Kshiteej Sheth

Insu Han, Michael Kapralov, Ekaterina Kochetkova et al.

Large language models (LLMs) have achieved impressive success, but their high memory requirements present challenges for long-context token generation. In this paper we study the streaming complexity of attention approximation, a key computational primitive underlying token generation. Our main contribution is BalanceKV, a streaming algorithm for $ε$-approximating attention computations based on geometric process for selecting a balanced collection of Key and Value tokens as per Banaszczyk's vector balancing theory. We complement our algorithm with space lower bounds for streaming attention computation. Besides strong theoretical guarantees, BalanceKV exhibits empirically validated performance improvements over existing methods, both for attention approximation and end-to-end performance on various long context benchmarks.

Piotr Indyk, Michael Kapralov, Kshiteej Sheth et al.

Motivated by the problem of fast processing of attention matrices, we study fast algorithms for computing matrix-vector products for asymmetric Gaussian Kernel matrices $K\in \mathbb{R}^{n\times n}$. $K$'s columns are indexed by a set of $n$ keys $k_1,k_2\ldots, k_n\in \mathbb{R}^d$, rows by a set of $n$ queries $q_1,q_2,\ldots,q_n\in \mathbb{R}^d $, and its $i,j$ entry is $K_{ij} = e^{-\|q_i-k_j\|_2^2/2σ^2}$ for some bandwidth parameter $σ>0$. Given a vector $x\in \mathbb{R}^n$ and error parameter $ε>0$, our task is to output a $y\in \mathbb{R}^n$ such that $\|Kx-y\|_2\leq ε\|x\|_2$ in time subquadratic in $n$ and linear in $d$. Our algorithms rely on the following modelling assumption about the matrices $K$: the sum of the entries of $K$ scales linearly in $n$, as opposed to worst case quadratic growth. We validate this assumption experimentally, for Gaussian kernel matrices encountered in various settings such as fast attention computation in LLMs. We obtain the first subquadratic-time algorithm that works under this assumption, for unrestricted vectors.

Kshiteej Sheth, Dinesh Garg, Anirban Dasgupta

Near isometric orthogonal embeddings to lower dimensions are a fundamental tool in data science and machine learning. In this paper, we present the construction of such embeddings that minimizes the maximum distortion for a given set of points. We formulate the problem as a non convex constrained optimization problem. We first construct a primal relaxation and then use the theory of Lagrange duality to create dual relaxation. We also suggest a polynomial time algorithm based on the theory of convex optimization to solve the dual relaxation provably. We provide a theoretical upper bound on the approximation guarantees for our algorithm, which depends only on the spectral properties of the dataset. We experimentally demonstrate the superiority of our algorithm compared to baselines in terms of the scalability and the ability to achieve lower distortion.

Ashish Mahabal, Kshiteej Sheth, Fabian Gieseke et al.

Astronomy light curves are sparse, gappy, and heteroscedastic. As a result standard time series methods regularly used for financial and similar datasets are of little help and astronomers are usually left to their own instruments and techniques to classify light curves. A common approach is to derive statistical features from the time series and to use machine learning methods, generally supervised, to separate objects into a few of the standard classes. In this work, we transform the time series to two-dimensional light curve representations in order to classify them using modern deep learning techniques. In particular, we show that convolutional neural networks based classifiers work well for broad characterization and classification. We use labeled datasets of periodic variables from CRTS survey and show how this opens doors for a quick classification of diverse classes with several possible exciting extensions.

Kshiteej Sheth

We propose novel methods of solving two tasks using Convolutional Neural Networks, firstly the task of generating HDR map of a static scene using differently exposed LDR images of the scene captured using conventional cameras and secondly the task of finding an optimal tone mapping operator that would give a better score on the TMQI metric compared to the existing methods. We quantitatively show the performance of our networks and illustrate the cases where our networks performs good as well as bad.