# A Comparative Study of Learning Paradigms in Large Language Models via Intrinsic Dimension

arXiv: https://arxiv.org/abs/2412.06245 · HTML: https://mlsanity.com/paper/2412.06245/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 29 references that are in the map.
- First posted on arXiv 9 Dec 2024.

## Builds on (most cited first, 21 of 21)

- [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)
- [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)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [PromptSource: An Integrated Development Environment and Repository for Natural Language Prompts](https://mlsanity.com/paper/2202.01279/) (2022)
- [Intrinsic dimension of data representations in deep neural networks](https://mlsanity.com/paper/1905.12784/) (2019)
- [Estimating the intrinsic dimension of datasets by a minimal neighborhood information](https://mlsanity.com/paper/1803.06992/) (2018)
- [Why Can GPT Learn In-Context? Language Models Implicitly Perform Gradient Descent as Meta-Optimizers](https://mlsanity.com/paper/2212.10559/) (2022)
- [Bilateral Multi-Perspective Matching for Natural Language Sentences](https://mlsanity.com/paper/1702.03814/) (2017)
- [The geometry of hidden representations of large transformer models](https://mlsanity.com/paper/2302.00294/) (2023)
- [Characterizing Truthfulness in Large Language Model Generations with Local Intrinsic Dimension](https://mlsanity.com/paper/2402.18048/) (2024)
- [Bridging Information-Theoretic and Geometric Compression in Language Models](https://mlsanity.com/paper/2310.13620/) (2023)
- [Geometric Signatures of Compositionality Across a Language Model's Lifetime](https://mlsanity.com/paper/2410.01444/) (2024)

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

- [Riemannian Geometry for Pre-trained Language Model Embeddings](https://mlsanity.com/paper/2607.07047/) (2026)

## Abstract (arXiv)

The performance of Large Language Models (LLMs) on natural language tasks can be improved through both supervised fine-tuning (SFT) and in-context learning (ICL), which operate via distinct mechanisms. Supervised fine-tuning updates the model's weights by minimizing loss on training data, whereas in-context learning leverages task demonstrations embedded in the prompt, without changing the model's parameters. This study investigates the effects of these learning paradigms on the hidden representations of LLMs using Intrinsic Dimension (ID). We use ID to estimate the number of degrees of freedom between representations extracted from LLMs as they perform specific natural language tasks. We first explore how the ID of LLM representations evolves during SFT and how it varies due to the number of demonstrations in ICL. We then compare the IDs induced by SFT and ICL and find that ICL consistently induces a higher ID compared to SFT, suggesting that representations generated during ICL reside in higher dimensional manifolds in the embedding space.