9 citations · 14 across the 5 of their papers we have counts for
8 papers
DynMuon: A Dynamic Spectral Shaping View of Muon
Fangzhou Wu, Rikhav Shah, Sandeep Silwal +1
In recent years, Muon has emerged as the dominant method for training large language models, and transformers more broadly. The essential difference, when compared to standard grad…
Even Faster Kernel Matrix Linear Algebra via Density Estimation
Rikhav Shah, Sandeep Silwal, Haike Xu
This paper studies the use of kernel density estimation (KDE) for linear algebraic tasks involving the kernel matrix of a collection of data points in . In particu…
Achieving the Highest Possible Elo Rating
Rikhav Shah
Elo rating systems measure the approximate skill of each competitor in a game or sport. A competitor's rating increases when they win and decreases when they lose. Increasing one's…
A Spectral Approach to Polytope Diameter
Hariharan Narayanan, Rikhav Shah, Nikhil Srivastava
We prove upper bounds on the graph diameters of polytopes in two settings. The first is a worst-case bound for polytopes defined by integer constraints in terms of the height of th…
Smoothed analysis of the condition number under low-rank perturbations
Rikhav Shah, Sandeep Silwal
Let be an arbitrary by matrix of rank . We study the condition number of plus a \emph{low-rank} perturbation where are by random Gaussian…
Determinants of binary matrices achieve every integral value up to
Rikhav Shah
This work shows that the smallest natural number that is not the determinant of some binary matrix is at least for . That same quantity natura…
Using Dimensionality Reduction to Optimize t-SNE
Rikhav Shah, Sandeep Silwal
t-SNE is a popular tool for embedding multi-dimensional datasets into two or three dimensions. However, it has a large computational cost, especially when the input data has many d…
Directed Random Geometric Graphs
Jesse Michel, Sushruth Reddy, Rikhav Shah +2
Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many other…