TLDR: CodeSeq is a new synthetic dataset and training pipeline designed to enhance the inductive reasoning abilities of large language models (LLMs). It converts number sequences into algorithmic coding problems, requiring LLMs to find general patterns. The pipeline involves generating and validating these problems, using iterative self-correction based on failed test cases for supervised finetuning, and employing a novel reward system for reinforcement learning that considers problem difficulty and self-generated case success. Experiments show CodeSeq significantly improves LLMs’ inductive reasoning and code generation skills, while maintaining overall performance on other tasks.
Large Language Models (LLMs) have shown impressive capabilities in various reasoning tasks. Among these, inductive reasoning, which involves drawing general conclusions from specific observations, is particularly important because it closely mirrors how humans learn and generalize knowledge. However, current research in this area faces significant hurdles. Existing datasets often focus on simple, surface-level patterns, lacking the complexity needed to truly challenge LLMs. Furthermore, training methods have typically been limited to basic prompting or finetuning on simple pairs, without providing models with precise thinking processes or mechanisms to control difficulty.
To tackle these challenges, a new approach introduces CodeSeq, a synthetic post-training dataset built from number sequences. This innovative method transforms number sequences into algorithmic problems, tasking LLMs with discovering their general terms through code. This process is called the General Term Generation (GTG) task. The core idea is to teach LLMs a human-like, case-based reasoning process, thereby boosting their inductive abilities.
The CodeSeq pipeline is structured in three main parts:
Sequence Algorithmization
This initial step involves gathering and filtering thousands of number sequences and their related information from various mathematical websites. A ‘working agent’ then packages each sequence into an algorithmic problem, complete with example cases. To ensure the problems are correctly formulated, a ‘guiding agent’ validates them by generating solutions based on the problem descriptions and example inputs. Only well-formatted and correct problems are retained, forming the ‘seed sequence data’ which is then split for further training.
Case-based Reflection Injection
For one group of the seed data, the working agent generates initial code solutions. These solutions are then rigorously tested against a set of ‘test cases’ in an isolated sandbox environment. If a solution fails a test, the guiding agent provides reasons for the failure, prompting the working agent to iteratively modify and correct the code. This iterative reflection process, where models learn to generate cases autonomously and self-check their solutions, is injected into the Chain-of-Thought (CoT) and forms the Supervised Finetuning (SFT) data, known as CodeSeqSFT.
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Solvability-Estimated Selection
For the second group of seed data, a model of comparable scale performs multiple attempts (rollouts) on each algorithmic problem to estimate its ‘solvability’ – essentially, how difficult it is. Problems that are moderately challenging (solved correctly only after multiple attempts) are selected for Reinforcement Learning (RL) training. A novel ‘Case-synergy Solvability Scaling Reward’ (CSSR) is introduced. This reward function considers both the problem’s solvability (lower solvability yields higher reward) and the success rate of the model’s self-directed case generation, ensuring a controlled learning process and improving the model’s proficiency in generating and using cases for reasoning. This data forms CodeSeqRL.
Experimental results demonstrate the effectiveness of CodeSeq. Models trained with this dataset, such as LLaMA3-8B-Instruct and Qwen2.5-7B-Instruct, show significant improvements in the in-domain GTG task. Crucially, these models also exhibit strong transfer performance on related code reasoning tasks like Humaneval, MBPP, and LiveCodeBench. This suggests that the inductive reasoning skills learned through CodeSeq are generalizable. Furthermore, the training does not compromise the models’ performance on out-of-domain comprehensive reasoning benchmarks like MMLU, BBH, and GaoKaoBench, indicating the robustness of the approach.
Ablation studies further confirm the importance of each component of CodeSeq, highlighting the benefits of case-based reflection in CoT and the carefully designed CSSR reward function. The research also explores scaling behaviors, showing that increasing reflection rounds and the diversity of number sequence patterns both contribute to improved performance. The study also found a positive correlation between the models’ success in autonomous case generation and the accuracy of their code solutions, indicating that models can indeed learn to reason effectively with cases.
In conclusion, CodeSeq offers a novel and effective way to enhance the inductive reasoning capabilities of LLMs by leveraging number sequences packaged as algorithmic coding problems. This work provides a fully automated pipeline for generating high-quality training data that incorporates precise reasoning processes, paving the way for more advanced and human-like AI reasoning. You can find the full research paper here.
