arXiv subjects

Jorge António

Publications and source records attributed to Jorge António.

6 recordsLinked to original sources

arXiv2024

Privacy-Preserving Decentralized AI with Confidential Computing

This paper addresses privacy protection in decentralized Artificial Intelligence (AI) using Confidential Computing (CC) within the Atoma Network, a decentralized AI platform designed for the Web3 domain. Decentralized AI distributes AI services among multiple entities without centralized oversight, fostering transparency and robustness. However, this structure introduces significant privacy challenges, as sensitive assets such as proprietary models and personal data may be exposed to untrusted participants. Cryptography-based privacy protection techniques such as zero-knowledge machine learning (zkML) suffers prohibitive computational overhead. To address the limitation, we propose leveraging Confidential Computing (CC). Confidential Computing leverages hardware-based Trusted Execution Environments (TEEs) to provide isolation for processing sensitive data, ensuring that both model parameters and user data remain secure, even in decentralized, potentially untrusted environments. While TEEs face a few limitations, we believe they can bridge the privacy gap in decentralized AI. We explore how we can integrate TEEs into Atoma's decentralized framework.

cs.CR↗

arXiv2020

Spreading out the Hodge filtration in non-archimedean geometry

The goal of the current text is to study non-archimedean analytic derived de Rham cohomology by means of formal completions. Our approach is inspired by the deformation to the normal cone provided in \cite{Gaitsgory_Study_II}. More specifically, given a morphism $f \colon X \to Y$ of (derived) $k$-analytic spaces we construct the \emph{non-archimedean deformation to the normal cone} associated to $f$. The latter can be thought as an $\mathbf A^1_k$-parametrized deformation whose fiber at $1 \in \mathbf A^1_k$ coincides with the formal completion of $f$ and the fiber at $0 \in \mathbf A^1_k$ with the (derived) normal cone associated to $f$. We further show that such deformation can be endowed with a natural filtration which spreads out the usual Hodge filtration on the (completed shifted) analytic tangent bundle to the formal completion. Such filtration agrees with the $I$-adic filtration in the case where $f$ is a locally complete intersection morphism between (derived) $k$-affinoid spaces. Along the way we develop the theory of (ind-inf)-$k$-analytic spaces or in other words $k$-analytic formal moduli problems.

math.AG↗

arXiv2020

Moduli of $p$-adic representations of a profinite group

Let $X$ be a smooth and proper scheme over an algebraically closed field. The purpose of the current text is twofold. First, we construct the moduli stack parametrizing rank $n$ continuous $p$-adic representations of the étale fundamental group $π_1^\textrm{ét}(X)$. Our construction realizes such object as a $\mathbb{Q}_p$-analytic stack, denoted $\mathrm{LocSys}_{p,n } (X)$. Secondly, we prove that $\mathrm{LocSys}_{p,n}(X)$ admits a canonical derived structure. This derived structure allow us to intrinsically recover the deformation theory of continuous $p$-adic representations, studied in [GV18]. Our proof of geometricity of $\mathrm{LocSys}_{p,n}(X)$ uses in an essential way the $\mathbb{Q}_p$-analytic analogue of Lurie-Artin representability, proved in [PY17].

math.AG↗

arXiv2020

Derived $\mathcal{O}_k$-adic geometry and derived Raynaud localization theorem

The goal of the present text is to state and prove a generalization of Raynaud localization theorem in the setting of derived geometry. More explicitly, we show that the $\infty$-category of quasi-paracompact and quasi-separated derived $k$-analytic spaces can be realized as a localization of the $\infty$-category of admissible derived formal schemes. We construct a derived rigidification functor generalizing Raynaud rigidification functor. In order to construct the latter we will need to formalize derived formal $\mathcal{O}_k$-adic formal geometry via a structured spaces approach. We prove that $\mathcal{O}_k$-adic Postnikov towers of derived $\mathcal{O}_k$-adic Deligne-Mumford stacks decompose and we relate these to Postnikov towers of derived $k$-analytic spaces. This is possible by a precise comparison between the $\mathcal{O}_k$-adic cotangent complex and the $k$-analytic cotangent complex.

math.AG↗

arXiv2019

Derived Non-archimedean analytic Hilbert space

In this short paper we combine the representability theorem introduced in [17, 18] with the theory of derived formal models introduced in [2] to prove the existence representability of the derived Hilbert space RHilb(X) for a separated k-analytic space X. Such representability results relies on a localization theorem stating that if X is a quasi-compact and quasi-separated formal scheme, then the \infty-category Coh^+(X^rig) of almost perfect complexes over the generic fiber can be realized as a Verdier quotient of the \infty-category Coh^+(X). Along the way, we prove several results concerning the the \infty-categories of formal models for almost perfect modules on derived k-analytic spaces.

math.AG↗

arXiv2019

Moduli of $\ell$-adic pro-étale local systems for smooth non-proper schemes

Let $X$ be a smooth scheme over an algebraically closed field. When $X$ is proper, it was proved in \cite{me1} that the moduli of $\ell$-adic continuous representations of $π_1^\et(X)$, $\LocSys(X)$, is representable by a (derived) $\Ql$-analytic space. However, in the non-proper case one cannot expect that the results of \cite{me1} hold mutatis mutandis. Instead, assuming $\ell$ is invertible in $X$, one has to bound the ramification at infinity of those considered continuous representations. The main goal of the current text is to give a proof of such representability statements in the open case. We also extend the representability results of \cite{me1}. More specifically, assuming $X$ is assumed to be proper, we show that $\LocSys(X)$ admits a canonical shifted symplectic form and we give some applications of such existence result.

math.AG↗