# MiCA Learns More Knowledge Than LoRA and Full Fine-Tuning

arXiv: https://arxiv.org/abs/2604.01694 · HTML: https://mlsanity.com/paper/2604.01694/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 18 references that are in the map.
- First posted on arXiv 2 Apr 2026.

## Builds on (most cited first, 15 of 15)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Prefix-Tuning: Optimizing Continuous Prompts for Generation](https://mlsanity.com/paper/2101.00190/) (2021)
- [The Power of Scale for Parameter-Efficient Prompt Tuning](https://mlsanity.com/paper/2104.08691/) (2021)
- [Finetuned Language Models Are Zero-Shot Learners](https://mlsanity.com/paper/2109.01652/) (2021)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models](https://mlsanity.com/paper/2404.02948/) (2024)
- [Anatomy of Catastrophic Forgetting: Hidden Representations and Task Semantics](https://mlsanity.com/paper/2007.07400/) (2020)
- [SoMA: Singular Value Decomposed Minor Components Adaptation for Domain Generalizable Representation Learning](https://mlsanity.com/paper/2412.04077/) (2024)
- [Learning Rate Matters: Vanilla LoRA May Suffice for LLM Fine-tuning](https://mlsanity.com/paper/2602.04998/) (2026)

## Built on by (most cited first, 1 of 1)

- [Frozen Factor or Spectral Band? Disentangling Two Choices in Low-Rank LoRA](https://mlsanity.com/paper/2610.06621/) (2026)

## Abstract (arXiv)

Minor Component Adaptation (MiCA) is a novel parameter-efficient fine-tuning method for large language models that focuses on adapting underutilized subspaces of model representations. Unlike conventional methods such as Low-Rank Adaptation (LoRA), which target dominant subspaces, MiCA leverages Singular Value Decomposition to identify subspaces related to minor singular vectors associated with the least significant singular values and constrains the update of parameters during fine-tuning to those directions. This strategy leads to up to 5.9x improvement in knowledge acquisition under optimized training hyperparameters and a minimal parameter footprint of 6-60% compared to LoRA. These results suggest that constraining adaptation to minor singular directions provides a more efficient and stable mechanism for integrating new knowledge into pre-trained language models.