# Understanding and Guiding Layer Placement in Parameter-Efficient Fine-Tuning of Large Language Models

arXiv: https://arxiv.org/abs/2602.04019 · HTML: https://mlsanity.com/paper/2602.04019/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 35 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 29 of 29)

- [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)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [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)
- [CIDEr: Consensus-based Image Description Evaluation](https://mlsanity.com/paper/1411.5726/) (2014)
- [BitFit: Simple Parameter-efficient Fine-tuning for Transformer-based Masked Language-models](https://mlsanity.com/paper/2106.10199/) (2021)
- [Few-Shot Parameter-Efficient Fine-Tuning is Better and Cheaper than In-Context Learning](https://mlsanity.com/paper/2205.05638/) (2022)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Towards a Unified View of Parameter-Efficient Transfer Learning](https://mlsanity.com/paper/2110.04366/) (2021)
- [AdapterFusion: Non-Destructive Task Composition for Transfer Learning](https://mlsanity.com/paper/2005.00247/) (2020)
- [Large Language Models](https://mlsanity.com/paper/2307.05782/) (2023)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey](https://mlsanity.com/paper/2403.14608/) (2024)
- [An Empirical Study of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning](https://mlsanity.com/paper/2308.08747/) (2023)
- [Layer by Layer: Uncovering Hidden Representations in Language Models](https://mlsanity.com/paper/2502.02013/) (2025)
- [AdapterDrop: On the Efficiency of Adapters in Transformers](https://mlsanity.com/paper/2010.11918/) (2020)
- [S-LoRA: Serving Thousands of Concurrent LoRA Adapters](https://mlsanity.com/paper/2311.03285/) (2023)
- [Are All Layers Created Equal?](https://mlsanity.com/paper/1902.01996/) (2019)
- [LISA: Layerwise Importance Sampling for Memory-Efficient Large Language Model Fine-Tuning](https://mlsanity.com/paper/2403.17919/) (2024)
- [LoRAPrune: Structured Pruning Meets Low-Rank Parameter-Efficient Fine-Tuning](https://mlsanity.com/paper/2305.18403/) (2023)
- [Understanding the Performance and Estimating the Cost of LLM Fine-Tuning](https://mlsanity.com/paper/2408.04693/) (2024)
- [Empirical Analysis of the Strengths and Weaknesses of PEFT Techniques for LLMs](https://mlsanity.com/paper/2304.14999/) (2023)
- [Investigating Layer Importance in Large Language Models](https://mlsanity.com/paper/2409.14381/) (2024)
- [Lessons and Insights from a Unifying Study of Parameter-Efficient Fine-Tuning (PEFT) in Visual Recognition](https://mlsanity.com/paper/2409.16434/) (2024)
- [PEFT-Bench: A Parameter-Efficient Fine-Tuning Methods Benchmark](https://mlsanity.com/paper/2511.21285/) (2025)
- [Efficient Layer-wise LLM Fine-tuning for Revision Intention Prediction](https://mlsanity.com/paper/2510.00268/) (2025)
- [zFLoRA: Zero-Latency Fused Low-Rank Adapters](https://mlsanity.com/paper/2510.25784/) (2025)

## Built on by (most cited first, 2 of 2)

- [Compiling Learning Problems into Adaptation Programs for Language Models](https://mlsanity.com/paper/2609.37371/) (2026)
- [Where to Adapt Matters: Layer-Selective Fine-Tuning for Capability Retention](https://mlsanity.com/paper/2610.11620/) (2026)

## Abstract (arXiv)

As large language models (LLMs) continue to grow, the cost of full-parameter fine-tuning has made parameter-efficient fine-tuning (PEFT) the default strategy for downstream adaptation. Constraints from inference latency in scalable serving and fine-tuning cost in edge or rapid-deployment settings make the choice of which layers to fine-tune unavoidable. Yet current practice typically applies PEFT uniformly across all layers, with limited understanding or leverage of layer selection. This paper develops a unified projected residual view of PEFT on top of a frozen base model. Under a local quadratic approximation, layerwise adaptation is governed by three quantities: (i) the projected residual norm (resnorm), which measures how much correctable bias a layer can capture; (ii) the activation energy, which determines feature conditioning; and (iii) layer coupling, which quantifies how strongly residuals interact across layers. We show that, for squared loss and linear adapters, the resnorm equals a normalized gradient norm, activation energy controls ill-conditioning and noise amplification, and weak coupling yields approximately additive layerwise contributions. Building on these insights, we introduce the Layer Card, a reusable diagnostic that summarizes residual signal strength, compute cost, and performance for each layer of a given model. With an identical model and LoRA configuration, Layer Card-guided placement refines the choice of adapted layers to flexibly prioritize different objectives, such as maximizing performance or reducing fine-tuning cost. Moreover, on Qwen3-8B, we show that selectively adapting a subset of layers can achieve performance close to full-layer LoRA while substantially reducing fine-tuning cost and the number of adapter-augmented layers during inference, offering a more cost-performance-aware alternative to full-layer insertion.