[2403.03867] On the Origins of Linear Representations in Large Language Models

Abstract:Recent works have argued that high-level semantic concepts are encoded "linearly" in the representation space of large language models. In this work, we study the origins of such linear representations. To that end, we introduce a simple latent variable model to abstract and formalize the concept dynamics of the next token prediction. We use this formalism to show that the next token prediction objective (softmax with cross-entropy) and the implicit bias of gradient descent together promote the linear representation of concepts. Experiments show that linear representations emerge when learning from data matching the latent variable model, confirming that this simple structure already suffices to yield linear representations. We additionally confirm some predictions of the theory using the LLaMA-2 large language model, giving evidence that the simplified model yields generalizable insights.

View PDF HTML (experimental) Abstract:Recent works have argued that high-level semantic concepts are encoded "linearly" in the representation space of large language models. In this work, we study the origins of such linear representations. To that end, we introduce a simple latent variable model to abstract and formalize the concept dynamics of the next token prediction. We use this formalism to show that the next token prediction objective (softmax with cross-entropy) and the implicit bias of gradient descent together promote the linear representation of concepts. Experiments show that…

saved by

• Timothy Kostolansky

related reading

• The Linear Representation Hypothesis and the Geometry of Large Language Modelsarxiv.org
• Verbalizable Representations Form a Global Workspace in Language Modelstransformer-circuits.pub
• The Geometry of Categorical and Hierarchical Concepts in Large Language Modelsarxiv.org
• The Linear Representation Hypothesis and the Geometry of Large Language Modelsarxiv.org
• A History of Large Language Modelsgregorygundersen.com
• GenAI Handbookgenai-handbook.github.io
• Emotion Concepts and their Function in a Large Language Modeltransformer-circuits.pub
• Large Language Model: world models or surface statistics?thegradient.pub
• Large Concept Models (LCMs) by Meta: The Era of AI After LLMs?aipapersacademy.com
• Mapping the Mind of a Large Language Model \ Anthropicanthropic.com
• [2412.06769] Training Large Language Models to Reason in a Continuous Latent Spacearxiv.org
• Training Large Language Models to Reason in a Continuous Latent Spacearxiv.org