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Dual-Process Scaffold Reasoning for Enhancing LLM Code Debugging
Hsieh, Po-Chung, Chen, Chin-Po, Li, Jeng-Lin, Chang, Ming-Ching
Recent LLMs have demonstrated sophisticated problem-solving capabilities on various benchmarks through advanced reasoning algorithms. However, the key research question of identifying reasoning steps that balance complexity and computational efficiency remains unsolved. Recent research has increasingly drawn upon psychological theories to explore strategies for optimizing cognitive pathways. The LLM's final outputs and intermediate steps are regarded as System 1 and System 2, respectively. However, an in-depth exploration of the System 2 reasoning is still lacking. Therefore, we propose a novel psychologically backed Scaffold Reasoning framework for code debugging, which encompasses the Scaffold Stream, Analytic Stream, and Integration Stream. The construction of reference code within the Scaffold Stream is integrated with the buggy code analysis results produced by the Analytic Stream through the Integration Stream. Our framework achieves an 88.91% pass rate and an average inference time of 5.36 seconds per-problem on DebugBench, outperforming other reasoning approaches across various LLMs in both reasoning accuracy and efficiency. Further analyses elucidate the advantages and limitations of various cognitive pathways across varying problem difficulties and bug types. Our findings also corroborate the alignment of the proposed Scaffold Reasoning framework with human cognitive processes.
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Infinite-Dimensional Operator/Block Kaczmarz Algorithms: Regret Bounds and $λ$-Effectiveness
Jeong, Halyun, Jorgensen, Palle E. T., Kwon, Hyun-Kyoung, Song, Myung-Sin
We present a variety of projection-based linear regression algorithms with a focus on modern machine-learning models and their algorithmic performance. We study the role of the relaxation parameter in generalized Kaczmarz algorithms and establish a priori regret bounds with explicit $λ$-dependence to quantify how much an algorithm's performance deviates from its optimal performance. A detailed analysis of relaxation parameter is also provided. Applications include: explicit regret bounds for the framework of Kaczmarz algorithm models, non-orthogonal Fourier expansions, and the use of regret estimates in modern machine learning models, including for noisy data, i.e., regret bounds for the noisy Kaczmarz algorithms. Motivated by machine-learning practice, our wider framework treats bounded operators (on infinite-dimensional Hilbert spaces), with updates realized as (block) Kaczmarz algorithms, leading to new and versatile results.
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Provable Accelerated Bayesian Optimization with Knowledge Transfer
Lin, Haitao, Zhao, Boxin, Kolar, Mladen, Liu, Chong
We study how Bayesian optimization (BO) can be accelerated on a target task with historical knowledge transferred from related source tasks. Existing works on BO with knowledge transfer either do not have theoretical guarantees or achieve the same regret as BO in the non-transfer setting, $\tilde{\mathcal{O}}(\sqrt{T γ_f})$, where $T$ is the number of evaluations of the target function and $γ_f$ denotes its information gain. In this paper, we propose the DeltaBO algorithm, in which a novel uncertainty-quantification approach is built on the difference function $δ$ between the source and target functions, which are allowed to belong to different reproducing kernel Hilbert spaces (RKHSs). Under mild assumptions, we prove that the regret of DeltaBO is of order $\tilde{\mathcal{O}}(\sqrt{T (T/N + γ_δ)})$, where $N$ denotes the number of evaluations from source tasks and typically $N \gg T$. In many applications, source and target tasks are similar, which implies that $γ_δ$ can be much smaller than $γ_f$. Empirical studies on both real-world hyperparameter tuning tasks and synthetic functions show that DeltaBO outperforms other baseline methods and support our theoretical claims.
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An Explanation-oriented Inquiry Dialogue Game for Expert Collaborative Recommendations
Shaheen, Qurat-ul-ain, Budzynska, Katarzyna, Sierra, Carles
This work presents a requirement analysis for collaborative dialogues among medical experts and an inquiry dialogue game based on this analysis for incorporating explainability into multiagent system design. The game allows experts with different knowledge bases to collaboratively make recommendations while generating rich traces of the reasoning process through combining explanation-based illocutionary forces in an inquiry dialogue. The dialogue game was implemented as a prototype web-application and evaluated against the specification through a formative user study. The user study confirms that the dialogue game meets the needs for collaboration among medical experts. It also provides insights on the real-life value of dialogue-based communication tools for the medical community.
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