Master's Thesis: Mechanistic Interpretability with Singular Value Decompositions

Background and Motivation Activation functions are a fundamental part of machine learning, as they introduce a non-linear component and thus make it possible to approximate arbitrary functions. In practice, these functions can have several million dimensions per layer of a neural network, which lead to the model’s prediction layer by layer through linear combinations and subsequent activation. Algebraically and numerically, it is also possible to transform the matrices in such a way that the products remain the same, while the factors are chosen cleverly so that individual features can be emphasized more strongly. Goal The thesis will investigate how exactly methods of mechanistic interpretability relate to the vector spaces of the activations, and whether, for example, safety features can be strengthened or weakened through targeted transformation of the matrices. Results The thesis should show whether manual transformations of the parameters are possible in principle, and whether a careful choice of bases, for example through orthogonalization, yields linear combinations that allow individual capabilities to be influenced in a targeted way.