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

• URL: http://arxiv.org/abs/2602.22911v2
• Date: Mon, 02 Mar 2026 22:35:44 GMT
• Title: CeRA: Breaking the Linear Ceiling of Low-Rank Adaptation via Manifold Expansion
• Abstract summary: Low-Rank Adaptation (LoRA) dominates parameter-efficient fine-tuning (PEFT)<n>We introduce CeRA (Capacity-enhanced Rank Adaptation), a weight-level parallel adapter that injects SiLU gating and structural dropout to induce manifold expansion.
• Score: 1.5736899098702974
• License: http://creativecommons.org/licenses/by/4.0/
• 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 mathematical reasoning, where CeRA achieves a perplexity of 1.97 on MathInstruct, significantly surpassing LoRA's saturation point of 2.07. 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.

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