# Code-driven Number Sequence Calculation: Enhancing the inductive Reasoning Abilities of Large Language Models

arXiv: https://arxiv.org/abs/2510.14620 · HTML: https://mlsanity.com/paper/2510.14620/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 50 of its 100 references that are in the map.
- First posted on arXiv 16 Oct 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 50)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [HybridFlow: A Flexible and Efficient RLHF Framework](https://mlsanity.com/paper/2409.19256/) (2024)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [The Rise and Potential of Large Language Model Based Agents: A Survey](https://mlsanity.com/paper/2309.07864/) (2023)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [SGLang: Efficient Execution of Structured Language Model Programs](https://mlsanity.com/paper/2312.07104/) (2023)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [DeepSeek-V3 Technical Report](https://mlsanity.com/paper/2412.19437/) (2024)
- [InternLM2 Technical Report](https://mlsanity.com/paper/2403.17297/) (2024)
- [Evaluating the Performance of Large Language Models on GAOKAO Benchmark](https://mlsanity.com/paper/2305.12474/) (2023)
- [Teaching Large Language Models to Reason with Reinforcement Learning](https://mlsanity.com/paper/2403.04642/) (2024)
- [Self-planning Code Generation with Large Language Models](https://mlsanity.com/paper/2303.06689/) (2023)
- [A Comprehensive Survey in LLM(-Agent) Full Stack Safety: Data, Training and Deployment](https://mlsanity.com/paper/2504.15585/) (2025)
- [Group Robust Preference Optimization in Reward-free RLHF](https://mlsanity.com/paper/2405.20304/) (2024)
- [Comprehensive Exploration of Synthetic Data Generation: A Survey](https://mlsanity.com/paper/2401.02524/) (2024)
- [On the Creativity of Large Language Models](https://mlsanity.com/paper/2304.00008/) (2023)
- [Scaling Laws for Downstream Task Performance of Large Language Models](https://mlsanity.com/paper/2402.04177/) (2024)
- [MathCoder2: Better Math Reasoning from Continued Pretraining on Model-translated Mathematical Code](https://mlsanity.com/paper/2410.08196/) (2024)
- [Inductive or Deductive? Rethinking the Fundamental Reasoning Abilities of LLMs](https://mlsanity.com/paper/2408.00114/) (2024)

## Built on by (most cited first, 2 of 2)

- [Beyond Accuracy: Unveiling Inefficiency Patterns in Tool-Integrated Reasoning](https://mlsanity.com/paper/2604.05404/) (2026)
- [Dual Attention Guided Defense Against Malicious Edits](https://mlsanity.com/paper/2512.14333/) (2025)

## Abstract (arXiv)

Large language models (LLMs) make remarkable progress in reasoning tasks. Among different reasoning modes, inductive reasoning, due to its better alignment with human learning, attracts increasing interest. However, research on inductive reasoning faces certain challenges. First, existing inductive data mostly focuses on superficial regularities while lacking more complex internal patterns. Second, current works merely prompt LLMs or finetune on simple prompt-response pairs, but do not provide precise thinking processes nor implement difficulty control. Unlike previous work, we address these challenges by introducing textitCodeSeq, a synthetic post-training dataset built from number sequences. We package number sequences into algorithmic problems to discover their general terms, defining a general term generation (GTG) task correspondingly. Our pipeline generates supervised finetuning data by reflecting on failed test cases and incorporating iterative corrections, thereby teaching LLMs to learn autonomous case generation and self-checking. Additionally, it leverages reinforcement learning with a novel Case-Synergy Solvability Scaling Reward based on both solvability, estimated from the problem pass rate, and the success rate of self-directed case generation, enabling models to learn more effectively from both successes and failures. Experimental results show that the models trained with textitCodeSeq improve on various reasoning tasks and can preserve the models' OOD performance.