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3 </head> <body class="fixed-top-nav "> <header> <nav id="navbar" class="navbar navbar-light navbar-expand-sm fixed-top" role="navigation"> <div class="container"> <a class="navbar-brand title font-weight-lighter" href="/"> <span class="font-weight-bold">Manuel</span> Lecha </a> <button class="navbar-toggler collapsed ml-auto" type="button" data-toggle="collapse" data-target="#navbarNav" aria-controls="navbarNav" aria-expanded="false" aria-label="Toggle navigation"> <span class="sr-only">Toggle navigation</span> <span class="icon-bar top-bar"></span> <span class="icon-bar middle-bar"></span> <span class="icon-bar bottom-bar"></span> </button> <div class="collapse navbar-collapse text-right" id="navbarNav"> <ul class="navbar-nav ml-auto flex-nowrap"> <li class="nav-item "> <a class="nav-link" href="/">about </a> </li> <li class="nav-item active"> <a class="nav-link" href="/publications/">publications <span class="sr-only">(current)</span> </a> </li> <li class="nav-item "> <a class="nav-link" href="/cv/">cv </a> </li> <li class="nav-item"> <button id="search-toggle" title="Search" onclick="openSearchModal()"> <span class="nav-link">ctrl k <i class="fa-solid fa-magnifying-glass"></i></span> </button> </li> <li class="toggle-container"> <button id="light-toggle" title="Change theme"> <i class="fa-half-sun-moon" id="light-toggle-system"></i> <i class="fa-solid fa-moon" id="light-toggle-dark"></i> <i class="fa-solid fa-sun" id="light-toggle-light"></i> </button> </li> </ul> </div> </div> </nav> <progress id="progress" value="0"> <div class="progress-container"> <span class="progress-bar"></span> </div> </progress> </header> <div class="container mt-5" role="main"> <div class="post"> <header class="post-header"> <h1 class="post-title">publications</h1> <p class="post-description"></p> </header> <article> 
3<script src="/assets/js/bibsearch.js?v=1bc438ca9037884cc579601c09afd847" type="module"></script>
3 <p><input type="text" id="bibsearch" spellcheck="false" autocomplete="off" class="search bibsearch-form-input" placeholder="Type to filter"></p> <div class="publications"> <h2 class="bibliography">2026</h2> <ol class="bibliography"><li> <div class="row"> <div class="col col-sm-2 abbr"> <abbr class="badge rounded w-100">ICLR</abbr> </div> <div id="lecha2026directed" class="col-sm-8"> <div class="title">Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding</div> <div class="author"> Manuel Lecha, Andrea Cavallo, Francesca Dominici, and <span class="more-authors" title="click to view 5 more authors" onclick=" var element=$(this); element.attr('title', ''); var more_authors_text=element.text() == '5 more authors' ? 'Ran Levi, Alessio Del Bue, Elvin Isufi, Pietro Morerio, Claudio Battiloro' : '5 more authors'; var cursorPosition=0; var textAdder=setInterval(function(){ element.html(more_authors_text.substring(0, cursorPosition + 1)); if (++cursorPosition == more_authors_text.length){ clearInterval(textAdder); } }, '10'); ">5 more authors</span> </div> <div class="periodical"> <em>In International Conference on Learning Representations (ICLR)</em>, 2026 </div> <div class="periodical"> </div> <div class="links"> <a class="abstract btn btn-sm z-depth-0" role="button">Abs</a> <a href="http://arxiv.org/abs/2505.17939" class="btn btn-sm z-depth-0" role="button" rel="external nofollow noopener" target="_blank">arXiv</a> <a class="bibtex btn btn-sm z-depth-0" role="button">Bib</a> <a href="https://github.com/ManuelLecha/ssns-brain" class="btn btn-sm z-depth-0" role="button" rel="external nofollow noopener" target="_blank">Code</a> </div> <div class="abstract hidden"> <p>Graph Neural Networks excel at learning from pairwise interactions but often overlook multi-way and hierarchical relationships. Topological Deep Learning addresses this limitation by leveraging combinatorial topological spaces. However, existing TDL models are restricted to undirected settings and fail to capture the higher-order directed patterns prevalent in many complex systems, e.g., brain networks, where such interactions are both abundant and functionally significant. To fill this gap, we introduce Semi-Simplicial Neural Networks (SSNs), a principled class of TDL models that operate on semi-simplicial sets — combinatorial structures that encode directed higher-order motifs and their directional relationships. To enhance scalability, we propose Routing-SSNs, which dynamically select the most informative relations in a learnable manner. SSNs achieve state-of-the-art performance on brain dynamics classification tasks, outperforming the second-best model by up to 27%, and message-passing GNNs by up to 50% in accuracy.</p> </div> <div class="bibtex hidden"> <figure class="highlight"><pre><code class="language-bibtex" data-lang="bibtex"><span class="nc">@inproceedings</span><span class="p">{</span><span class="nl">lecha2026directed</span><span class="p">,</span>
4  <span class="na">title</span> <span class="p">=</span> <span class="s">{Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding}</span><span class="p">,</span>
5  <span class="na">author</span> <span class="p">=</span> <span class="s">{Lecha, Manuel and Cavallo, Andrea and Dominici, Francesca and Levi, Ran and Del Bue, Alessio and Isufi, Elvin and Morerio, Pietro and Battiloro, Claudio}</span><span class="p">,</span>
6  <span class="na">booktitle</span> <span class="p">=</span> <span class="s">{International Conference on Learning Representations (ICLR)}</span><span class="p">,</span>
7  <span class="na">year</span> <span class="p">=</span> <span class="s">{2026}</span><span class="p">,</span>
8  <span class="na">url</span> <span class="p">=</span> <span class="s">{https://openreview.net/forum?id=YR3CNvFfCr}</span>
9<span class="p">}</span></code></pre></figure> </div> </div> </div> </li></ol> <h2 class="bibliography">2025</h2> <ol class="bibliography"> <li> <div class="row"> <div class="col col-sm-2 abbr"> <abbr class="badge rounded w-100">ICASSP</abbr> </div> <div id="lecha2025higherorder" class="col-sm-8"> <div class="title">Higher-Order Topological Directionality and Directed Simplicial Neural Networks</div> <div class="author"> Manuel Lecha, Andrea Cavallo, Francesca Dominici, and <span class="more-authors" title="click to view 2 more authors" onclick=" var element=$(this); element.attr('title', ''); var more_authors_text=element.text() == '2 more authors' ? 'Elvin Isufi, Claudio Battiloro' : '2 more authors'; var cursorPosition=0; var textAdder=setInterval(function(){ element.html(more_authors_text.substring(0, cursorPosition + 1)); if (++cursorPosition == more_authors_text.length){ clearInterval(textAdder); } }, '10'); ">2 more authors</span> </div> <div class="periodical"> <em>In IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)</em>, 2025 </div> <div class="periodical"> </div> <div class="links"> <a class="abstract btn btn-sm z-depth-0" role="button">Abs</a> <a href="http://arxiv.org/abs/2409.08389" class="btn btn-sm z-depth-0" role="button" rel="external nofollow noopener" target="_blank">arXiv</a> <a class="bibtex btn btn-sm z-depth-0" role="button">Bib</a> <a href="https://github.com/andrea-cavallo-98/DirSNN" class="btn btn-sm z-depth-0" role="button" rel="external nofollow noopener" target="_blank">Code</a> </div> <div class="abstract hidden"> <p>We introduce a notion of higher-order directionality and design Directed Simplicial Neural Networks (Dir-SNNs), message-passing networks operating on directed simplicial complexes that leverage directed interactions among simplices. To our knowledge, this is the first TDL model using a notion of higher-order directionality. We prove that Dir-SNNs are strictly more expressive than their directed graph counterparts in distinguishing isomorphic directed graphs, and show empirically that they outperform undirected SNNs when the underlying complex is directed.</p> </div> <div class="bibtex hidden"> <figure class="highlight"><pre><code class="language-bibtex" data-lang="bibtex"><span class="nc">@inproceedings</span><span class="p">{</span><span class="nl">
9lecha2025higherorder</span><span class="p">,</span>
10  <span class="na">title</span> <span class="p">=</span> <span class="s">{Higher-Order Topological Directionality and Directed Simplicial Neural Networks}</span><span class="p">,</span>
11  <span class="na">author</span> <span class="p">=</span> <span class="s">{Lecha, Manuel and Cavallo, Andrea and Dominici, Francesca and Isufi, Elvin and Battiloro, Claudio}</span><span class="p">,</span>
12  <span class="na">booktitle</span> <span class="p">=</span> <span class="s">{IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}</span><span class="p">,</span>
13  <span class="na">year</span> <span class="p">=</span> <span class="s">{2025}</span><span class="p">,</span>
14<span class="p">}</span></code></pre></figure> </div> </div> </div> </li> <li> <div class="row"> <div class="col col-sm-2 abbr"> <abbr class="badge rounded w-100">DMLR</abbr> </div> <div id="telyatnikov2025topobench" class="col-sm-8"> <div class="title">TopoBench: A Framework for Benchmarking Topological Deep Learning</div> <div class="author"> Lev Telyatnikov, Guillermo Bernárdez, Marco Montagna, and <span class="more-authors" title="click to view 4 more authors" onclick=" var element=$(this); element.attr('title', ''); var more_authors_text=element.text() == '4 more authors' ? 'Mustafa Hajij, Miquel Ferriol Galmés, Manuel Lecha, others' : '4 more authors'; var cursorPosition=0; var textAdder=setInterval(function(){ element.html(more_authors_text.substring(0, cursorPosition + 1)); if (++cursorPosition == more_authors_text.length){ clearInterval(textAdder); } }, '10'); ">4 more authors</span> </div> <div class="periodical"> <em>Data-centric Machine Learning Research (DMLR)</em>, 2025 </div> <div class="periodical"> </div> <div class="links"> <a href="http://arxiv.org/abs/2406.06642" class="btn btn-sm z-depth-0" role="button" rel="external nofollow noopener" target="_blank">arXiv</a> <a class="bibtex btn btn-sm z-depth-0" role="button">Bib</a> <a href="https://github.com/geometric-intelligence/TopoBench" class="btn btn-sm z-depth-0" role="button" rel="external nofollow noopener" target="_blank">Code</a> </div> <div class="bibtex hidden"> <figure class="highlight"><pre><code class="language-bibtex" data-lang="bibtex"><span class="nc">@article</span><span class="p">{</span><span class="nl">telyatnikov2025topobench</span><span class="p">,</span>
15  <span class="na">title</span> <span class="p">=</span> <span class="s">{{TopoBench}: A Framework for Benchmarking Topological Deep Learning}</span><span class="p">,</span>
16  <span class="na">author</span> <span class="p">=</span> <span class="s">{Telyatnikov, Lev and Bernárdez, Guillermo and Montagna, Marco and Hajij, Mustafa and Ferriol Galmés, Miquel and Lecha, Manuel and others}</span><span class="p">,</span>
17  <span class="na">journal</span> <span class="p">=</span> <span class="s">{Data-centric Machine Learning Research (DMLR)}</span><span class="p">,</span>
18  <span class="na">year</span> <span class="p">=</span> <span class="s">{2025}</span><span class="p">,</span>
19<span class="p">}</span></code></pre></figure> </div> </div> </div> </li> <li> <div class="row"> <div class="col col-sm-2 abbr"> <abbr class="badge rounded w-100">JMLR</abbr> </div> <div id="hajij2025topox" class="col-sm-8"> <div class="title">TopoX: A Suite of Python Packages for Machine Learning on Topological Domains</div> <div class="author"> Mustafa Hajij, Mathilde Papillon, Florian Frantzen, and <span class="more-authors" title="click to view 4 more authors" onclick=" var element=$(this); element.attr('title', ''); var more_authors_text=element.text() == '4 more authors' ? 'Jens Agerberg, Ibrahem AlJabea, Rubén Ballester, others' : '4 more authors'; var cursorPosition=0; var textAdder=setInterval(function(){ element.html(more_authors_text.substring(0, cursorPosition + 1)); if (++cursorPosition == more_authors_text.length){ clearInterval(textAdder); } }, '10'); ">4 more authors</span> </div> <div class="periodical"> <em>Journal of Machine Learning Research (JMLR)</em>, 2025 </div> <div class="periodical"> </div> <div class="links"> <a href="http://arxiv.org/abs/2402.02441" class="btn btn-sm z-depth-0" role="button" rel="external nofollow noopener" target="_blank">arXiv</a> <a class="bibtex btn btn-sm z-depth-0" role="button">Bib</a> <a href="https://github.com/pyt-team" class="btn btn-sm z-depth-0" role="button" rel="external nofollow noopener" target="_blank">Code</a> </div> <div class="bibtex hidden"> <figure class="highlight"><pre><code class="language-bibtex" data-lang="bibtex"><span class="nc">@article</span><span class="p">{</span><span class="nl">hajij2025topox</span><span class="p">,</span>
20  <span class="na">title</span> <span class="p">=</span> <span class="s">{{TopoX}: A Suite of Python Packages for Machine Learning on Topological Domains}</span><span class="p">,</span>
21  <span class="na">author</span> <span class="p">=</span> <span class="s">{Hajij, Mustafa and Papillon, Mathilde and Frantzen, Florian and Agerberg, Jens and AlJabea, Ibrahem and Ballester, Rubén and others}</span><span class="p">,</span>
22  <span class="na">
22journal</span> <span class="p">=</span> <span class="s">{Journal of Machine Learning Research (JMLR)}</span><span class="p">,</span>
23  <span class="na">year</span> <span class="p">=</span> <span class="s">{2025}</span><span class="p">,</span>
24<span class="p">}</span></code></pre></figure> </div> </div> </div> </li> <li> <div class="row"> <div class="col col-sm-2 abbr"> <abbr class="badge rounded w-100">TAG-DS</abbr> </div> <div id="bernardez2025tdl2025" class="col-sm-8"> <div class="title">Topological Deep Learning Challenge 2025: Expanding the Data Landscape</div> <div class="author"> Guillermo Bernárdez, Lev Telyatnikov, Mathilde Papillon, and <span class="more-authors" title="click to view 4 more authors" onclick=" var element=$(this); element.attr('title', ''); var more_authors_text=element.text() == '4 more authors' ? 'Marco Montagna, Raphaël Theiler, Manuel Lecha, others' : '4 more authors'; var cursorPosition=0; var textAdder=setInterval(function(){ element.html(more_authors_text.substring(0, cursorPosition + 1)); if (++cursorPosition == more_authors_text.length){ clearInterval(textAdder); } }, '10'); ">4 more authors</span> </div> <div class="periodical"> <em>In Topology, Algebra, and Geometry in Data Science Workshop (TAG-DS)</em>, 2025 </div> <div class="periodical"> </div> <div class="links"> <a class="bibtex btn btn-sm z-depth-0" role="button">Bib</a> </div> <div class="bibtex hidden"> <figure class="highlight"><pre><code class="language-bibtex" data-lang="bibtex"><span class="nc">@inproceedings</span><span class="p">{</span><span class="nl">bernardez2025tdl2025</span><span class="p">,</span>
25  <span class="na">title</span> <span class="p">=</span> <span class="s">{Topological Deep Learning Challenge 2025: Expanding the Data Landscape}</span><span class="p">,</span>
26  <span class="na">author</span> <span class="p">=</span> <span class="s">{Bernárdez, Guillermo and Telyatnikov, Lev and Papillon, Mathilde and Montagna, Marco and Theiler, Raphaël and Lecha, Manuel and others}</span><span class="p">,</span>
27  <span class="na">booktitle</span> <span class="p">=</span> <span class="s">{Topology, Algebra, and Geometry in Data Science Workshop (TAG-DS)}</span><span class="p">,</span>
28  <span class="na">year</span> <span class="p">=</span> <span class="s">{2025}</span>
29<span class="p">}</span></code></pre></figure> </div> </div> </div> </li> <li> <div class="row"> <div class="col col-sm-2 abbr"> <abbr class="badge rounded w-100">arXiv</abbr> </div> <div id="islam2025em3rf" class="col-sm-8"> <div class="title">E-M3RF: An Equivariant Multimodal 3D Re-assembly Framework</div> <div class="author"> Adeela Islam, Stefano Fiorini, Manuel Lecha, and <span class="more-authors" title="click to view 4 more authors" onclick=" var element=$(this); element.attr('title', ''); var more_authors_text=element.text() == '4 more authors' ? 'Theodore Tsesmelis, Stuart James, Pietro Morerio, Alessio Del Bue' : '4 more authors'; var cursorPosition=0; var textAdder=setInterval(function(){ element.html(more_authors_text.substring(0, cursorPosition + 1)); if (++cursorPosition == more_authors_text.length){ clearInterval(textAdder); } }, '10'); ">4 more authors</span> </div> <div class="periodical"> 2025 </div> <div class="periodical"> arXiv preprint </div> <div class="links"> <a class="bibtex btn btn-sm z-depth-0" role="button">Bib</a> </div> <div class="bibtex hidden"> <figure class="highlight"><pre><code class="language-bibtex" data-lang="bibtex"><span class="nc">@misc</span><span class="p">{</span><span class="nl">islam2025em3rf</span><span class="p">,</span>
30  <span class="na">title</span> <span class="p">=</span> <span class="s">{{E-M3RF}: An Equivariant Multimodal 3D Re-assembly Framework}</span><span class="p">,</span>
31  <span class="na">author</span> <span class="p">=</span> <span class="s">{Islam, Adeela and Fiorini, Stefano and Lecha, Manuel and Tsesmelis, Theodore and James, Stuart and Morerio, Pietro and Del Bue, Alessio}</span><span class="p">,</span>
32  <span class="na">year</span> <span class="p">=</span> <span class="s">{2025}</span><span class="p">,</span>
33  <span class="na">note</span> <span class="p">=</span> <span class="s">{arXiv preprint}</span>
34<span class="p">}</span></code></pre></figure> </div> </div> </div> </li> </ol> <h2 class="bibliography">2024</h2> <ol class="bibliography"><li> <div class="row"> <div class="col col-sm-2 abbr"> <abbr class="badge rounded w-100">ICML-W</abbr> </div> <div id="bernardez2024tdl2024" class="col-sm-8"> <div class="title">ICML Topological Deep Learning Challenge 2024: Beyond the Graph Domain</div> <div class="author"> Guillermo Bernárdez, Lev Telyatnikov, Marco Montagna, and <span class="more-authors" title="click to view 4 more authors" onclick=" var element=$(this); element.attr('title', ''); var more_authors_text=element.text() == '4 more authors' ? 'Federica Baccini, Mathilde Papillon, Manuel Lecha, others' : '4 more authors'; var cursorPosition=0; var textAdder=setInterval(function(){ element.html(more_authors_text.substring(0, cursorPosition + 1)); if (++cursorPosition == more_authors_text.length){ clearInterval(textAdder); } }, '10'); ">4 more authors</span> </div> <div class="periodical"> <em>In ICML 2024 Workshop on Geometry-grounded Representation Learning and Generative Modeling (GRaM)</em>, 2024 </div> <div class="periodical"> </div> <div class="links"> <a href="http://arxiv.org/abs/2409.05211" class="btn btn-sm z-depth-0" role="button" rel="external nofollow noopener" target="_blank">arXiv</a> <a class="bibtex btn btn-sm z-depth-0" role="button">Bib</a> <a href="https://github.com/ManuelLecha/challenge-icml-2024" class="btn btn-sm z-depth-0" role="button" rel="external nofollow noopener" target="_blank">Code</a> </div> <div class="bibtex hidden"> <figure class="highlight"><pre><code class="language-bibtex" data-lang="bibtex"><span class="nc">@inproceedings</span><span class="p">{</span><span class="nl">bernardez2024tdl2024</span><span class="p">,</span>
35  <span class="na">title</span> <span class="p">=</span> <span class="s">{{ICML} Topological Deep Learning Challenge 2024: Beyond the Graph Domain}</span><span class="p">,</span>
36  <span class="na">author</span> <span class="p">=</span> <span class="s">{Bernárdez, Guillermo and Telyatnikov, Lev and Montagna, Marco and Baccini, Federica and Papillon, Mathilde and Lecha, Manuel and others}</span><span class="p">,</span>
37  <span class="na">booktitle</span> <span class="p">=</span> <span class="s">{ICML 2024 Workshop on Geometry-grounded Representation Learning and Generative Modeling (GRaM)}</span><span class="p">,</span>
38  <span class="na">year</span> <span class="p">=</span> <span class="s">{2024}</span><span class="p">,</span>
39<span class="p">}</span></code></pre></figure> </div> </div> </div> </li></ol> <h2 class="bibliography">2023</h2> <ol class="bibliography"><li> <div class="row"> <div class="col col-sm-2 abbr"> <abbr class="badge rounded w-100">PMLR</abbr> </div> <div id="papillon2023tdl2023" class="col-sm-8"> <div class="title">ICML 2023 Topological Deep Learning Challenge: Design and Results</div> <div class="author"> Mathilde Papillon, Mustafa Hajij, Audun Myers, and <span class="more-authors" title="click to view 5 more authors" onclick=" var element=$(this); element.attr('title', ''); var more_authors_text=element.text() == '5 more authors' ? 'Helen Jenne, Johan Mathe, Theodore Papamarkou, Manuel Lecha, others' : '5 more authors'; var cursorPosition=0; var textAdder=setInterval(function(){ element.html(more_authors_text.substring(0, cursorPosition + 1)); if (++cursorPosition == more_authors_text.length){ clearInterval(textAdder); } }, '10'); ">5 more authors</span> </div> <div class="periodical"> <em>In Topological, Algebraic and Geometric Learning Workshops</em>, 2023 </div> <div class="periodical"> </div> <div class="links"> <a class="bibtex btn btn-sm z-depth-0" role="button">Bib</a> </div> <div class="bibtex hidden"> <figure class="highlight"><pre><code class="language-bibtex" data-lang="bibtex"><span class="nc">@inproceedings</span><span class="p">{</span><span class="nl">papillon2023tdl2023</span><span class="p">,</span>
40  <span class="na">title</span> <span class="p">=</span> <span class="s">{{ICML} 2023 Topological Deep Learning Challenge: Design and Results}</span><span class="p">,</span>
41  <span class="na">author</span> <span class="p">=</span> <span class="s">{Papillon, Mathilde and Hajij, Mustafa and Myers, Audun and Jenne, Helen and Mathe, Johan and Papamarkou, Theodore and Lecha, Manuel and others}</span><span class="p">,</span>
42  <span class="na">booktitle</span> <span class="p">=</span> <span class="s">{Topological, Algebraic and Geometric Learning Workshops}</span><span class="p">,</span>
43  <span class="na">year</span> <span class="p">=</span> <span class="s">{2023}</span><span class="p">,</span>
44  <span class="na">url</span> <span class="p">=</span> <span class="s">{https://proceedings.mlr.press/v221/papillon23a/papillon23a.pdf}</span>
45<span class="p">}</span></code></pre></figure> </div> </div> </div> </li></ol> </div> </article> </div> </div> <footer class="fixed-bottom" role="contentinfo"> <div class="container mt-0"> © Copyright 2026 Manuel Lecha. © {{ "now" | date: "%Y" }} Manuel Lecha. Built with <a href="https://jekyllrb.com/" target="_blank" rel="external nofollow noopener">Jekyll</a> and the <a href="https://github.com/alshedivat/al-folio" rel="external nofollow noopener" target="_blank">al-folio</a> theme. </div> </footer> 
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