Related papers: Tokenisation is NP-Complete
We propose task-adaptive tokenization as a way to adapt the generation pipeline to the specifics of a downstream task and enhance long-form generation in mental health. Inspired by insights from cognitive science, our task-adaptive…
Reducing the conditions under which a given set satisfies the stipulations of the subset sum proposition to a set of linear relationships, the question of whether a set satisfies subset sum may be answered in a polynomial number of steps by…
Large Language Models have proven highly successful at modelling a variety of tasks. However, this comes at a steep computational cost that hinders wider industrial uptake. In this paper, we present MWT: a Multi-Word Tokenizer that goes…
Digitization provides a sound and complete method to reduce the problem of verifying whether a real-time system satisfies a property under dense-time semantics to whether the same real-time system satisfies the property over discrete-time.…
Dataset distillation aims to find a synthetic training set such that training on the synthetic data achieves similar performance to training on real data, with orders of magnitude less computational requirements. Existing methods can be…
Tokenization - the practice of converting strings of characters from an alphabet into sequences of tokens over a vocabulary - is a critical step in the NLP pipeline. The use of token representations is widely credited with increased model…
We introduce Tokenization with Split Trees (ToaST), a subword tokenization method that directly optimizes compression under a new recursive inference procedure. ToaST greedily splits each pretoken into a full binary tree using precomputed…
When writing SQL queries, it is often convenient to use correlated subqueries. However, for the database engine, these correlated queries are very difficult to evaluate efficiently. The query optimizer will therefore try to eliminate the…
Given an input dataset (i.e., a set of tuples), query definability in Ontology-based Data Management (OBDM) amounts to find a query over the ontology whose certain answers coincide with the tuples in the given dataset. We refer to such a…
Sumsets are central objects in additive combinatorics. In 2007, Granville asked whether one can efficiently recognize whether a given set $S$ is a sumset, i.e. whether there is a set $A$ such that $A+A=S$. Granville suggested an algorithm…
Abduction is a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining how the world behaves it aims at finding an explanation for some observed manifestation. In this paper we focus on propositional…
Let $\Lambda^{\ast}$ be the free monoid of (finite) words over a not necessarily finite alphabet $\Lambda$, which is equipped with some (partial) order. This ordering lifts to $\Lambda^{\ast}$, where it extends the divisibility ordering of…
In this paper, we present a proof of the NP-completeness of computing the smallest Deterministic Finite Automaton (DFA) that distinguishes two given regular languages as DFAs. A distinguishing DFA is an automaton that recognizes a language…
Matrix completion is a classical problem in data science wherein one attempts to reconstruct a low-rank matrix while only observing some subset of the entries. Previous authors have phrased this problem as a nuclear norm minimization…
In this paper, we propose two new methods for solving Set Constraint Problems, as well as a potential polynomial solution for NP-Complete problems using quantum computation. While current methods of solving Set Constraint Problems focus on…
We settle the parameterized complexities of several variants of independent set reconfiguration and dominating set reconfiguration, parameterized by the number of tokens. We show that both problems are XL-complete when there is no limit on…
Vector quantization is a technique in machine learning that discretizes continuous representations into a set of discrete vectors. It is widely employed in tokenizing data representations for large language models, diffusion models, and…
The original knapsack problem is well known to be NP-complete. In a multidimensional version one have to decide whether a $p\in \N^k$ is in a sumset-sum of a set $X \subseteq \N^k$ or not. In this paper we are going to investigate a…
We prove computational intractability of variants of checkers: (1) deciding whether there is a move that forces the other player to win in one move is NP-complete; (2) checkers where players must always be able to jump on their turn is…
Clustering token-level contextualized word representations produces output that shares many similarities with topic models for English text collections. Unlike clusterings of vocabulary-level word embeddings, the resulting models more…