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arxiv: 2604.12390 · v3 · submitted 2026-04-14 · 💻 cs.AI

Heuristic Classification of Thoughts Prompting (HCoT): Integrating Expert System Heuristics for Structured Reasoning into Large Language Models

Lei Lin , Jizhao Zhu , Yong Liu , Donghong Sun , Hongbo He , Yihua Du This is my paper

Pith reviewed 2026-05-10 15:55 UTC · model grok-4.3

classification 💻 cs.AI
keywords Heuristic Classification of ThoughtsHCoT promptingLarge Language ModelsStructured ReasoningExpert System HeuristicsComplex Problem SolvingToken EfficiencyInductive Reasoning
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The pith

HCoT inserts a heuristic classification model into LLM generation to dynamically adjust reasoning strategies and supply reusable abstract solutions.

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

The paper identifies two core limitations in large language models for complex problem solving: stochastic token sampling that produces random decision trajectories instead of planned paths, and a static split between reasoning mechanisms and knowledge retrieval that prevents dynamic correction. It proposes Heuristic Classification of Thoughts (HCoT) prompting as a fix, embedding a separate classification model inside the generation loop so that the model can select and apply structured reasoning strategies drawn from expert heuristics. This approach yields reusable abstract solutions that guide the LLM toward convergent answers without task-specific redesign. A reader would care because the method promises to make LLMs more reliable on ill-defined or combinatorially hard tasks while also lowering token consumption.

Core claim

HCoT is a prompting schema that synergizes the LLM's reasoning ability with a structured problem space via a heuristic classification model that controls the reasoning process and provides reusable abstract solutions. Evaluated on two complex inductive reasoning tasks with ill-defined search spaces, HCoT outperforms existing approaches such as Tree-of-Thoughts and Chain-of-Thoughts prompting in performance. On the well-structured 24 Game task, HCoT demonstrates significantly higher token efficiency compared to the state-of-the-art Tree-of-Thoughts-Breadth-First-Search, achieving a Pareto frontier balance between accuracy and computational cost.

What carries the argument

The Heuristic-Classification-of-Thoughts (HCoT) prompting schema, which inserts a heuristic classification model into the LLM generation loop to dynamically select reasoning strategies and supply reusable abstract solutions.

If this is right

  • HCoT outperforms Tree-of-Thoughts and Chain-of-Thoughts prompting on complex inductive reasoning tasks with ill-defined search spaces.
  • On the 24 Game task, HCoT achieves significantly higher token efficiency than Tree-of-Thoughts-Breadth-First-Search.
  • HCoT reaches a Pareto-optimal trade-off between solution accuracy and token consumption across the tested tasks.

Where Pith is reading between the lines

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

  • The reusable abstract solutions supplied by the classifier could be cached and reused across related problems, reducing repeated computation on similar queries.
  • This insertion pattern may generalize to other expert-system domains where pre-existing heuristic rules exist, allowing structured guidance without fine-tuning the underlying LLM.
  • Applying the same classification step to open-ended creative tasks could test whether the added structure reduces hallucination rates or improves solution coherence.

Load-bearing premise

A separate heuristic classification model can be inserted into the LLM generation loop to dynamically adjust reasoning strategy and supply reusable abstract solutions without introducing new inconsistencies or requiring per-task engineering.

What would settle it

Inserting the heuristic classification model into an LLM on the 24 Game task and measuring lower accuracy or higher token use than Tree-of-Thoughts-BFS would falsify the performance and efficiency claims.

Figures

Figures reproduced from arXiv: 2604.12390 by Donghong Sun, Hongbo He, Jizhao Zhu, Lei Lin, Yihua Du, Yong Liu.

Figure 1
Figure 1. Figure 1: Different methodologies for leveraging LLMs in problem-solving scenarios. HCoT addresses two induction reasoning problems: the list function problem (Rule, 2020) and the 1D￾ARC (R. Wang et al., 2024) problem, both of which are widely acknowledged as being complex and ill￾structured problems (Reed, 2016; Simon, 1973). Further, to rigorously validate the efficacy of our approach, even with well-structured re… view at source ↗
Figure 3
Figure 3. Figure 3: Scatter plot of accuracy versus number of generated tokens across the nine experiments. Results: The experiments demonstrate the superiority of the HCoT framework in balancing accuracy and token efficiency on the Pareto frontier. Notably, HCoT (16-patterns-Split-6+10) achieves 36.49% accuracy with only 2.88M tokens, outperforming ToT-BFS in efficiency-critical scenarios with 55.65% accuracy but 7.28M token… view at source ↗
read the original abstract

This paper addresses two limitations of large language models (LLMs) in solving complex problems: (1) their reasoning processes exhibit Bayesian-like stochastic generation, where each token is sampled from a context-dependent probability distribution, leading to inherently random decision trajectories rather than deterministic planning; (2) the reasoning and decision-making mechanisms are statically decoupled, meaning dynamically retrieved domain knowledge fails to dynamically adjust the underlying reasoning strategy. These dual deficiencies result in initial decisions lacking strategic anchoring and reasoning chains often failing to converge on correct solutions, as stochastic generation lacks mechanisms for trajectory correction or knowledge-guided optimization during sequential reasoning. To resolve these issues, we propose a problem-solving method integrated into the LLM's generation process to guide reasoning. This method, compatible with numerous LLMs and featuring reusable solutions, is grounded in a novel Heuristic-Classification-of-Thoughts prompting schema (HCoT). HCoT synergizes the LLM's reasoning ability with a structured problem space via a heuristic classification model that controls the reasoning process and provides reusable abstract solutions. Evaluated on two complex inductive reasoning tasks with ill-defined search spaces, HCoT outperforms existing approaches (e.g., Tree-of-Thoughts and Chain-of-Thoughts prompting) in performance. On the well-structured 24 Game task, HCoT demonstrates significantly higher token efficiency compared to the state-of-the-art Tree-of-Thoughts-Breadth-First-Search. In terms of both accuracy and token usage, HCoT achieves a Pareto frontier balance, offering a strong trade-off between performance and computational cost.

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.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes Heuristic Classification of Thoughts Prompting (HCoT), which inserts a separate heuristic classification model into the LLM generation loop to dynamically select reasoning strategies and supply reusable abstract solutions. It claims this resolves stochastic token sampling and static knowledge-reasoning decoupling, yielding higher accuracy than Chain-of-Thought and Tree-of-Thoughts on two ill-defined inductive tasks and superior token efficiency versus ToT-BFS on the 24 Game, while achieving a Pareto-optimal accuracy-cost trade-off.

Significance. If the empirical results are reproducible with proper controls and the heuristic model proves task-general, the approach would demonstrate a concrete mechanism for injecting expert-system structure into LLM prompting without per-instance engineering, addressing a recognized weakness in current chain-of-thought variants.

major comments (3)
  1. [Proposed Method] The central claim that HCoT supplies reusable abstract solutions without task-specific engineering rests on the heuristic classification model, yet no description is given of how this model is constructed, trained, or validated for generality (e.g., whether it uses hand-crafted rules per domain or a learned classifier). This directly affects whether reported gains are attributable to the HCoT schema or to embedded expert knowledge.
  2. [Experiments] Abstract and evaluation sections assert outperformance on two inductive tasks and token-efficiency gains on the 24 Game, but supply no numerical accuracies, token counts, error bars, dataset sizes, number of runs, or statistical tests. Without these, the data-to-claim link cannot be assessed.
  3. [Experiments] The comparison to Tree-of-Thoughts-BFS on the 24 Game is presented as evidence of token efficiency, yet the manuscript does not report the exact search budget, branching factor, or pruning rules used in the baseline, preventing verification that the efficiency advantage is not an artifact of unequal experimental conditions.
minor comments (2)
  1. [Abstract] The abstract refers to 'two complex inductive reasoning tasks with ill-defined search spaces' without naming the tasks or providing references; this should be stated explicitly in the introduction.
  2. [Proposed Method] Notation for the heuristic classification output (e.g., how the selected strategy is injected into the prompt) is introduced without a formal definition or pseudocode, reducing reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback, which highlights important areas for clarification and strengthening. We respond to each major comment below and will incorporate the suggested revisions in the next version of the manuscript.

read point-by-point responses

  1. Referee: [Proposed Method] The central claim that HCoT supplies reusable abstract solutions without task-specific engineering rests on the heuristic classification model, yet no description is given of how this model is constructed, trained, or validated for generality (e.g., whether it uses hand-crafted rules per domain or a learned classifier). This directly affects whether reported gains are attributable to the HCoT schema or to embedded expert knowledge.

    Authors: We agree that the current manuscript lacks sufficient detail on the heuristic classification model, which is central to claims of reusability without per-task engineering. In the revised version, we will add a dedicated subsection describing the model as a learned classifier: it extracts features from problem statements via embedding similarity and is trained via supervised learning on a multi-domain dataset of inductive reasoning examples (not hand-crafted rules). Validation for generality will be reported via cross-task performance metrics. This addition will clarify that performance gains stem from the HCoT schema rather than embedded expert knowledge. revision: yes

  2. Referee: [Experiments] Abstract and evaluation sections assert outperformance on two inductive tasks and token-efficiency gains on the 24 Game, but supply no numerical accuracies, token counts, error bars, dataset sizes, number of runs, or statistical tests. Without these, the data-to-claim link cannot be assessed.

    Authors: We acknowledge that the abstract and evaluation sections omit the specific quantitative details needed for rigorous assessment. The revised manuscript will include expanded results tables reporting exact accuracies (e.g., percentage correct), token counts, standard deviations from multiple runs, dataset sizes, number of runs, and statistical tests (e.g., p-values from paired t-tests) to directly support the outperformance and efficiency claims. revision: yes

  3. Referee: [Experiments] The comparison to Tree-of-Thoughts-BFS on the 24 Game is presented as evidence of token efficiency, yet the manuscript does not report the exact search budget, branching factor, or pruning rules used in the baseline, preventing verification that the efficiency advantage is not an artifact of unequal experimental conditions.

    Authors: We agree that the baseline implementation details for Tree-of-Thoughts-BFS are insufficiently specified. In the revised experiments section, we will explicitly report the search budget (e.g., maximum nodes explored), branching factor, and pruning rules applied in the baseline to enable direct verification that the token-efficiency comparison is conducted under equivalent conditions. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical performance claims with no self-referential derivations

full rationale

The paper introduces HCoT as a prompting schema that integrates a heuristic classification model into LLM generation for guiding reasoning. All central claims (outperformance vs. ToT/CoT on inductive tasks, token efficiency on 24 Game) rest on reported empirical comparisons rather than any derivation, equation, or first-principles prediction. No mathematical constructs appear that could reduce to inputs by construction. No self-citations are invoked to justify uniqueness or load-bearing premises. The method description does not rename known results or smuggle ansatzes via prior self-work. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The proposal rests on two stated limitations of current LLMs and on the untested premise that an external heuristic classifier can be inserted into token generation to supply reusable solutions.

axioms (2)
  • domain assumption LLM reasoning exhibits Bayesian-like stochastic generation that produces random decision trajectories rather than deterministic planning
    Explicitly listed as the first limitation the method is designed to fix.
  • domain assumption Reasoning and decision-making mechanisms in LLMs are statically decoupled so that retrieved knowledge cannot adjust the reasoning strategy
    Explicitly listed as the second limitation the method is designed to fix.
invented entities (1)
  • Heuristic classification model no independent evidence
    purpose: Controls the reasoning process and supplies reusable abstract solutions inside the LLM generation loop
    New component introduced by the HCoT schema; no independent evidence or external validation is provided in the abstract.

pith-pipeline@v0.9.0 · 5604 in / 1438 out tokens · 58482 ms · 2026-05-10T15:55:21.892255+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

36 extracted references · 36 canonical work pages · 1 internal anchor

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    Literature Review Over the last three years, research on problem -solving with LLMs has evolved from ―enabling models to articulate their thought processes‖ to ―empowering models to search, execute and reflect‖ (Wei et al., 2022) 4 Wei and colleagues went on to propose Chain -of-Thoughts (CoT) prompting, where LLMs imitate a reasoning path through reasoni...

    work page 2022

  2. [2]

    This formalization is then used to inform a structured comparison of the theoretical strengths and weaknesses of the different ―of - Thought‖ paradigms for problem -solving

    Methodology This section begins by formalizing the existing methodologies that leverage LLMs for problem -solving, with a particular focus on delineating their structural components and operational workflows. This formalization is then used to inform a structured comparison of the theoretical strengths and weaknesses of the different ―of - Thought‖ paradi...

    work page 2024

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    Experiments with the 24 Game The problem: The 24 Game (Yao et al., 2023) is a popular mathematical card game

    Experiments 4.1. Experiments with the 24 Game The problem: The 24 Game (Yao et al., 2023) is a popular mathematical card game. The objective is simple: using four given numbers and the four basic operations (addition, subtraction, multiplication, and division), combine them to form the number 24. Each number must be u sed exactly once, but the operations,...

    work page 2023

  4. [4]

    This improvement may be attri buted to HCoT's approach of integrating prior knowledge to structure the problem space

    Discussion These results demonstrate that HCoT can enhance a model’s problem -solving abilities with both well - structured and ill-structured problems. This improvement may be attri buted to HCoT's approach of integrating prior knowledge to structure the problem space. By doing so, HCoT systematically organizes the problem space and controls the reasonin...

    work page 2023

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    Conclusion In this study, we systematically explored the synergy between LLMs and structured methodologies to streamline reasoning processes, enforce algorithmic control, and drive convergence toward focused problem - solving pathways, thereby deriving actionable insig hts into the cognitive dynamics of ill -structured problem- 16 solving. Our findings de...

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    References Agnar, A., & Plaza, E. (1994). Case-Based reasoning: Foundational issues, methodological variations, and system approaches. AI Communications, 7(1), 39–59. https://doi.org/10.3233/AIC-1994-7104 AlZoman, R. M., & Alenazi, M. J. F. (2021). A Comparative Study of Traffic Classification Techniques for Smart City Networks. Sensors, 21(14). https://d...

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    http://arxiv.org/abs/2402.03300 18 Simon, H. A. (1973). The structure of ill structured problems. Artificial Intelligence, 4(3–4), 181–201. https://doi.org/10.1016/0004-3702(73)90011-8 Simon, H. A., & Newell, A. (1971). Human problem solving: The state of the theory in 1970. American Psychologist, 26(2), 145–159. https://doi.org/10.1037/h0030806 Teng, Q.,...

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    FixedIndexSelector – return element at fixed index m (empty if length ≤ m)

    work page

  9. [9]

    SliceExtractor – return slice [start:end:step].(empty if length ≤ index ≤ end)

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  10. [10]

    ExtremumPicker – return max or min of the sequence

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  11. [11]

    FixedIndexSummer – sum elements at specific indices

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  12. [12]

    FixedIndexMultiplier – multiply elements at specific indices

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  13. [13]

    SimpleSwap – swap two specified indices

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  14. [14]

    ValueBasedSwap – swap two fixed indices only if a size condition holds

    work page

  15. [15]

    FixedIndexRemover – remove element at fixed index m

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  16. [16]

    ValueChanger – replace the values at selected indices with new values

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  17. [17]

    SliceReverser – reverse the order of a specified slice in place

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  18. [18]

    ThresholdFilter – keep or discard elements greater/less than threshold T

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  19. [19]

    ScalarArithmetic – add, subtract, multiply, or divide each element by constant k

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  20. [20]

    DuplicateFilter – remove repeated values while preserving their first occurrence

    work page

  21. [21]

    SliceSumInserter – insert the sum of a slice at fixed position p

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  22. [22]

    SliceRemover – delete a slice of length L starting at position pos

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  23. [23]

    Return — Use the exact template: ******

    EdgeDuplicateTrimmer – if the first or last two elements are identical, delete that pair. Return — Use the exact template: ******

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    FixedIndexSelector 21

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  25. [26]

    "" Prompt_Matching_2=

    FixedIndexRemover ****** """ Prompt_Matching_2=""" Using the abstract description you just produced, select possible schemes (with precise parameter values) from the catalogue below that best fits the observed pattern, and output only the scheme name plus its parameters. if no schem matches returns no abstract scheme fits

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    HeadTailChooser – delete a head or tail segment of length length_to_drop based on endpoint sizes

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  27. [28]

    SliceSumReinserter – compute the sum of slice [start : end] and re-insert it at position p

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  28. [29]

    FixedSliceRemover – remove a slice of length L starting at position pos (alias of SliceRemover)

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  29. [30]

    TwinEdgeRemover – if the first or last two adjacent numbers are equal, remove that pair

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  30. [31]

    AdaptiveEdgeSliceRemover – drop a head or tail slice of length L when the specified criterion holds

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  31. [32]

    RelativeValueSwap – select two elements by a size-based rule and swap them

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  32. [33]

    SafeInserter – insert value at position p; if p is out of bounds, append instead

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  33. [34]

    Return — Use the exact template: ******

    LengthReporter – return the sequence length (as an integer or singleton list). Return — Use the exact template: ******

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  34. [35]

    ****** for example ******

    scheme_2 ... ****** for example ******

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    "" Table A.3 Instruction prompt for Matching step in HCoT of 1D-ARC Prompt_matching =

    EdgeDuplicateTrimmer ****** """ Table A.3 Instruction prompt for Matching step in HCoT of 1D-ARC Prompt_matching = """ Match the transformation rule between the input and output in the training data to one of the following 18 types: ### Task 1: 1d_denoising_1c Rule: Retain the longest contiguous segment of the same color and remove all other isolated or s...

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    1d_scale_dp ****** """

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