7 citations · 11 across the 10 of their papers we have counts for
11 papers
Product-Aware Deterministic Rounding for Quantized Matrix Multiplication
Piyush Sao, Narasinga Miniskar, Pedro Valero-Lara +2
Scalar rounding decisions interact through matrix multiplication. We study deterministic product-aware rounding after scales, clipping bounds, and grids are fixed, with each active…
A Nuclear-Norm Lower Bound for Dithered Scalar Quantization of Matrix Products
Piyush Sao, Narasinga Miniskar, Pedro Valero-Lara +2
We consider the problem of minimizing error in quantized matrix multiplication . Scalar quantization of the factors introduces rounding errors whose scale depends on the maxi…
Exact Limits of Random Projections for Preserving Geometry: Distance Recovery, Nearest-Neighbor Rankings, and Covariance Shape in Gaussian Models
Piyush Sao
The Johnson-Lindenstrauss (JL) lemma guarantees that a random projection of points to dimensions preserves pairwise squared distances within relat…
A Second-Moment Theory for Floating-Point Reduction Trees
Piyush Sao, Narasinga Miniskar, Pedro Valero-Lara +2
Summation error depends on partial-sum order, which standard worst-case bounds omit. To capture this dependence, we derive an exact mean-square error (MSE) recurrence for a binary…
Contraction-Gauge Preconditioning for Quantized Matrix Multiplication
Piyush Sao, Narasinga Miniskar, Pedro Valero-Lara +2
We study low-precision computation of C=AB with both factors quantized. We derive an exact finite-dimensional identity for the expected squared product error under independent, zer…
Ghosts of Softmax: Complex Singularities That Limit Safe Step Sizes in Cross-Entropy
Piyush Sao
Optimization analyses for cross-entropy training rely on local Taylor models of the loss to predict whether a proposed step will decrease the objective. These surrogates are reliab…
Fast Evaluation of Truncated Neumann Series by Low-Product Radix Kernels
Piyush Sao
Truncated Neumann series are used in approximate matrix inversion and polynomial preconditioning. In dense settings, matrix-matrix products dominate the…
What Trace Powers Reveal About Log-Determinants: Closed-Form Estimators, Certificates, and Failure Modes
Piyush Sao
Computing for large symmetric positive definite matrices arises in Gaussian process inference and Bayesian model comparison. Standard methods combine matrix-vector pr…
Interface for Sparse Linear Algebra Operations
Ahmad Abdelfattah, Willow Ahrens, Hartwig Anzt +32
The standardization of an interface for dense linear algebra operations in the BLAS standard has enabled interoperability between different linear algebra libraries, thereby boosti…
PANDORA: A Parallel Dendrogram Construction Algorithm for Single Linkage Clustering on GPU
Piyush Sao, Andrey Prokopenko, Damien Lebrun-Grandié
This paper presents \pandora, a novel parallel algorithm for efficiently constructing dendrograms for single-linkage hierarchical clustering, including \hdbscan. Traditional dendro…
A single-tree algorithm to compute the Euclidean minimum spanning tree on GPUs
Andrey Prokopenko, Piyush Sao, Damien Lebrun-Grandié
Computing the Euclidean minimum spanning tree (EMST) is a computationally demanding step of many algorithms. While work-efficient serial and multithreaded algorithms for computing…