{"id":1841,"date":"2026-09-15T09:40:00","date_gmt":"2026-09-15T09:40:00","guid":{"rendered":"https:\/\/prg.inf.unibe.ch\/?page_id=1841"},"modified":"2026-09-15T09:41:11","modified_gmt":"2026-09-15T09:41:11","slug":"thesis-learning-resolution-consistent-representations-for-graph-neural-networks","status":"publish","type":"page","link":"https:\/\/prg.inf.unibe.ch\/index.php\/education\/thesis-learning-resolution-consistent-representations-for-graph-neural-networks\/","title":{"rendered":"thesis-Learning Resolution-Consistent Representations for Graph Neural Networks"},"content":{"rendered":"\n
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Learning Resolution-Consistent Representations for Graph Neural Networks<\/h2>\n\n\n\n

Co-Supervised by:<\/strong> Kalvin Dobler<\/p>\n\n\n\n

If you are interested in this topic or have further questions, do not hesitate to contact: kalvin.dobler@unibe.ch<\/a><\/p>\n\n\n\n

Background \/ Context<\/h3>\n\n\n\n

Graphs are often used to represent the same underlying system at different resolutions. For example, a physical, biological, or molecular system may be represented using fine-grained nodes or by aggregating them into coarser entities. Ideally, a Graph Neural Network (GNN) should produce consistent representations and predictions when the resolution changes. However, recent work shows that standard message-passing GNNs can assign substantially different latent representations to graphs describing the same underlying object at different resolutions.<\/p>\n\n\n\n

This raises a fundamental question about the scale consistency and generalization of GNNs: can GNNs learn representations that are stable across different graph resolutions?<\/p>\n\n\n\n

Research Question(s) \/ Goals<\/h3>\n\n\n\n

The project will investigate:<\/p>\n\n\n\n

    \n
  • How sensitive are common GNN architectures to changes in graph resolution?<\/li>\n\n\n\n
  • How does the choice of graph coarsening\/refinement affect learned representations and predictions?<\/li>\n\n\n\n
  • Can training objectives or architectural modifications improve cross-resolution consistency?<\/li>\n\n\n\n
  • Does resolution consistency improve generalization to graph resolutions not observed during training?<\/li>\n<\/ul>\n\n\n\n

    <\/p>\n\n\n\n

    Approach \/ Methods<\/h3>\n\n\n\n

    The project will construct multiple representations of the same underlying graphs at different resolutions using controlled graph coarsening\/refinement procedures. Standard architectures such as GCN, GIN, GraphSAGE, and potentially Graph Transformers will be evaluated.<\/p>\n\n\n\n

    Experiments will measure:<\/p>\n\n\n\n

      \n
    1. Representation consistency between corresponding graphs at different resolutions.<\/li>\n\n\n\n
    2. Prediction consistency for graph- and node-level tasks.<\/li>\n\n\n\n
    3. Cross-resolution generalization, training at one resolution and testing at another.<\/li>\n\n\n\n
    4. The influence of graph size, topology, and coarsening ratio.<\/li>\n<\/ol>\n\n\n\n

      <\/p>\n\n\n\n

      Expected Contributions \/ Outcomes<\/h3>\n\n\n\n

      The project is expected to provide:<\/p>\n\n\n\n

        \n
      • A systematic empirical evaluation of GNN behavior across graph resolutions.<\/li>\n\n\n\n
      • A benchmark for cross-resolution generalization of common GNN architectures.<\/li>\n\n\n\n
      • An analysis of which architectural and training choices improve scale consistency.<\/li>\n\n\n\n
      • Potentially, a simple method for improving resolution-invariant graph representations.<\/li>\n\n\n\n
      • An open-source implementation and experimental results that can serve as a basis for further research.<\/li>\n<\/ul>\n\n\n\n

        <\/p>\n\n\n\n

        Required Skills<\/h3>\n\n\n\n
          \n
        • Familiarity with graph theoretic concepts, machine learning experimentation and evaluation, or willingness to learn them.<\/li>\n\n\n\n
        • Basic programming skills in Python.<\/li>\n\n\n\n
        • Interest in graph neural networks and deep learning.<\/li>\n<\/ul>\n\n\n\n

          <\/p>\n\n\n\n

          Further Readings<\/h3>\n\n\n\n
            \n
          • Loukas & Vandergheynst, \u201cSpectrally Approximating Large Graphs with Smaller Graphs,\u201d ICML 2018.<\/li>\n\n\n\n
          • Loukas, \u201cGraph Reduction with Spectral and Cut Guarantees,\u201d JMLR 2019.<\/li>\n\n\n\n
          • Koke et al., \u201cGraph Neural Networks Are Not Continuous Across Graph Resolutions,\u201d ICML 2026.<\/li>\n<\/ul>\n<\/div>\n<\/div><\/section>\n","protected":false},"excerpt":{"rendered":"

            Learning Resolution-Consistent Representations for Graph Neural Networks Co-Supervised by: Kalvin Dobler If you are interested in this topic or have further questions, do not hesitate to contact: kalvin.dobler@unibe.ch Background \/ Context Graphs are often used to represent the same underlying system at different resolutions. For example, a physical, biological, or molecular system may be represented […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":731,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_uag_custom_page_level_css":"","site-sidebar-layout":"no-sidebar","site-content-layout":"plain-container","ast-site-content-layout":"normal-width-container","site-content-style":"unboxed","site-sidebar-style":"unboxed","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"enabled","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"set","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-1841","page","type-page","status-publish","hentry"],"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false},"uagb_author_info":{"display_name":"prg-admin","author_link":"https:\/\/prg.inf.unibe.ch\/index.php\/author\/prg-admin\/"},"uagb_comment_info":0,"uagb_excerpt":"Learning Resolution-Consistent Representations for Graph Neural Networks Co-Supervised by: Kalvin Dobler If you are interested in this topic or have further questions, do not hesitate to contact: kalvin.dobler@unibe.ch Background \/ Context Graphs are often used to represent the same underlying system at different resolutions. For example, a physical, biological, or molecular system may be represented…","_links":{"self":[{"href":"https:\/\/prg.inf.unibe.ch\/index.php\/wp-json\/wp\/v2\/pages\/1841","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/prg.inf.unibe.ch\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/prg.inf.unibe.ch\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/prg.inf.unibe.ch\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/prg.inf.unibe.ch\/index.php\/wp-json\/wp\/v2\/comments?post=1841"}],"version-history":[{"count":2,"href":"https:\/\/prg.inf.unibe.ch\/index.php\/wp-json\/wp\/v2\/pages\/1841\/revisions"}],"predecessor-version":[{"id":1845,"href":"https:\/\/prg.inf.unibe.ch\/index.php\/wp-json\/wp\/v2\/pages\/1841\/revisions\/1845"}],"up":[{"embeddable":true,"href":"https:\/\/prg.inf.unibe.ch\/index.php\/wp-json\/wp\/v2\/pages\/731"}],"wp:attachment":[{"href":"https:\/\/prg.inf.unibe.ch\/index.php\/wp-json\/wp\/v2\/media?parent=1841"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}