Pith. sign in

REVIEW 4 major objections 5 minor 41 references

Language Models Coupled with Metacognition Can Outperform Reasoning Models

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A training-free metacognitive feedback loop lets a fast LLM match or beat a dedicated reasoning model on graph coloring and code debugging while using less time.

desk verdict Plausible hybrid architecture with a genuinely useful domain-contrast finding, but the headline accuracy claim is undercut by an undefined treatment of unsolvable graph instances and post-hoc configuration picking. read the letter →

arxiv 2508.17959 v1 pith:SBUVN2LM submitted 2025-08-25 cs.AI

Vedant Khandelwal , Francesca Rossi , Keerthiram Murugesan , Erik Miehling , Murray Campbell , Karthikeyan Natesan Ramamurthy , Lior Horesh This is my paper · ORCID
classification cs.AI
keywords metacognitionfeedbackloopfastandslowreasoninggraphcoloringcodedebugginglargemodelstraining-freeadaptationselectivefallback
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 establish that an ordinary, fast language model, when run in a loop with a module that checks its answers and feeds targeted corrections back to it, can solve hard reasoning problems as well as or better than a larger, slower reasoning model. The authors generalize the SOFAI fast-and-slow cognitive architecture into SOFAI-LM, replacing fine-tuning with runtime feedback and using the slow model only as a selective fallback. In their experiments on graph coloring and on Python and C++ debugging, the feedback-driven LLM closes or reverses the accuracy gap and does so with lower average inference time. If right, this matters because it points to a cheaper way to get reliable reasoning from language models without retraining.

What carries the argument

The load-bearing mechanism is the metacognitive governance module (MC) interposed between the System-1 LLM and the System-2 LRM. MC computes a correctness score—fraction of properly colored edges or test pass ratio—turns the specific failures into feedback, and re-prompts the LLM for up to T iterations, tracking stagnation and storing the episode in memory. When the LLM loop fails, MC invokes the LRM with one of three prompt levels: problem-only, best LLM attempt, or full feedback history. The same module, without model fine-tuning, applies to both domains; only the evaluation and feedback-generation pieces are domain-specific.

What would settle it

Run SOFAI-LM and the standalone LRM on the same set of known-unsolvable graph instances with 5-25 vertices and count how often each emits exactly 'NOT SOLVABLE' rather than an invalid coloring; if the pipeline is not reliably correct on those instances, the claimed advantage over the LRM applies only to the solvable subset and the decision-problem claim fails.

Watch

Extended reading notes

Core claim

SOFAI-LM's central claim is that a metacognitive controller can make a fast LLM surpass a standalone reasoning model on two contrasting reasoning tasks. The controller evaluates each candidate answer with a domain-specific correctness function, generates iterative feedback (structured multi-line feedback or compressed single-line feedback, plus adaptive subproblems), stores a limited episodic memory, and after a fixed number of iterations decides whether to invoke the slower LRM. In the paper's head-to-head comparison, the complete pipeline solves 70% of Python and 73% of C++ debugging problems while taking less time, versus 37% and 40% for the standalone LRM; on size-25 graph coloring it solves 42% versus 2%. The authors also report that feedback format changes outcomes: multi-line feedback beats single-line feedback and minimal memory beats extended history, and that passing failed-attempt history to the LRM helps in code debugging but hurts in graph coloring.

Load-bearing premise

The load-bearing premise is that the graph-coloring correctness score—the fraction of properly colored edges—adequately captures success on the decision problem, even though the paper never specifies how a 'NOT SOLVABLE' answer is scored and reports results only for solvable instances.

Editorial extensions

If this is right

  • Increasing the number of feedback iterations (5, 10, 15) monotonically improves LLM success rate in both domains, with the largest jump at LLM@5.
  • The architecture is model-agnostic: the same feedback loop raises success rates for different base LLMs, and the selective fallback outperforms multiple standalone LRMs.
  • Feedback design is consequential: multi-line feedback with minimal episodic memory is the best configuration tested on graph coloring, while single-line feedback is used for debugging.
  • For local-repair tasks like debugging, giving the LRM the LLM's best attempt or full history raises success; for global-consistency tasks like graph coloring, it lowers success.
  • Because the slow LRM is invoked only after the LLM loop fails, average inference cost per solved instance can fall even while accuracy rises.

Reading between the lines

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

  • An implication not developed in the paper: the same architecture could be applied to any domain with an external verifier that can name concrete failures—formal proof checking, constraint satisfaction, database query repair—so the feedback loop would replace task-specific fine-tuning.
  • A testable extension suggested by the global/local asymmetry: measure the locality of corrections automatically and use it to choose PO versus BA/FH prompting for the fallback, potentially eliminating the need to hand-tune the strategy per domain.
  • If unsolvable graph instances were scored explicitly, the graph-coloring advantage might narrow, because the correctness function currently gives no separate credit for correctly answering 'NOT SOLVABLE'; this is the main unresolved boundary of the decision-problem claim.
  • The authors leave implicit that iteration count T is a cost lever: at small T the loop is cheap but may under-perform, at large T it approaches LRM-level compute; a policy that stops early on detected stagnation may be the real driver of the efficiency gain.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper introduces SOFAI-LM, a training-free metacognitive architecture that pairs a fast LLM (System 1) with a slower LRM (System 2) under a metacognitive governance module. The LLM iteratively refines solutions using correctness feedback from a domain-specific evaluator, optionally with episodic memory; if the LLM does not converge within a fixed number of iterations, the LRM is invoked with one of three prompting strategies (problem-only, best attempt, or full history). The authors evaluate the architecture on the graph coloring decision problem and on DebugBench (Python and C++ subsets), across multiple LLM/LRM combinations. They report that the feedback-driven LLM alone can match or exceed standalone LRMs (RQ1), that multi-line feedback with minimal memory is best in graph coloring while single-line feedback is used for code debugging (RQ2), that the value of passing LLM context to the LRM differs by domain (RQ3), and that the full SOFAI-LM pipeline outperforms standalone LRMs in both accuracy and inference time (RQ4).

Significance. If the empirical claims hold, the paper makes a practical contribution: a training-free, model-agnostic way to raise the accuracy of a fast LLM on constraint-heavy reasoning tasks while using the expensive LRM only selectively. The strengths include the use of exact verifiers for graph coloring, execution-based evaluation via the LeetCode API for code debugging, comparisons against external benchmarks (DebugBench), and ablations across multiple LLM and LRM combinations. The central claim is plausible but the supporting evidence is weakened by an undefined evaluation protocol for unsolvable graph coloring instances, post-hoc selection of feedback, memory, and prompting variants on the test sets, and inconsistent timing statements. These issues directly affect the headline RQ4 numbers, which carry the paper's main argument.

major comments (4)
  1. [Problem domains; Supplementary Algorithm 1] Eq. (2) defines C(y) as the fraction of properly colored edges, so a response of 'NOT SOLVABLE' cannot be assigned a score by this function. Algorithm 1 (lines 3-30) contains no branch that recognizes the 'NOT SOLVABLE' token; it always calls ParseColoring on the final response and returns a coloring. Since the Experimental Setting states that both solvable and unsolvable graph instances are generated, the RQ4 solve rates (e.g., 42% vs 2% for size 25) are ambiguous as decision-problem rates: if unsolvable instances are in the denominator, the pipeline as specified cannot solve them; if they are excluded, the claim about solving the decision problem is narrower than stated. Please specify how unsolvable instances were handled and report the success rates separately for solvable and unsolvable instances.
  2. [Results RQ2/RQ3/RQ4] The headline RQ4 comparison uses per-domain variants chosen from the same test sets: MLF+MEM for graph coloring (Fig. 3) and SLF+MEM for code debugging (adopted 'because of this analysis'), and LRM prompting with PO for graph coloring versus FH for code debugging (Fig. 4). No held-out validation split is described, and no significance tests or error bars are reported; with 100 graph instances per size, the RQ4 advantage could be substantially inflated by selection. Please provide a validation protocol or report how sensitive the RQ4 conclusions are to the choice of feedback, memory, and prompting variants.
  3. [Results RQ1 and footnote 2] The timing statements are inconsistent. The RQ1 text says 'the LRM, though faster on average, performs substantially worse on larger graph sizes,' while footnote 2 says 'iterating the use of the LLM dominates the LRM, since it can solve many more problem instances while using much less time.' These two statements cannot both be true as written. Please clarify which configuration is faster on average, and define the sense in which one configuration dominates another (e.g., Pareto dominance on success rate and time), so that the efficiency claim is unambiguous.
  4. [Supplementary Algorithm 1, lines 18-30] Algorithm 1 invokes all three LRM prompting variants (PO, BA, FH) on every fallback and only afterward selects a final response ('Choose final r* based on selected variant'). This contradicts the described 'selective fallback' mechanism and, if all three calls are executed, would triple the LRM inference cost. Please specify which variant is actually executed in each reported experiment and how the reported time accounts for any unused LRM calls.
minor comments (5)
  1. [Introduction; Experimental Setting] There are typographical errors: 'stduy' should be 'study' and 'employes' should be 'employed' (or 'employees' depending on intent).
  2. [Figure 5 caption] The caption says the comparison is between 'SOFAI-LM and LLM approaches,' but the comparison is actually against the LRM; the caption should refer to the LRM.
  3. [Supplementary Figure 6 sample prompt] The sample graph coloring prompt says 'Graph Coloring Decision Problem (< 5 colors)' and 'Use < 5 distinct colors' while the instance has k=4; the formal definition is 'at most k colors.' The phrasing should be rendered as at most 4, or equivalently less than 5, to avoid confusion.
  4. [Equation (2)] The numerator of Eq. (2) appears to contain a sum that is typeset as a bare 'P'; please typeset it as a summation symbol.
  5. [References] Several related-work references use a truncated format (e.g., 'Wei, J. e. a. 2022'), which is inconsistent with the full author lists in the main reference list; the bibliography should be unified.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity detected: the SOFAI-LM claims are supported by external-benchmark experiments and deterministic evaluation functions, not by self-referential definitions or fitted predictions.

full rationale

I walked the paper's claimed derivation chain. The central claims (RQ1-RQ4) are empirical comparisons on DebugBench and generated graph-coloring instances, with success measured by deterministic checkers: the graph-coloring correctness function C(y) in Eq. 2 (fraction of properly colored edges), the code-debugging pass ratio Pass(y) in Eq. 3, and measured per-instance runtime. No parameter is fitted to the comparison data and then relabeled as a prediction; the S1 and S2 models are off-the-shelf, the iteration limit T is an experimental design choice, and the feedback is generated by rule-based checkers rather than learned from the test outcomes. The SOFAI prior work is cited as architectural inspiration, but the paper does not rely on a SOFAI result to establish its own empirical outcome; the experiments are self-contained against external benchmarks. The unsolvable-instance ambiguity in the graph-coloring evaluation is a correctness or measurement concern, not a circularity concern, because no equation or fitted parameter reduces the reported solve rate to an input of the derivation. Thus no circular step is present.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The architecture introduces no new physical or theoretical entities. All free parameters are design choices for the metacognitive loop, selected either by explicit sweep (T) or post hoc on the test set (feedback type, memory type, LRM prompting). The domain assumptions are the evaluation oracles and the representativeness of the generated benchmarks.

free parameters (5)
  • Max iterations T = 5, 10, 15; full pipeline T not specified
    Success rate increases with T, so T is a tunable cost-accuracy knob. The final SOFAI-LM configuration relies on a chosen T or adaptive stopping.
  • Feedback type (MLF vs SLF) = MLF for graph coloring, SLF for code debugging
    MLF outperformed SLF on graph coloring; the paper adopted SLF for code debugging without testing it there, based on the assumption that local fixes benefit from concise feedback.
  • Episodic memory type (MEM vs EEM) = MEM (minimal memory)
    MEM outperformed EEM in graph coloring experiments, so MEM was used throughout.
  • LRM prompting strategy (PO vs BA vs FH) = PO for graph coloring, FH for code debugging
    RQ3 results on the test data showed PO is best for graph coloring and BA/FH improve code debugging. These choices are post hoc.
  • Correctness threshold theta = 1.0 (implicit)
    The architecture accepts a solution when C(y)=1.0 or Pass(y)=1.0; the exact threshold θ is mentioned but not specified.
assumptions (5)
  • domain assumption The fraction of properly colored edges correctly measures solution quality for graph coloring.
    Used for metacognitive evaluation and feedback; assumes edge conflicts are the right signal for the LLM to improve.
  • domain assumption The LeetCode API's pass ratio over hidden tests correctly measures program correctness.
    Used as the correctness function for code debugging; hidden tests are assumed to be a fair oracle.
  • domain assumption Greedy decoding with temperature 0 is a representative inference setting.
    All experiments use seed=12345, temperature=0, top_k=1, top_p=1; assumes this does not bias results.
  • domain assumption Random graphs with edge probabilities in [0.1,0.9] are representative of graph coloring difficulty.
    The benchmark is synthetic; assumes this distribution captures the difficulty spectrum.
  • domain assumption The stagnation detection mechanism in the metacognitive module works as intended.
    Algorithms 1 and 2 mention 'If stagnation detected, it invokes LRM', but no specific detection method is defined in the main text.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Language Models Coupled with Metacognition Can Outperform Reasoning Models." pith.science (2026). https://pith.science/paper/SBUVN2LM

@misc{pith2026250817959,
  author       = {Pith},
  title        = {Pith review of: Language Models Coupled with Metacognition Can Outperform Reasoning Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SBUVN2LM}},
  note         = {Machine review of arXiv:2508.17959}
}
read the original abstract

Large language models (LLMs) excel in speed and adaptability across various reasoning tasks, but they often struggle when strict logic or constraint enforcement is required. In contrast, Large Reasoning Models (LRMs) are specifically designed for complex, step-by-step reasoning, although they come with significant computational costs and slower inference times. To address these trade-offs, we employ and generalize the SOFAI (Slow and Fast AI) cognitive architecture into SOFAI-LM, which coordinates a fast LLM with a slower but more powerful LRM through metacognition. The metacognitive module actively monitors the LLM's performance and provides targeted, iterative feedback with relevant examples. This enables the LLM to progressively refine its solutions without requiring the need for additional model fine-tuning. Extensive experiments on graph coloring and code debugging problems demonstrate that our feedback-driven approach significantly enhances the problem-solving capabilities of the LLM. In many instances, it achieves performance levels that match or even exceed those of standalone LRMs while requiring considerably less time. Additionally, when the LLM and feedback mechanism alone are insufficient, we engage the LRM by providing appropriate information collected during the LLM's feedback loop, tailored to the specific characteristics of the problem domain and leads to improved overall performance. Evaluations on two contrasting domains: graph coloring, requiring globally consistent solutions, and code debugging, demanding localized fixes, demonstrate that SOFAI-LM enables LLMs to match or outperform standalone LRMs in accuracy while maintaining significantly lower inference time.

Figures

Figures reproduced from arXiv: 2508.17959 by the authors.

Figure 1
Figure 1. The SOFAI-LM architecture. 2. MC evaluates y using the correctness function C(y). 3. If y does not meet the correctness threshold, MC gener￾ates feedback F(y) and calls again the S1 solver, moni￾toring progress for up to T iterations. 4. If no satisfactory solution is found after T iterations, or if improvement stagnates, MC invokes the S2 solver to produce the final solution y ∗ . Experimental Setting To use SOFAI-… view at source ↗
Figure 2
Figure 2. Each point corresponds to a configuration: [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. The x-axis shows the average time per instance [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (64 more)
Figure 4
Figure 4. Figure 4: Left: graph coloring, with graph size 25. Right: code debugging (Python and C++). The x-axis shows the average time [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: The x-axis shows the average time per instance [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Sample input prompts for the Graph Coloring and Code Debugging domains. [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 12
Figure 12. Figure 12: Visualization of the LLM’s second incorrect at [PITH_FULL_IMAGE:figures/full_fig_p013_12.png]
Figure 9
Figure 9. Figure 9: Visualization of the LLM’s first incorrect attempt. [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]
Figure 7
Figure 7. Figure 7: The initial prompt given to the LLM for the graph coloring task. [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 10
Figure 10. Figure 10: Feedback generated by the MC module, including concise (SLF), structured (MLF), and adaptive example formats. [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]
Figure 13
Figure 13. Figure 13: The LLM’s second, and correct, candidate solution. [PITH_FULL_IMAGE:figures/full_fig_p015_13.png]
Figure 15
Figure 15. Figure 15: Comparison of memory storage variants. MEM stores the final solution, while EEM stores the full interaction history. [PITH_FULL_IMAGE:figures/full_fig_p015_15.png]
Figure 16
Figure 16. Figure 16: The initial prompt for the code debugging task ’the-kth-factor-of-n’. [PITH_FULL_IMAGE:figures/full_fig_p017_16.png]
Figure 17
Figure 17. Figure 17: The LLM’s first, incorrect attempt to fix the buggy code. [PITH_FULL_IMAGE:figures/full_fig_p017_17.png]
Figure 18
Figure 18. Figure 18: Feedback generated after the first attempt failed a test case. [PITH_FULL_IMAGE:figures/full_fig_p017_18.png]
Figure 19
Figure 19. Figure 19: The LLM’s second, successful attempt at fixing the bug. [PITH_FULL_IMAGE:figures/full_fig_p018_19.png]
Figure 20
Figure 20. Figure 20: A second, different incorrect attempt from the LLM. [PITH_FULL_IMAGE:figures/full_fig_p018_20.png]
Figure 21
Figure 21. Figure 21: RQ1 - Model Combination 1, Size 5: Success [PITH_FULL_IMAGE:figures/full_fig_p019_21.png]
Figure 22
Figure 22. Figure 22: RQ1 - Model Combination 1, Size 10: Success [PITH_FULL_IMAGE:figures/full_fig_p020_22.png]
Figure 24
Figure 24. Figure 24: RQ1 - Model Combination 1, Size 20: Success [PITH_FULL_IMAGE:figures/full_fig_p020_24.png]
Figure 23
Figure 23. Figure 23: RQ1 - Model Combination 1, Size 15: Success [PITH_FULL_IMAGE:figures/full_fig_p020_23.png]
Figure 27
Figure 27. Figure 27: RQ1 - Model Combination 2, Size 15 [PITH_FULL_IMAGE:figures/full_fig_p021_27.png]
Figure 28
Figure 28. Figure 28: RQ1 - Model Combination 2, Size 20 [PITH_FULL_IMAGE:figures/full_fig_p021_28.png]
Figure 26
Figure 26. Figure 26: RQ1 - Model Combination 2, Size 10 [PITH_FULL_IMAGE:figures/full_fig_p021_26.png]
Figure 32
Figure 32. Figure 32: RQ1 - Model Combination 3, Size 15 [PITH_FULL_IMAGE:figures/full_fig_p022_32.png]
Figure 30
Figure 30. Figure 30: RQ1 - Model Combination 3, Size 5 [PITH_FULL_IMAGE:figures/full_fig_p022_30.png]
Figure 31
Figure 31. Figure 31: RQ1 - Model Combination 3, Size 10 [PITH_FULL_IMAGE:figures/full_fig_p022_31.png]
Figure 37
Figure 37. Figure 37: RQ1 - Model Combination 4, Size 15 [PITH_FULL_IMAGE:figures/full_fig_p023_37.png]
Figure 35
Figure 35. Figure 35: RQ1 - Model Combination 4, Size 5 [PITH_FULL_IMAGE:figures/full_fig_p023_35.png]
Figure 36
Figure 36. Figure 36: RQ1 - Model Combination 4, Size 10 [PITH_FULL_IMAGE:figures/full_fig_p023_36.png]
Figure 41
Figure 41. Figure 41: RQ2 - LLM: Granite 3.3B, Size 10 [PITH_FULL_IMAGE:figures/full_fig_p024_41.png]
Figure 42
Figure 42. Figure 42: RQ2 - LLM: Granite 3.3B, Size 15 [PITH_FULL_IMAGE:figures/full_fig_p024_42.png]
Figure 43
Figure 43. Figure 43: RQ2 - LLM: Granite 3.3B, Size 20 [PITH_FULL_IMAGE:figures/full_fig_p024_43.png]
Figure 46
Figure 46. Figure 46: RQ2 - LLM: Llama 3.1, Size 15 [PITH_FULL_IMAGE:figures/full_fig_p025_46.png]
Figure 44
Figure 44. Figure 44: RQ2 - LLM: Llama 3.1, Size 5 [PITH_FULL_IMAGE:figures/full_fig_p025_44.png]
Figure 45
Figure 45. Figure 45: RQ2 - LLM: Llama 3.1, Size 10 [PITH_FULL_IMAGE:figures/full_fig_p025_45.png]
Figure 50
Figure 50. Figure 50: RQ3 - Pipeline: Granite 3.3B → DeepSeek R1 8B, Size 10 [PITH_FULL_IMAGE:figures/full_fig_p026_50.png]
Figure 51
Figure 51. Figure 51: RQ3 - Pipeline: Granite 3.3B → DeepSeek R1 8B, Size 15 [PITH_FULL_IMAGE:figures/full_fig_p026_51.png]
Figure 52
Figure 52. Figure 52: RQ3 - Pipeline: Granite 3.3B → DeepSeek R1 8B, Size 20 [PITH_FULL_IMAGE:figures/full_fig_p026_52.png]
Figure 55
Figure 55. Figure 55: RQ3 - Pipeline: Granite 3.3B → Granite 3.3B, Size 15 [PITH_FULL_IMAGE:figures/full_fig_p027_55.png]
Figure 53
Figure 53. Figure 53: RQ3 - Pipeline: Granite 3.3B → Granite 3.3B, Size 5 [PITH_FULL_IMAGE:figures/full_fig_p027_53.png]
Figure 54
Figure 54. Figure 54: RQ3 - Pipeline: Granite 3.3B → Granite 3.3B, Size 10 [PITH_FULL_IMAGE:figures/full_fig_p027_54.png]
Figure 60
Figure 60. Figure 60: RQ3 - Pipeline: Granite 3.3B → Qwen 2.5 Pro, Size 15 [PITH_FULL_IMAGE:figures/full_fig_p028_60.png]
Figure 58
Figure 58. Figure 58: RQ3 - Pipeline: Granite 3.3B → Qwen 2.5 Pro, Size 5 [PITH_FULL_IMAGE:figures/full_fig_p028_58.png]
Figure 59
Figure 59. Figure 59: RQ3 - Pipeline: Granite 3.3B → Qwen 2.5 Pro, Size 10 [PITH_FULL_IMAGE:figures/full_fig_p028_59.png]
Figure 65
Figure 65. Figure 65: RQ3 - Pipeline: Llama 3.1 → DeepSeek R1 8B, Size 15 [PITH_FULL_IMAGE:figures/full_fig_p029_65.png]
Figure 63
Figure 63. Figure 63: RQ3 - Pipeline: Llama 3.1 → DeepSeek R1 8B, Size 5 [PITH_FULL_IMAGE:figures/full_fig_p029_63.png]
Figure 64
Figure 64. Figure 64: RQ3 - Pipeline: Llama 3.1 → DeepSeek R1 8B, Size 10 [PITH_FULL_IMAGE:figures/full_fig_p029_64.png]
Figure 70
Figure 70. Figure 70: RQ4 - Combination 1: SOFAI-LM (Granite → DeepSeek) vs. LRM (DeepSeek), Size 15 [PITH_FULL_IMAGE:figures/full_fig_p030_70.png]
Figure 68
Figure 68. Figure 68: RQ4 - Combination 1: SOFAI-LM (Granite → DeepSeek) vs. LRM (DeepSeek), Size 5 [PITH_FULL_IMAGE:figures/full_fig_p030_68.png]
Figure 71
Figure 71. Figure 71: RQ4 - Combination 1: SOFAI-LM (Granite → DeepSeek) vs. LRM (DeepSeek), Size 20 [PITH_FULL_IMAGE:figures/full_fig_p030_71.png]
Figure 74
Figure 74. Figure 74: RQ4 - Combination 2: SOFAI-LM (Granite → Granite) vs. LRM (Granite), Size 15 [PITH_FULL_IMAGE:figures/full_fig_p031_74.png]
Figure 72
Figure 72. Figure 72: RQ4 - Combination 2: SOFAI-LM (Granite → Granite) vs. LRM (Granite), Size 5 [PITH_FULL_IMAGE:figures/full_fig_p031_72.png]
Figure 73
Figure 73. Figure 73: RQ4 - Combination 2: SOFAI-LM (Granite → Granite) vs. LRM (Granite), Size 10 [PITH_FULL_IMAGE:figures/full_fig_p031_73.png]
Figure 79
Figure 79. Figure 79: RQ4 - Combination 3: SOFAI-LM (Granite → Qwen) vs. LRM (Qwen), Size 15 [PITH_FULL_IMAGE:figures/full_fig_p032_79.png]
Figure 77
Figure 77. Figure 77: RQ4 - Combination 3: SOFAI-LM (Granite → Qwen) vs. LRM (Qwen), Size 5 [PITH_FULL_IMAGE:figures/full_fig_p032_77.png]
Figure 78
Figure 78. Figure 78: RQ4 - Combination 3: SOFAI-LM (Granite → Qwen) vs. LRM (Qwen), Size 10 [PITH_FULL_IMAGE:figures/full_fig_p032_78.png]
Figure 84
Figure 84. Figure 84: RQ4 - Combination 4: SOFAI-LM (Llama → DeepSeek) vs. LRM (DeepSeek), Size 15 [PITH_FULL_IMAGE:figures/full_fig_p033_84.png]
Figure 82
Figure 82. Figure 82: RQ4 - Combination 4: SOFAI-LM (Llama → DeepSeek) vs. LRM (DeepSeek), Size 5 [PITH_FULL_IMAGE:figures/full_fig_p033_82.png]
Figure 83
Figure 83. Figure 83: RQ4 - Combination 4: SOFAI-LM (Llama → DeepSeek) vs. LRM (DeepSeek), Size 10 [PITH_FULL_IMAGE:figures/full_fig_p033_83.png]
Figure 88
Figure 88. Figure 88: Comparison of success rate versus average time [PITH_FULL_IMAGE:figures/full_fig_p034_88.png]
Figure 87
Figure 87. Figure 87: Comparison of success rate versus average time [PITH_FULL_IMAGE:figures/full_fig_p034_87.png]
Figure 89
Figure 89. Figure 89: Comparison of success rate versus average time [PITH_FULL_IMAGE:figures/full_fig_p034_89.png]
Figure 91
Figure 91. Figure 91: Comparison of SOFAI-LM performance using [PITH_FULL_IMAGE:figures/full_fig_p036_91.png]
Figure 92
Figure 92. Figure 92: Comparison of SOFAI-LM performance using [PITH_FULL_IMAGE:figures/full_fig_p036_92.png]
Figure 94
Figure 94. Figure 94: Overall performance comparison between the [PITH_FULL_IMAGE:figures/full_fig_p037_94.png]
Figure 95
Figure 95. Figure 95: Overall performance comparison between the a [PITH_FULL_IMAGE:figures/full_fig_p037_95.png]

Review history (2 revisions) →

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

41 extracted references · 22 canonical work pages

  1. [1]

    Amizadeh, S. e. a. 2020. NeuroSAT: End-to-End SAT Solver Learning. ICLR

    work page 2020

  2. [2]

    Besta, M. e. a. 2023. ThinkGPT: Enhancing LLM Reasoning with Chain-of-Thought Fine-Tuning. arXiv preprint arXiv:2309.02664

    work page Pith review arXiv 2023

  3. [3]

    Booch, G.; Fabiano, F.; Horesh, L.; Kate, K.; Lenchner, J.; Linck, N.; Loreggia, A.; Murugesan, K.; Mattei, N.; and Rossi, F. e. a. 2021. Thinking fast and slow in AI. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 35, 15042--15046

    work page 2021

  4. [4]

    B.; Mann, B.; Ryder, N.; Subbiah, M.; Kaplan, J.; Dhariwal, P.; Neelakantan, A.; Shyam, P.; Sastry, G.; and Askell, A

    Brown, T. B.; Mann, B.; Ryder, N.; Subbiah, M.; Kaplan, J.; Dhariwal, P.; Neelakantan, A.; Shyam, P.; Sastry, G.; and Askell, A. e. a. 2020. Language Models are Few-Shot Learners. arXiv preprint arXiv:2005.14165

    arXiv 2020

  5. [5]

    Chen, M.; Tworek, J.; Jun, H.; Yuan, Q.; Pinto, H. P. D. O.; Kaplan, J.; Edwards, H.; Burda, Y.; Joseph, N.; Brockman, G.; et al. 2021. Evaluating large language models trained on code. arXiv preprint arXiv:2107.03374

    arXiv 2021

  6. [6]

    Dubey, A.; Jauhri, A.; Pandey, A.; Kadian, A.; Al-Dahle, A.; Letman, A.; Mathur, A.; Schelten, A.; Yang, A.; and Fan, A. e. a. 2024. The Llama 3 Herd of Models. CoRR

    work page 2024

  7. [7]

    Evans, R. e. a. 2021. Making Neural Deduction Differentiable. Nature Machine Intelligence

    work page 2021

  8. [8]

    B.; Loreggia, A.; Mattei, N.; Murugesan, K.; Pallagani, V.; Rossi, F.; Srivastava, B.; and Venable, K

    Fabiano, F.; Ganapini, M. B.; Loreggia, A.; Mattei, N.; Murugesan, K.; Pallagani, V.; Rossi, F.; Srivastava, B.; and Venable, K. B. 2025. Thinking Fast and Slow in Human and Machine Intelligence. Commun. ACM, 68(8): 72–79

    work page 2025

Show all 41 references
  1. [9]

    B.; Horesh, L.; Loreggia, A.; Murugesan, K.; Rossi, F.; and Srivastava, B

    Fabiano, F.; Pallagani, V.; Ganapini, M. B.; Horesh, L.; Loreggia, A.; Murugesan, K.; Rossi, F.; and Srivastava, B. 2023. Plan-SOFAI: A Neuro-Symbolic Planning Architecture. In Neuro-Symbolic Learning and Reasoning in the era of Large Language Models

    2023

  2. [10]

    B.; Campbell, M.; Fabiano, F.; Horesh, L.; Lenchner, J.; Loreggia, A.; Mattei, N.; Rossi, F.; Srivastava, B.; and Venable, K

    Ganapini, M. B.; Campbell, M.; Fabiano, F.; Horesh, L.; Lenchner, J.; Loreggia, A.; Mattei, N.; Rossi, F.; Srivastava, B.; and Venable, K. B. e. a. 2022. Combining Fast and Slow Thinking for Human-like and Efficient Decisions in Constrained Environments. In NeSy, 171--185

    2022

  3. [11]

    Guo, D.; Yang, D.; Zhang, H.; Song, J.; Zhang, R.; Xu, R.; Zhu, Q.; Ma, S.; Wang, P.; and Bi, X. e. a. 2025. Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning. arXiv preprint arXiv:2501.12948

    2025 arXiv

  4. [12]

    Han, J. e. a. 2023. PiVe: Prompting with iterative verification improving graph-based generative capability of LLMs. arXiv:2305.12392

    2023 arXiv

  5. [13]

    IBM Research . 2025. Granite 3.3 8B Instruct Model Card . https://huggingface.co/ibm-granite/granite-3.3-8b-instruct. Accessed on 2025-08-01

    2025

  6. [14]

    Jiang, Y.; Wang, Y.; Zeng, X.; Zhong, W.; Li, L.; Mi, F.; Shang, L.; Jiang, X.; Liu, Q.; and Wang, W. 2023. FollowBench: A Multi-Level Fine-Grained Constraints Following Benchmark for Large Language Models. arXiv preprint arXiv:2310.20410

    2023 arXiv

  7. [15]

    S.; and Trick, M

    Johnson, D. S.; and Trick, M. A. 1996. Cliques, coloring, and satisfiability: second DIMACS implementation challenge, October 11-13, 1993, volume 26. American Mathematical Soc

    1996

  8. [16]

    Kahneman, D. 2011. Thinking, fast and slow. Farrar, Straus and Giroux

    2011

  9. [17]

    Kambhampati, S. 2024. Can large language models reason and plan? Annals of the New York Academy of Sciences, 1534(1): 15--18

    2024

  10. [18]

    S.; Reid, M.; Matsuo, Y.; and Iwasawa, Y

    Kojima, T.; Gu, S. S.; Reid, M.; Matsuo, Y.; and Iwasawa, Y. 2022. Large language models are zero-shot reasoners. Advances in neural information processing systems, 35: 22199--22213

    2022

  11. [19]

    Li, Y. e. a. 2023. Improving Factuality via Multi-Agent Debate and Self-Consistency. arXiv preprint arXiv:2305.14325

    2023 arXiv

  12. [20]

    Lightman, A. e. a. 2023. Let's Verify Step by Step. arXiv preprint arXiv:2305.20050

    2023 arXiv

  13. [21]

    Y.; Fu, Y.; Yang, K.; Brahman, F.; Huang, S.; Bhagavatula, C.; Ammanabrolu, P.; Choi, Y.; and Ren, X

    Lin, B. Y.; Fu, Y.; Yang, K.; Brahman, F.; Huang, S.; Bhagavatula, C.; Ammanabrolu, P.; Choi, Y.; and Ren, X. 2024. Swiftsage: A generative agent with fast and slow thinking for complex interactive tasks. Advances in Neural Information Processing Systems, 36

    2024

  14. [22]

    Madaan, A. e. a. 2023. Self-Refine: Iterative Refinement with Self-Feedback. arXiv preprint arXiv:2303.17651

    2023 arXiv

  15. [23]

    S.; Gala, A.; Magalh \ a es, R.; Perez de Britto, F.; Dur \ a es, D.; and Novais, P

    Marcondes, F. S.; Gala, A.; Magalh \ a es, R.; Perez de Britto, F.; Dur \ a es, D.; and Novais, P. 2025. Using ollama. In Natural Language Analytics with Generative Large-Language Models: A Practical Approach with Ollama and Open-Source LLMs, 23--35. Springer

    2025

  16. [24]

    McConnell, S. 2004. Code complete. Pearson Education

    2004

  17. [25]

    Nye, M. e. a. 2021. Show your work: Scratchpads for intermediate computation with language models. arXiv:2112.00114

    2021 arXiv

  18. [26]

    Paranjape, A.; and Chen, X. e. a. 2023. Hindsight Chain-of-Thought Reasoning. In NeurIPS

    2023

  19. [27]

    Paul, D. e. a. 2023. Chain-of-Verification Reduces Hallucination in LLM Reasoning. arXiv preprint arXiv:2309.11495

    2023 arXiv

  20. [28]

    Polu, S.; and Sutskever, I. 2022. Minerva: Solving Quantitative Reasoning Problems with Language Models. arXiv preprint arXiv:2206.14858

    2022 arXiv

  21. [29]

    Schick, T.; Dwivedi-Yu, J.; and Lazaridou, A. e. a. 2023. Toolformer: Language Models Can Teach Themselves to Use Tools. arXiv preprint arXiv:2302.04761

    2023 arXiv

  22. [30]

    Selsam, D. e. a. 2019. Learning a SAT Solver from Single-Bit Supervision. ICML

    2019

  23. [31]

    Shinn, N.; and Cassano, F. e. a. 2023. Reflexion: An Autonomous Agent with Dynamic Memory and Self-Reflection. arXiv preprint arXiv:2303.11366

    2023 arXiv

  24. [32]

    Stechly, K.; Valmeekam, K.; and Kambhampati, S. 2024. On the self-verification limitations of large language models on reasoning and planning tasks. arXiv preprint arXiv:2402.08115

    2024 arXiv

  25. [33]

    Tian, R.; Ye, Y.; Qin, Y.; Cong, X.; Lin, Y.; Pan, Y.; Wu, Y.; Haotian, H.; Weichuan, L.; and Liu, Z. e. a. 2024. DebugBench: Evaluating Debugging Capability of Large Language Models. In Findings of the Association for Computational Linguistics ACL 2024, 4173--4198

    2024

  26. [34]

    Valmeekam, K.; Olmo, A.; Sreedharan, S.; and Kambhampati, S. 2022. Large Language Models Still Can’t Plan: A Benchmark for LLMs on Planning and Reasoning about Change. In NeurIPS 2022 Foundation Models for Decision Making Workshop

    2022

  27. [35]

    Valmeekam, K. e. a. 2022. Large language models still can’t plan: A benchmark for LLMs on planning and reasoning about change. In NeurIPS Foundation Models for Decision Making Workshop

    2022

  28. [36]

    Wang, X. e. a. 2022. Self-consistency improves chain-of-thought reasoning in language models. arXiv:2203.11171

    2022 arXiv

  29. [37]

    Wei, J. e. a. 2022. Chain-of-thought prompting elicits reasoning in large language models. In NeurIPS

    2022

  30. [38]

    Welleck, S. e. a. 2022. NaturalProofs: Formal Theorem Proving with LLMs. In ICML

    2022

  31. [39]

    Yang, A.; Li, A.; Yang, B.; Zhang, B.; Hui, B.; Zheng, B.; Yu, B.; Gao, C.; Huang, C.; and Lv, C. e. a. 2025. Qwen3 technical report. arXiv preprint arXiv:2505.09388

    2025 arXiv

  32. [40]

    , " * write output.state after.block = add.period write newline

    ENTRY address archivePrefix author booktitle chapter edition editor eid eprint howpublished institution isbn journal key month note number organization pages publisher school series title type volume year label extra.label sort.label short.list INTEGERS output.state before.all...

  33. [41]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.