Recent work utilizes plan-and-solve decomposition to decrease the complexity and leverage self-tests to refine the generated program.

Despite recent progress made by large language models in code generation, they still struggle with programs that meet complex requirements. Recent work utilizes plan-and-solve decomposition to decrease the complexity and leverage self-tests to refine the generated program. Yet, planning deep-inside requirements in advance can be challenging, and the tests need to be accurate to accomplish self-improvement. To this end, we propose FunCoder, a code generation framework incorporating the divide-and-conquer strategy with functional consensus. Specifically, FunCoder recursively branches off sub-functions as smaller goals during code generation, represented by a tree hierarchy. These sub-functions are then composited to attain more complex objectives. Additionally, we designate functions via a consensus formed by identifying similarities in program behavior, mitigating error propagation. FunCoder outperforms state-of-the-art methods by +9.8% on average in HumanEval, MBPP, xCodeEval and MATH with GPT-3.5 and GPT-4. Moreover, our method demonstrates superiority on smaller models: With FunCoder, StableCode-3b surpasses GPT-3.5 by +18.6% and achieves 97.7% of GPT-4's performance on HumanEval. Further analysis reveals that our proposed dynamic function decomposition is capable of handling complex requirements, and the functional consensus prevails over self-testing in correctness evaluation.

This chapter defines a new concept and framework for constructing fusion rules for evidences. This framework is based on a referee function, which does a decisional arbitrament conditionally to basic decisions provided by the several sources of information. A simple sampling method is derived from this framework. The purpose of this sampling approach is to avoid the combinatorics which are inherent to the definition of fusion rules of evidences. This definition of the fusion rule by the means of a sampling process makes possible the construction of several rules on the basis of an algorithmic implementation of the referee function, instead of a mathematical formulation. Incidentally, it is a versatile and intuitive way for defining rules. The framework is implemented for various well known evidence rules. On the basis of this framework, new rules for combining evidences are proposed, which takes into account a consensual evaluation of the sources of information.