Disentangling Optimization Geometry via Hierarchical Polar Adapters for Class-Incremental Learning

Deep neural networks suffer from catastrophic forgetting when learning on sequence tasks because standard adaptation mechanisms update a monolithic set of Cartesian weights, inherently entangling feature intensity with spatial displacement and destructively overwriting ancestral representations. Inspired by the brain’s multi-timescale consolidation and frequency-aware memory dynamics, we propose HiPo(Hierarchical Polar Adapters), a novel continual learning framework that fundamentally redefines how neural knowledge is parameterized, stored, and consolidated. First, HiPo projects token representations into a complex orthogonal Fourier basis and explicitly parametrizes the adapter weights in polar coordinates, decoupling feature intensity from geometric correlation to probabilistically isolate task updates. Second, we embed these polar weights within a multi-tiered hierarchical memory stack, functionally separating a highly plastic working memory from a deep, stabilizing long-term memory. Finally, an adaptively thresholded snapshot Fisher mechanism evaluates parameter criticality in the decoupled polar space. By executing mathematically safe, Cartesian-invariant knowledge transfers into the deep memory tiers, HiPo safely hollows out the working memory, paralyzing obsolete gradients and preserving plasticity without inducing structural distortion. Extensive experiments across standard CIL benchmarks demonstrate that HiPo establishes a highly resilient optimization manifold, achieving state-of-the-art performance and exceptional geometric stability, particularly under severe out-of-distribution shifts.