# Investigating the Impact of Model Complexity in Large Language Models

arXiv: https://arxiv.org/abs/2410.00699 · HTML: https://mlsanity.com/paper/2410.00699/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 40 of its 48 references that are in the map.
- First posted on arXiv 1 Oct 2024.

## Builds on (most cited first, 30 of 40)

- [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)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Deep contextualized word representations](https://mlsanity.com/paper/1802.05365/) (2018)
- [Reconciling modern machine learning practice and the bias-variance trade-off](https://mlsanity.com/paper/1812.11118/) (2018)
- [Fine-Tuning can Distort Pretrained Features and Underperform Out-of-Distribution](https://mlsanity.com/paper/2202.10054/) (2022)
- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Benign Overfitting in Linear Regression](https://mlsanity.com/paper/1906.11300/) (2019)
- [A Theoretical Analysis of Contrastive Unsupervised Representation Learning](https://mlsanity.com/paper/1902.09229/) (2019)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Provable Guarantees for Self-Supervised Deep Learning with Spectral Contrastive Loss](https://mlsanity.com/paper/2106.04156/) (2021)
- [Transformers as Statisticians: Provable In-Context Learning with In-Context Algorithm Selection](https://mlsanity.com/paper/2306.04637/) (2023)
- [Towards Revealing the Mystery behind Chain of Thought: A Theoretical Perspective](https://mlsanity.com/paper/2305.15408/) (2023)
- [High-dimensional dynamics of generalization error in neural networks](https://mlsanity.com/paper/1710.03667/) (2017)
- [Two models of double descent for weak features](https://mlsanity.com/paper/1903.07571/) (2019)
- [Theoretical Analysis of Self-Training with Deep Networks on Unlabeled Data](https://mlsanity.com/paper/2010.03622/) (2020)
- [Predicting What You Already Know Helps: Provable Self-Supervised Learning](https://mlsanity.com/paper/2008.01064/) (2020)
- [Contrastive learning, multi-view redundancy, and linear models](https://mlsanity.com/paper/2008.10150/) (2020)
- [Tensor Programs II: Neural Tangent Kernel for Any Architecture](https://mlsanity.com/paper/2006.14548/) (2020)
- [Modality Competition: What Makes Joint Training of Multi-modal Network Fail in Deep Learning? (Provably)](https://mlsanity.com/paper/2203.12221/) (2022)
- [Harmless interpolation of noisy data in regression](https://mlsanity.com/paper/1903.09139/) (2019)
- [A Kernel-Based View of Language Model Fine-Tuning](https://mlsanity.com/paper/2210.05643/) (2022)
- [On the Optimal Weighted ℓ2 Regularization in Overparameterized Linear Regression](https://mlsanity.com/paper/2006.05800/) (2020)
- [Double Trouble in Double Descent : Bias and Variance(s) in the Lazy Regime](https://mlsanity.com/paper/2003.01054/) (2020)
- [Why Do Pretrained Language Models Help in Downstream Tasks? An Analysis of Head and Prompt Tuning](https://mlsanity.com/paper/2106.09226/) (2021)
- [Precise Tradeoffs in Adversarial Training for Linear Regression](https://mlsanity.com/paper/2002.10477/) (2020)
- [Inverse scaling can become U-shaped](https://mlsanity.com/paper/2211.02011/) (2022)

## Abstract (arXiv)

Large Language Models (LLMs) based on the pre-trained fine-tuning paradigm have become pivotal in solving natural language processing tasks, consistently achieving state-of-the-art performance. Nevertheless, the theoretical understanding of how model complexity influences fine-tuning performance remains challenging and has not been well explored yet. In this paper, we focus on autoregressive LLMs and propose to employ Hidden Markov Models (HMMs) to model them. Based on the HMM modeling, we investigate the relationship between model complexity and the generalization capability in downstream tasks. Specifically, we consider a popular tuning paradigm for downstream tasks, head tuning, where all pre-trained parameters are frozen and only individual heads are trained atop pre-trained LLMs. Our theoretical analysis reveals that the risk initially increases and then decreases with rising model complexity, showcasing a "double descent" phenomenon. In this case, the initial "descent" is degenerate, signifying that the "sweet spot" where bias and variance are balanced occurs when the model size is zero. Obtaining the presented in this study conclusion confronts several challenges, primarily revolving around effectively modeling autoregressive LLMs and downstream tasks, as well as conducting a comprehensive risk analysis for multivariate regression. Our research is substantiated by experiments conducted on data generated from HMMs, which provided empirical support and alignment with our theoretical insights.