Related papers: Faster truncated integer multiplication
One of the crucial generic techniques for quantum computation is amplitude encoding. Although several approaches have been proposed, each of them often requires exponential classical-computational cost or an oracle whose explicit…
The number of n-gram features grows exponentially in n, making it computationally demanding to compute the most frequent n-grams even for n as small as 3. Motivated by our production machine learning system built on n-gram features, we ask:…
For two integers $a$ and $b$, the plum-blossom product of $a$ and $b$ is defined as the ones of the usual product of $a$ and $b$ if the ones is less than or equal to $3$, or otherwise as the ones minus $10$. Under this operation, all…
Matrix multiplication is a fundamental kernel in high performance computing. Many algorithms for fast matrix multiplication can only be applied to enormous matrices ($n>10^{100}$) and thus cannot be used in practice. Of all algorithms…
Recent trends show recognition accuracy increasing even more profoundly. Inference process of Deep Convolutional Neural Networks (DCNN) has a large number of parameters, requires a large amount of computation, and can be very slow. The…
We observe that any $T(n)$ time algorithm (quantum or classical) for several central linear algebraic problems, such as computing $\det(A)$, $tr(A^3)$, or $tr(A^{-1})$ for an $n \times n$ integer matrix $A$, yields a $O(T(n)) + \tilde…
We improve the number of $T$ gates needed for a $b$-bit approximation of a multiplexed quantum gate with $c$ controls applying $n$ single-qubit arbitrary phase rotations from $4n b+\mathcal{O}(\sqrt{cn b})$ to $2n b+\mathcal{O}(\sqrt{cn…
We consider the problem of private distributed matrix multiplication under limited resources. Coded computation has been shown to be an effective solution in distributed matrix multiplication, both providing privacy against the workers and…
We further develop the group-theoretic approach to fast matrix multiplication introduced by Cohn and Umans, and for the first time use it to derive algorithms asymptotically faster than the standard algorithm. We describe several families…
Fast approximations to matrix multiplication have the potential to dramatically reduce the cost of neural network inference. Recent work on approximate matrix multiplication proposed to replace costly multiplications with table-lookups by…
Efficient handling of sparse data is a key challenge in Computer Science. Binary convolutions, such as polynomial multiplication or the Walsh Transform are a useful tool in many applications and are efficiently solved. In the last decade,…
In this paper we give an algorithm for computing the mth base-b digit (m=1 is the least significant digit) of an integer n (actually, it finds sharp approximations to n/b^m mod 1), where n is defined as the last number in a sequence of…
Ternary Neural Networks (TNNs) have received much attention due to being potentially orders of magnitude faster in inference, as well as more power efficient, than full-precision counterparts. However, 2 bits are required to encode the…
We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra…
Asymptotically tight lower bounds are derived for the I/O complexity of a general class of hybrid algorithms computing the product of $n \times n$ square matrices combining ``\emph{Strassen-like}'' fast matrix multiplication approach with…
This paper develops fast and efficient algorithms for computing Tucker decomposition with a given multilinear rank. By combining random projection and the power scheme, we propose two efficient randomized versions for the truncated…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
We present efficient algorithms to generate a bit string in which each bit is set with arbitrary probability. By adopting a hybrid algorithm, i.e., a finite-bit density approximation with correction techniques, we achieve 3.8 times faster…
We establish new lower-bounds for the information complexity of mixed-integer convex optimization under two "bit-wise" oracles. The first oracle provides bits of first-order information in the standard coordinate model, and the second…
We show that multiplication can be done in polynomial time on a three counter machine that receives its input as the contents of two counters. The technique is generalized to functions of two variables computable by deterministic Turing…