A series exploring how curved geometric structure in neural network representations mirrors the conceptual structure of the world—and how that geometry can be leveraged to control and understand AI systems.
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 curved manifolds in representation space produces cleaner, more targeted behavior changes than conventional linear steering vectors.
Wurgaft et al. · May 7, 2025
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.
Feucht et al. · May 14, 2025
Can we use sparse autoencoder features – i.e., straight lines – to reconstruct curved geometry? We study how, and implement an unsupervised pipeline for discovering manifolds using SAE features.
Bhalla et al. · May 21, 2025
While reading stories, LLMs represent human emotions both geometrically (in activation space) and temporally (changing across the course of a story).
Bhalla et al. · May 21, 2025
More posts coming soon!
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