reviews: 
Comments: This paper presents a novel approach for efficient fine-tuning of large-scale models. It addresses the challenge of substantial memory consumption associated with such models by introducing L-MSA, a method that fine-tunes only selected layers based on a new metric derived from the Method of Successive Approximations (MSA). This metric guides layer selection and optimizes their fine-tuning, resulting in better model performance with reduced computational costs.

The paper provides a theoretical analysis within deep linear networks and evaluates L-MSA across various datasets and tasks. It compares the proposed method with other layer-wise fine-tuning techniques, demonstrating its superior performance. The experimental results show that L-MSA consistently identifies the most impactful layers for fine-tuning and optimizes them effectively, outperforming baseline methods.
Strengths: 1. **Novel Layer Selection Metric:** The paper introduces a new metric for layer selection based on the Method of Successive Approximations (MSA), which is theoretically grounded and offers a fresh perspective on fine-tuning strategies.

2. **Theoretical Foundations:** The authors provide a comprehensive theoretical analysis within the context of deep linear networks, which strengthens the credibility of the proposed approach.

3. **Empirical Validation:** The paper demonstrates the effectiveness of L-MSA across multiple datasets and tasks, showing consistent improvement over several existing layer-wise fine-tuning methods.

4. **Parameter-Efficiency Focus:** By targeting specific layers for fine-tuning, the method aims to reduce computational costs, addressing a key challenge in training large-scale models.

5. **Clear Contributions to Layer-Wise Fine-Tuning:** The research highlights the potential of selectively fine-tuning layers to achieve better performance, contributing to the growing field of parameter-efficient fine-tuning methods.
Weaknesses: 1. **Lack of Comparison with State-of-the-Art Methods:** The paper does not compare L-MSA with prominent methods like **LoRA**[Hu et, al], which limits the evaluation of its relative effectiveness and practical impact.

2. **Disjointed Presentation:** The flow of the paper is disrupted by referencing equations and concepts out of order, requiring readers to frequently navigate back and forth, which hampers comprehension and readability.

3. **Inadequate Contextualization of Contributions:** The novelty of the proposed method is not sufficiently contextualized against a broader range of parameter-efficient fine-tuning techniques, making it harder to assess its uniqueness and value.

4. **Generalization Concerns:** The paper acknowledges that the approximated updated loss may not always guarantee strong generalization to test data, which raises questions about the robustness of the approach in diverse real-world scenarios.

5. **Computational Demands:** Despite aiming for parameter efficiency, the method still involves substantial computational overhead due to both forward and backward propagation, which could limit its practicality for very large-scale models.

6. **Limited Scope of Empirical Comparisons:** While the paper evaluates L-MSA across several tasks, the range of comparative baselines is not exhaustive, potentially missing out on broader insights.

[Hu et. al, ICLR 2022, LoRA: Low-Rank Adaptation of Large Language Models]
Recommendation: 3
Reviewer confidence: 4
Soundness/correctness: 2
Clarity: 2