Beyond Isolated Mechanisms: Coordinated Representation Learning for Systemic Reasoning in Large Language Models

Existing methods typically enhance the reasoning capabilities of large language models through four mechanisms, which are often studied in isolation: explicit supervision, implicit knowledge transfer, optimization tuning, and structural constraints. Since these mechanisms are frequently introduced as independent components rather than optimized under a unified objective, their interactions remain under-explored, and potential synergies may be overlooked. We propose Coordinated Representation Learning (CRL), a unified training framework that jointly optimizes these signals: grain-invariant chain-of-thought supervision ensures consistency in reasoning across different trajectory lengths; multi-teacher distillation injects expert knowledge into hidden states; difficulty-aware curriculum learning stabilizes training dynamics; and a structured subspace adapter enables efficient updates. To investigate the interactions among these mechanisms, we compare CRL with an independent compositional baseline that includes the same four components but optimizes them as separate, uncoordinated objectives. Across various model scales and in mathematics, logic, and coding benchmarks, CRL consistently outperforms supervised fine-tuning and standard distillation baselines. More importantly, CRL outperforms the independent combination baseline, revealing positive synergies: the gains from coordinated joint optimization exceed the sum of the individual mechanisms. Ablation experiments further demonstrate that removing any component degrades performance, and the synergy is particularly evident in terms of robustness and sample efficiency under distribution shifts and adversarial conditions. These results suggest that explicitly modeling and coordinating complementary training signals toward a unified objective is a promising path toward achieving stronger system reasoning.