Case2Code: Learning Inductive Reasoning with Synthetic Data

Complex reasoning is an impressive ability shown by large language models (LLMs). Most LLMs are skilled in deductive reasoning, such as chain-of-thought prompting or iterative tool-using to solve challenging tasks step-by-step. In this paper, we hope to focus on evaluating and teaching LLMs to conduct inductive reasoning, that is, LLMs are supposed to infer underlying rules by observing examples or sequential transformations. However, collecting large-scale and diverse human-generated inductive data is challenging. We focus on data synthesis in the code domain and propose a \textbf{Case2Code} task by exploiting the expressiveness and correctness of programs. Specifically, we collect a diverse set of executable programs, synthesize input-output transformations for each program, and force LLMs to infer the underlying code implementations based on the synthetic I/O cases. We first evaluate representative LLMs on the synthesized Case2Code task and demonstrate that the Case-to-code induction is challenging for LLMs. Then, we synthesize large-scale Case2Code training samples to train LLMs to perform inductive reasoning. Experimental results show that such induction training benefits not only in distribution Case2Code performance but also enhances various coding abilities of trained LLMs, demonstrating the great potential of learning inductive reasoning via synthetic data.

InternLM-Math: Open Math Large Language Models Toward Verifiable Reasoning

The math abilities of large language models can represent their abstract reasoning ability. In this paper, we introduce and open-source our math reasoning LLMs InternLM-Math which is continue pre-trained from InternLM2. We unify chain-of-thought reasoning, reward modeling, formal reasoning, data augmentation, and code interpreter in a unified seq2seq format and supervise our model to be a versatile math reasoner, verifier, prover, and augmenter. These abilities can be used to develop the next math LLMs or self-iteration. InternLM-Math obtains open-sourced state-of-the-art performance under the setting of in-context learning, supervised fine-tuning, and code-assisted reasoning in various informal and formal benchmarks including GSM8K, MATH, Hungary math exam, MathBench-ZH, and MiniF2F. Our pre-trained model achieves 30.3 on the MiniF2F test set without fine-tuning. We further explore how to use LEAN to solve math problems and study its performance under the setting of multi-task learning which shows the possibility of using LEAN as a unified platform for solving and proving in math. Our models, codes, and data are released at \url{https://github.com/InternLM/InternLM-Math}.

Multi: Multimodal Understanding Leaderboard with Text and Images

Rapid progress in multimodal large language models (MLLMs) highlights the need to introduce challenging yet realistic benchmarks to the academic community. Existing benchmarks primarily focus on simple natural image understanding, but Multi emerges as a cutting-edge benchmark for MLLMs, offering a comprehensive dataset for evaluating MLLMs against understanding complex figures and tables, and scientific questions. This benchmark, reflecting current realistic examination styles, provides multimodal inputs and requires responses that are either precise or open-ended, similar to real-life school tests. It challenges MLLMs with a variety of tasks, ranging from formula derivation to image detail analysis, and cross-modality reasoning. Multi includes over 18,000 questions, with a focus on science-based QA in diverse formats. We also introduce Multi-Elite, a 500-question subset for testing the extremities of MLLMs, and Multi-Extend, which enhances In-Context Learning research with more than 4,500 knowledge pieces. Our evaluation indicates significant potential for MLLM advancement, with GPT-4V achieving a 63.7% accuracy rate on Multi, in contrast to other MLLMs scoring between 31.3% and 53.7%. Multi serves not only as a robust evaluation platform but also paves the way for the development of expert-level AI.