Check out our latest work on Geometric Machine Learning at #ICML2026 this week: I’ll be speaking at the @weightsymmetry workshop about Model-Agnostic Equivariance for Efficient Learning under Symmetry. *Main Conference:* 🔹 Neural Feature Geometry Evolves as Discrete Ricci Flow (Spotlight). Led by Moritz Hehl, w/ Max von Renesse. openreview.net/pdf?id=YPH5yC… The evolution of the feature geometry of neural networks during training resembles a discrete Ricci flow, offering a geometric view of class separation and practical signals for early stopping and depth selection. 🔹 Adaptive symmetry discovery for dynamical system identification. Led by @B_Tahmasebi. openreview.net/pdf?id=crYiAj… Unknown symmetries in dynamical systems can be learned from a single trajectory and then used to identify the system just as efficiently as if the symmetries were known in advance. 🔹Unitary Convolutions for Message-passing and Positional Encodings on Directed Graphs. Led by Lukas Fesser w/ @bobak_kiani . openreview.net/pdf?id=QhNO3q… Directed graphs need message passing that respects edge direction without collapsing at depth; Dune uses unitary convolutions with edge features to avoid oversmoothing, stay trainable beyond 100 layers, and provide positional information for graph transformers. *High-dimensional Learning Dynamics Workshop:* 🔹 Dimension-Free Scaling Laws for Invariant Score Matching. Led by @B_Tahmasebi. openreview.net/pdf?id=xnhs25… Score estimators that respect symmetries can be learned on sets or graphs of one size and transferred to much larger domains, with error rates that do not grow with ambient dimension.

Moving from individual proofs to large-scale autoformalization requires new tools. We introduce Choir, an open protocol for multi-agent autoformalization that decomposes projects into tasks, coordinates contributions through GitHub, and deterministically checks them before merging. Choir is modular, open source, and supports Lean 4, Isabelle, and Rocq. Repository: github.com/Weber-GeoML/Choir Preprint: arxiv.org/abs/2609.31903 Led by @yidi_qi. Supported by @darpa expMath.

Nice example of AI-assisted mathematics led by @tle_96: AI-guided search, human refinement, formal verification. Details here: github.com/steven-le-thien/v…

@theNASciences meeting on "Organizing Mathematical Knowledge in the Age of AI and Formalization" Registration for virtual attendance closes tomorrow: nationalacademies.org/units/…

Our #ICML2026 Spotlight shows that Neural Feature Geometry evolves as discrete Ricci Flow. Poster on Wed, Jul 8, 2026, 3:30 PM – 5:15 PM HST, HALL A #1705, presented by Moritz Hehl.

Happy that GraphBench has been accepted as an oral at the GFM workshop @ICML. 🚀 We also updated GraphBench🆕: - Extensive documentation📔, - more baselines📊, - bugfixes🪲, - extended 80+ page preprint 📰(arxiv.org/abs/2512.04475). Check it out: graphbench.io/.

#COLT2026 Data augmentation offers a model-agnostic route to equivariance, using symmetry-transformed samples rather than architectural changes. Can partial data augmentation recover the benefits of full augmentation? We analyze this through Fourier methods and group representations, showing random subsets achieve full-augmentation minimax rates up to vanishing error. Led by @B_Tahmasebi, w/ @StefanieJegelka Details here: arxiv.org/pdf/2606.24418

@bostonsymmetry is hosting a poster session (4-5:30pm) + social on Tuesday, June 9th, at Northeastern! All are welcome to come chat about geometry, symmetries, + AI! Location: Raytheon Amphitheater, maps.app.goo.gl/oDZc3Rw7iN4q… Register here: neu.co1.qualtrics.com/jfe/fo…

Submissions are open through June 15th AOE for all tracks of TAG-DS/ Boston Symmetry Day 2026. Submit your latest work and open problems in Geometric and Topological Machine Learning. Join us in Boston in August! Details here: tagds.com/events/tag-ds-2026

Just under two weeks until the submission deadline for the Boston TAG Party 2026– a joint conference organized collaboratively by the Boston Symmetry Group and TAG-DS! Papers are due June 12th— full archival papers, extended abstracts, and open problem tracks!

Looking forward to @NetSciConf 2026 in Boston! We will be presenting recent work from the group on Geometric Machine Learning for Network Science: June 1, 11:45am-12:30pm - Invited talk at the Network Geometry Satellite: Curvature-based Community Detection in Complex Networks June 1, 2:30–6:00pm - Invited lecture at the @NetSciConf School: Deep Learning on Networks through a Geometric Lens June 2, 9:05-9:50am - Invited talk @TopoNets Satellite: A Geometric Lens on Higher-Order Information in Graph Machine Learning: Challenges, Insights, and Remedies June 3, 6:30pm — @tle_96 will present new work on graph coloring: Neural Algorithmic Reasoning for Graph Coloring via Lovász-ϑ with Contrastive Learning (Poster #382)

Can we learn the curvature of a data manifold from a finite sample? We study continuum limits of Ollivier’s Ricci curvature on geometric graphs, proving pointwise consistency and showing that positive lower bounds on the underlying manifold are inherited by the graph with high probability. We further discuss applications to heat kernels and manifold learning. With Nicolás García Trillos. Now published in Discrete & Computational Geometry: link.springer.com/article/10…

Excited for the new issue of Dædalus, the journal of @americanacad, with many thought-provoking essays on AI & Science, edited by James Manyika: amacad.org/daedalus/ai-scien… My contribution explores geometry-informed AI and its role in advancing scientific discovery.

Can small models solve combinatorial optimization problems by learning from larger source models? We study when distillation succeeds using a GNN that is algorithmically aligned with the solution procedure. We prove that this alignment enables efficient distillation when the underlying algorithm has low decision-tree complexity. Led by Thien Le. Learn more here: arxiv.org/pdf/2605.20074

Check out our latest work on Geometric Machine Learning at #ICLR2026 this week: 🔹Achieving Approximate Symmetry Is Exponentially Easier than Exact Symmetry. Led by @B_Tahmasebi. openreview.net/pdf?id=ncOJYF… Approximate symmetry, enforced via sparse group averaging, can deliver much of the benefit of exact symmetry in ML at exponentially lower cost. 🔹Priors in Time: Missing Inductive Biases for Language Model Interpretability. Led by @EkdeepL @can_rager @sumedh_hrs. openreview.net/pdf?id=4J2e3n… Language model activations are strongly context-dependent over time. We propose Temporal SAEs, which add a temporal inductive bias that yields more meaningful interpretability features than standard token-wise SAEs. 🔹Adaptive Symmetry Discovery for Dynamical System Identification Led by @B_Tahmasebi. openreview.net/pdf?id=6SkG3U… Unknown symmetries in dynamical systems can be learned from a single trajectory and then used to identify the system just as efficiently as if the symmetries were known in advance.

#ICLR2026 Can approximate symmetry offer the same benefits as exact symmetry in practice? We study the tradeoff between enforcing symmetry exactly versus approximately in machine learning models, showing that approximate symmetry can be exponentially cheaper, while preserving the benefits of symmetry-based inductive bias. Led by @B_Tahmasebi. Details here: arxiv.org/pdf/2512.11855

How are emotions represented in the latent geometry of LLMs? We analyze affective representations in latent space and show that they mirror classic valence-arousal models from psychology (similar to concurrent work @AnthropicAI @1e0sun) and display nonlinear structure that supports uncertainty quantification and steering in emotion tasks with implications for model transparency and AI safety.

Interesting read on arxiv: Shaping the Future of Mathematics in the Age of AI By Johan Commelin, Mateja Jamnik, Rodrigo Ochigame, Lenny Taelman, and Akshay Venkatesh Artificial intelligence is transforming mathematics at a speed and scale that demand active engagement from the mathematical community. We examine five areas where this transformation is particularly pressing: values, practice, teaching, technology, and ethics. We offer recommendations on safeguarding our intellectual autonomy, rethinking our practice, broadening curricula, building academically oriented infrastructure, and developing shared ethical principles - with the aim of ensuring that the future of mathematics is shaped by the community itself. arxiv.org/abs/2603.24914