RL as a Reasoning Synthesizer

• RL as a reasoning synthesizer is a framework that uses reinforcement learning to aggregate, reweight, and refine pre-existing reasoning strategies for enhanced multi-step processing.
• Empirical results show that RL rebalances choice patterns, increasing optimal strategy usage from 20–40% pre-training to as high as 70–90% post-training.
• Integrating adaptive partial-supervision, reverse curricula, and hierarchical tool-augmentation, RL improves the synthesis of compositional reasoning while leveraging atomic skills.

Reinforcement learning as a reasoning synthesizer refers to the use of RL algorithms not merely to amplify pre-existing reasoning patterns in LLMs, but to actively aggregate, refine, and in some regimes generate new, compositional reasoning strategies. Recent research delineates sharp boundaries between the capabilities of RL to select, orchestrate, and even synthesize multi-step reasoning processes, dissecting the interplay between reward-driven pattern selection, curriculum, and the inductive biases carried over by supervised pretraining. This article reviews the principal theoretical models, convergence regimes, empirical methodologies, and mechanistic analyses underpinning RL as a reasoning synthesizer.

1. Theoretical Foundations: Pattern Selection in RL with Verifiable Rewards

The dominant abstraction is the RLVR (Reinforcement Learning with Verifiable Rewards) framework, which models LLM reasoning as a two-stage process: pattern selection followed by answer generation. Given a question $q$, the model samples a reasoning pattern $r\in\mathcal R$ with probability $\pi_\theta(r\mid q)$ and then generates an answer $a$ conditioned on $(r, q)$. Each $r$ has an intrinsic success rate $p_{\rm succ}(r)=\pi_\theta(a_T\mid r, q)$. RLVR training dynamics, formalized by the gradient flow

$$\frac{d}{dt}\,\pi_{\theta(t)}(r\mid q) = \pi_{\theta(t)}(r\mid q)\,\bigl[p_{\rm succ}(r) - \mathrm{Acc}_{\theta(t)}\bigr],$$

where $\mathrm{Acc}_{\theta(t)}$ is the current average accuracy, naturally amplify the usage of patterns with higher success rates while suppressing inferior patterns. The essential empirical finding (Assumption 5.1) is that RLVR does not significantly alter $p_{\rm succ}(r)$, instead reweighing $\pi_\theta(r\mid q)$ so that, post-training, the highest-success pattern dominates (typically $70$–$90\%$ usage versus $20$–$40\%$ pre-RLVR).

RLVR convergence exhibits two regimes:

• Regime 1 (rapid): If the initialization mass gives sufficient weight to the optimal pattern $r^*$, convergence to $\pi_\theta(r^*\mid q)\to1$ is $\mathcal{O}(1/\varepsilon)$.
• Regime 2 (entangled/slow): If the suboptimal $r'$ dominates initially, breakout to $r^*$ can be super-exponentially slow in the ratio $$\gamma_{\rm ref} = \sum_{r\ne r'}\pi_{\rm ref}(r\mid q)/\pi_{\rm ref}(r^*\mid q)$$ (Chen et al., 5 Jun 2025).

These regimes are highly sensitive to the initialization, motivating the use of a brief SFT stage to front-load mass onto reliable patterns and catalyze fast RLVR convergence.

2. Empirical Mechanisms: Aggregation, Amplification, and the Limits of Pattern Reweighting

Comprehensive task-wide measurements assert that RLVR-trained models retain stable per-pattern $p_{\rm succ}(r)$ (within $\pm 1$–$3\%$), indicating that RLVR seldom invents new patterns but powerfully aggregates and rebalances pre-existing reasoning strategies. On benchmarks such as Easy Countdown, Geometry, and OlympiadBench, the frequency of the top pattern increases dramatically post-RLVR (to as high as $90\%$), while the usage of low-success patterns recedes to negligible levels.

This mechanism has been further dissected using multi-layer analytic frameworks [e.g., SPARKLE in (Wang et al., 5 Jun 2025)], which show that RL does not primarily enhance plan-execution per se, but rather improves the model's ability to synthesize and internally follow plans attuned to its strengths. Moreover, knowledge integration (the ability to incorporate external facts) is robustly improved by RL, as evidenced by gains of $+4\%$ in knowledge-augmented settings.

However, research also establishes that for more complex or out-of-distribution reasoning, RLVR is limited: it cannot "synthesize" new strategies unless the atomic skills are already present via SFT. For example, in complementary reasoning (blending parametric and contextual reasoning), RL enables synthesis of composite strategies only if both atomic capabilities are previously mastered (Cheng et al., 1 Dec 2025).

3. Augmenting Reasoning Synthesis: Curriculum, Partial Demonstrations, and Self-Supervision

Standard RL struggles with sparse rewards in long chains; several algorithmic advances address this bottleneck:

• Adaptive Partial-Supervision Curricula (AdaBack): The AdaBack algorithm dynamically reveals only a partial gold rationale prefix per sample, shrinking supervision as reward improves. This decomposes the exponential search for correct full chains into tractable subproblems and was shown to solve otherwise intractable tasks (e.g., degree-3 parity) (Amani et al., 22 Jun 2025). AdaBack consistently outperforms both naive RL and SFT+RL, with the strongest gains in OOD settings (e.g., GSM8k, where pass@k is expanded for larger $k$).
• Reverse Curriculum RL (R³): The R³ framework slides the start state backward along expert demonstrations, successively training from (almost) the solution to the full problem (Xi et al., 8 Feb 2024). This method bridges the benefits of process supervision and outcome-based RL, yielding $+4.1$ points over standard RL on average.
• Unsupervised Curriculum in Label-Free RL: For weak base models (sub-3B), label-free RL alone is inadequate for reasoning synthesis, often failing to bootstrap longer chains. Only with curriculum learning, difficulty-controlled synthetic datasets, and masked majority-vote reward assignment can self-supervised RL enable consistent improvements (e.g., from $23.4\%$ to $32.8\%$ on Math-500 at 0.5B scale) (Roy et al., 7 Nov 2025).

4. Hierarchical and Tool-Augmented Reasoning Synthesis

Recent research extends RL as a reasoning synthesizer along two critical axes:

• Hierarchical Reasoning and Tool Integration (THOR): The THOR framework formalizes RL with a hierarchical objective, optimizing both trajectory-level solution accuracy and step-level tool execution success. Empirically, step-level tool success is a strong predictor of final correctness; accordingly, THOR assigns dense step-level rewards for successful tool calls, enabling fine-grained code synthesis and dynamic self-correction during inference. This joint optimization improves mathematical reasoning and code generation performance beyond standard SFT and pure RL baselines, reaching state-of-the-art for 8B models (Chang et al., 17 Sep 2025).
• Abstraction Discovery: RLAD frames reasoning as a two-player RL process: one agent proposes concise, reusable natural-language "abstractions," while another constructs full solutions informed by these abstractions. By separately rewarding effective abstraction proposals and their downstream use, RLAD guides models toward discovering subgoals and intermediate procedures (e.g., "use logarithm to estimate digit count") that enhance generalization (Qu et al., 2 Oct 2025).
• Process-Supervision and Stepwise Credit Assignment: Innovations such as DRER (He et al., 7 Sep 2025) introduce reasoning-quality rewards based on the improvement in answer likelihood from CoT tokens and dynamic length normalization, directly incentivizing logically beneficial intermediate steps and penalizing excessively short or verbose chains.

5. Multimodal Reasoning and RL Synthesis

RL-based reasoning synthesis also extends to multimodal LLMs (MLLMs), where each token in a chain-of-thought trajectory corresponds to actions in a Markov process that may rely on cross-modal evidence (e.g., vision, audio). RL empowers the alignment of perceptual and symbolic components, and tailored reward functions—covering output format, accuracy, and process-level evidence—have been shown to boost multimodal reasoning, especially on out-of-domain tasks and "hard" splits by $5$–$15$ points (Zhou et al., 30 Apr 2025). Here, RL enhances not only the alignment of intermediate reasoning steps but also the compositionality of cross-modal inferences.

6. Synthesis Limits and Prerequisites: When Is RL a Reasoning Synthesizer?

A central finding is that RL cannot synthesize high-level composite strategies from scratch. Rather, RL only acts as a genuine reasoning synthesizer when built on a foundation of atomic skills (e.g., parametric and contextual reasoning), typically instilled via SFT. This is evidenced by the inability of RL on composite reasoning tasks to generalize out-of-distribution when the model has not first mastered both atomic components (Cheng et al., 1 Dec 2025). RL as a pure probability amplifier reweights existing behaviors but does not break new ground in compositional reasoning. In contrast, the atomic–composite curriculum (SFT on atomic, RL on composite) unlocks zero-shot transfer to novel combinations of reasoning steps.

Mechanistically, analyses using dimension reduction (e.g., PCA of hidden states) confirm that RL can reorganize the model's internal representation such that composite task representations lie in the span of the atomic skills, indicating real synthesis as opposed to rote memorization or shortcut reweighting.

7. Practical Implications and Future Directions

The insights from recent work yield several practical recommendations and open research avenues:

• Brief, high-quality SFT on targeted reasoning patterns can dramatically accelerate RL-driven reasoning synthesis by avoiding entanglement and slow convergence.
• Partial-supervision curricula and reverse-curriculum methods can bridge sparse-reward barriers, making RL tractable even in long-horizon, multi-step reasoning tasks.
• Reward mechanisms must be designed to incentivize not only final correctness but also the utility of intermediate reasoning steps, with dynamic penalties for deviation in chain length or logical coherence.
• Research continues into whether RL can be extended to synthesize genuinely novel algorithmic procedures not present in any form in the base model, as opposed to efficiently combining existing primitives.

A plausible implication is that the full power of RL as a reasoning synthesizer depends on carefully staged curricula and reward design, as well as the presence of atomic reasoning competencies. The precise delineation of RL’s creative boundary—synthesis versus amplification—remains an active frontier.

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References

• "On the Mechanism of Reasoning Pattern Selection in Reinforcement Learning for LLMs" (Chen et al., 5 Jun 2025)
• "THOR: Tool-Integrated Hierarchical Optimization via RL for Mathematical Reasoning" (Chang et al., 17 Sep 2025)
• "RL of Thoughts: Navigating LLM Reasoning with Inference-time Reinforcement Learning" (Hao et al., 20 May 2025)
• "RL for Reasoning by Adaptively Revealing Rationales" (Amani et al., 22 Jun 2025)
• "Rethinking Reasoning Quality in LLMs through Enhanced Chain-of-Thought via RL" (He et al., 7 Sep 2025)
• "RL Tango: Reinforcing Generator and Verifier Together for Language Reasoning" (Zha et al., 21 May 2025)
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• "Training LLMs for Reasoning through Reverse Curriculum Reinforcement Learning" (Xi et al., 8 Feb 2024)
• "Reasoning Core: A Scalable RL Environment for LLM Symbolic Reasoning" (Lacombe et al., 22 Sep 2025)
• "From Atomic to Composite: Reinforcement Learning Enables Generalization in Complementary Reasoning" (Cheng et al., 1 Dec 2025)
• "RLAD: Training LLMs to Discover Abstractions for Solving Reasoning Problems" (Qu et al., 2 Oct 2025)
• "Reinforced MLLM: A Survey on RL-Based Reasoning in Multimodal LLMs" (Zhou et al., 30 Apr 2025)
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• "You Need Reasoning to Learn Reasoning: The Limitations of Label-Free RL in Weak Base Models" (Roy et al., 7 Nov 2025)
• "SWE-RL: Advancing LLM Reasoning via Reinforcement Learning on Open Software Evolution" (Wei et al., 25 Feb 2025)
• "Exploring the Potential of Offline RL for Reasoning in LLMs: A Preliminary Study" (Tian et al., 4 May 2025)
• "Enhancing Analogical Reasoning in the Abstraction and Reasoning Corpus via Model-Based RL" (Lee et al., 27 Aug 2024)