Related papers: On the equivalence of different presentations of T…

We introduce a new combinatorial object called tower diagrams and prove fundamental properties of these objects. We also introduce an algorithm that allows us to slide words to tower diagrams. We show that the algorithm is well-defined only…

Transformers are a type of neural network that have demonstrated remarkable performance across various domains, particularly in natural language processing tasks. Motivated by this success, research on the theoretical understanding of…

We obtain an upper and lower bound for the number of reduced words for a permutation in terms of the number of braid classes and the number of commutation classes of the permutation. We classify the permutations that achieve each of these…

In this paper we derive and analyze an algorithm for inverting quaternion matrices. The algorithm is an analogue of the Frobenius algorithm for the complex matrix inversion. On the theory side, we prove that our algorithm is more efficient…

Humans and many animals show remarkably adaptive behavior and can respond differently to the same input depending on their internal goals. The brain not only represents the intermediate abstractions needed to perform a computation but also…

We present here a more general version of the balanced pair algorithm. This version works in the reducible case and terminates more often than the standard algorithm. We present examples to illustrate this point. Lastly, we discuss the…

The advancements in deep learning, particularly the introduction of transformers, have been pivotal in enhancing various natural language processing (NLP) tasks. These include text-to-text applications such as machine translation, text…

Typing of lambda-terms in Elementary and Light Affine Logic (EAL, LAL, resp.) has been studied for two different reasons: on the one hand the evaluation of typed terms using LAL (EAL, resp.) proof-nets admits a guaranteed polynomial…

Transformers are widely used in natural language processing, where they consistently achieve state-of-the-art performance. This is mainly due to their attention-based architecture, which allows them to model rich linguistic relations…

Evaluating translation models is a trade-off between effort and detail. On the one end of the spectrum there are automatic count-based methods such as BLEU, on the other end linguistic evaluations by humans, which arguably are more…

In this manuscript, we show that any neural network with any activation function can be represented as a decision tree. The representation is equivalence and not an approximation, thus keeping the accuracy of the neural network exactly as…

The field of quantum computing is at an exciting time where we are constructing novel hardware, evaluating algorithms, and finding out what works best. As qubit technology grows and matures, we need to be ready to design and program larger…

Static program analysis is a valuable tool for any programming language that people write programs in. The prevalence of scripting languages in the world suggests programming language interpreters are relatively easy to write. Users of…

We prove that orthogonal constructor term rewrite systems and lambda-calculus with weak (i.e., no reduction is allowed under the scope of a lambda-abstraction) call-by-value reduction can simulate each other with a linear overhead. In…

This paper aims to provide an analysis of what it means when we say that a pair of theories, very generously construed, are equivalent in the sense that they are interdefinable. With regard to theories articulated in first order logic, we…

We consider automatically identifying the defined term within a mathematical definition from the text of an academic article. Inspired by the development of transformer-based natural language processing applications, we pose the problem as…

Text simplification aims at reducing the lexical, grammatical and structural complexity of a text while keeping the same meaning. In the context of machine translation, we introduce the idea of simplified translations in order to boost the…

Neural machine translation is a recently proposed approach to machine translation. Unlike the traditional statistical machine translation, the neural machine translation aims at building a single neural network that can be jointly tuned to…

Batch normalization has become ubiquitous in many state-of-the-art nets. It accelerates training and yields good performance results. However, there are various other alternatives to normalization, e.g. orthonormalization. The objective of…

With the wide spread of deep learning and gradient descent inspired optimization algorithms, differentiable programming has gained traction. Nowadays it has found applications in many different areas as well, such as scientific computing,…