# Generalization of RLVR Using Causal Reasoning as a Testbed

arXiv: https://arxiv.org/abs/2512.20760 · HTML: https://mlsanity.com/paper/2512.20760/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Reinforcement learning for reasoning, one of 17 directions in LLM reasoning.
- Builds on 22 of its 40 references that are in the map.
- First posted on arXiv 23 Dec 2025.

## Placed in

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

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [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)
- [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)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Causal Reasoning and Large Language Models: Opening a New Frontier for Causality](https://mlsanity.com/paper/2305.00050/) (2023)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data](https://mlsanity.com/paper/2405.14333/) (2024)
- [SFT or RL? An Early Investigation into Training R1-Like Reasoning Large Vision-Language Models](https://mlsanity.com/paper/2504.11468/) (2025)
- [Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.11354/) (2025)
- [Causal Parrots: Large Language Models May Talk Causality But Are Not Causal](https://mlsanity.com/paper/2308.13067/) (2023)
- [Can Large Language Models Infer Causation from Correlation?](https://mlsanity.com/paper/2306.05836/) (2023)
- [The Illusion of Diminishing Returns: Measuring Long Horizon Execution in LLMs](https://mlsanity.com/paper/2509.09677/) (2025)
- [All Roads Lead to Likelihood: The Value of Reinforcement Learning in Fine-Tuning](https://mlsanity.com/paper/2503.01067/) (2025)
- [UFT: Unifying Supervised and Reinforcement Fine-Tuning](https://mlsanity.com/paper/2505.16984/) (2025)
- [Training a Scientific Reasoning Model for Chemistry](https://mlsanity.com/paper/2506.17238/) (2025)
- [Decomposing Elements of Problem Solving: What "Math" Does RL Teach?](https://mlsanity.com/paper/2505.22756/) (2025)
- [Metis-RISE: RL Incentivizes and SFT Enhances Multimodal Reasoning Model Learning](https://mlsanity.com/paper/2506.13056/) (2025)
- [CARL-GT: Evaluating Causal Reasoning Capabilities of Large Language Models](https://mlsanity.com/paper/2412.17970/) (2024)

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

- [Which Tokens Matter? Adaptive Token Selection for RLVR with the Relative Surprisal Index](https://mlsanity.com/paper/2606.31575/) (2026)
- [Minerva: Reinforcement Learning with Verifiable Rewards for Cyber Threat Intelligence LLMs](https://mlsanity.com/paper/2602.00513/) (2026)

## Abstract (arXiv)

Reinforcement learning with verifiable rewards (RLVR) has emerged as a promising paradigm for post-training large language models (LLMs) on complex reasoning tasks. Yet, the conditions under which RLVR yields robust generalization remain underexplored. This paper provides an empirical study of RLVR generalization in the setting of probabilistic inference over causal graphical models. This setting offers two natural axes along which to examine generalization: (i) the level of the probabilistic query -- associational, interventional, or counterfactual -- and (ii) the structural complexity of the query, measured by the size of its relevant subgraph. We construct a dataset of causal graphs and queries spanning these difficulty axes and fine-tune Qwen-2.5-Instruct models using RLVR or supervised fine-tuning (SFT). We vary both the model scale (3B-32B) and the query level included in training. We find that RLVR yields stronger within-level and across-level generalization than SFT, but only for specific combinations of model size and training query level. Further analysis shows that RLVR's effectiveness depends on the model's initial reasoning competence. With sufficient initial competence, RLVR improves an LLM's marginalization strategy and reduces errors in intermediate probability calculations, producing substantial accuracy gains, particularly on more complex queries. These results show that RLVR can improve specific causal reasoning subskills, with its benefits emerging only when the model has sufficient initial competence. Our code and data is available at https://github.com/zhichul/rlcausal.