We hypothesize that the layer-dependent emergence of linear structure is due to LLMs hierarchically developing understanding of input data, progressing from surface features to more abstract concepts

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• We hypothesize that the layer-wise emergence of linear structure is due to LLMs hierarchically developing understanding of their input data, progressing from surface level features to more abstract conceptshypothesis0.955
  Stated explicitly in App. C to explain why linear structure emerges later for conjunctive statements
• LLMs hierarchically develop understanding of their input data, progressing from surface-level features in early layers to more abstract concepts in later layersclaim0.877
  Interpretation of the layer-by-layer PCA visualizations showing linear structure emerging in early-middle layers
• In intermediate regimes of scale or layer depth, LLMs may linearly represent features at intermediate levels of abstraction such as 'accurate factual recall' or 'close association' rather than abstract truthclaim0.798
  Theoretical interpretation of antipodal alignment and misalignment phenomena in PCA visualizations
• As LLMs scale, they develop increasingly general abstractions, with large models linearly representing abstract concepts like truth that capture shared properties of diverse inputsclaim0.778
  Interpretive claim connecting scale to abstraction level in LLM representations
• In LLaMA-2-13B, salient linear structure in the top PCs rapidly emerges in early-middle layers, with this emergence occurring later for conjunctive statements than simple statementsfinding0.771
  Layer-wise emergence pattern supporting hierarchical development hypothesis
• Causal emergence may be a previously undisclosed axis of reorganization of neural representations in RL agents.claim0.760
  Authors' interpretive assertion that the observed alignment reveals a novel organizing principle of neural representation dynamics.
• Connecting the Dots: LLMs Can Infer and Verbalize Latent Structure from Disparate Training Data (Treutlein et al. 2024)concept0.758
  Out-of-context reasoning work directly related to synthetic document fine-tuning experiments
• Life and living structure will appear in the world inevitably because the mathematical way space gives rise to structure necessarily reinforces wholeness as part of its most normal evolution.claim0.757
  Alexander's strongest ontological claim: living structure is not probabilistically improbable but mathematically necessary given the principle of unfolding wholeness