15 citations · 36 across the 11 of their papers we have counts for
14 papers
Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures
Mathilde Papillon, Sophia Sanborn, Johan Mathe +8
The enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern mach…
The Selective G-Bispectrum and its Inversion: Applications to G-Invariant Networks
Simon Mataigne, Johan Mathe, Sophia Sanborn +2
An important problem in signal processing and deep learning is to achieve \textit{invariance} to nuisance factors not relevant for the task. Since many of these factors are describ…
Harmonics of Learning: Universal Fourier Features Emerge in Invariant Networks
Giovanni Luca Marchetti, Christopher Hillar, Danica Kragic +1
In this work, we formally prove that, under certain conditions, if a neural network is invariant to a finite group then its weights recover the Fourier transform on that group. Thi…
Identifying Interpretable Visual Features in Artificial and Biological Neural Systems
David Klindt, Sophia Sanborn, Francisco Acosta +2
Single neurons in neural networks are often interpretable in that they represent individual, intuitively meaningful features. However, many neurons exhibit $\textit{mixed selectivi…
A General Framework for Robust G-Invariance in G-Equivariant Networks
Sophia Sanborn, Nina Miolane
We introduce a general method for achieving robust group-invariance in group-equivariant convolutional neural networks (-CNNs), which we call the -triple-correlation (-TC)…
ICML 2023 Topological Deep Learning Challenge : Design and Results
Mathilde Papillon, Mustafa Hajij, Helen Jenne +53
This paper presents the computational challenge on topological deep learning that was hosted within the ICML 2023 Workshop on Topology and Geometry in Machine Learning. The competi…
Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks
Mathilde Papillon, Sophia Sanborn, Mustafa Hajij +1
The natural world is full of complex systems characterized by intricate relations between their components: from social interactions between individuals in a social network to elec…
Equivariant Representation Learning in the Presence of Stabilizers
Luis Armando Pérez Rey, Giovanni Luca Marchetti, Danica Kragic +2
We introduce Equivariant Isomorphic Networks (EquIN) -- a method for learning representations that are equivariant with respect to general group actions over data. Differently from…
Quantifying Extrinsic Curvature in Neural Manifolds
Francisco Acosta, Sophia Sanborn, Khanh Dao Duc +2
The neural manifold hypothesis postulates that the activity of a neural population forms a low-dimensional manifold whose structure reflects that of the encoded task variables. In…
Improved Representation of Asymmetrical Distances with Interval Quasimetric Embeddings
Tongzhou Wang, Phillip Isola
Asymmetrical distance structures (quasimetrics) are ubiquitous in our lives and are gaining more attention in machine learning applications. Imposing such quasimetric structures in…
Bispectral Neural Networks
Sophia Sanborn, Christian Shewmake, Bruno Olshausen +1
We present a neural network architecture, Bispectral Neural Networks (BNNs) for learning representations that are invariant to the actions of compact commutative groups on the spac…
ICLR 2022 Challenge for Computational Geometry and Topology: Design and Results
Adele Myers, Saiteja Utpala, Shubham Talbar +25
This paper presents the computational challenge on differential geometry and topology that was hosted within the ICLR 2022 workshop ``Geometric and Topological Representation Learn…
Efficient Neuromorphic Signal Processing with Loihi 2
Garrick Orchard, E. Paxon Frady, Daniel Ben Dayan Rubin +4
The biologically inspired spiking neurons used in neuromorphic computing are nonlinear filters with dynamic state variables -- very different from the stateless neuron models used…
Representational efficiency outweighs action efficiency in human program induction
Sophia Sanborn, David D. Bourgin, Michael Chang +1
The importance of hierarchically structured representations for tractable planning has long been acknowledged. However, the questions of how people discover such abstractions and h…