Related papers: An Introduction to Motivic Integration
These notes are meant to provide a rapid introduction to triangulated categories. We start with the definition of an additive category and end with a glimps of tilting theory. Some exercises are included.
Despite the recent progress in deep learning and reinforcement learning, transfer and generalization of skills learned on specific tasks is very limited compared to human (or animal) intelligence. The lifelong, incremental building of…
There is a growing interest and literature on intrinsic motivations and open-ended learning in both cognitive robotics and machine learning on one side, and in psychology and neuroscience on the other. This paper aims to review some…
We prove that the moduli spaces of twisted $\mathrm{SL}_n$ and $\mathrm{PGL}_n$-Higgs bundles on a smooth projective curve have the same (stringy) class in the Grothendieck ring of rational Chow motives. On the level of Hodge numbers this…
Interacting particles on graphs are routinely used to study magnetic behaviour in physics, disease spread in epidemiology, and opinion dynamics in social sciences. The literature on mean-field approximations of such systems for large graphs…
These notes are the write-up of my 2008 PCMI lectures on multiplier ideals. They aim to give an introduction to the algebro-geometric side of the theory, with an emphasis on its global aspects. The focus is on concrete examples and…
This is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic motivations, coming from discrete probability,…
This is a non-standard paper, containing some problems, mainly in model theory, which I have, in various degrees, been interested in. Sometimes with a discussion on what I have to say; sometimes, of what makes them interesting to me,…
Let X be a smooth projective curve over a field of characteristic zero. We calculate the motivic class of the moduli stack of semistable Higgs bundles on X. We also calculate the motivic class of the moduli stack of vector bundles with…
We regard explanations as a blending of the input sample and the model's output and offer a few definitions that capture various desired properties of the function that generates these explanations. We study the links between these…
The apparatus of motivic stable homotopy theory provides a notion of Euler characteristic for smooth projective varieties, valued in the Grothendieck-Witt ring of the base field. Previous work of the first author and recent work of…
Well-known principles of induction include monotone induction and different sorts of non-monotone induction such as inflationary induction, induction over well-founded sets and iterated induction. In this work, we define a logic formalizing…
The paper gives a soundness and completeness proof for the implicative fragment of intuitionistic calculus with respect to the semantics of computability logic, which understands intuitionistic implication as interactive algorithmic…
We use dualities of quiver moduli induced by reflection functors to describe generating series of motives of Kronecker moduli spaces of central slope as solutions of algebraic and q-difference equations.
This monograph aims at providing an introduction to key concepts, algorithms, and theoretical results in machine learning. The treatment concentrates on probabilistic models for supervised and unsupervised learning problems. It introduces…
"Intrinsic motivation" refers to the capacity for intelligent systems to be motivated endogenously, i.e. by features of agential architecture itself rather than by learned associations between action and reward. This paper views active…
This is my habilitation thesis. As the tradition wants, I tried to give an introduction of my field of research. I post it on the ArXiv with the hope it can be useful to young researchers looking for a short and friendly text on…
This article gives an overview of recent results on the relation between quantum field theory and motives, with an emphasis on two different approaches: a "bottom-up" approach based on the algebraic geometry of varieties associated to…
We extend the definitions of upper and lower valuations on partially ordered sets, and consider the metrics they induce, in particular the metrics available (or not) based on the logarithms of such valuations. Motivating applications in…
This article is based on lecture notes for the Marie Curie Training school "Initial Training on Numerical Methods for Active Matter". It provides an introductory overview of modeling approaches for active matter and is primarily targeted at…