Can the geometry of thought reveal how alignment works?
I develop differential-geometric frameworks for understanding how large language models encode, transform, and ultimately suppress beliefs — with a focus on mechanistic interpretability and AI alignment. The Torsional Belief Vector Field (TBVF), models transformer hidden states as discrete curves on a Riemannian belief manifold equipped with a Cartan torsion connection. This reveals, for the first time, where and how DPO/RLHF alignment geometrically reshapes model internals — creating what I call "brake layers": localized, geometrically distinct suppression mechanisms.
I am actively seeking fully-funded PhD positions at world-class research universities in mechanistic interpretability, geometric deep learning, and AI alignment.
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Torsional Belief Vector Field treats each transformer layer's hidden state as a point on a high-dimensional Riemannian manifold with Fisher-Rao metric. The torsion tensor — antisymmetric component of cross-layer covariance — measures rotational mismatch between consecutive belief updates. |
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