Related papers: Rhymes in primes
This paper introduces a greedy parser based on neural networks, which leverages a new compositional sub-tree representation. The greedy parser and the compositional procedure are jointly trained, and tightly depends on each-other. The…
This is an expository article detailing results concerning large arcs in finite projective spaces, which attempts to cover the most relevant results on arcs, simplifying and unifying proofs of known old and more recent theorems. The article…
This report presents our participation to the WSDM Cup 2026 shared task on multilingual document retrieval from English queries. The task provides a challenging benchmark for cross-lingual generalization. It also provides a natural testbed…
Abhyankar proved that every field of finite transcendence degree over $\mathbb{Q}$ or over a finite field is a homomorphic image of a subring of the ring of polynomials $\mathbb{Z}[T_1, \dots, T_n]$ (for some $n$ depending on the field). We…
We propose a model of network formation based on reinforcement learning, which can be seen as a generalization as the one proposed by Skyrms for signaling games. On a discrete graph, whose vertices represent individuals, at any time step…
Despite being trained exclusively on speech data, speech foundation models (SFMs) like Whisper have shown impressive performance in non-speech tasks such as audio classification. This is partly because speech shares some common traits with…
In this paper we get two new classes of regular sequences in the polynomial ring over the field of complex numbers.
This text was written to support a Bourbaki seminar given in January 2026 on the subject of the model theory of perfectoid fields, especially on the work of Jahnke and Kartas in their paper "Beyond the Fontaine-Wintenberger theorem", J.…
The game INFLUENCE is a scoring combinatorial game that has been introduced in 2020 by Duchene et al. It is a good representative of Milnor's universe of scoring games, i.e. games where it is never interesting for a player to miss his turn.…
Human language is known to exhibit a nested, hierarchical structure, allowing us to form complex sentences out of smaller pieces. However, many state-of-the-art neural networks models such as Transformers have no explicit hierarchical…
Andrei Okounkov received the Fields Medal at the ICM 2006 in Madrid "for his contributions bridging probability, representation theory and algebraic geometry". This is a brief account of his work.
Large language models (LLMs) have achieved remarkable success in natural language processing tasks, yet their internal knowledge structures remain poorly understood. This study examines these structures through the lens of historical…
This work is the continuation of the earlier efforts to apply the mean field approximation to the world sheet formulation of planar phi^3 theory. The previous attempts were either simple but without solid foundation or well founded but…
As Machine Learning (ML) systems becomes more ubiquitous, ensuring the fair and equitable application of their underlying algorithms is of paramount importance. We argue that one way to achieve this is to proactively cultivate public…
Professional sports enhance interaction among athletes through training groups, sponsored events and competitions. Among these, the Olympic Games represent the largest competition with a global impact, providing the participants with a…
The Music Emotion Recognition (MER) field has seen steady developments in recent years, with contributions from feature engineering, machine learning, and deep learning. The landscape has also shifted from audio-centric systems to bimodal…
Let us denote the nth difference between consecutive primes by d_n. The Prime Number Theorem clearly implies that d_n is logn on average. Paul Erd\H{o}s conjectured about 60 years ago that the sequence d_n/logn is everywhere dense on the…
I give some claims on primorial prime numbers for interested readers in number theory.
This paper revisits the solution of the word problem for $\omega$-terms interpreted over finite aperiodic semigroups, obtained by J. McCammond. The original proof of correctness of McCammond's algorithm, based on normal forms for such…
Non-cooperative and cooperative games with a very large number of players have many applications but remain generally intractable when the number of players increases. Introduced by Lasry and Lions, and Huang, Caines and Malham\'e, Mean…