School of Mathematics and Statistics - Research Publications

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Deep Learning Is Singular, and That's Good

Wei, S ; Murfet, D ; Gong, M ; Li, H ; Gell-Redman, J ; Quella, T (IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2023-12)

In singular models, the optimal set of parameters forms an analytic set with singularities, and a classical statistical inference cannot be applied to such models. This is significant for deep learning as neural networks are singular, and thus, "dividing" by the determinant of the Hessian or employing the Laplace approximation is not appropriate. Despite its potential for addressing fundamental issues in deep learning, a singular learning theory appears to have made little inroads into the developing canon of a deep learning theory. Via a mix of theory and experiment, we present an invitation to the singular learning theory as a vehicle for understanding deep learning and suggest an important future work to make the singular learning theory directly applicable to how deep learning is performed in practice.
On conformal field theories based on takiff superalgebras

Quella, T (IOP Publishing, 2020-07-01)

Abstract We revisit the construction of conformal field theories based on Takiff algebras and superalgebras that was introduced by Babichenko and Ridout. Takiff superalgebras can be thought of as truncated current superalgebras with Z -grading which arise from taking p copies of a Lie superalgebra g and placing them in the degrees s = 0 , … , p − 1 . Using suitably defined non-degenerate invariant forms we show that Takiff superalgebras give rise to families of conformal field theories with central charge c = p sdim g . The resulting conformal field theories are defined in the standard way, i.e. they lend themselves to a Lagrangian description in terms of a WZW model and their chiral energy momentum tensor is the one obtained naturally from the usual Sugawara construction. In view of their intricate representation theory they provide interesting examples of conformal field theories.
Asymmetrically gauged WZNW models

Quella, T ; Schomerus, V (WILEY-V C H VERLAG GMBH, 2003)

Abstract Many interesting exactly solvable backgrounds can be obtained by gauging WZNW models asymmetrically. These include the base of the conifold and the time dependent Nappi‐Witten background in which a 3‐dimensional universe passes through a series of big‐bang big‐crunch singularities. In this short note we review recent results on the conformal field theory description of asymmetric cosets. In particular, we present formulas for their bulk modular invariant partition functions and for a large number of D‐brane boundary states.
Non-chiral current algebras for deformed supergroup WZW models

Konechny, A ; Quella, T (SPRINGER, 2011-03)
Conformal superspace σ-models

Mitev, V ; Quella, T ; Schomerus, V (ELSEVIER, 2011-09)
Infinite matrix product states for long-range SU(N) spin models

Bondesan, R ; Quella, T (ELSEVIER, 2014-09)
An algorithm for twisted fusion rules

Quella, T ; Runkel, I ; Schweigert, C (International Press of Boston, 2002-01-01)
The abelian cosets of the Heisenberg group

D'Appollonio, G ; Quella, T (SPRINGER, 2007-11)
The diagonal cosets of the Heisenberg group

D'Appollonio, G ; Quella, T (SPRINGER, 2008-05)
Topological and symmetry broken phases of Z_N parafermions in one dimension

Bondesan, R ; Quella, T (IOP PUBLISHING LTD, 2013-10)

School of Mathematics and Statistics - Research Publications

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