Related papers: A Tighter Complexity Analysis of SparseGPT
We present an optimized single-precision implementation of the Sparse Approximate Matrix Multiply (\SpAMM{}) [M. Challacombe and N. Bock, arXiv {\bf 1011.3534} (2010)], a fast algorithm for matrix-matrix multiplication for matrices with…
Deep Learning (DL) acceleration support in CPUs has recently gained a lot of traction, with several companies (Arm, Intel, IBM) announcing products with specialized matrix engines accessible via GEMM instructions. CPUs are pervasive and…
In prior work, Gupta et al. (SPAA 2022) presented a distributed algorithm for multiplying sparse $n \times n$ matrices, using $n$ computers. They assumed that the input matrices are uniformly sparse--there are at most $d$ non-zeros in each…
Let $G = (V, E)$ be an $m_1 \times \ldots \times m_k$ grid. Assuming that each $v \in V$ is occupied by a robot and a robot may move to a neighboring vertex in a step via synchronized rotations along cycles of $G$, we first establish that…
Recent work on simultaneous trajectory estimation and mapping (STEAM) for mobile robots has found success by representing the trajectory as a Gaussian process. Gaussian processes can represent a continuous-time trajectory, elegantly handle…
We give two algorithms for output-sparse matrix multiplication (OSMM), the problem of multiplying two $n \times n$ matrices $A, B$ when their product $AB$ is promised to have at most $O(n^{\delta})$ many non-zero entries for a given value…
We present a nearly-linear time algorithm for finding a minimum-cost flow in planar graphs with polynomially bounded integer costs and capacities. The previous fastest algorithm for this problem is based on interior point methods (IPMs) and…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
Due to its optimality on a single machine for the problem of minimizing average flow time, Shortest-Remaining-Processing-Time (\srpt) appears to be the most natural algorithm to consider for the problem of minimizing average flow time on…
Structured dilated attention has an appealing inference-time efficiency knob: it reduces the FLOPs of attention and the KV cache size by a factor of the dilation size D, while preserving long-range connectivity. While prior work studies it…
An efficient attention implementation is essential for large models due to its quadratic time complexity. Fortunately, attention commonly exhibits sparsity, i.e., many values in the attention map are near zero, allowing for the omission of…
We improve the current best running time value to invert sparse matrices over finite fields, lowering it to an expected $O\big(n^{2.2131}\big)$ time for the current values of fast rectangular matrix multiplication. We achieve the same…
We consider the problem of finding a dense submatrix of a matrix with i.i.d. Gaussian entries, where density is measured by average value. This problem arose from practical applications in biology and social sciences…
In this paper, we study the $d$-dimensional update-query problem. We provide lower bounds on update and query running times, assuming a long-standing conjecture on min-plus matrix multiplication, as well as algorithms that are close to the…
We perform forward error analysis for a large class of recursive matrix multiplication algorithms in the spirit of [D. Bini and G. Lotti, Stability of fast algorithms for matrix multiplication, Numer. Math. 36 (1980), 63--72]. As a…
The classic algorithm [Papadimitriou, J.ACM '81] for IPs has a running time $n^{O(m)}(m\cdot\max\{\Delta,\|\textbf{b}\|_{\infty}\})^{O(m^2)}$, where $m$ is the number of constraints, $n$ is the number of variables, and $\Delta$ and…
A major enterprise in compressed sensing and sparse approximation is the design and analysis of computationally tractable algorithms for recovering sparse, exact or approximate, solutions of underdetermined linear systems of equations. Many…
Latent position models (LPMs) are a large and popular class of models for random graphs. However, fitting Bayesian LPMs is computationally challenging - computing the likelihood even once takes time that is quadratic in the number of…
In this paper, we consider the following inverse maintenance problem: given $A \in \mathbb{R}^{n\times d}$ and a number of rounds $r$, we receive a $n\times n$ diagonal matrix $D^{(k)}$ at round $k$ and we wish to maintain an efficient…
Greedy algorithms for minimizing L0-norm of sparse decomposition have profound application impact on many signal processing problems. In the sparse coding setup, given the observations $\mathrm{y}$ and the redundant dictionary…