99 citations · 157 across the 39 of their papers we have counts for
43 papers
The Era of Vibe Tapeout: Dark Age or Golden Age for Analog Circuit Design?
Kentaro Yoshioka
LLM agents now write their own schematic and layout generators, run EDA tools, read the results, and fix the design. This "vibe tapeout" is becoming practical for analog circuits a…
Understanding Clustering in Slot Attention via Particle Dynamics
Vasudev Joy, Rajat Rasal, Avinash Kori +2
Studying attention through the lens of interacting particle dynamics has shown how token clustering can emerge from the underlying dynamics. We extend this perspective to slot atte…
Density-Robust Spherical Coordinates from Persistent Cohomology
Nick Nordwald, Inés García-Redondo, Anthea Monod
Persistent cohomology provides a principled framework for constructing nonlinear coordinates that reflect the topology of data. However, these topological coordinates can be severe…
Tracking Representation Dynamics in Large Language Models with Persistent Homology
Naman Malhotra, Jay Ambadkar, Abhinav Gupta +4
Large language models are commonly aligned through supervised fine-tuning, yet little is known about how their internal representations evolve during this process. We study alignme…
Generative Modeling on Metric Graphs via Neural Optimal Transport
Alessandro Micheli, Yueqi Cao, Anthea Monod +1
We introduce, to our knowledge, the first deep generative modeling framework for probability distributions continuously supported on compact metric graphs. Given source and target…
Non-Archimedean Polydisc Spaces and Applications to Optimisation
Paul Lezeau, Yiannis Fam, Anthea Monod +1
We propose a new framework for optimisation over non-Archimedean spaces inspired by Berkovich geometry. Specifically, we introduce polydisc spaces, which consists of products of cl…
Topological Signatures of Grokking
Yifan Tang, Qiquan Wang, Inés García-Redondo +1
We study the grokking phenomenon through the lens of topology. Using persistent homology on point clouds derived from the embedding matrices of a range of models trained on modular…
Feature Starvation as Geometric Instability in Sparse Autoencoders
Faris Chaudhry, Keisuke Yano, Anthea Monod
Sparse autoencoders (SAEs) are used to disentangle the dense, polysemantic internal representations of large language models (LLMs) into interpretable, monosemantic concepts. Howev…
Entropic Riemannian Neural Optimal Transport
Alessandro Micheli, Silvia Sapora, Anthea Monod +1
Many machine learning problems involve data supported on curved spaces such as spheres, rotation groups, hyperbolic spaces, and general Riemannian manifolds, where Euclidean geomet…
Trajectory-Restricted Optimization Conditions and Geometry-Aware Linear Convergence
Faris Chaudhry, Anthea Monod, Keisuke Yano
Linear convergence of first-order methods is typically characterized by global optimization conditions whose constants reflect worst-case geometry of the ambient space. In high-dim…
On the Uniqueness of Fréchet Means for Polytope Norms
Roan Talbut, Andrew McCormack, Anthea Monod
Fréchet means are a popular type of average for non-Euclidean datasets, defined as those points which minimise the average squared distance to a set of data points. We consider the…
Breaking Symmetry Bottlenecks in GNN Readouts
Mouad Talhi, Arne Wolf, Anthea Monod
Graph neural networks (GNNs) are widely used for learning on structured data, yet their ability to distinguish non-isomorphic graphs is fundamentally limited. These limitations are…
Riemannian Neural Optimal Transport
Alessandro Micheli, Yueqi Cao, Anthea Monod +1
Computational optimal transport (OT) offers a principled framework for generative modeling. Neural OT methods, which use neural networks to learn an OT map (or potential) from data…
Generalized Persistent Laplacians and their Spectral Properties
Arne Wolf, Jiyu Fan, Anthea Monod
Laplacian operators are classical objects that are fundamental in both pure and applied mathematics and are becoming increasingly prominent in modern computational and data science…
The Shape of Adversarial Influence: Characterizing LLM Latent Spaces with Persistent Homology
Aideen Fay, Inés García-Redondo, Qiquan Wang +2
Existing interpretability methods for Large Language Models (LLMs) predominantly capture linear directions or isolated features. This overlooks the high-dimensional, relational, an…
Metric Graph Kernels via the Tropical Torelli Map
Yueqi Cao, Anthea Monod
We introduce the first graph kernels for metric graphs via tropical algebraic geometry. In contrast to conventional graph kernels based on graph combinatorics such as nodes, edges,…
Computing the Tropical Abel--Jacobi Transform and Tropical Distances for Metric Graphs
Yueqi Cao, Anthea Monod
Metric graphs are important models for capturing the structure of complex data across various domains. While much effort has been devoted to extracting geometric and topological fe…
Confidence Bands for Multiparameter Persistence Landscapes
Inés García-Redondo, Anthea Monod, Qiquan Wang
Multiparameter persistent homology is a generalization of classical persistent homology, a central and widely-used methodology from topological data analysis, which takes into acco…
Tropical Fréchet Means: a polyhedral approach to exact optimization
Kamillo Ferry, Bo Lin, Carlos Améndola +2
The Fréchet mean is a fundamental notion of central tendency defined as a minimizer of a sum of squared distances in a general metric space. In this paper, we study Fréchet means i…
A Topological Gaussian Mixture Model for Bone Marrow Morphology in Leukaemia
Qiquan Wang, Anna Song, Antoniana Batsivari +2
Acute myeloid leukaemia (AML) is a type of blood and bone marrow cancer characterized by the proliferation of abnormal clonal haematopoietic cells in the bone marrow leading to bon…
On the Limitations of Fractal Dimension as a Measure of Generalization
Charlie B. Tan, Inés García-Redondo, Qiquan Wang +2
Bounding and predicting the generalization gap of overparameterized neural networks remains a central open problem in theoretical machine learning. There is a recent and growing bo…
A Computational Tropical Geometry Framework for Neural Networks
Paul Lezeau, Thomas Walker, Yueqi Cao +2
We propose a computational tropical geometry framework for the symbolic analysis of neural networks with tropical activations. The number of linear regions of a neural network has…
Tropical Gradient Descent
Roan Talbut, Anthea Monod
We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interes…
Topological Community Detection: A Sheaf-Theoretic Approach
Arne Wolf, Anthea Monod
We propose a model for network community detection using topological data analysis, a branch of modern data science that leverages theory from algebraic topology to statistical ana…