Compositional learning systems must balance plasticity, the ability to acquire new knowledge, with stability, the preservation of previously learned components, especially when tasks share structure and risk interference. We study how modular architecture, task similarity, and representational dimensionality jointly shape compositional continual learning in a sequential A-B-A paradigm, comparing a task-partitioned recurrent network to a single-network baseline while inducing high- and low-dimensional regimes via weight-scale manipulations. In a high-dimensional "lazy" regime, both architectures achieve similar performance and internal geometry, suggesting that explicit modular structure has little impact when representations are weakly constrained. In a lower-dimensional "rich" regime, modularity becomes decisive: the modular network develops graded task-specific subspaces that overlap for similar tasks, partially align for moderately dissimilar tasks, and separate for dissimilar tasks, yielding a more compositional and interpretable organization than the single network. These findings identify the representational regime induced by initialization scale, which co-varies with representational dimensionality, as a key factor governing when compositional, modular structure is functionally beneficial in continual learning, and support viewing safety and robustness as problems of adaptive allocation of representational subspaces rather than fixed separation versus sharing.

翻译：组合学习系统必须在可塑性（获取新知识的能力）与稳定性（保留已学组件的能力）之间取得平衡，尤其当任务共享结构且存在干扰风险时。我们研究模块化架构、任务相似性与表征维度如何共同塑造序列式A-B-A范式下的组合持续学习，通过权重尺度操控诱发高维与低维状态，将任务分区循环网络与单网络基线进行比较。在高维"惰性"状态下，两种架构的性能与内部几何结构相似，表明当表征约束较弱时，显式模块化结构影响甚微。在低维"丰富"状态下，模块化变得至关重要：模块化网络会形成分级任务特定子空间，相似任务间子空间重叠、中度不相似任务部分对齐、不相似任务完全分离，从而比单网络形成更具组合性与可解释性的组织结构。这些发现揭示了由初始化尺度（与表征维度共变）诱发的表征状态，是决定组合式模块化结构在持续学习中何时具有功能优势的关键因素，并支持将安全性与鲁棒性视为表征子空间自适应分配问题（而非固定分离或共享）的观点。