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Hidden Activations are not Enough I: Knowledge Matrices as Higher Representations
Marco Armenta
We study the knowledge matrix of a trained feedforward network as a higher representation of its inputs. A network is a pair , a thin representation of its quiver and an…
The Serre--Hochschild plane of a finite-dimensional algebra
Marco Armenta
For a finite-dimensional algebra over a field we organize the Hochschild cohomology of with coefficients in all derived tensor powers of the Serre bimodule $ω=\D A$ into a…
Protected corners and a trichotomy for Han's conjecture
Marco Armenta
Han's conjecture predicts that a finite-dimensional algebra with eventually vanishing Hochschild homology has finite global dimension. In the tau-Hochschild framework of Cibils, La…
-Hochschild (co)homology, the square of the Serre bimodule, and the Coxeter automorphism of the Tamarkin--Tsygan calculus
Marco Armenta
We relate two recent enrichments of the Hochschild theory of a finite-dimensional algebra $\Lm$: the -Hochschild (co)homology of Cibils, Lanzilotta, Marcos and Solotar, built fr…
The Coxeter transformation as an automorphism of the Tamarkin--Tsygan calculus
Marco Armenta
Let be a finite-dimensional algebra over a field $\kk$. We show that the Auslander--Reiten bimodule $\ar_A:=\D A[-1]$ is central in the derived Picard group of and that, wh…