The Depth Flow of Token Representations Is Nonlinear and Does Not Descend Its Own Density

arXiv:2608.29706 · cs.CL · Submitted 2026-08-30 · Read on arXiv

cs.CL

Submitted: 2026-08-30

Updated: 2026-08-30

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Transformer — 11× in this paper · explained in 2 episodes
• Alignment — 7× in this paper · explained in 1 episode
• In International Conference on Learning Representations — 3× in this paper
• Gradient Flow — 2× in this paper · explained in 2 episodes
• Bayesian Inference — 1× in this paper · explained in 5 episodes
• Calibration — 1× in this paper · explained in 7 episodes
• Embeddings — 1× in this paper · explained in 2 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Generative Modeling — 1× in this paper · explained in 3 episodes
• Generative Models — 1× in this paper · explained in 2 episodes
• Interpretability — 1× in this paper · explained in 15 episodes
• Langevin Dynamics — 1× in this paper · explained in 2 episodes
• Ornstein–Uhlenbeck Process — 1× in this paper · explained in 3 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Sampling Biases — 1× in this paper · explained in 2 episodes
• Spectral Geometry — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Transformer Architecture — 1× in this paper · explained in 2 episodes

Sources

• Eliciting Latent Predictions from Transformers with the Tuned Lens
• Pythia: A Suite for Analyzing Large Language Models Across Training and Scaling
• A Statistical Physics of Language Model Reasoning
• The Curved Spacetime of Transformer Architectures
• Transformer Dynamics: A neuroscientific approach to interpretability of large language models
• Dynamics of the Transformer Residual Stream: Coupling Spectral Geometry to Network Topology
• A mathematical perspective on Transformers
• The Remarkable Robustness of LLMs: Stages of Inference?
• A Geometric Perspective on Next-Token Prediction in Large Language Models: Three Emerging Phases
• All-but-the-Top: Simple and Effective Postprocessing for Word Representations
• Sinkformers: Transformers with Doubly Stochastic Attention
• Lines of Thought in Large Language Models
• Jump to Conclusions: Short-Cutting Transformers With Linear Transformations
• YuriiFormer: A Suite of Nesterov-Accelerated Transformers

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