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Publications
Uncovering a Universal Abstract Algorithm for Modular Addition in Neural Networks
We propose a testable universality hypothesis, asserting that seemingly disparate neural network solutions observed in the simple task of mo… (see more)dular addition are unified under a common abstract algorithm. While prior work interpreted variations in neuron-level representations as evidence for distinct algorithms, we demonstrate - through multi-level analyses spanning neurons, neuron clusters, and entire networks - that multilayer perceptrons and transformers universally implement the abstract algorithm we call the approximate Chinese Remainder Theorem. Crucially, we introduce approximate cosets and show that neurons activate exclusively on them. Furthermore, our theory works for deep neural networks (DNNs). It predicts that universally learned solutions in DNNs with trainable embeddings or more than one hidden layer require only O(log n) features, a result we empirically confirm. This work thus provides the first theory-backed interpretation of multilayer networks solving modular addition. It advances generalizable interpretability and opens a testable universality hypothesis for group multiplication beyond modular addition.
We introduce a machine learning approach to determine the transition dynamics of silicon atoms on a single layer of carbon atoms, when stimu… (see more)lated by the electron beam of a scanning transmission electron microscope (STEM). Our method is data-centric, leveraging data collected on a STEM. The data samples are processed and filtered to produce symbolic representations, which we use to train a neural network to predict transition probabilities. These learned transition dynamics are then leveraged to guide a single silicon atom throughout the lattice to pre-determined target destinations. We present empirical analyses that demonstrate the efficacy and generality of our approach.
