Towards Worst-Case Guarantees with Scale-Aware Interpretability

Neural networks organize information according to the hierarchical, multi-scale structure of natural data. Methods to interpret model internals should be similarly scale-aware, explicitly tracking how features compose across resolutions and guaranteeing bounds on the influence of fine-grained structure that is discarded as irrelevant noise. We posit that the renormalisation framework from physics can meet this need by offering technical tools that can overcome limitations of current methods. Moreover, relevant work from adjacent fields has now matured to a point where scattered research threads can be synthesized into practical, theory-informed tools. To combine these threads in an AI safety context, we propose a unifying research agenda -- \emph{scale-aware interpretability} -- to develop formal machinery and interpretability tools that have robustness and faithfulness properties supported by statistical physics.

Mathematical Models of Computation in Superposition

Superposition -- when a neural network represents more ``features'' than it has dimensions -- seems to pose a serious challenge to mechanistically interpreting current AI systems. Existing theory work studies \emph{representational} superposition, where superposition is only used when passing information through bottlenecks. In this work, we present mathematical models of \emph{computation} in superposition, where superposition is actively helpful for efficiently accomplishing the task. We first construct a task of efficiently emulating a circuit that takes the AND of the $\binom{m}{2}$ pairs of each of $m$ features. We construct a 1-layer MLP that uses superposition to perform this task up to $\varepsilon$-error, where the network only requires $\tilde{O}(m^{\frac{2}{3}})$ neurons, even when the input features are \emph{themselves in superposition}. We generalize this construction to arbitrary sparse boolean circuits of low depth, and then construct ``error correction'' layers that allow deep fully-connected networks of width $d$ to emulate circuits of width $\tilde{O}(d^{1.5})$ and \emph{any} polynomial depth. We conclude by providing some potential applications of our work for interpreting neural networks that implement computation in superposition.