# Reasoning Depth and Environment Complexity: A Controlled Study of RLVR Data Allocation across Logical Reasoning Tasks

arXiv: https://arxiv.org/abs/2605.26934 · HTML: https://mlsanity.com/paper/2605.26934/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 11 of its 63 references that are in the map.
- First posted on arXiv 26 May 2026.

## Placed in

- LLM reasoning / [Reinforcement learning for reasoning](https://mlsanity.com/lr/reinforcement-learning-for-reasoning/)

## Builds on (most cited first, 11 of 11)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [Phi-4-reasoning Technical Report](https://mlsanity.com/paper/2504.21318/) (2025)
- [RLEP: Reinforcement Learning with Experience Replay for LLM Reasoning](https://mlsanity.com/paper/2507.07451/) (2025)
- [VCRL: Variance-based Curriculum Reinforcement Learning for Large Language Models](https://mlsanity.com/paper/2509.19803/) (2025)
- [EFRame: Deeper Reasoning via Exploration-Filter-Replay Reinforcement Learning Framework](https://mlsanity.com/paper/2506.22200/) (2025)
- [Can GRPO Help LLMs Transcend Their Pretraining Origin?](https://mlsanity.com/paper/2510.15990/) (2025)
- [MolQuest: A Benchmark for Agentic Evaluation of Abductive Reasoning in Chemical Structure Elucidation](https://mlsanity.com/paper/2603.25253/) (2026)
- [Can RL Teach Long-Horizon Reasoning to LLMs? Expressiveness Is Key](https://mlsanity.com/paper/2605.06638/) (2026)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards (RLVR) has become central to post-training reasoning models, yet a key limitation of existing studies is their narrow view of the reasoning space: difficulty is treated as reasoning depth alone, and reward is concentrated on forward deductive state tracking. We instead characterize the reasoning space along two dimensions. Difficulty. Beyond reasoning depth, we study environment complexity, where models must identify the correct path amid distractors and interacting structures. Rewarded reasoning form. We consider four abilities core to real-world reasoning: deductive state tracking, abductive recovery of hidden events or facts, inductive rule induction, and analogical transfer. To disentangle these factors, we construct a synthetic knowledge-graph environment with controlled pre- and post-training distributions, where each instance varies along depth, complexity, and task family. Three findings emerge: joint depth-complexity coverage outperforms single-axis recipes; reasoning families respond non-uniformly, with abductive reasoning degrading outside the RL-covered region and task correlations clustering into deductive-abductive and inductive-analogy pairs; and uniform mixing outperforms staged curricula under a fixed budget. We also find that recent off-the-shelf models exhibit the same deductive-over-abductive asymmetry, suggesting that this gap is not merely an artifact of our controlled setup.