Related papers: Tokenisation is NP-Complete
The problem Defensive $\delta$-Covering, for some covering range $\delta > 0$, is a continuous facility location problem on undirected graphs where all edges have unit length. It is a generalization of Defensive Dominating Set and…
This work aims to produce translations that convey source language content at a formality level that is appropriate for a particular audience. Framing this problem as a neural sequence-to-sequence task ideally requires training triplets…
Mathematical optimization, although often leading to NP-hard models, is now capable of solving even large-scale instances within reasonable time. However, the primary focus is often placed solely on optimality. This implies that while…
Kernelization is a general theoretical framework for preprocessing instances of NP-hard problems into (generally smaller) instances with bounded size, via the repeated application of data reduction rules. For the fundamental Max Cut…
We continue the investigation of problems concerning correlation clustering or clustering with qualitative information, which is a clustering formulation that has been studied recently. The basic setup here is that we are given as input a…
Neural machine translation with millions of parameters is vulnerable to unfamiliar inputs. We propose Token Drop to improve generalization and avoid overfitting for the NMT model. Similar to word dropout, whereas we replace dropped token…
We sketch a tentative proof of P-completeness for the $\beta$-convertibility problem on untyped planar (a.k.a. ordered or non-commutative) $\lambda$-terms.
Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new…
Correlation clustering is a technique for aggregating data based on qualitative information about which pairs of objects are labeled 'similar' or 'dissimilar.' Because the optimization problem is NP-hard, much of the previous literature…
A $k$-attractor is a combinatorial object unifying dictionary-based compression. It allows to compare the repetitiveness measures of different dictionary compressors such as Lempel-Ziv 77, the Burrows-Wheeler transform, straight line…
In this thesis, we propose a multitask learning based method to improve Neural Sign Language Translation (NSLT) consisting of two parts, a tokenization layer and Neural Machine Translation (NMT). The tokenization part focuses on how Sign…
The class of known constraint automata for which the constrained synchronization problem is in NP all admit a special form. In this work, we take a closer look at them. We characterize a wider class of constraint automata that give…
A proper labeling of a graph is an assignment of integers to some elements of a graph, which may be the vertices, the edges, or both of them, such that we obtain a proper vertex coloring via the labeling subject to some conditions. The…
Subword regularization, used widely in NLP, improves model performance by reducing the dependency on exact tokenizations, augmenting the training corpus, and exposing the model to more unique contexts during training. BPE and MaxMatch, two…
In this note we show that pattern matching in permutations is polynomial time reducible to pattern matching in set partitions. In particular, pattern matching in set partitions is NP-Complete.
We give a new expression of the multiple harmonic sum, which serves as a refinement of the iterated integral expression of the multiple zeta value, and prove it using the so-called connected sum method. Based on this fact, by taking two…
Let A be a finite or countable alphabet and let $\theta$ be a literal (anti-)automorphism onto A * (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under…
Data representation remains a fundamental challenge in machine learning, particularly when adapting sequence-based architectures like Transformers and Large Language Models (LLMs) for structured tabular data. Existing methods often fail to…
In many-particle problems involving interacting fermions or bosons, the most natural language for expressing the Hamiltonian, the observables, and the basis states is the language of the second-quantization operators. It thus appears…
We prove that the problem of counting the number of colourings of the vertices of a graph with at most two colours, such that the colour classes induce connected subgraphs is #P-complete. We also show that the closely related problem of…