Functional compatibility as a determinant of persistent neural learning

Neural networks can acquire new capabilities while damaging existing ones, but what determines whether new learning persists remains unclear. We identify functional compatibility, the extent to which incoming learning can coexist with behaviour that must be preserved, as an experimentally manipulable causal determinant of persistence. From identical neural states, we vary compatibility while matching unrestricted learning opportunity and imposing a common retention requirement. Persistent learning increases with compatibility across independent directions, convolutional and transformer architectures, vision and text, and a ten-seed replication. Learning rules and retention constraints determine how much compatible opportunity is retained, whereas nonlinear geometry limits the matched intervention at larger update norms. Functional compatibility therefore reframes stability-plasticity from preventing forgetting to determining which new learning can coexist with existing function and persist.

Continual Learning as a Multiphase Moving-Boundary Problem

Continual learning struggles to balance retaining past knowledge with absorbing new tasks. Stefan-CL elegantly resolves this stability-plasticity dilemma through the physics of melting. It frames consolidated knowledge as a protected "solid" and unused capacity as an adaptable "liquid." As the network learns, this boundary expands, governed by a "latent heat" tuning dial. By mathematically freezing the learned interior, Stefan-CL cuts forgetting to near zero, matching memory-heavy baselines without storing raw data, forging a beautiful, physics-grounded path for AI.

When Does Structure Matter in Continual Learning? Dimensionality Controls When Modularity Shapes Representational Geometry

To preserve previously learned representations, continual learning systems must strike a balance between plasticity, the ability to acquire new knowledge, and stability. This stability-plasticity dilemma affects how representations can be reused across tasks: shared structure enables transfer when tasks are similar but may also induce interference when new learning disrupts existing representations. However, it remains unclear when and why structural separation influences this trade-off. In this study, we examine how network architecture, task similarity, and representational dimensionality jointly shape learning in a sequential task paradigm inspired by transfer-interference studies. We compare a task-partitioned modular recurrent network with a single-module baseline by systematically varying task similarity (low, medium, high) and the scale of weight initialization, which induces different learning regimes that we empirically characterize through the effective dimensionality of the learned representations. We find that architecture has minimal impact in high-dimensional regimes where representations are sufficiently unconstrained to accommodate multiple tasks without strong interference. In contrast, in lower-dimensional (rich) regimes, architectural separation is decisive: modular networks exhibit graded alignment of task-specific subspaces with overlap for similar tasks, partial orthogonalization for moderately dissimilar tasks, and stronger separation for dissimilar tasks. This graded geometry is absent in the single network baseline. Our findings suggest that representational dimensionality acts as a key organizing variable governing when structural separation becomes functionally relevant, and highlight adaptive geometry as a central principle for designing continual learning systems.