizon symbolic tasks; progress would have to come from an external planner, memory structure, or training on explicit solution trajectories.
  • The same stepwise and agentic ablations could be applied to other recursively structured benchmarks to see whether the eight-disk cliff is specific to Hanoi or a general signature of current reasoning models.
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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

4 major / 6 minor

Summary. This paper replicates and refines two benchmarks from Shojaee et al.'s 'The Illusion of Thinking' using Gemini 2.5 Pro. For Towers of Hanoi, the authors introduce stepwise prompting (breaking the solution into requests of p moves each) and a two-agent dialogue protocol; they report that success rates still decline sharply around N = 8 disks, interpreting this as evidence that the difficulty is not merely an output-window artifact but reflects structural complexity. For River Crossing, they argue the original study tested unsolvable configurations (k = 3, N > 5) and show that when restricted to solvable instances, the model solves large configurations, including N = 100 with k = 4, using few tokens. The paper concludes that LRM performance is task- and formulation-dependent, and that failure modes are better described as limitations in long-horizon consistency than as simple output limits.

Significance. If the central claim about Towers of Hanoi were fully established, the paper would make a useful contribution to the debate: it proposes a concrete methodology (stepwise decomposition and agentic dialogue) for separating output-window constraints from planning limitations, and it corrects a likely artifact in the River Crossing benchmark. The River Crossing result is a valuable falsifiable prediction—solvable instances are reported as solvable even at large N—and the authors' reliance on external formal solvability criteria (Efimova; Spahn & Zeilberger) is appropriate. The manuscript is also transparent in acknowledging that the comparison curves from the original study are approximate. However, the central claim is currently underdetermined because the stepwise protocol's key parameter p is unreported and no same-model single-pass baseline is provided; these are fixable reporting and control gaps rather than internal inconsistencies.

major comments (4)
  1. [Section III.B.1 and IV.A.1] The parameter p, the number of moves requested per substage, is defined but never assigned a value anywhere in the text or figures. The stepwise and agentic protocols are only valid as controls for the output-window confound if p is small enough that each per-request output stays well below the model's maximum output length. Without reporting p (and the output limit of Gemini 2.5 Pro), the claim in Section V that 'the difficulty lies not in the output length or window size' is not established; if p were large, a single request could still approach the window limit. Please report p for each configuration and, ideally, include an ablation over p.
  2. [Section V (Fig. 4a)] The comparison showing that stepwise and agentic performance 'does not significantly improve' over the original study is made against manually estimated curves from Claude 3.7 Sonnet and DeepSeek-R1 (from Shojaee et al.), not against a single-pass baseline using the same model (Gemini 2.5 Pro) and the same prompts. Without this same-model control, the observed failure around N = 8 cannot be attributed to the structural complexity of the task rather than to a Gemini-specific weakness or to residual output-window effects. A single-pass Gemini baseline is necessary to support the paper's central conclusion.
  3. [Section IV.A and IV.B] No exact success rates or confidence intervals are reported; the results are presented only as figures and qualitative descriptions, with 10 trials per configuration. In particular, the claim that the model solves River Crossing 'effortlessly' for N = 100, k = 4 rests on an unreported success count out of 10 trials. Given that the paper's contribution is empirical, exact per-configuration success rates (with confidence intervals or raw trial data) are required to assess the strength of the claims, especially the steep drop in Towers of Hanoi near N = 8 and the high success at N = 100 in River Crossing.
  4. [Section III.B.2 and IV.A.2] The agentic dialogue protocol is underspecified. The paper does not state whether both agents are the same model (Gemini 2.5 Pro), how the shared memory is implemented, what information is passed between turns, or what value of p is used in that setting. Furthermore, the interpretation that sustained token investment indicates the agents 'recognize the task as solvable' (Section V) is an unsupported inference; the continued effort could simply reflect the absence of a termination signal in the multi-agent loop. Please provide the full protocol and a more cautious interpretation of token dynamics.
minor comments (6)
  1. [Section VI] The final sentence of the conclusion contains a grammatical error: 'inside a large, into discrete search space' should read 'inside a large, discrete search space.'
  2. [Throughout] The paper alternates between referring to 'Apple' and 'Shojaee et al.'; consider standardizing on the citation label for consistency.
  3. [Section II] The sentence 'The minimal solution path was known and recursive, the models failed' is a comma splice; consider splitting it into two sentences for readability.
  4. [Section III.B.3] The sentence 'we replicate the original River Crossing experiments while restricting our tests to configurations that are mathematically solvable' is slightly misleading because the authors also vary boat capacity k (from 2 to 4), which the original study did not; the wording should clarify that this is a modified replication.
  5. [Figure 2 caption] The caption states 'p indicates the number of moves requested per substage'; since p is not reported in the text, consider adding the actual value(s) in the caption or in the main text.
  6. [References [11]–[13]] The cited Gemini references describe Gemini 1.5 models, whereas the experiments use Gemini 2.5 Pro; an updated reference for Gemini 2.5 would be appropriate.

Circularity Check

1 steps flagged · score 1.0 of 10

One localized token-drop-as-recognition interpretive loop exists, but the central Hanoi and River Crossing claims are externally grounded and not circular.

  1. other [Section IV.A.1 (Towers of Hanoi, Stepwise Resolution), paragraph beginning 'The evolution of token usage...']
    "However, when the puzzle exceeds the LRM's capabilities, the token rate drops, reflecting early-stage failures and an implicit recognition of task infeasibility."

    The only evidence adduced for the model's 'implicit recognition' is the observed token-rate drop itself, and the drop is then presented as reflecting that recognition; the explanatory construct is therefore the observation relabeled, so this token-effort finding cannot independently support the claim that LRMs perceive infeasibility. This is a localized interpretive loop rather than a fitted identity, and it does not carry the paper's structural-complexity conclusion.

full rationale

The paper's main derivation chain is not circular. The Towers of Hanoi difficulty claim rests on new stepwise and agentic experiments whose failure rates are measured directly, not fitted from the conclusion; the River Crossing reframing uses externally cited solvability criteria (Efimova; Spahn and Zeilberger) to select instances, and the resulting success rates are observed rather than imported. The comparison with Shojaee et al. is explicitly labeled as manually estimated approximations and used only for qualitative trend contrast, so no benchmark equation is defined by the conclusion. The only mild circular element is localized: the sharp token-rate drop at high N is presented as evidence of the model's 'implicit recognition of task infeasibility,' and that recognition is then cited as the explanation for the drop; the explanatory construct is the observation relabeled. This loop does not support the paper's main structural-complexity conclusion. Separately, Section III.B.1 defines the stepwise protocol via a parameter p but never reports its value, and no same-model single-pass Gemini baseline is shown; these are reporting and control gaps that underdetermine the 'not output length' claim, but underdetermination is a validity issue rather than a circularity. The central claims are not reduced by construction to their inputs.

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

There is no fitted theory or derived constant. The only hand-chosen protocol parameter is p. The paper leans on an external solvability theorem, a single-model generalization, and manual estimates of the original study's plots, all of which are assumptions rather than derived results.

free parameters (1)
  • p (moves per substage)
    Chosen by authors to split Towers of Hanoi into subproblems; value not reported in the manuscript. It controls output length per request and therefore directly bears on the claim that output constraints are not the cause of failure.
assumptions (3)
  • domain assumption River Crossing solvability criterion: a configuration is solvable iff k >= 4 or N <= 2k - 1.
    Paper restricts all River Crossing tests to configurations satisfying this criterion, citing Efimova [9] and Spahn/Zeilberger [10]. If this criterion were wrong, the 'solvable only' results would be invalid.
  • domain assumption Gemini 2.5 Pro is representative of the broader class of LRMs.
    All new experiments use a single model, yet the abstract and conclusion make general claims about 'LRMs'. Cross-model replication is left to future work in Section V.
  • domain assumption Apple's success-rate curves, manually estimated from published plots, are adequate qualitative baselines.
    Section V states exact values are not public and curves are 'manually estimated from the published plots'. The comparison of stepwise performance against these estimates supports the no-improvement claim.

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Cite this review

Pith. "Pith review of Rethinking the Illusion of Thinking." pith.science (2026). https://pith.science/paper/IPZSK3TX

@misc{pith2026250701231,
  author       = {Pith},
  title        = {Pith review of: Rethinking the Illusion of Thinking},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IPZSK3TX}},
  note         = {Machine review of arXiv:2507.01231}
}
read the original abstract

Earlier this year, Apple ignited controversy by publishing "The Illusion of Thinking," prompting heated debate within the AI community. Critics seized upon the findings as conclusive evidence that Large Reasoning Models (LRMs) lack genuine reasoning capabilities, branding them as mere stochastic parrots. Meanwhile, defenders-spearheaded by Lawsen et al. (2025)-fired back, condemning the experimental setup as flawed and the conclusions overstated. We clarify this debate by replicating and refining two of the original study's most contentious benchmarks: Towers of Hanoi and River Crossing. By introducing incremental stepwise prompting and agentic collaborative dialogue, we show that previously reported failures solving the Towers of Hanoi were not purely result of output constraints, but also partly a result of cognition limitations: LRMs still stumble when complexity rises moderately (around 8 disks). Moreover, the River Crossing results initially heralded as catastrophic failures turn out to hinge upon testing unsolvable configurations. Once we limit tests strictly to solvable problems-LRMs effortlessly solve large instances involving over 100 agent pairs. Our findings ultimately defy simplistic narratives: today's LRMs are stochastic, RL-tuned searchers in a discrete state space we barely understand. Real progress in symbolic, long-horizon reasoning demands mapping that terrain through fine-grained ablations like those introduced here.

Figures

Figures reproduced from arXiv: 2507.01231 by the authors.

Figure 1
Figure 1. FIG. 1. Illustration of the two benchmark puzzles analyzed in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Comparison of performance across two solving strate [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Performance of the LRM in the River Crossing puzzle [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Comparison of success rate trends between our experimental results and those reported by Shojaee et al. [2]. [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

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Forward citations

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Reference graph

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