Park et al. formalize the linear representation hypothesis (LRH) as a framework for interpreting concepts within large language models like Llama 2. Their work demonstrates that concepts such as gender or tense are linearly represented in specific spaces within the model's architecture, with empirical validation on Llama 2.

However, the limited dimensionality of these spaces (2K-16K) creates challenges for representing the vast number of language features. Anthropic introduces superposition as a solution, showing how nonlinear activation functions (like ReLU) enable models to manage interference between orthogonal concepts in high-dimensional spaces, allowing sparse features to coexist productively. This research provides valuable mathematical tools for understanding how LLMs capture complex language patterns through linear representations and superposition.