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In this paper, we propose AdaBB, an adaptive gradient method based on the Barzilai-Borwein stepsize. The algorithm is line-search-free and parameter-free, and it essentially provides a convergent variant of the Barzilai-Borwein method for general convex optimization problems. We analyze the ergodic convergence of the objective function value and the convergence of the iterates for solving general convex optimization problems. Compared with existing works along this line of research, our algorithm gives the best lower bounds on the stepsize and the average of the stepsizes. Furthermore, we present extensions of the proposed algorithm for solving locally strongly convex and composite convex optimization problems where the objective function is the sum of a smooth function and a nonsmooth function. In the case of local strong convexity, we achieve linear convergence. Our numerical results also demonstrate very promising potential of the proposed algorithms on some representative examples. Funding: S. Ma is supported by the National Science Foundation [Grants DMS-2243650, CCF-2308597, CCF-2311275, and ECCS-2326591] and a startup fund from Rice University. J. Yang is supported by the National Natural Science Foundation of China [Grants 12431011 and 12371301] and the Natural Science Foundation for Distinguished Young Scholars of Gansu Province [Grant 22JR5RA223]. 

Code Large Language Models (Code LLMs) have excelled at tasks like code completion but often miss deeper semantics such as execution effects and dynamic states. This paper aims to bridge the gap between Code LLMs' reliance on static text data and the need for semantic understanding for complex tasks like debugging and program repair. We introduce a novel strategy, monologue reasoning, to train Code LLMs to reason comprehensive semantics, encompassing high-level functional descriptions, local execution effects of individual statements, and overall input/output behavior, thereby linking static code text with dynamic execution states. We begin by collecting PyX, a clean Python corpus of fully executable code samples with functional descriptions and test cases. We propose training Code LLMs not only to write code but also to understand code semantics by reasoning about key properties, constraints, and execution behaviors using natural language, mimicking human verbal debugging, i.e., rubber-duck debugging. This approach led to the development of SemCoder, a Code LLM with only 6.7B parameters, which shows competitive performance with GPT-3.5-turbo on code generation and execution reasoning tasks. SemCoder achieves 79.3% on HumanEval (GPT-3.5-turbo: 76.8%), 63.6% on CRUXEval-I (GPT-3.5-turbo: 50.3%), and 63.9% on CRUXEval-O (GPT-3.5-turbo: 59.0%). We also study the effectiveness of SemCoder's monologue-style execution reasoning compared to concrete scratchpad reasoning, showing that our approach integrates semantics from multiple dimensions more smoothly. Finally, we demonstrate the potential of applying learned semantics to improve Code LLMs' debugging and self-refining capabilities. Our data, code, and models are available at: https://github.com/ARiSE-Lab/SemCoder.