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Valentina Di Proietto

Publications and source records attributed to Valentina Di Proietto.

7 recordsLinked to original sources
arXiv2024

CARMIL: Context-Aware Regularization on Multiple Instance Learning models for Whole Slide Images

Multiple Instance Learning (MIL) models have proven effective for cancer prognosis from Whole Slide Images. However, the original MIL formulation incorrectly assumes the patches of the same image to be independent, leading to a loss of spatial context as information flows through the network. Incorporating contextual knowledge into predictions is particularly important given the inclination for cancerous cells to form clusters and the presence of spatial indicators for tumors. State-of-the-art methods often use attention mechanisms eventually combined with graphs to capture spatial knowledge. In this paper, we take a novel and transversal approach, addressing this issue through the lens of regularization. We propose Context-Aware Regularization for Multiple Instance Learning (CARMIL), a versatile regularization scheme designed to seamlessly integrate spatial knowledge into any MIL model. Additionally, we present a new and generic metric to quantify the Context-Awareness of any MIL model when applied to Whole Slide Images, resolving a previously unexplored gap in the field. The efficacy of our framework is evaluated for two survival analysis tasks on glioblastoma (TCGA GBM) and colon cancer data (TCGA COAD).

cs.CV↗
arXiv2024

Drinfeld-Lau Descent over Fibered Categories

Let ${\mathcal X}$ be a category fibered in groupoids over a finite field $\mathbb{F}_q$, and let $k$ be an algebraically closed field containing $\mathbb{F}_q$. Denote by $ϕ_k\colon {\mathcal X}_k\to {\mathcal X}_k$ the arithmetic Frobenius of ${\mathcal X}_k/k$ and suppose that ${\mathcal M}$ is a stack over $\mathbb{F}_q$ (not necessarily in groupoids). Then there is a natural functor $α_{{\mathcal M},{\mathcal X}}\colon{\mathcal M}({\mathcal X})\to{\mathcal M}({\mathbf D_k}({\mathcal X}))$, where ${\mathcal M}({\mathbf D_k}({\mathcal X}))$ is the category of $ϕ_k$-invariant maps ${\mathcal X}_k\to {\mathcal M}$. A version of Drinfeld's lemma states that if ${\mathcal X}$ is a projective scheme and ${\mathcal M}$ is the stack of quasi-coherent sheaves of finite presentation, then $α_{{\mathcal M},{\mathcal X}}$ is an equivalence. We extend this result in several directions. For proper algebraic stacks or affine gerbes ${\mathcal X}$, we prove Drinfeld's lemma and deduce that $α_{{\mathcal M},{\mathcal X}}$ is an equivalence for very general algebraic stacks ${\mathcal M}$. For arbitrary ${\mathcal X}$, we show that $α_{{\mathcal M},{\mathcal X}}$ is an equivalence when ${\mathcal M}$ is the stack of immersions, the stack of quasi-compact separated étale morphisms or any quasi-separated Deligne-Mumford stack with separated diagonal.

math.AG↗
arXiv2021

A crystalline incarnation of Berthelot's conjecture and Künneth formula for isocrystals

Berthelot's conjecture predicts that under a proper and smooth morphism of schemes in characteristic $p$, the higher direct images of an overconvergent $F$-isocrystal are overconvergent $F$-isocrystals. In this paper we prove that this is true for crystals up to isogeny. As an application we prove a Künneth formula for the crystalline fundamental group.

math.NT↗
arXiv2020

Comparison of relatively unipotent log de Rham fundamental groups

In this paper, we prove compatibilities of various definitions of relatively unipotent log de Rham fundamental groups for certain proper log smooth integral morphisms of fine log schemes of characteristic zero. Our proofs are purely algebraic. As an application, we give a purely algebraic calculation of the monodromy action on the unipotent log de Rham fundamental group of a stable log curve. As a corollary we give a purely algebraic proof to the transcendental part of Andreatta-Iovita-Kim's article: obtaining in this way a complete algebraic criterion for good reduction for curves.

math.NT↗
arXiv2014

On $p$-adic differential equations on semistable varieties II

This paper is a complement to the paper "On $p$-adic differential equations on semistable varieties" written by V. Di Proietto. Given an open variety over a DVR with semistable reduction, the author constructed in that paper a fully faithful algebraization functor from the category of certain log overconvergent isocrystals on the special fiber to the category of modules with regular integrable connection on the generic fiber. In this paper, we prove that, with convenable hypothesis, this functor is a tensor functor whose essential image is closed under extensions and subquotients. As a consequence, we can find suitable Tannakian subcategories of log overconvergent isocrystals and of modules with regular integrable connection on which the algebraization functor is an equivalence of Tannakian categories.

math.NT↗
arXiv2012

On $p$-adic differential equations on semistable varieties

In this paper we prove a comparison theorem between the category of certain modules with integrable connection on the complement of a normal crossing divisor of the generic fiber of a proper semistable variety over a DVR and the category of certain log overconvergent isocystrals on the special fiber of the same open.

math.NT↗