4 citations · 16 across the 12 of their papers we have counts for
13 papers
An expressivity analysis of hierarchical modelling in deep transformers via bounded-depth grammars
Vinoth Nandakumar, Qiang Qu, Pramod Thebe +2
Deep neural networks are widely believed to derive their expressive power from their ability to form \textbf{hierarchical representations}, capturing progressively more abstract an…
A theoretical model for task routing in mixture-of-expert transformers
Vinoth Nandakumar, Yongli Xiang, Yunzhi Yao +2
Mixture-of-experts (MoE) layers enable the scaling of transformer models while keeping the inference compute fixed. While task-expert specialization has been observed in empirical…
Why do CNNs excel at feature extraction? A mathematical explanation
Vinoth Nandakumar, Arush Tagade, Tongliang Liu
Over the past decade deep learning has revolutionized the field of computer vision, with convolutional neural network models proving to be very effective for image classification b…
State space models can express n-gram languages
Vinoth Nandakumar, Qiang Qu, Peng Mi +1
Recent advancements in recurrent neural networks (RNNs) have reinvigorated interest in their application to natural language processing tasks, particularly with the development of…
Categorification via blocks of modular representations II
Vinoth Nandakumar, Gufang Zhao
Bernstein, Frenkel and Khovanov have constructed a categorification of tensor products of the standard representation of using singular blocks of category $\mathc…
Irreducible Components of Exotic Springer fibres II: The Exotic Robinson-Schensted Algorithm
Vinoth Nandakumar, Daniele Rosso, Neil Saunders
Kato's exotic nilpotent cone was introduced as a substitute for the ordinary nilpotent cone of type C with cleaner properties. The geometric Robinson-Schensted correspondence is ob…
Modular representations in type A with a two-row nilpotent central character
Galyna Dobrovolska, Vinoth Nandakumar, David Yang
We study the category of representations of in positive characteristic, whose p-character is a nilpotent whose Jordan type is the two-row partition (m+n,n).…
Categorification via blocks of modular representations for sl(n)
Vinoth Nandakumar, Gufang Zhao
Bernstein, Frenkel, and Khovanov have constructed a categorification of tensor products of the standard representation of , where they use singular blocks of categ…
Irreducible components of exotic Springer fibres
Vinoth Nandakumar, Daniele Rosso, Neil Saunders
Kato introduced the exotic nilpotent cone to be a substitute for the ordinary nilpotent cone of type C with cleaner properties. Here we describe the irreducible components of exoti…
Quiver varieties and crystals in symmetrizable type via modulated graphs
Vinoth Nandakumar, Peter Tingley
Kashiwara and Saito have a geometric construction of the infinity crystal for any symmetric Kac-Moody algebra. The underlying set consists of the irreducible components of Lusztig'…
Exotic t-structures for two-block Springer fibers
Rina Anno, Vinoth Nandakumar
We study the exotic t-structure on the derived category of coherent sheaves on two-block Springer fibre (i.e. for a nilpotent matrix of type (m+n,n) in type A). The exotic t-struct…
Stability conditions for Gelfand-Kirillov subquotients of category O
Vinoth Nandakumar
Recently, Anno, Bezrukavnikov and Mirkovic have introduced the notion of a "real variation of stability conditions" (which is related to Bridgeland's stability conditions), and con…
Equivariant coherent sheaves on the exotic nilpotent cone
Vinoth Nandakumar
Let , and be Kato's exotic nilpotent cone. Following techniques used by Bezrukavnikov in [5] to establish a bijection between , the domin…