{"title": "Limitations in Reasoning Models When Provided with Explicit Algorithms", "report_sections": [{"header": "Overview", "content": "

Recent studies have indicated that even when a complete algorithm is provided in the prompt, reasoning models fail to execute it accurately. This phenomenon highlights a deeper issue: these models have substantial limitations in both verifying the correctness of each step and following logical sequences as prescribed. The models\u2019 inability to benefit from explicit algorithmic guidance exposes critical weaknesses in their reasoning capabilities. The text from the source explains that despite being given a recursive algorithm for the Tower of Hanoi, the model\u2019s performance does not improve, and the failure point remains unchanged.

", "media": [{"caption": "Figure 3: Illustration of the four puzzle environments. Columns show the progression from initial state (top) through intermediate state (middle) to target state (bottom) for puzzles: Tower of Hanoi (disk transfer across pegs), Checkers Jumping (position swapping of colored tokens), River Crossing (transporting entities across a river), and Blocks World (stack reconfiguration).", "url": "https://askpandipro.s3.eu-west-1.amazonaws.com/users/1/documents/401/figures/2.png", "source_url": null, "title": null, "s3_key": "users/1/documents/401/figures/2.png", "type": "image", "id": 208219, "html": null, "carousel_h5": "Figure 3: Illustration of the four puzzle environments. Columns show the progression from initial state (top) through intermediate state (middle) to target state (bottom) for puzzles: Tower of Hanoi (disk transfer across pegs), Checkers Jumping (position swapping of colored tokens), River Crossing (transporting entities across a river), and Blocks World (stack reconfiguration).", "alt": null}]}, {"header": "Inadequate Execution of Prescribed Algorithms", "content": "

A key observation made in the study is that providing the exact solution algorithm does not lead to improved performance. For instance, in the Tower of Hanoi experiments, even when the recursive method was explicitly provided in the prompt, the failure in executing the solution occurred at nearly the same point as when the algorithm was not given. The source text states: \"even when we provide the algorithm in the prompt\u2014so that the model only needs to execute the prescribed steps\u2014performance does not improve, and the observed collapse still occurs at roughly the same point.\" This clearly indicates that these models face difficulties with consistent logical step execution, regardless of whether they must discover the algorithm independently or merely follow provided instructions.

", "media": [{"caption": "Figure 9: Compositional depth (number of moves required) across different problem sizes for our four puzzle environments.", "url": "https://askpandipro.s3.eu-west-1.amazonaws.com/users/1/documents/401/figures/7.png", "source_url": null, "title": null, "s3_key": "users/1/documents/401/figures/7.png", "type": "image", "id": 208221, "html": null, "carousel_h5": "Figure 9: Compositional depth (number of moves required) across different problem sizes for our four puzzle environments.", "alt": null}, {"caption": "Figure 4: Accuracy of thinking models (Claude 3.7 Sonnet with thinking, DeepSeek-R1) versus their non-thinking counterparts (Claude 3.7 Sonnet, DeepSeek-V3) across all puzzle environments and varying levels of problem complexity.", "url": "https://askpandipro.s3.eu-west-1.amazonaws.com/users/1/documents/401/figures/3.png", "source_url": null, "title": null, "s3_key": "users/1/documents/401/figures/3.png", "type": "image", "id": 208218, "html": null, "carousel_h5": "Figure 4: Accuracy of thinking models (Claude 3.7 Sonnet with thinking, DeepSeek-R1) versus their non-thinking counterparts (Claude 3.7 Sonnet, DeepSeek-V3) across all puzzle environments and varying levels of problem complexity.", "alt": null}]}, {"header": "Limitations in Verification and Consistency", "content": "

The inability to effectively follow and verify algorithmic steps is central to the failure of reasoning models when explicit algorithms are provided. The source material emphasizes that \"finding and devising a solution should require substantially more computation (e.g., for search and verification) than merely executing a given algorithm.\" This suggests that the models are not only challenged by the process of devising novel solutions but also by the execution of known and provided methods. The internal process of verifying the correctness of every step appears to be insufficient. Due to these verification limitations, the models tend to collapse in performance as soon as the complexity increases, leading to an early error in the sequence of operations. This inconsistency in reasoning and verification means that even the simplest hints in the form of explicit algorithms do not translate into better performance during problem solving.

", "media": [{"caption": "Figure 2: Comparative analysis of thinking versus non-thinking models across math benchmarks reveals inconsistent performance patterns. While results on the MATH-500 dataset show comparable performance between both model types, the thinking models demonstrate superior performance on AIME24 and AIME25 benchmarks. Additionally, the observed performance degradation from AIME24 to AIME25 highlights the vulnerability of these benchmarks to data contamination issues.", "url": "https://askpandipro.s3.eu-west-1.amazonaws.com/users/1/documents/401/figures/1.png", "source_url": null, "title": null, "s3_key": "users/1/documents/401/figures/1.png", "type": "image", "id": 208217, "html": null, "carousel_h5": "Figure 2: Comparative analysis of thinking versus non-thinking models across math benchmarks reveals inconsistent performance patterns. While results on the MATH-500 dataset show comparable performance between both model types, the thinking models demonstrate superior performance on AIME24 and AIME25 benchmarks. Additionally, the observed performance degradation from AIME24 to AIME25 highlights the vulnerability of these benchmarks to data contamination issues.", "alt": null}]}, {"header": "Underlying Computational and Logical Barriers", "content": "

The experiments described in the text reveal that the reasoning models have inherent computational and logical scaling limits. As the complexity of the tasks increases, the models initially invest more tokens to reason through the problem; however, near a critical complexity threshold, their reasoning effort decreases despite the problems becoming harder. This counterintuitive behavior underscores a primary limitation: a shortfall in the capacity to dynamically adjust their verification routines as problem complexity increases. Even with the algorithm provided, the expected benefit of reduced search space and simpler execution conditions is not realized because these models still fail to properly track state transitions and maintain logical consistency across multiple steps. In essence, the failure is not solely due to the inability to find a solution, but also due to an intrinsic mismanagement of the execution process when following a set of explicit directives.

", "media": [{"caption": "Figure 5: Pass@k performance of thinking vs. non-thinking models across equivalent compute budgets in puzzle environments of low , medium , and high complexity. Non-thinking models excel in simple problems, thinking models show advantages at medium complexity, while both approaches fail at high complexity regardless of compute allocation.", "url": "https://askpandipro.s3.eu-west-1.amazonaws.com/users/1/documents/401/figures/4.png", "source_url": null, "title": null, "s3_key": "users/1/documents/401/figures/4.png", "type": "image", "id": 208220, "html": null, "carousel_h5": "Figure 5: Pass@k performance of thinking vs. non-thinking models across equivalent compute budgets in puzzle environments of low , medium , and high complexity. Non-thinking models excel in simple problems, thinking models show advantages at medium complexity, while both approaches fail at high complexity regardless of compute allocation.", "alt": null}, {"caption": "Figure 6: Accuracy and thinking tokens vs. problem complexity for reasoning models across puzzle environments. As complexity increases, reasoning models initially spend more tokens while accuracy declines gradually, until a critical point where reasoning collapses\u2014performance drops sharply and reasoning effort decreases.", "url": "https://askpandipro.s3.eu-west-1.amazonaws.com/users/1/documents/401/figures/5.png", "source_url": null, "title": null, "s3_key": "users/1/documents/401/figures/5.png", "type": "image", "id": 208223, "html": null, "carousel_h5": "Figure 6: Accuracy and thinking tokens vs. problem complexity for reasoning models across puzzle environments. As complexity increases, reasoning models initially spend more tokens while accuracy declines gradually, until a critical point where reasoning collapses\u2014performance drops sharply and reasoning effort decreases.", "alt": null}]}, {"header": "Implications for Future Research", "content": "

The failure of reasoning models to harness the benefits of a provided algorithm calls for further investigation into their symbolic manipulation and logical verification capabilities. The observed limitations suggest that current training methods, although effective in generating chain-of-thoughts, are insufficient for developing robust, algorithmic reasoning skills that are crucial for precise and error-free problem solving. This shortfall indicates that future models may need enhanced mechanisms for exact computation and improved frameworks that focus on consistency in step-by-step logical execution. Researchers are thereby encouraged to explore hybrid approaches that combine both pattern recognition and strict algorithmic verification to overcome these fundamental barriers.

", "media": [{"caption": "Figure 11: The first failure move versus problem complexity (N) comparison for thinking and non-thinking models across puzzle environments. Top: Claude-3.7-Sonnet comparison; Bottom: DeepSeek-R1 vs DeepSeek-V3.", "url": "https://askpandipro.s3.eu-west-1.amazonaws.com/users/1/documents/401/figures/9.png", "source_url": null, "title": null, "s3_key": "users/1/documents/401/figures/9.png", "type": "image", "id": 208226, "html": null, "carousel_h5": "Figure 11: The first failure move versus problem complexity (N) comparison for thinking and non-thinking models across puzzle environments. Top: Claude-3.7-Sonnet comparison; Bottom: DeepSeek-R1 vs DeepSeek-V3.", "alt": null}, {"caption": "Figure 12: Density distribution of first failure moves for thinking and non-thinking models across puzzle environments. Top: Claude-3.7-Sonnet comparison; Bottom: DeepSeek-R1 vs DeepSeek-V3.", "url": "https://askpandipro.s3.eu-west-1.amazonaws.com/users/1/documents/401/figures/10.png", "source_url": null, "title": null, "s3_key": "users/1/documents/401/figures/10.png", "type": "image", "id": 208225, "html": null, "carousel_h5": "Figure 12: Density distribution of first failure moves for thinking and non-thinking models across puzzle environments. Top: Claude-3.7-Sonnet comparison; Bottom: DeepSeek-R1 vs DeepSeek-V3.", "alt": null}]}, {"header": "Conclusion", "content": "

In summary, reasoning models fail to benefit from explicitly provided algorithms due to their inherent limitations in step verification and logical consistency. Despite improved chain-of-thought mechanisms, the failure to translate an algorithm into a reliable sequence of actions highlights a major challenge in artificial intelligence research. The verification process remains inadequate, and models exhibit similar performance collapse regardless of whether the algorithm is self-generated or supplied. This points to a need for future work focused on enhancing the symbolic and verification capabilities of reasoning models to ensure that explicit guidance can be effectively executed in practice.

", "media": [{"caption": "Figure 10: Accuracy versus compositional depth (number of moves required) for three LRMs (DeepSeek-R1, Claude-3.7-Sonnet with thinking, and o3-mini) across four puzzle environments.", "url": "https://askpandipro.s3.eu-west-1.amazonaws.com/users/1/documents/401/figures/8.png", "source_url": null, "title": null, "s3_key": "users/1/documents/401/figures/8.png", "type": "image", "id": 208224, "html": null, "carousel_h5": "Figure 10: Accuracy versus compositional depth (number of moves required) for three LRMs (DeepSeek-R1, Claude-3.7-Sonnet with thinking, and o3-mini) across four puzzle environments.", "alt": null}, {"caption": "Figure 13: Detailed results on reasoning effort (measured in inference thinking tokens) versus problem complexity (N) for three LRMs (DeepSeek-R1, Claude-3.7-Sonnet with thinking, and o3-mini) across four puzzle environments.", "url": "https://askpandipro.s3.eu-west-1.amazonaws.com/users/1/documents/401/figures/11.png", "source_url": null, "title": null, "s3_key": "users/1/documents/401/figures/11.png", "type": "image", "id": 208227, "html": null, "carousel_h5": "Figure 13: Detailed results on reasoning effort (measured in inference thinking tokens) versus problem complexity (N) for three LRMs (DeepSeek-R1, Claude-3.7-Sonnet with thinking, and o3-mini) across four puzzle environments.", "alt": null}]}]}

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