Related papers: Subtraction makes computing integers faster
We propose efficient algorithms for enumerating maximal common subsequences (MCSs) of two strings. Efficiency of the algorithms are estimated by the preprocessing-time, space, and delay-time complexities. One algorithm prepares a…
In this paper we review main ideas mentioned in several other papers which talk about optimization techniques used by compilers. Here we focus on loop unrolling technique and its effect on power consumption, energy usage and also its impact…
Over the past decade, there has been increasing interest in distributed/parallel algorithms for processing large-scale graphs. By now, we have quite fast algorithms -- usually sublogarithmic-time and often $poly(\log\log n)$-time, or even…
We consider computing the longest palindrome in a text of length $n$ in the streaming model, where the characters arrive one-by-one, and we do not have random access to the input. While computing the answer exactly using sublinear memory is…
Matrix multiplication is the foundation from much of the success from high performance technologies like deep learning, scientific simulations, and video graphics. High level programming languages like Python and R rely on highly optimized…
In modern graph analytics, the shortest path is a fundamental concept. Numerous \rrev{recent works} concentrate mostly on the distance of these shortest paths. Nevertheless, in the era of betweenness analysis, the counting of the shortest…
The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…
Finding an Approximate Longest Common Substring (ALCS) within a given set $S=\{s_1,s_2,\ldots,s_m\}$ of $m \ge 2$ strings is a key problem in computational biology, such as identifying related mutations across multiple genetic sequences. We…
We study the Parallel Task Scheduling problem $Pm|size_j|C_{\max}$ with a constant number of machines. This problem is known to be strongly NP-complete for each $m \geq 5$, while it is solvable in pseudo-polynomial time for each $m \leq 3$.…
Algebraic Subspace Clustering (ASC) is a simple and elegant method based on polynomial fitting and differentiation for clustering noiseless data drawn from an arbitrary union of subspaces. In practice, however, ASC is limited to…
We consider the following "partition and sum" operation on a natural number: Treating the number as a long string of digits insert several plus signs in between some of the digits and carry out the indicated sum. This results in a smaller…
Transformers are widely deployed in large language models (LLMs), yet most models still fail on basic arithmetic tasks such as multidigit addition. In contrast, we show that small transformers trained from scratch can solve n-digit addition…
Finding the minimum of a multivariate real polynomial is a well-known hard problem with various applications. We present a polynomial time algorithm to approximate such lower bounds via sums of nonnegative circuit polynomials (SONC). As a…
The brain efficiently performs nonlinear computations through its intricate networks of spiking neurons, but how this is done remains elusive. While nonlinear computations can be implemented successfully in spiking neural networks, this…
This paper analyzes the effects of approximate multiplication when performing inferences on deep convolutional neural networks (CNNs). The approximate multiplication can reduce the cost of the underlying circuits so that CNN inferences can…
Data structures that allow efficient distance estimation (distance oracles, distance sketches, etc.) have been extensively studied, and are particularly well studied in centralized models and classical distributed models such as CONGEST. We…
Making large language models (LLMs) more efficient in memory, latency, and serving cost is crucial for edge deployment, interactive applications, and sustainable inference at scale. Pruning is a promising technique, but existing pruning…
In real-world applications, it is important for machine learning algorithms to be robust against data outliers or corruptions. In this paper, we focus on improving the robustness of a large class of learning algorithms that are formulated…
Speculative decoding (SD) accelerates language model inference by drafting tokens from a cheap proposal model and verifying them against an expensive target model via rejection sampling. Because rejection truncates the draft block at the…
A caveat to many applications of the current Deep Learning approach is the need for large-scale data. One improvement suggested by Kolmogorov Complexity results is to apply the minimum description length principle with computationally…