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A tweet describing a talk at Carnegie Mellon University that explains OpenAI's recent proof of the existence of non-sofic groups, covering concepts like Cayley graphs, LEF groups, and the use of Thompson group V and property T.
OpenAI announces research results spanning sphere packing, coding theory, group theory, quantum complexity, lattice cryptography, and extremal combinatorics, including establishing the existence of non-sofic groups and exponential improvements to high-dimensional sphere packing bounds.
Introduces Schreier-Coset Graph Rewiring, a group-theoretic method to rewire graphs for GNNs, mitigating over-squashing by improving spectral gap and effective resistance. Empirical results show significant reduction in effective resistance across learning tasks.
This paper applies graph neural networks to predict the solvability of finite groups, demonstrating an AI-driven approach to a classic problem in group theory.
This paper theoretically demonstrates that two-layer neural networks trained on group composition tasks learn spectral representations, with neurons converging to irreducible representations and achieving rotational rank-one alignment, providing a representation-theoretic account of feature learning.
This paper provides a theoretical analysis of how neural networks learn structured representations during group composition tasks, proving that training dynamics drive neurons to converge to irreducible group representations with exponential convergence rates. The work establishes a representation-theoretic account of feature learning and characterizes a low-rank compression phenomenon for matrix-valued group representations.
This exploratory study empirically measures the symmetry–data exchange rate predicted by equivariance theory on controlled C_n-symmetric tasks, finding that wrong-group constraints are actively harmful, augmentation with test-time orbit averaging matches equivariant models exactly, and the empirical exchange rate is broadly consistent with theory but statistically inconclusive. The authors emphasize the study's exploratory nature and call for registered replications.
This paper introduces a theoretical framework to analyze the generalization error of canonization methods for symmetric data, proving that Hilbert curve serialization offers polynomial growth in covering number compared to exponential growth in lexicographical sorting.