From Atomic to Composite: Reinforcement Learning Enables Generalization in Complementary Reasoning (2512.01970v1)

Abstract: The mechanism by which RL contributes to reasoning capabilities-whether it incentivizes the synthesis of new skills or merely amplifies existing behaviors-remains a subject of intense debate. In this work, we investigate this question through the lens of Complementary Reasoning, a complex task that requires integrating internal parametric knowledge with external contextual information. Using a controlled synthetic dataset of human biographies, we strictly decouple this ability into two atomic skills: Parametric Reasoning (relying on internal knowledge) and Contextual Reasoning (depending on external information). To rigorously assess capability boundaries, we evaluate generalization across three distinct levels of difficulty: I.I.D., Composition, and Zero-shot settings. We find that while SFT is sufficient for in-distribution performance, it struggles with O.O.D. generalization, particularly in Zero-shot settings where relational combinations are novel. Crucially, we identify the SFT Generalization Paradox: Models supervised solely on the composite task achieve near-perfect in-distribution accuracy but collapse on out-of-distribution generalization, indicating their reliance on rote memorization of path shortcuts. In contrast, we find that RL acts as a reasoning synthesizer rather than a probability amplifier. However, we uncover a strict atomic prerequisite: RL can only synthesize these complex strategies if the base model has first mastered the independent atomic skills (Parametric and Contextual) via SFT. These findings challenge the view of RL as a mere amplifier, suggesting that given sufficient atomic foundations, RL can actively synthesize complex reasoning strategies from learned primitives without explicit supervision on such complex strategies. This indicates that decoupled atomic training followed by RL offers a scalable path to generalization for complex reasoning tasks.

• The paper demonstrates that applying reinforcement learning after atomic skill SFT synthesizes new composite reasoning circuits essential for generalization.
• The study reveals that while SFT achieves high I.I.D. accuracy, it fails in zero-shot settings unless reinforced by targeted RL training.
• Ablative analysis confirms both parametric and contextual skills are necessary, indicating RL actively synthesizes reasoning rather than merely amplifying memorized patterns.

Reinforcement Learning as a Synthesizer of Complementary Reasoning in LLMs

Motivation and Problem Definition

The paper investigates the nuanced interplay between Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) in post-training LLMs, focusing on the mechanisms enabling generalization in composite reasoning tasks. The core scenario concerns Complementary Reasoning, where the model must integrate internal parametric knowledge with external contextual cues—a setting emblematic of real-world information demands, such as multi-hop QA on knowledge bases or RAG systems. Crucially, the work isolates two atomic reasoning skills: Parametric Reasoning (Mem) and Contextual Reasoning (Ctx), and studies their composition (Comp), elucidating logical prerequisites for advanced reasoning.

Three distinct generalization levels are formulated:

• I.I.D.: The test requires only seen relational paths.
• Composition: The test requires unseen combinations of seen atomic relations.
• Zero-shot: The test requires at least one relation never seen during training.

Synthetic Experimental Design

Addressing the confounding effects of data contamination in web-scale corpora, experiments are conducted on a large, highly-controlled synthetic dataset of human biographies, with knowledge graph-based entity relations and carefully segmented training/test splits. This unique design ensures strict separation between parametric and contextual skills, facilitating robust formal evaluation across differing generalization levels.

Figure 1: Definition and evaluation protocol for complementary reasoning, showing compositional requirements and generalization analysis.

The parametric/contextual split enables controlled synthesis of multi-hop QA pairs, with chain-of-thought (CoT) answers used to probe stepwise reasoning.

SFT Generalization Paradox and Baseline Analysis

Empirical results demonstrate:

• SFT on composite data achieves high I.I.D. accuracy (≈90%) but catastrophically fails on Zero-shot (≈18%).
• SFT on atomic skills (Mem+Ctx) does not generally compose: achieving only ≈24–35% on Comp, with little transfer.

This establishes the SFT generalization paradox: SFT incentivizes superficial memorization rather than true algorithmic reasoning, unable to transcend distributional boundaries present in Zero-shot settings.

RL as a Reasoning Synthesizer

The central claim is that RL is not merely a probability amplifier, but a synthesizer of new logical reasoning circuits—conditional on the mastery of atomic skills. The experimental curriculum is:

1. SFT on atomic skills (Mem+Ctx).
2. RL on composite skills (Comp).

Results indicate:

• RL over SFT models with sufficient atomic abilities consistently unlocks generalization, especially in Zero-shot scenarios, regardless of data scale.
• SFT directly on composite data fails to yield the same gains, even under matched RL training.

  Figure 2: RL generalization gain across varying composite data proportions.

A crucial sample efficiency finding is that atomic pretraining is more data-efficient for building compositional reasoning; once atomic skills are primed, RL requires few composite samples to unlock generalization.

Figure 3: Sample efficiency comparison, showing superior adaptation in Comp after atomic SFT and RL.

Necessity of Atomic Skills and RL for Generalization

Ablative analysis confirms that both atomic skills are strictly necessary for RL to compose complementary reasoning—models lacking either parametric or contextual capability post-SFT fail to generalize after RL, despite similar initial performance levels. Furthermore, RL is required to actively synthesize skills; further SFT or LoRA adaptation only amplifies memorization with little effects on unseen combination generalization.

Figure 4: RL generalization gains strictly depend on atomic skill sufficiency in the base model.

Mechanistic Insights: Synthesis vs. Amplification

To dissect RL’s mechanism, pass@k metrics reveal a persistent performance gap even at high k for models with atomic skills, indicating synthesis rather than mere amplification. Conversely, models SFTed only on composite data show that RL is an amplifier—their pass@k curves converge.

Figure 5: Pass@k curves confirm synthesis in atomic-SFT+RL models and amplification in composite-SFT+RL models.

Model scaling (e.g., Qwen-2.5-3B) confirms robustness: atomic skill SFT followed by RL remains optimal as model capacity increases.

Figure 6: Trends persist across model families and scaling.

Learning Dynamics and Latent Mechanism Analysis

Training dynamics show emergent gains in complementary reasoning ability as SFT progresses over atomic data, with robust generalization only manifesting past key convergence thresholds. PCA analysis demonstrates explicit latent disentanglement of atomic skills in SFT→RL setups, while composite-task SFT leads to entangled representations.

Figure 7: Training dynamics for emergence of Comp ability.

Figure 8: Generalization emergence as SFT loss decreases.

Figure 9: PCA latent space shifts, highlighting representation disentanglement in atomic SFT→RL.

Error analysis reveals that RL-augmented models transition failure points towards later stages in multi-hop chains, consistent with improved knowledge integration.

Implications and Future Directions

The results advocate a scalable strategy for building reasoning LLMs: maximize learning of atomic skills via SFT, then apply RL to synthesize complex composites with minimal additional supervision. This paradigm obviates the need for expensive collection of composite reasoning traces. Theoretical implications challenge prior conceptualizations of RL as a mere reweighting mechanism and instead establish its role as an active algorithmic synthesizer.

Practically, future developments in AI reasoning may draw on these insights to design architectures and curricula optimizing for atomic skill acquisition followed by RL-driven synthesis, especially in OOD domains or high-complexity reasoning environments. Validation on real-world, strictly split datasets remains a crucial avenue. Mechanistic interpretability of synthesized circuits and the application to large-scale models represent further opportunities.

Conclusion

This work provides compelling empirical and mechanistic evidence that RL can synthesize complex, compositional reasoning in LLMs when the base model has mastered atomic skills, challenging the paradigm of RL as mere amplification. The atomic-SFT-then-RL curriculum offers a robust, efficient path to scalable generalization in knowledge-intensive reasoning, substantiated across data scales, model families, and reasoning difficulties.