# Strategic Over-Parameterization for Generalizable Low-Rank Adaptation

arXiv: https://arxiv.org/abs/2605.16470 · HTML: https://mlsanity.com/paper/2605.16470/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 44 of its 53 references that are in the map.
- First posted on arXiv 15 May 2026.

## Builds on (most cited first, 30 of 44)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [WizardLM: Empowering large pre-trained language models to follow complex instructions](https://mlsanity.com/paper/2304.12244/) (2023)
- [Analyzing Multi-Head Self-Attention: Specialized Heads Do the Heavy Lifting, the Rest Can Be Pruned](https://mlsanity.com/paper/1905.09418/) (2019)
- [A Convergence Theory for Deep Learning via Over-Parameterization](https://mlsanity.com/paper/1811.03962/) (2018)
- [DoRA: Weight-Decomposed Low-Rank Adaptation](https://mlsanity.com/paper/2402.09353/) (2024)
- [Gradient Descent Provably Optimizes Over-parameterized Neural Networks](https://mlsanity.com/paper/1810.02054/) (2018)
- [Pre-trained Models for Natural Language Processing: A Survey](https://mlsanity.com/paper/2003.08271/) (2020)
- [LoRA+: Efficient Low Rank Adaptation of Large Models](https://mlsanity.com/paper/2402.12354/) (2024)
- [AdaLoRA: Adaptive Budget Allocation for Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2303.10512/) (2023)
- [Learning and Generalization in Overparameterized Neural Networks, Going Beyond Two Layers](https://mlsanity.com/paper/1811.04918/) (2018)
- [The Lottery Ticket Hypothesis for Pre-trained BERT Networks](https://mlsanity.com/paper/2007.12223/) (2020)
- [PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models](https://mlsanity.com/paper/2404.02948/) (2024)
- [DynaBERT: Dynamic BERT with Adaptive Width and Depth](https://mlsanity.com/paper/2004.04037/) (2020)
- [Tensorizing Neural Networks](https://mlsanity.com/paper/1509.06569/) (2015)
- [OpenCodeInterpreter: Integrating Code Generation with Execution and Refinement](https://mlsanity.com/paper/2402.14658/) (2024)
- [A Rank Stabilization Scaling Factor for Fine-Tuning with LoRA](https://mlsanity.com/paper/2312.03732/) (2023)
- [Proving the Lottery Ticket Hypothesis: Pruning is All You Need](https://mlsanity.com/paper/2002.00585/) (2020)
- [FedPara: Low-Rank Hadamard Product for Communication-Efficient Federated Learning](https://mlsanity.com/paper/2108.06098/) (2021)
- [KronA: Parameter Efficient Tuning with Kronecker Adapter](https://mlsanity.com/paper/2212.10650/) (2022)

## Abstract (arXiv)

Adapting large language models (LLMs) to downstream tasks via full fine-tuning is increasingly impractical due to its computational and memory demands. Parameter-efficient fine-tuning (PEFT) approaches such as Low-Rank Adaptation (LoRA) mitigate this by confining updates to a compact set of trainable parameters, but this aggressive reduction often sacrifices generalization, especially under transfer across heterogeneous tasks and domains. We revisit the tension between parameter efficiency and adaptation capacity, and ask whether the two are truly at odds. We answer in the negative by introducing LoRA-Over, a framework grounded in a simple principle: enrich the optimization landscape during training, then collapse the enrichment at inference. LoRA-Over injects auxiliary parameters into the low-rank adapters during training to broaden the effective hypothesis space, and through a decomposition-based reformulation folds them back into a standard low-rank structure with negligible reconstruction error, keeping inference cost identical to vanilla LoRA. Since not all weight matrices benefit equally from added capacity, we further propose two scheduling strategies, one statically predefined and one dynamically determined at runtime, that direct extra capacity where most needed. We evaluate LoRA-Over on language understanding (GLUE, T5-Base), dialogue (MT-Bench), arithmetic reasoning (GSM8K), and code generation (HumanEval), using LLaMA 2-7B and LLaMA 3.1-8B. Across all benchmarks and scales, LoRA-Over consistently outperforms vanilla LoRA, showing that principled over-parameterization designed to vanish at inference is an effective lever for improving PEFT generalization. Code will be released upon acceptance.