Luke Sciarappa
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View article: Neural Group Actions
Neural Group Actions Open
We introduce an algorithm for designing Neural Group Actions, collections of deep neural network architectures which model symmetric transformations satisfying the laws of a given finite group. This generalizes involutive neural networks $…
View article: Computable decision making on the reals and other spaces
Computable decision making on the reals and other spaces Open
Though many safety-critical software systems use floating point to represent real-world input and output, the mathematical specifications of these systems' behaviors use real numbers. Significant deviations from those specifications can ca…
View article: Computable decision making on the reals and other spaces via partiality and nondeterminism
Computable decision making on the reals and other spaces via partiality and nondeterminism Open
Though many safety-critical software systems use floating point to represent real-world input and output, programmers usually have idealized versions in mind that compute with real numbers. Significant deviations from the ideal can cause e…
View article: Simple commutative algebras in Deligne's categories Rep($S_t$)
Simple commutative algebras in Deligne's categories Rep($S_t$) Open
We show that in the Deligne categories $\mathrm{Rep}(S_t)$ for $t$ a transcendental number, the only simple algebra objects are images of simple algebras in the category of representations of a symmetric group under a canonical induction f…