Related papers: An O(1) Solution to the Prefix Sum Problem on a Sp…
Stemming or suffix stripping, an important part of the modern Information Retrieval systems, is to find the root word (stem) out of a given cluster of words. Existing algorithms targeting this problem have been developed in a haphazard…
Causal language modeling (LM) uses word history to predict the next word. BERT, on the other hand, makes use of bi-directional word information in a sentence to predict words at masked positions. While BERT is effective in sequence…
For time-frequency (TF) domain speech enhancement (SE) methods, the overlap-and-add operation in the inverse TF transformation inevitably leads to an algorithmic delay equal to the window size. However, typical causal SE systems fail to…
We present a new FPTAS for the Subset Sum Ratio problem, which, given a set of integers, asks for two disjoint subsets such that the ratio of their sums is as close to $1$ as possible. Our scheme makes use of exact and approximate…
The notions of synchronizing and partitioning sets are recently introduced variants of locally consistent parsings with great potential in problem-solving. In this paper we propose a deterministic algorithm that constructs for a given…
We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the…
Fermat's well-known factorization algorithm is based on finding a representation of natural numbers $N$ as the difference of squares. In 1895, Lawrence generalized this idea and applied it to multiples $kN$ of the original number. A…
Retrieval augmented language models have recently become the standard for knowledge intensive tasks. Rather than relying purely on latent semantics within the parameters of large neural models, these methods enlist a semi-parametric memory…
We present algorithms for length-constrained maximum sum segment and maximum density segment problems, in particular, and the problem of finding length-constrained heaviest segments, in general, for a sequence of real numbers. Given a…
Memory management is vital for LLM agents to handle long-term interaction and personalization. Most research focuses on how to organize and use memory summary, but often overlooks the initial memory extraction stage. In this paper, we argue…
We investigate some extremal problems in Fourier analysis and their connection to a problem in prime number theory. In particular, we improve the current bounds for the largest possible gap between consecutive primes assuming the Riemann…
Given a text $T$ of length $n$, we propose a deterministic online algorithm computing the sparse suffix array and the sparse longest common prefix array of $T$ in $O(c \sqrt{\lg n} + m \lg m \lg n \lg^* n)$ time with $O(m)$ words of space…
The solution of a Caputo time fractional diffusion equation of order $0<\alpha<1$ is expressed in terms of the solution of a corresponding integer order diffusion equation. We demonstrate a linear time mapping between these solutions that…
We introduce a differentiable random access memory module with $O(1)$ performance regardless of size, scaling to billions of entries. The design stores entries on points of a chosen lattice to calculate nearest neighbours of arbitrary…
We propose the first reduction-based approach to obtaining long-term memory guarantees for online learning in the sense of Bousquet and Warmuth, 2002, by reducing the problem to achieving typical switching regret. Specifically, for the…
The impressive generalization performance of modern neural networks is attributed in part to their ability to implicitly memorize complex training patterns. Inspired by this, we explore a novel mechanism to improve model generalization via…
In this paper we present algorithms for several string problems in the Congested Clique model. In the Congested Clique model, $n$ nodes (computers) are used to solve some problem. The input to the problem is distributed among the nodes, and…
Large Language Models (LLMs) have been widely adopted in commercial code completion engines, significantly enhancing coding efficiency and productivity. However, LLMs may generate code with quality issues that violate coding standards and…
Prefix-tuning, or more generally continuous prompt tuning, has become an essential paradigm of parameter-efficient transfer learning. Using a large pre-trained language model (PLM), prefix-tuning can obtain strong performance by training…
The suffix array and the suffix tree are the two most fundamental data structures for string processing. For a length-$n$ text, however, they use $\Theta(n \log n)$ bits of space, which is often too costly. To address this, Grossi and…