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.
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.
Steering Along Manifolds to Control Neural Networks
Steering along curved manifolds in representation space produces cleaner, more targeted behavior changes than conventional linear steering vectors.
A Geometric Calculator Inside a Neural Network
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.
Can SAEs Capture Neural Geometry?
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.
Meandering on Manifolds: The Neural Geometry of Stories Over Time
To fully understand LLM representations, we must understand how they change dynamically over the course of a prompt or conversation. We investigate these temporal dynamics with a simple case study: how do LLMs represent emotions while reading short stories, both geometrically (in activation space) and temporally (changing from sentence to sentence)?
Uncovering Neural Geometry in Vision Models With Block-Sparse Featurizers
We introduce Block-Sparse Featurizers (BSF), a family of methods to decompose a model's activations into multidimensional subspaces rather than single directions. Applied to vision models, we find that BSFs find interpretable, multidimensional features which offer a more parsimonious explanation of model internals; that those features enable fine-grained steering; and that most concepts in the models are multidimensional.
More posts coming soon!
