TDL tutorial at ACML 2026

Tutorial at the 18th Asian Conference on Machine Learning

Topological Deep Learning for Robust Representation Learning

Foundations, architectures, and applications

When
Tuesday 1 December 2026, session time to be announced
Where
ACML 2026, Melbourne, Australia (in person)
Length
150 minutes
Presenters
Ali Zia (La Trobe University) and Abdelwahed Khamis (CSIRO Data61)
See the programme Register through ACML 2026

Connected components (β0): 26 Loops (β1): 0

Persistent homology, the first idea in the tutorial. Grow a ball around every point and connect points whose balls meet. Components merge and loops open, then fill in. Each bar records how long a feature survives: the two longer amber bars are the two rings in the data, and the short one is noise. Drag the slider to explore.

What the tutorial covers

Deep networks are very good at local and pairwise structure. Topology gives us tools for the rest: the shape, connectivity, and higher-order organisation of data and of the representations a model learns.

Standard models can miss global structure, weak signals, and the properties of data that stay the same under noise, sampling variation, or domain shift. Topological methods measure exactly those properties, and over the past few years they have moved from an analysis tool applied after training to something that can sit inside the learning pipeline.

This tutorial introduces the foundations and current practice of topological deep learning. We start from persistent homology, filtrations, and persistence diagrams, then show how topological summaries become features, losses, and differentiable layers. From there we move to neural networks defined on graphs, simplicial and cellular complexes, hypergraphs, and sheaves.

We also spend time on the practical questions: when topology actually helps, how to combine it with a deep network, how to show that it contributed, and what still does not work. Examples come from visual recognition, hyperspectral imaging, biomedical analysis, and representation learning with foundation models.

From data to a topology-aware model Five stages connected by arrows: data, filtration, persistence diagram, vector summary, and a deep model that uses the summary as a feature, a loss, or a layer. birth death DataFiltrationPersistence diagramVector summaryDeep model points, images, graphsstructure at every scalewhat persists, and for how longlandscapes, imagesfeature, loss, or layer
Figure 1. The route the first half of the tutorial follows. A filtration turns data into a nested family of shapes, persistent homology summarises which features survive across scales, and the summary enters a network as an input feature, a regularising loss, or a differentiable layer.

Programme

Six parts over two and a half hours, moving from intuition to foundations, architectures, applications, and open problems.

  1. 0:0015 minutes

    Motivation: why topology in machine learning?

    Local distances and pairwise graphs do not always capture global structure, holes, connectedness, representation collapse, domain shift, or weak signals. We introduce topology as a complementary tool for analysing and improving learned representations.

  2. 0:1520 minutes

    Persistent homology for machine learning

    Point clouds, simplicial complexes, Vietoris–Rips and sublevel-set filtrations, barcodes, persistence diagrams, landscapes and images, stability, and interpretation.

  3. 0:3520 minutes

    Topology in deep learning pipelines

    Topological summaries as features, topology-aware regularisation, differentiable topology layers, topology-preserving segmentation, and representation diagnostics, along with practical issues such as batching, scalability, differentiability, and ablations.

  4. 0:5520 minutes

    From topological data analysis to topological deep learning

    Neural learning on graphs, simplicial complexes, cellular complexes, hypergraphs, and sheaves. We compare graph message passing with higher-order message passing and discuss when pairwise modelling is not enough.

  5. 1:1540 minutes

    Applications and case studies

    Representative uses in computer vision, medical imaging, hyperspectral and remote sensing data, anomaly detection, molecular data, and robustness analysis. One case study shows how topology and geometry can diagnose out-of-distribution behaviour and weak-signal representations.

  6. 1:5535 minutes

    Open challenges and discussion

    Scalability, differentiable topology, benchmark design, integration with foundation models, uncertainty, interpretability, and convincing evaluation protocols for topology-based machine learning.

Times are measured from the start of the session. The session slot and room will be added here once the ACML 2026 schedule is published.

Four domains for neural networks, drawn on the same six nodes A graph with pairwise edges; a simplicial complex with two filled triangles; a cell complex with an additional four-sided cell; and a hypergraph in which three hyperedges group several nodes at once. GraphSimplicial complexCell complexHypergraph pairwise relations onlyadds filled trianglesadds cells of any shapegroups of any size
Figure 2. The domains compared in part four. Message passing on a graph exchanges information along edges. Higher-order domains let a network pass messages between nodes, edges, faces, and groups, which matters when the signal lives in a relationship among several things at once.

Where topology earns its place

The longest part of the session looks at problems where connectivity and shape carry information that pixel-level or pairwise objectives miss.

Vision and medical imaging

Vessels, roads, and cell boundaries must stay connected. Topology-aware losses penalise a broken branch that barely changes pixel accuracy.

Hyperspectral and remote sensing

Hundreds of bands, few labels, and faint targets. Topological summaries help separate weak but persistent signals from noise.

Anomaly detection and robustness

Anomalies and distribution shift change the shape of a representation. Topology and geometry give diagnostics for detecting that change.

Molecular and scientific data

Rings, cavities, and functional groups are higher-order structures. Cell-complex and simplicial networks represent them directly.

Presenters

Both presenters work on topological and higher-order representation learning and its use in imaging and sensing.

Dr Ali Zia

Research Fellow, La Trobe University, Australia

Ali works across machine learning, computer vision, hyperspectral imaging, and topological representation learning. His work includes a field-level review of topological deep learning, topology-aware representation learning, robustness diagnostics, weak-signal detection, and scientific imaging applications.

a.zia@latrobe.edu.auali-zia.me

Dr Abdelwahed Khamis

Research Scientist, CSIRO Data61, Australia

Abdelwahed's research spans machine learning, optimal transport, multimodal sensing, radar perception, and higher-order representation learning.

Abdelwahed.Khamis@data61.csiro.au

Materials

Slides and supporting resources will be posted here before the tutorial.

Coming soon

Slides

The full slide deck, released ahead of the session so you can follow along.

Coming soon

Worked examples

Short examples that reproduce the figures and case studies shown in the session.

Software to explore now

TopoX is an open-source suite of Python packages for learning on topological domains, described in reference 3 below.

References covered

The tutorial draws on these papers. The first is the most complete single starting point.

  1. Zia, A., Khamis, A., Nichols, J., Tayab, U. B., Hayder, Z., et al. Topological Deep Learning: A Review of an Emerging Paradigm. Artificial Intelligence Review, 57, 77, 2024.
  2. Zia, A., Ali, U., Rehman, A., Ramzan, M. U., Han, K., Faheem, M., Qureshi, S., and Xiang, W. Learning Topology-Aware Representations via Test-Time Adaptation for Anomaly Segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2026, accepted.
  3. Hajij, M., Papillon, M., Frantzen, F., Agerberg, J., AlJabea, I., Ballester, R., Zia, A., et al. TopoX: A Suite of Python Packages for Machine Learning on Topological Domains. Journal of Machine Learning Research, 25(374), 1–8, 2024.
  4. Papillon, M., Hajij, M., Myers, A., Jenne, H., Mathe, J., Papamarkou, T., Zia, A., et al. ICML 2023 Topological Deep Learning Challenge: Design and Results. Topological, Algebraic and Geometric Learning Workshops, 2023.
  5. Zia, A., Ali, U., Ramzan, M. U., Rehman, A., Khamis, A., and Xiang, W. Test-Time Adaptation for Anomaly Segmentation via Topology-Aware Optimal Transport Chaining. arXiv:2601.20333, 2026.
  6. Carlsson, G. Topology and Data. Bulletin of the American Mathematical Society, 2009.
  7. Hofer, C., Kwitt, R., Niethammer, M., and Uhl, A. Deep Learning with Topological Signatures. NeurIPS, 2017.
  8. Moor, M., Horn, M., Rieck, B., and Borgwardt, K. Topological Autoencoders. ICML, 2020.
  9. Hajij, M., Zamzmi, G., Papamarkou, T., et al. Topological Deep Learning: Going Beyond Graph Data. arXiv:2206.00606, 2023.