Related papers: Tokenisation is NP-Complete

Bottom-up knowledge compilation is a paradigm for generating representations of functions by iteratively conjoining constraints using a so-called apply function. When the input is not efficiently compilable into a language - generally a…

We present a new generalization of the bin covering problem that is known to be a strongly NP-hard problem. In our generalization there is a positive constant $\Delta$, and we are given a set of items each of which has a positive size. We…

Subword tokenization is a commonly used input pre-processing step in most recent NLP models. However, it limits the models' ability to leverage end-to-end task learning. Its frequency-based vocabulary creation compromises tokenization in…

Despite the impressive quality improvements yielded by neural machine translation (NMT) systems, controlling their translation output to adhere to user-provided terminology constraints remains an open problem. We describe our approach to…

The first step in any NLP pipeline is to split the text into individual tokens. The most obvious and straightforward approach is to use words as tokens. However, given a large text corpus, representing all the words is not efficient in…

Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…

Let $G=(V,E)$ be a graph. A subset $D\subseteq V$ is a dominating set if every vertex not in $D$ is adjacent to a vertex in $D$. A dominating set $D$ is called a total dominating set if every vertex in $D$ is adjacent to a vertex in $D$.…

We study the satisfiability problem of symbolic finite automata and decompose it into the satisfiability problem of the theory of the input characters and the monadic second-order theory of the indices of accepted words. We use our…

Deep hashing has shown to be a complexity-efficient solution for the Approximate Nearest Neighbor search problem in high dimensional space. Many methods usually build the loss function from pairwise or triplet data points to capture the…

Language models typically tokenize text into subwords, using a deterministic, hand-engineered heuristic of combining characters into longer surface-level strings such as 'ing' or whole words. Recent literature has repeatedly shown the…

In the recently introduced framework of solution discovery via reconfiguration [Fellows et al., ECAI 2023], we are given an initial configuration of $k$ tokens on a graph and the question is whether we can transform this configuration into…

This paper focuses on the noiseless complete dictionary learning problem, where the goal is to represent a set of given signals as linear combinations of a small number of atoms from a learned dictionary. There are two main challenges faced…

Traditional greedy tokenization methods have been a critical step in Natural Language Processing (NLP), influencing how text is converted into tokens and directly impacting model performance. While subword tokenizers like Byte-Pair Encoding…

Tokenization is the first - and often underappreciated - layer of computation in language models. While Chain-of-Thought (CoT) prompting enables transformer models to approximate recurrent computation by externalizing intermediate steps, we…

Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even…

Deep learning technology has developed unprecedentedly in the last decade and has become the primary choice in many application domains. This progress is mainly attributed to a systematic collaboration in which rapidly growing computing…

Distribution networks with periodically repeating events often hold great promise to exploit economies of scale. Joint replenishment problems are a fundamental model in inventory management, manufacturing, and logistics that capture these…

We show that any submodular minimization (SM) problem defined on a linear constraint set with constraints having up to two variables per inequality, are 2-approximable in polynomial time. If the constraints are monotone (the two variables…

When can $n$ given numbers be combined using arithmetic operators from a given subset of $\{+, -, \times, \div\}$ to obtain a given target number? We study three variations of this problem of Arithmetic Expression Construction: when the…

Improving the explainability of the results from machine learning methods has become an important research goal. Here, we study the problem of making clusters more interpretable by extending a recent approach of [Davidson et al., NeurIPS…