Скачать или смотреть Topology and Geometry of Modular Addition

In this AI Research Roundup episode, Alex discusses the paper: 'On the geometry and topology of representations: the manifolds of modular addition(2512.25060v1)' This research challenges the idea that modular addition is solved by two distinct circuits depending on model architecture. By analyzing groups of neurons as single entities, the authors show that uniform and learnable attention models actually implement the same algorithm. The study uses topological and geometric tools to reveal that these learned representations are equivalent manifolds. These findings provide strong evidence for the universality hypothesis by showing consistent internal circuits across different neural network designs. Paper URL: https://arxiv.org/pdf/2512.25060 #AI #MachineLearning #DeepLearning #ModularAddition #UniversalityHypothesis #NeuralCircuits #TopologicalDataAnalysis