The Neural Geometry Series
A series about mapping the inner geometry of neural networks: the multidimensional structures in models' activations, the computations that those structures support, and new methods that let us recover, understand, and control them. How neural geometry will unlock understanding and control of AI Neural networks develop rich geometric structure in their activations, mirroring the structure of the world they are trained on: days of the week form circles, colors form an HSL manifold, and the tree of life appears in genomic representations. This opening post makes the case that this "neural geometry" is a crucial frontier for understanding, improving, and controlling AI models. Steering along curved manifolds in representation space produces cleaner, more targeted behavior changes than conventional linear steering vectors. We found a neural mechanism that operates over manifolds: a general-purpose addition module inside Llama 3.1 8B which manipulates circular representations of numbers. Ca
The World Inside Neural Networks How neural geometry will unlock understanding and control of AI Neural networks develop rich geometric structure in their activations, mirroring the structure of the world they are trained on: days of the week form circles, colors form an HSL manifold, and the tree of life appears in genomic representations. This opening post makes the case that this "neural geometry" is a crucial frontier for understanding, improving, and controlling AI models. Geiger et al. · May 7, 2026 Steering Along Manifolds to Control Neural Networks Steering along curved…
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