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<li><a href="#idée-principale" id="toc-idée-principale" class="nav-link active" data-scroll-target="#idée-principale"><span class="header-section-number">1</span> Idée principale</a></li>
<li><a href="#apprentissage-contrastif" id="toc-apprentissage-contrastif" class="nav-link" data-scroll-target="#apprentissage-contrastif"><span class="header-section-number">2</span> Apprentissage contrastif</a>
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<li><a href="#hypersphère-méga-cool" id="toc-hypersphère-méga-cool" class="nav-link" data-scroll-target="#hypersphère-méga-cool"><span class="header-section-number">2.1</span> Hypersphère méga cool</a></li>
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<h1 class="title">Variational Graph AutoEncoder with Wasserstein</h1>
<div class="quarto-categories">
<div class="quarto-category">convolution</div>
<div class="quarto-category">machine learning</div>
<div class="quarto-category">vae</div>
<div class="quarto-category">graphes</div>
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<div class="quarto-title-meta-author">
<div class="quarto-title-meta-heading">Auteur·rice</div>
<div class="quarto-title-meta-heading">Affiliation</div>
<div class="quarto-title-meta-contents">
<p class="author">Louis Lacoste <a href="mailto:louis.lacoste@agroparistech.fr" class="quarto-title-author-email"><i class="bi bi-envelope"></i></a> <a href="https://orcid.org/0009-0004-0178-9821" class="quarto-title-author-orcid"> <img src="data:image/png;base64,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"></a></p>
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<div class="quarto-title-meta-contents">
<p class="affiliation">
MIA Paris-Saclay, INRAE, AgroParisTech, Université Paris-Saclay
</p>
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<div class="quarto-title-meta-heading">Date de publication</div>
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<p class="date">11 mai 2026</p>
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<div>
<div class="quarto-title-meta-heading">Modifié</div>
<div class="quarto-title-meta-contents">
<p class="date-modified">11 mai 2026</p>
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</header>
<p>Suite à la discussion avec Julian jinscris ce que lon sest dit.</p>
<section id="idée-principale" class="level1" data-number="1">
<h1 data-number="1"><span class="header-section-number">1</span> Idée principale</h1>
<p>Les VAE avec convolution de graphes (GCN) permettent dapprendre une représentation latente des noeuds dun graphe basée sur les interactions entre noeuds.</p>
<p><strong>Objectif</strong> : apprendre un même encodeur et donc un espace latent structuré pour clusteriser une collection de réseaux sur la base de la structure. <em>Sous-objectif</em> : pouvoir prendre en compte des covariables (Fused Wasserstein ?).</p>
<p>Principe du VAE:</p>
<p>Soit <span class="math inline">Y</span> une matrice dadjacence (ou de bi-adjacence pour les graphes bipartites), <span class="math inline">X</span> une matrice de covariables.</p>
<p>Soit <span class="math inline">D_1</span> la matrice des degrés en ligne, <span class="math inline">D_2</span> la matrice des degrés en colonne.</p>
<p><span class="math inline">\widetilde{Y} = D_1^{-1/2} Y D_2^{-1/2}</span></p>
<p><strong>à compléter</strong></p>
</section>
<section id="apprentissage-contrastif" class="level1" data-number="2">
<h1 data-number="2"><span class="header-section-number">2</span> Apprentissage contrastif</h1>
<p>Puisque lon voudrait marquer la séparation entre différentes structures de réseaux, on pourrait vouloir faire de l<a href="https://u9534056.medium.com/an-overview-of-contrastive-learning-fa520f5f2c23">apprentissage contrastif pour V(G)AE</a>.</p>
<section id="hypersphère-méga-cool" class="level2" data-number="2.1">
<h2 data-number="2.1" class="anchored" data-anchor-id="hypersphère-méga-cool"><span class="header-section-number">2.1</span> Hypersphère méga cool</h2>
<p>Il faut creuser : forcer les contraintes des <em>embeddings</em> à vivre sur la surface dune hypersphère car, daprès Julian et la littérature, par rapport à un espace euclidien cela permet davoir :</p>
<ul>
<li>position latente bornée : stabilisation de lapprentissage et évite lexplosion dans une ou plusieurs directions.</li>
<li>couverture “uniforme” de la sphère : tendance à faciliter lapprentissage contrastif, avec lidée de bien séparer les graphes aux structures différentes.</li>
</ul>
<p><a href="https://www.envisioning.com/vocab/hyperspherical-representation-learning">Première source</a></p>
<p>Le softmax est remplacée par la loi de von Mises-Fisher. Daprès <a href="https://fr.wikipedia.org/wiki/Loi_de_von_Mises-Fisher#Relation_avec_la_loi_normale">Wikipédia</a> équivalent de la loi normale multivariée à covariance isotrope restreinte à lhypersphère unité.</p>
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let height = null;
let parent = null;
if (lineIds.length > 0) {
//compute the position of the single el (top and bottom and make a div)
const el = window.document.getElementById(lineIds[0]);
top = el.offsetTop;
height = el.offsetHeight;
parent = el.parentElement.parentElement;
if (lineIds.length > 1) {
const lastEl = window.document.getElementById(lineIds[lineIds.length - 1]);
const bottom = lastEl.offsetTop + lastEl.offsetHeight;
height = bottom - top;
}
if (top !== null && height !== null && parent !== null) {
// cook up a div (if necessary) and position it
let div = window.document.getElementById("code-annotation-line-highlight");
if (div === null) {
div = window.document.createElement("div");
div.setAttribute("id", "code-annotation-line-highlight");
div.style.position = 'absolute';
parent.appendChild(div);
}
div.style.top = top - 2 + "px";
div.style.height = height + 4 + "px";
div.style.left = 0;
let gutterDiv = window.document.getElementById("code-annotation-line-highlight-gutter");
if (gutterDiv === null) {
gutterDiv = window.document.createElement("div");
gutterDiv.setAttribute("id", "code-annotation-line-highlight-gutter");
gutterDiv.style.position = 'absolute';
const codeCell = window.document.getElementById(targetCell);
const gutter = codeCell.querySelector('.code-annotation-gutter');
gutter.appendChild(gutterDiv);
}
gutterDiv.style.top = top - 2 + "px";
gutterDiv.style.height = height + 4 + "px";
}
selectedAnnoteEl = annoteEl;
}
};
const unselectCodeLines = () => {
const elementsIds = ["code-annotation-line-highlight", "code-annotation-line-highlight-gutter"];
elementsIds.forEach((elId) => {
const div = window.document.getElementById(elId);
if (div) {
div.remove();
}
});
selectedAnnoteEl = undefined;
};
// Handle positioning of the toggle
window.addEventListener(
"resize",
throttle(() => {
elRect = undefined;
if (selectedAnnoteEl) {
selectCodeLines(selectedAnnoteEl);
}
}, 10)
);
function throttle(fn, ms) {
let throttle = false;
let timer;
return (...args) => {
if(!throttle) { // first call gets through
fn.apply(this, args);
throttle = true;
} else { // all the others get throttled
if(timer) clearTimeout(timer); // cancel #2
timer = setTimeout(() => {
fn.apply(this, args);
timer = throttle = false;
}, ms);
}
};
}
// Attach click handler to the DT
const annoteDls = window.document.querySelectorAll('dt[data-target-cell]');
for (const annoteDlNode of annoteDls) {
annoteDlNode.addEventListener('click', (event) => {
const clickedEl = event.target;
if (clickedEl !== selectedAnnoteEl) {
unselectCodeLines();
const activeEl = window.document.querySelector('dt[data-target-cell].code-annotation-active');
if (activeEl) {
activeEl.classList.remove('code-annotation-active');
}
selectCodeLines(clickedEl);
clickedEl.classList.add('code-annotation-active');
} else {
// Unselect the line
unselectCodeLines();
clickedEl.classList.remove('code-annotation-active');
}
});
}
const findCites = (el) => {
const parentEl = el.parentElement;
if (parentEl) {
const cites = parentEl.dataset.cites;
if (cites) {
return {
el,
cites: cites.split(' ')
};
} else {
return findCites(el.parentElement)
}
} else {
return undefined;
}
};
var bibliorefs = window.document.querySelectorAll('a[role="doc-biblioref"]');
for (var i=0; i<bibliorefs.length; i++) {
const ref = bibliorefs[i];
const citeInfo = findCites(ref);
if (citeInfo) {
tippyHover(citeInfo.el, function() {
var popup = window.document.createElement('div');
citeInfo.cites.forEach(function(cite) {
var citeDiv = window.document.createElement('div');
citeDiv.classList.add('hanging-indent');
citeDiv.classList.add('csl-entry');
var biblioDiv = window.document.getElementById('ref-' + cite);
if (biblioDiv) {
citeDiv.innerHTML = biblioDiv.innerHTML;
}
popup.appendChild(citeDiv);
});
return popup.innerHTML;
});
}
}
});
</script>
</div> <!-- /content -->
</body></html>