# CeRA: Breaking the Linear Ceiling of Low-Rank Adaptation with Non-linearity Retained at Inference

arXiv: https://arxiv.org/abs/2602.22911 · HTML: https://mlsanity.com/paper/2602.22911/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 26 references that are in the map.
- First posted on arXiv 26 Feb 2026.

## Builds on (most cited first, 20 of 20)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [MAmmoTH: Building Math Generalist Models through Hybrid Instruction Tuning](https://mlsanity.com/paper/2309.05653/) (2023)
- [AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.10512/) (2023)
- [A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA](https://mlsanity.com/paper/2312.03732/) (2023)
- [S-LoRA: Serving Thousands of Concurrent LoRA Adapters](https://mlsanity.com/paper/2311.03285/) (2023)
- [Punica: Multi-Tenant LoRA Serving](https://mlsanity.com/paper/2310.18547/) (2023)
- [CoLA: Compute-Efficient Pre-Training of LLMs via Low-Rank Activation](https://mlsanity.com/paper/2502.10940/) (2025)
- [AuroRA: Breaking Low-Rank Bottleneck of LoRA with Nonlinear Mapping](https://mlsanity.com/paper/2505.18738/) (2025)
- [EdgeLoRA: An Efficient Multi-Tenant LLM Serving System on Edge Devices](https://mlsanity.com/paper/2507.01438/) (2025)
- [Learning Rate Matters: Vanilla LoRA May Suffice for LLM Fine-tuning](https://mlsanity.com/paper/2602.04998/) (2026)
- [PEANuT: Parameter-Efficient Adaptation with Weight-aware Neural Tweakers](https://mlsanity.com/paper/2410.01870/) (2024)
- [CoLA: Collaborative Low-Rank Adaptation](https://mlsanity.com/paper/2505.15471/) (2025)
- [Dynamic DropConnect: Enhancing Neural Network Robustness through Adaptive Edge Dropping Strategies](https://mlsanity.com/paper/2502.19948/) (2025)

## Abstract (arXiv)

Low-Rank Adaptation (LoRA) dominates parameter-efficient fine-tuning (PEFT). However, it faces a ``linear ceiling'': increasing the rank yields diminishing returns in expressive capacity due to linear constraints. We introduce CeRA (Capacity-enhanced Rank Adaptation), a weight-level parallel adapter that injects SiLU gating and dropout to induce non-linearity during inference, thereby placing it in a different function class from adapters whose non-linearity exists during training and collapses to an affine map at inference time. On both the basic arithmetic (GSM8K) and the complex MATH benchmark, CeRA is markedly more parameter-efficient. Across a full rank × learning rate sweep, CeRA at rank 64 achieves the highest MATH pass@1 of any configuration in the grid (23.6%), matching or exceeding both a rank-512 LoRA (22.4%) and DoRA (19.8%) while using only 1/8 of the parameter budget. With the rank and learning rate fixed, CeRA equals or outperforms LoRA in 10 of 12 matched settings. Spectrally, CeRA's learned updates utilize the singular-value spectrum more broadly than linear adapters, which exhibit rank collapse at high rank, although a scale-matched control shows that this difference stems mostly from output scale and partially from non-linearity. Additionally, dropout appears to contribute to regularization rather than rank expansion. We release the code for reproducibility: https://github.com/hhchen1105/cera.