# Exploring the LLM Journey from Cognition to Expression with Linear Representations

arXiv: https://arxiv.org/abs/2405.16964 · HTML: https://mlsanity.com/paper/2405.16964/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 28 of its 34 references that are in the map.
- First posted on arXiv 27 May 2024.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [CommonsenseQA: A Question Answering Challenge Targeting Commonsense Knowledge](https://mlsanity.com/paper/1811.00937/) (2018)
- [Understanding intermediate layers using linear classifier probes](https://mlsanity.com/paper/1610.01644/) (2016)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Interpretability Beyond Feature Attribution: Quantitative Testing with Concept Activation Vectors (TCAV)](https://mlsanity.com/paper/1711.11279/) (2017)
- [A General Language Assistant as a Laboratory for Alignment](https://mlsanity.com/paper/2112.00861/) (2021)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Large Language Models as Optimizers](https://mlsanity.com/paper/2309.03409/) (2023)
- [RACE: Large-scale ReAding Comprehension Dataset From Examinations](https://mlsanity.com/paper/1704.04683/) (2017)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Baichuan 2: Open Large-scale Language Models](https://mlsanity.com/paper/2309.10305/) (2023)
- [Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task](https://mlsanity.com/paper/2210.13382/) (2022)
- [Explainability for Large Language Models: A Survey](https://mlsanity.com/paper/2309.01029/) (2023)
- [Linearity of Relation Decoding in Transformer Language Models](https://mlsanity.com/paper/2308.09124/) (2023)
- [Arcee's MergeKit: A Toolkit for Merging Large Language Models](https://mlsanity.com/paper/2403.13257/) (2024)
- [Exploiting Similarities among Languages for Machine Translation](https://mlsanity.com/paper/1309.4168/) (2013)
- [Aligning Large Language Models with Human Preferences through Representation Engineering](https://mlsanity.com/paper/2312.15997/) (2023)
- [Evaluating Hallucinations in Chinese Large Language Models](https://mlsanity.com/paper/2310.03368/) (2023)

## Built on by (most cited first, 5 of 5)

- [Reward-Robust RLHF in LLMs](https://mlsanity.com/paper/2409.15360/) (2024)
- [Can DPO Learn Diverse Human Values? A Theoretical Scaling Law](https://mlsanity.com/paper/2408.03459/) (2024)
- [Lens: Rethinking Multilingual Enhancement for Large Language Models](https://mlsanity.com/paper/2410.04407/) (2024)
- [Relational Knowledge Distillation Using Fine-tuned Function Vectors](https://mlsanity.com/paper/2601.08169/) (2026)
- [RepBench: Compiling Benchmarks into Capability Representations for Large Language Models](https://mlsanity.com/paper/2607.28008/) (2026)

## Abstract (arXiv)

This paper presents an in-depth examination of the evolution and interplay of cognitive and expressive capabilities in large language models (LLMs), with a specific focus on Baichuan-7B and Baichuan-33B, an advanced bilingual (Chinese and English) LLM series. We define and explore the model's cognitive and expressive capabilities through linear representations across three critical phases: Pretraining, Supervised Fine-Tuning (SFT), and Reinforcement Learning from Human Feedback (RLHF). Cognitive capability is defined as the quantity and quality of information conveyed by the neuron output vectors within the network, similar to the neural signal processing in human cognition. Expressive capability is defined as the model's capability to produce word-level output. Our findings unveil a sequential development pattern, where cognitive abilities are largely established during Pretraining, whereas expressive abilities predominantly advance during SFT and RLHF. Statistical analyses confirm a significant correlation between the two capabilities, suggesting that cognitive capacity may limit expressive potential. The paper also explores the theoretical underpinnings of these divergent developmental trajectories and their connection to the LLMs' architectural design. Moreover, we evaluate various optimization-independent strategies, such as few-shot learning and repeated sampling, which bridge the gap between cognitive and expressive capabilities. This research reveals the potential connection between the hidden space and the output space, contributing valuable insights into the interpretability and controllability of their training processes.