Title: A*-Thought: Efficient Reasoning via Bidirectional Compression for Low-Resource Settings
Venue: NeurIPS 2025
Accepted: yes
Keywords: long-to-short

thought compression

reasoning

efficient CoT
Abstract: Large Reasoning Models (LRMs) achieve superior performance by extending the thought length. However, a lengthy thinking trajectory leads to reduced efficiency. Most of the existing methods are stuck in the assumption of overthinking and attempt to reason efficiently by compressing the Chain-of-Thought, but this often leads to performance degradation. To address this problem, we introduce A*-Thought, an efficient tree search-based unified framework designed to identify and isolate the most essential thoughts from the extensive reasoning chains produced by these models. It formulates the reasoning process of LRMs as a search tree, where each node represents a reasoning span in the giant reasoning space. By combining the A* search algorithm with a cost function specific to the reasoning path, it can efficiently compress the chain of thought and determine a reasoning path with high information density and low cost. In addition, we also propose a bidirectional importance estimation mechanism, which further refines this search process and enhances its efficiency beyond uniform sampling. Extensive experiments on several advanced math tasks show that A*-Thought effectively balances performance and efficiency over a huge search space. Specifically, A*-Thought can improve the performance of QwQ-32B by 2.39$\times$ with low-budget and reduce the length of the output token by nearly 50\% with high-budget. The proposed method is also compatible with several other LRMs, demonstrating its generalization capability. The code can be accessed at: https://github.com/AI9Stars/AStar-Thought.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces A*-Thought, a novel framework designed to enhance the reasoning efficiency of Large Reasoning Models (LRMs) by compressing their lengthy reasoning chains. The authors propose a bidirectional importance estimation mechanism to evaluate the significance of each reasoning step based on its relevance to both the question and the solution. This mechanism assigns a bidirectional importance score (BIS) to each step, which is then used in conjunction with the A* search algorithm to identify and isolate the most essential thoughts from the extensive reasoning chains. The A* search algorithm employs cost functions that assess the quality of the current path and estimate the future cost to reach a desirable final solution, thereby efficiently compressing the chain of thought and determining a reasoning path with high information density and low cost. Extensive experiments on various advanced math tasks demonstrate that A*-Thought effectively balances performance and efficiency over a huge search space. For instance, it can improve the performance of QwQ-32B by 2.39× with low-budget and reduce the length of the output token by nearly 50% with high-budget. The proposed method is also compatible with several other LRMs, showcasing its generalization capability.\n\nSTRENGTHS AND WEAKNESSES:\n### Strengths\n\n1. The paper is novel and presents a well-defined problem formulation. Both the **Step-Level Bidirectional Importance Score** and the **Path-Level A\\* Search** are intuitively motivated and thoroughly described.  \n2. The proposed method achieves strong empirical performance, demonstrating a **2.39× speedup** over the 32B model.  \n3. The overall structure of the paper is clear and easy to follow.\n\n### Weaknesses\n\n1. It would be helpful to include a more detailed analysis of the **computational cost** incurred by the A* search process when selecting training samples across benchmarks.  \n2. The paper would benefit from a broader evaluation across **different model scales** to better assess robustness.\n\nQUESTIONS:\n### Questions\n\n1. What validation model is used during the A* search process? The paper does not seem to specify this, which raises concerns about reproducibility and implementation clarity.\n\n2. The teaser figure is difficult to interpret. What do the circles of different sizes and depths represent? A legend or further explanation would greatly improve readability.\n\n3. Does using `\\n\\n` as a delimiter for segmenting thought steps risk omitting essential intermediate reasoning steps, especially in multi-line or complex CoT outputs?\n\n4. Have the authors explored **test-time scaling strategies**, such as self-consistency or diverse sampling? Such evaluations would help better understand the upper-bound performance of the method.\n\nLIMITATIONS:\nNo.", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-23"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper presents an approach for decreasing the length of chain-of-thought reasoning traces while maintaining accuracy. To do so, they design an algorithm that searches for subtraces that can still reach the final answer, and then conduct supervised fine-tuning (I think?) on those subtraces. Evaluated on mathematical reasoning benchmarks, the resulting models are much more accurate for a given token budget, and maintain accuracy when answering without a budget too. The algorithm for discovering subtraces is said to be a form of A* search that sorts tokens based on their importance in determining the solution, then chooses which tokens to in an expand-then-greedily-select step until the current subtrace is verified to produce a correct solution.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\nThe approach works really well compared to baselines.\nThe paper is well-written. Most of it is easy to understand and clear. \nThe approach is interesting and novel. At first when I read the paper, I was skeptical that such an approach would lead to useful results, so it's surprising to see that it works.\nThe interesting part of the approach is the fine-grained importance score as the basis of discovering useful traces. It's based on attention weights and the likelihood of the model producing the solution given the tokens up to that point, but using GPT-2 instead of whatever model is generating the reasoning traces.\nI find it quite surprising that GPT-2 could yield useful scores this way, given how weak of a model it is.\n\n## Weaknesses\nThe A* algorithm and the bidirectional score could be explained more clearly. See questions section.\nThere are some other confusing parts of the paper, see questions section.\nThe baselines the approach is being compared to seem quite weak — see appendix E for prompts.\n\nQUESTIONS:\nQ1. Is a reasoning step $t^(n)$ a single token? Or is it like a sentence? If it's not a token, is the splitting of an answer into thoughts given by your dataset? For the rest of my answer, I'll assume it's a single token..\nQ1. For the NLL part of the BIS, it looks like $NLL(s | t^(n))$ is the probability of generating the solution given the single reasoning step? Isn't that going to be very hard for the model? Similarly, it seems odd to calculate the $NLL(t^(n) | q)$. But I guess even though it's weird, there's enough signal there to be useful?\nQ3. I don't understand the $A^*$ search algorithm. Is this even A^*? Here is my understanding:\n    1. sort tokens by BIS score. start with empty trace T.\n    2. take the top W tokens. For each one, score using cost function f. Take the best scoring token and add it to the trace.\n    3. check if current trace leads to solution using verifier. If it does, return current trace. Otherwise, repeat step 2.\n\nQuestions about this algorithm:\nQ3.1: why are there two different scoring functions, BIS and the cost function? It seems like BIS more efficient to evaluate, and f more expensive? Why not just use the same exact function for the two, but use a cheap model for the initial sorting function and then the full model for the cost function? \nQ3.2: what is the value of W? is this stated somewhere?\nQ3.3: the tokens after being sorted by BIS are out of order, right? when added to the trace, they are put back into their order, right?\nQ3.4: after expanding W options, are the ones that aren't finally selected put back into the queue, or discarded?\nQ4. how does the verifier work? You just say which model it is, but I don't understand what the model is doing.\n\nLIMITATIONS:\nN/A", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 3, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 4, "DATE": "2025-06-30"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper proposes A*-Thought, an inference-time framework that prunes large language models’ long chain-of-thought (CoT) traces. Each step receives a bidirectional importance score (BIS) derived from attention statistics and token-level NLL with respect to both the question and the predicted answer. An A* search then selects a compact subset of spans that minimises a cost combining current-path verification loss and a heuristic future cost. Experiments on four math-reasoning benchmarks with three 32 B models show accuracy gains (up to +18 pp) and shorter outputs (≈50 % fewer tokens) under fixed token budgets compared with prompt- and training-based baselines.\n\nSTRENGTHS AND WEAKNESSES:\nStrengths\n\n- Potential to lower inference cost of LRMs, an important problem.\n\n- Empirical improvements on math tasks under tight budgets (Table 1). \n\nWeaknesses\n\n- Evaluation limited to synthetic math datasets; no evidence on open-domain, multimodal or non-numeric reasoning.\n\n- Variance/error bars omitted despite stochastic search; single-run results may be fragile. \n\n- Conceptually close to Retro-Search and TokenSkip; contribution may be incremental (reuse of A* and attention/NLL saliency).\n\n- Gains are shown only for already-compressed 32 B distillations; unclear impact on frontier ( >70 B) models or real latency on hardware.\n\n- Training still demands multi-epoch passes over the entire CoT corpus (8 × A100 80 G, 3 epochs) — energy savings may be overstated.\n\nQUESTIONS:\nQ1: Have you tried GSM-like natural-language tasks, code reasoning, or commonsense QA to demonstrate domain robustness?\n\nQ2: The verifier V is distilled from the same dataset used for pruning; could this inflate acceptance probability? \n\nWhile the idea is interesting and results promising, the narrow evaluation scope, missing robustness analyses, and incomplete limitation discussion prevent a confident acceptance at this stage.\n\nLIMITATIONS:\nThey do not discuss: (a) sensitivity to α, β, k_max across tasks; (b) potential semantic drift when critical but low-BIS steps are pruned; (c) ethical risks of deploying compressed reasoning that may omit safety checks. Hence the limitations section is insufficient.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 2, "IMPACT": 3, "ORIGINALITY": 2, "DATE": "2025-07-02"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces A-Thought*, a framework that compresses lengthy Chain-of-Thought (CoT) outputs from large reasoning models using an A* search guided by a bidirectional importance score (BIS). The method addresses the efficiency challenges posed by verbose CoT reasoning, aiming to retain performance while significantly reducing token output.\n\nSTRENGTHS AND WEAKNESSES:\n## Strengths\n\n1. **Clear Motivation and Relevance**: The problem of excessive reasoning length in LRMs is well-known, and addressing it aligns with growing interest in cost-efficient inference.\n\n2. **Methodological Innovation**: The integration of a bidirectional importance score with A* search to identify high-value reasoning steps is novel.\n\n3. **Empirical Performance**: Substantial gains are reported in accuracy and accuracy per computation unit (ACU), especially under constrained budgets (e.g., 2.39× improvement for QwQ-32B).\n\n## Weaknesses\n\n1. **Lack of Theoretical Analysis**: There is no rigorous theoretical justification for why BIS + A* would yield better CoT compression than alternatives.\n\n2. **Limited Performance Gains in High-Budget Scenarios**: While A*-Thought shows impressive improvements under strict token constraints, its advantages diminish—and even reverse—when larger token budgets are available. In high-budget settings (e.g., 4096 tokens), A*-Thought underperforms compared to several baselines in terms of raw accuracy. This suggests that the proposed method may overly prioritize brevity at the cost of completeness.\n\nQUESTIONS:\n1. Can you explain why A*-Thought underperforms in high-budget scenarios? Is there an inherent trade-off in the compression strategy that degrades solution completeness?\n\n2. How sensitive is the method to the selection of $\\alpha$ (in BIS) and $\\beta$ (in the cost function)? Have you performed any systematic hyperparameter tuning?\n\n3. Have you tested A*-Thought on non-mathematical reasoning tasks (e.g., commonsense QA, multi-hop QA)? If not, what are the anticipated limitations?\n\nLIMITATIONS:\nYes", "TITLE": "Official Review", "RECOMMENDATION": 4, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-07-03"}