CeRA: Breaking the Linear Ceiling of Low-Rank Adaptation via Manifold Expansion

Abstract

Low-Rank Adaptation (LoRA) dominates parameter-efficient fine-tuning (PEFT). However, it faces a critical ``linear ceiling'' in complex reasoning tasks: simply increasing the rank yields diminishing returns due to intrinsic linear constraints. We introduce CeRA (Capacity-enhanced Rank Adaptation), a weight-level parallel adapter that injects SiLU gating and structural dropout to induce manifold expansion. On the SlimOrca benchmark, CeRA breaks this linear barrier: at rank 64 (PPL 3.89), it outperforms LoRA at rank 512 (PPL 3.90), demonstrating superior spectral efficiency. This advantage generalizes to downstream mathematical reasoning. We reveal a profound impact of task complexity: In fundamental arithmetic (GSM8K), CeRA matches standard baselines, but in the highly complex MATH dataset, CeRA demonstrates extreme parameter efficiency. Remarkably, CeRA at rank 64 (Pass@1 16.36\%) outperforms LoRA at rank 512 (Pass@1 15.72\%), achieving superior reasoning accuracy with only 1/8 of the parameter budget. Mechanism analysis via Singular Value Decomposition (SVD) confirms that CeRA activates the dormant tail of the singular value spectrum, effectively preventing the rank collapse observed in linear methods.

Reproductions