Daily Papers

We study the classic Text-to-Pattern Hamming Distances problem: given a pattern P of length m and a text T of length n, both over a polynomial-size alphabet, compute the Hamming distance between P and T[i, ., . , i+m-1] for every shift i, under the standard Word-RAM model with Theta(log n)-bit words. - We provide an O(nm) time Las Vegas randomized algorithm for this problem, beating the decades-old O(n m log m) running time [Abrahamson, SICOMP 1987]. We also obtain a deterministic algorithm, with a slightly higher O(nm(log mloglog m)^{1/4}) running time. Our randomized algorithm extends to the k-bounded setting, with running time Obig(n+nk{m}big), removing all the extra logarithmic factors from earlier algorithms [Gawrychowski and Uzna\'{n}ski, ICALP 2018; Chan, Golan, Kociumaka, Kopelowitz and Porat, STOC 2020]. - For the (1+epsilon)-approximate version of Text-to-Pattern Hamming Distances, we give an O(epsilon^{-0.93}n) time Monte Carlo randomized algorithm, beating the previous O(epsilon^{-1}n) running time [Kopelowitz and Porat, FOCS 2015; Kopelowitz and Porat, SOSA 2018]. Our approximation algorithm exploits a connection with 3SUM, and uses a combination of Fredman's trick, equality matrix product, and random sampling; in particular, we obtain new results on approximate counting versions of 3SUM and Exact Triangle, which may be of independent interest. Our exact algorithms use a novel combination of hashing, bit-packed FFT, and recursion; in particular, we obtain a faster algorithm for computing the sumset of two integer sets, in the regime when the universe size is close to quadratic in the number of elements. We also prove a fine-grained equivalence between the exact Text-to-Pattern Hamming Distances problem and a range-restricted, counting version of 3SUM.

Recently, large language models (LLMs) have emerged as a groundbreaking technology and their unparalleled text generation capabilities have sparked interest in their application to the fundamental sentence representation learning task. Existing methods have explored utilizing LLMs as data annotators to generate synthesized data for training contrastive learning based sentence embedding models such as SimCSE. However, since contrastive learning models are sensitive to the quality of sentence pairs, the effectiveness of these methods is largely influenced by the content generated from LLMs, highlighting the need for more refined generation in the context of sentence representation learning. Building upon this premise, we propose MultiCSR, a multi-level contrastive sentence representation learning framework that decomposes the process of prompting LLMs to generate a corpus for training base sentence embedding models into three stages (i.e., sentence generation, sentence pair construction, in-batch training) and refines the generated content at these three distinct stages, ensuring only high-quality sentence pairs are utilized to train a base contrastive learning model. Our extensive experiments reveal that MultiCSR enables a less advanced LLM to surpass the performance of ChatGPT, while applying it to ChatGPT achieves better state-of-the-art results. Comprehensive analyses further underscore the potential of our framework in various application scenarios and achieving better sentence representation learning with LLMs.