Towards enhancing the chain-of-thought (CoT) reasoning of large language models (LLMs), much existing work has revealed the effectiveness of straightforward learning on annotated/generated CoT paths. However, there is less evidence yet that reasoning capabilities can be enhanced through a reverse learning process, i.e., learning from potential mistakes in reasoning. To investigate whether LLMs can learn from mistakes, we construct mistake-correction datasets, using GPT-4 to identify and correct the mistakes in inaccurate CoTs. With these mistake-correction datasets, we fine-tune open-source LLMs and arrive at the following conclusions. (1) LLMs can indeed learn from mistakes to enhance their CoT reasoning performances. (2) Compared to CoT data, the mistake-correction data provides additional knowledge on the explanations and reasons for the potential mistakes in CoTs, which consistently contributes to the effectiveness of learning from mistakes. (3) Evolution techniques, especially the correction-centric evolution we introduced, can further enhance the effectiveness of learning from mistakes.

Few-shot learning is a challenging task that requires language models to generalize from limited examples. Large language models like GPT-3 and PaLM have made impressive progress in this area, but they still face difficulties in reasoning tasks such as GSM8K, a benchmark for arithmetic problems. To improve their reasoning skills, previous work has proposed to guide the language model with prompts that elicit a series of reasoning steps before giving the final answer, achieving a significant improvement on GSM8K from 17.9% to 58.1% in problem-solving rate. In this paper, we present DiVeRSe (Diverse Verifier on Reasoning Step), a novel approach that further enhances the reasoning capability of language models. DiVeRSe has three main components: first, it generates diverse prompts to explore different reasoning paths for the same question; second, it uses a verifier to filter out incorrect answers based on a weighted voting scheme; and third, it verifies each reasoning step individually instead of the whole chain. We evaluate DiVeRSe on the latest language model code-davinci-002 and show that it achieves new state-of-the-art results on six of eight reasoning benchmarks (e.g., GSM8K 74.4% to 83.2%).

Compositional generalization–understanding unseen combinations of seen primitives–is an essential reasoning capability in human intelligence. The AI community mainly studies this capability by fine-tuning neural networks on lots of training samples, while it is still unclear whether and how in-context learning–the prevailing few-shot paradigm based on large language models–exhibits compositional generalization. In this paper, we present CoFe, a test suite to investigate in-context compositional generalization. We find that the compositional generalization performance can be easily affected by the selection of in-context examples, thus raising the research question what the key factors are to make good in-context examples for compositional generalization. We study three potential factors: similarity, diversity and complexity. Our systematic experiments indicate that in-context examples should be structurally similar to the test case, diverse from each other, and individually simple. Furthermore, two strong limitations are observed: in-context compositional generalization on fictional words is much weaker than that on commonly used ones; it is still critical that the in-context examples should cover required linguistic structures, even though the backbone model has been pre-trained on large corpus. We hope our analysis would facilitate the understanding and utilization of in-context learning paradigm.

*In-context learning* is the paradigm that adapts large language models to downstream tasks by providing a few examples. *Few-shot selection*—selecting appropriate examples for each test instance separately—is important for in-context learning. In this paper, we propose **Skill-KNN**, a skill-based few-shot selection method for in-context learning. The key advantages of Skill-KNN include: (1) it addresses the problem that existing methods based on pre-trained embeddings can be easily biased by surface natural language features that are not important for the target task; (2) it does not require training or fine-tuning of any models, making it suitable for frequently expanding or changing example banks. The key insight is to optimize the inputs fed into the embedding model, rather than tuning the model itself. Technically, Skill-KNN generates the skill-based descriptions for each test case and candidate example by utilizing a pre-processing few-shot prompting, thus eliminating unimportant surface features. Experimental results across five cross-domain semantic parsing datasets and six backbone models show that Skill-KNN significantly outperforms existing methods.

Reasoning over natural language is a long-standing goal for the research community. However, studies have shown that existing language models are inadequate in reasoning. To address the issue, we present POET, a novel reasoning pre-training paradigm. Through pre-training language models with programs and their execution results, POET empowers language models to harvest the reasoning knowledge possessed by program executors via a data-driven approach. POET is conceptually simple and can be instantiated by different kinds of program executors. In this paper, we showcase two simple instances POET-Math and POET-Logic, in addition to a complex instance, POET-SQL. Experimental results on six benchmarks demonstrate that POET can significantly boost model performance in natural language reasoning, such as numerical reasoning, logical reasoning, and multi-hop reasoning. POET opens a new gate on reasoning-enhancement pre-training, and we hope our analysis would shed light on the future research of reasoning like program executors.

With the rapid development of pre-training techniques, a number of language models have been pre-trained on large-scale code corpora and perform well in code generation. In this paper, we investigate how to equip pre-trained language models with the ability of code generation for private libraries. In practice, it is common for programmers to write code using private libraries. However, this is a challenge for language models since they have never seen private APIs during training. Motivated by the fact that private libraries usually come with elaborate API documentation, we propose a novel framework with two modules: the APIRetriever finds useful APIs, and then the APICoder generates code using these APIs. For APIRetriever, we present a dense retrieval system and also design a friendly interaction to involve uses. For APICoder, we can directly use off-the-shelf language models, or continually pre-train the base model on a code corpus containing API information. Both modules are trained with data from public libraries and can be generalized to private ones. Furthermore, we craft three benchmarks for private libraries, named TorchDataEval, MonkeyEval, and BeatNumEval. Experimental results demonstrate the impressive performance of our framework.