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Amit Sehgal

Publications and source records attributed to Amit Sehgal.

4 recordsLinked to original sources

Photonic convolutional neural network with pre-trained in situ training

Convolutional neural networks (CNNs) have transformed image processing, but the energy consumption and inference latency of electronic based implementations remain fundamental bottlenecks. These limitations have motivated the search for alternative hardware architectures beyond Complementary metal-oxide-semiconductor (CMOS) chips. Optical systems can perform linear matrix operations at the speed of light with extremely low energy dissipation, making them attractive for CNN acceleration. However, building a fully coherent photonic CNN that performs both linear and nonlinear operations and training it efficiently remains an open challenge. Here we present a fully photonic convolutional neural network (PCNN) that executes image classification in the optical domain, including convolution, max-pooling, nonlinear activation, and fully connected layers. The network achieves 94.49 percent accuracy on the MNIST dataset distributed across Mach Zehnder Interferometer (MZI) meshes, weighted Multimode Interferometer (MMI) trees, and a microring resonator based nonlinearity. A mathematically exact differentiable digital twin, enables backpropagation for ex situ pre training, reaches 97.45 percent digital accuracy. Trained phases are transferred one-to-one to the photonic hardware and refined via a gradient free algorithm that estimates the full gradient with only two forward passes. The architecture exhibits inherent robustness to non idealities, under the compound effect of propagation loss, MZI insertion loss, fabrication disorder, and thermal crosstalk. A bottom-up power analysis yields 10.83 W static chip consumption and 843 ns inference latency, translating to 220 to 330 times greater energy efficiency than state of the art electronic GPUs for single-image inference.

cs.ET

Co-Prime Order graph of a finite abelian Group and Dihedral Group

The \textbf{Co-Prime Order Graph} $Θ(G)$ of a given finite group is a simple undirected graph whose vertex set is the group $G$ itself, and any two vertexes x,y in $Θ(G)$ are adjacent if and only if $gcd(o(x),o(y))=1$ or prime. In this paper, we find a precise formula to count the degree of a vertex in the Co-Prime Order graph of a finite abelian group or Dihedral group $D_n$.We also investigate the Laplacian spectrum of the Co-Prime Order Graph $Θ(G)$ when G is finite abelian p-group, ${\mathbb{Z}_p}^t \times {\mathbb{Z}_q}^s$ or Dihedral group $D_{p^n}$. Key Words and Phrases: Co-Prime Order graph,finite abelian group,Dihedral group, Laplacian spectrum.

math.GR

The degree of a vertex in the power graph of a finite abelian group

The power graph of a given finite group is a simple undirected graph whose vertex set is the group itself, and there is an edge between any two distinct vertices if one is a power of the other. In this paper, we find a precise formula to count the degree of a vertex in the power graph of a finite abelian group of prime-power order. By using the degree formula, we give a new proof to show that the power graph of a cyclic group of prime-power order is complete. We finally determine the degree of a vertex in the power graph of a finite abelian group.

math.GR

Counting subgroups of fixed order in finite abelian groups

We use recurrence relations to derive explicit formulas for counting the number of subgroups of given order (or index) in rank 3 finite abelian p-groups and use these to derive similar formulas in few cases for rank 4. As a consequence, we answer some questions by M. T$\ddot{a}$rn$\ddot{a}$uceanu in \cite{MT} and L. T$\dot{\acute{o}}$th in \cite{LT}. We also use other methods such as the method of fundamental group lattices introduced in \cite{MT} to derive a similar counting function in a special case of arbitrary rank finite abelian p-groups.

math.GR