New Skills or Sharper Primitives? A Probabilistic Perspective on the Emergence of Reasoning in RLVR

• URL: http://arxiv.org/abs/2602.08281v1
• Date: Mon, 09 Feb 2026 05:23:13 GMT
• Title: New Skills or Sharper Primitives? A Probabilistic Perspective on the Emergence of Reasoning in RLVR
• Authors: Zhilin Wang, Yafu Li, Shunkai Zhang, Zhi Wang, Haoran Zhang, Xiaoye Qu, Yu Cheng,
• Abstract summary: We propose a probabilistic framework where capability is defined by instance-level solvability.<n>We train models exclusively on single-step operations and evaluate their performance on unseen multi-step tasks.<n>Our work offers a novel explanation for emergent abilities in RLVR, suggesting that the iterative optimization of solvable problems enables models to develop the capabilities to tackle previously unsolvable scenarios.
• Score: 44.98294610511283
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Whether Reinforcement Learning with Verifiable Rewards (RLVR) endows Large Language Models (LLMs) with new capabilities or merely elicits latent traces remains a central debate. In this work, we align with the former view, proposing a probabilistic framework where capability is defined by instance-level solvability. We hypothesize that the emergence of complex reasoning can be driven by sharpening atomic step probabilities, which enables models to overcome the exponential decay of success rates inherent in multi-step reasoning chains. Utilizing the Algebrarium framework, we train models exclusively on single-step operations and evaluate their performance on unseen multi-step tasks. Our empirical results confirm that: (1) RLVR incentivizes the exploration of previously inaccessible solution paths by amplifying the model's existing skills; (2) composite performance is strictly governed by the joint probability of atomic steps, evidenced by high Pearson correlation coefficients ($ρ\in [0.69, 0.96]$); and (3) RLVR, acting as a global optimizer, can cause specific skills to be sacrificed to maximize aggregate reward. Our work offers a novel explanation for emergent abilities in RLVR, suggesting that the iterative optimization of solvable problems enables models to develop the capabilities to tackle previously unsolvable scenarios.

Related papers

• Adaptive Ability Decomposing for Unlocking Large Reasoning Model Effective Reinforcement Learning [82.91265691530351]
  A$2$D is an Adaptive Ability Decomposing method for enhancing the effectiveness ofReinforcement Learning with verifiable rewards.<n>We first train a decomposer via RLVR without distillation, enabling it to decompose complex questions into a set of simpler sub-questions.<n>Next, we use this decomposer to annotate sub-questions for each question in the training dataset, and then train the reasoner under RLVR with sub-question guidance.
  arXiv  Detail & Related papers  (2026-01-31T14:48:23Z)
• Generalization of RLVR Using Causal Reasoning as a Testbed [20.97376329817835]
  Reinforcement learning with verifiable rewards (RLVR) has emerged as a promising paradigm for post-training large language models.<n>This paper provides an empirical study of RLVR generalization in the setting of probabilistic inference over causal models.
  arXiv  Detail & Related papers  (2025-12-23T20:45:31Z)
• Limits of Generalization in RLVR: Two Case Studies in Mathematical Reasoning [3.437656066916039]
  Reinforcement with Verifiable Rewards (RLVR) has emerged as a promising approach for enhancing such capabilities.<n>We investigate RLVR on two problems with fully verifiable solutions.<n>We find that RLVR improves evaluation metrics but often by reinforcing superficial Learning metrics rather than acquiring new reasoning strategies.
  arXiv  Detail & Related papers  (2025-10-30T23:16:02Z)
• How LLMs Learn to Reason: A Complex Network Perspective [14.638878448692493]
  Training large language models with Reinforcement Learning from Verifiable Rewards exhibits a set of puzzling behaviors.<n>We propose that these seemingly disparate phenomena can be explained using a single unifying theory.<n>Our work provides a new physical intuition for engineering the emergent reasoning capabilities of future AI systems.
  arXiv  Detail & Related papers  (2025-09-28T04:10:37Z)
• The Invisible Leash: Why RLVR May or May Not Escape Its Origin [47.488691410579925]
  It remains unclear whether the current practice of RLVR truly expands a model's reasoning boundary.<n>Under current training conditions, RLVR can operate as a support-constrained optimization mechanism.<n>While RLVR reliably enhances precision, it may progressively narrow exploration and potentially overlook correct yet underrepresented solutions.
  arXiv  Detail & Related papers  (2025-07-20T07:04:08Z)
• Reshaping Reasoning in LLMs: A Theoretical Analysis of RL Training Dynamics through Pattern Selection [35.268183415853976]
  We provide an explanation of the RL training process through empirical analysis and rigorous theoretical modeling.<n>We develop a theoretical framework to understand the training dynamics of RL with two typical rewards: reward (RLVR) and model's internal feedback (RLIF)
  arXiv  Detail & Related papers  (2025-06-05T07:17:04Z)
• LARES: Latent Reasoning for Sequential Recommendation [96.26996622771593]
  We present LARES, a novel and scalable LAtent REasoning framework for Sequential recommendation.<n>Our proposed approach employs a recurrent architecture that allows flexible expansion of reasoning depth without increasing parameter complexity.<n>Our framework exhibits seamless compatibility with existing advanced models, further improving their recommendation performance.
  arXiv  Detail & Related papers  (2025-05-22T16:22:54Z)
• Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model? [66.61292196146016]
  Reinforcement Learning with Verifiable Rewards (RLVR) has recently demonstrated notable success in enhancing the reasoning performance of large language models (LLMs)<n>This study critically examines the current state of RLVR.<n>We find that the current training setup does not elicit fundamentally new reasoning patterns.
  arXiv  Detail & Related papers  (2025-04-18T17:59:56Z)
• Vintix: Action Model via In-Context Reinforcement Learning [78.11130335098936]
  We present the first steps toward scaling ICRL by introducing a fixed, cross-domain model capable of learning behaviors through in-context reinforcement learning.<n>Our results demonstrate that Algorithm Distillation, a framework designed to facilitate ICRL, offers a compelling and competitive alternative to expert distillation to construct versatile action models.
  arXiv  Detail & Related papers  (2025-01-31T18:57:08Z)
• Understanding, Predicting and Better Resolving Q-Value Divergence in Offline-RL [86.0987896274354]
  We first identify a fundamental pattern, self-excitation, as the primary cause of Q-value estimation divergence in offline RL. We then propose a novel Self-Excite Eigenvalue Measure (SEEM) metric to measure the evolving property of Q-network at training. For the first time, our theory can reliably decide whether the training will diverge at an early stage.
  arXiv  Detail & Related papers  (2023-10-06T17:57:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.