From the 1 of 6 linked papers with an AI index.
6 papers
New non-Euclidean neural quantum states from hyperbolic Lorentz recurrent architectures
H. L. Dao
The paper introduces new hyperbolic recurrent neural network architectures (Poincaré RNN, Lorentz RNN, Lorentz GRU) for neural quantum states and shows they consistently outperform…
Two-dimensional Hyperbolic RNN Neural Quantum State
H. L. Dao
In the first part of this work, we construct the first type of two-dimensional (2D) hyperbolic neural quantum state (NQS) in the form of the Lorentz 2DRNN (Recurrent Neural Network…
Hierarchical Reinforcement Learning for Sparse-Reward Search in Commutative Algebra
Giorgi Butbaia, Paul Orland, Coco Huang +7
Applying machine learning techniques to solving long-standing mathematical conjectures can be particularly challenging due to their extreme reward sparsity. As an illustrative exam…
Quasipolynomial behavior via constructibility in multigraded algebra
Hailong Dao, Ezra Miller, Jonathan Montaño +2
Piecewise quasipolynomial growth of Presburger counting functions combines with tame persistent homology module theory to conclude piecewise quasipolynomial behavior of constructib…
Periodicity of ideals of minors in free resolutions
Michael K. Brown, Hailong Dao, Prashanth Sridhar
We study the asymptotic behavior of the ideals of minors in minimal free resolutions over local rings. In particular, we prove that such ideals are eventually 2-periodic over compl…
Syzygies of the residue field over Golod rings
Doan Trung Cuong, Hailong Dao, David Eisenbud +3
Let be a Golod ring. We show a recurrent formula for high syzygies of interms of previous ones. In the case of embedding dimension at most , we provided complete d…