About

Nina Miolane is an Assistant Professor in the Department of Electrical and Computer Engineering at UC Santa Barbara. Her research interests include Geometric Statistics, Geometric Deep Learning, Topological Deep Learning, Equivariant Deep Learning, Shape Analysis, Computational Medicine, Theoretical Neuroscience, and Computational Neuroscience. She is affiliated with the Geometric Intelligence Lab and can be contacted via phone at +1 805-893-2037 or email at ninamiolane@ece.ucsb.edu. Her office is located in Harold Frank Hall, Room 3155.

Research topics

• Computer Science
• Mathematics
• Machine Learning
• Artificial Intelligence
• Pure mathematics
• Algorithm
• Computational science
• Theoretical computer science
• Programming language
• Geometry
• Chemistry
• Mathematical analysis
• Data science

Selected publications

• Projecting Latent RL Actions: Towards Generalizable and Scalable Graph Combinatorial Optimization

  ArXiv.org · 2026-05-19

  articleOpen access

  Graph combinatorial optimization (GCO) has attracted growing interest, as many NP-hard problems naturally admit graph formulations, yet their combinatorial explosion renders exact methods computationally intractable. Recent advances in Reinforcement Learning (RL) combined with Graph Neural Networks (GNNs) have significantly improved learning-based GCO solvers. However, existing approaches face limitations in both generalization across diverse graph instances and computational scalability as action spaces grow. To address both challenges, we introduce projection agents, a novel RL-GCO approach that operates directly in a continuous GNN-based action embedding space, predicting a desired latent action in a single forward pass and subsequently decoding it into a valid discrete action. Additionally, we enable fair comparison across RL methods through a shared embedding space for both observations and actions. Across diverse benchmarks, our approach achieves up to 16.2x faster inference and up to 40% better generalization than existing solutions using only simple nearest-neighbor decoding, while opening the door to strong RL performance in super-linear decision spaces with multiple interdependent variables. Finally, we release LaGCO-RL, a Python library that automates latent action-space construction and supports existing RL-GCO solutions, promoting reproducibility and adaptation to new GCO benchmarks.

  PublisherOA PDF

• OgBench: A Framework for Evaluating Graph Neural Networks on Omics Data

  arXiv (Cornell University) · 2026-05-15

  preprintOpen accessSenior author

  Graph Neural Networks (GNNs) have become the dominant framework for inductive graph-level learning. Yet most benchmarks focus on the regime $n \gg p$, where the number of graphs $n$ greatly exceeds the number of nodes per graph $p$. This overlooks biological domains such as omics, which operate in the opposite $n \ll p$ regime, characterized by large graphs of genes, transcripts, or proteins across few patient samples. This raises the question: \textit{how do GNNs perform in this low-sample, high-node omics setting?} We introduce \texttt{OgBench} (Omics-Graph Bench), the first benchmarking platform for graph-level prediction in the $n \ll p$ regime characteristic of omics data. We provide a standardized, end-to-end modular infrastructure from raw omics data to families of featured graphs with varied structural properties. We benchmark classical GNNs, as well as GNNs designed for large graphs and omics applications, alongside MLPs and machine learning baselines to establish reference performances. Our results show that widely used GNNs often do not outperform simple MLPs and classical baselines. These findings challenge the prevailing assumption that graph structure inherently adds value in this domain, fostering a critical reassessment of current learning paradigms. Ultimately, by exposing these limitations, OgBench provides the open-source ecosystem necessary for the community to develop and validate novel architectures explicitly tailored for biological graphs. The code is available at https://github.com/geometric-intelligence/ogbench.

  PublisherDOI

• bispectrum: Selective $G$-Bispectra Made Practical

  arXiv (Cornell University) · 2026-05-08

  preprintOpen accessSenior author

  Many machine learning tasks are invariant under the action of a group $G$ of transformations: signal classification can be invariant under translations, image classification under 2D rotations, and spherical-image classification under 3D rotations. The $G$-bispectrum is a principled complete invariant of a signal (retaining all all signal's information up to the group action) with proven benefits in machine learning and as a pooling layer in deep networks. However, its deployment has been hampered by high computational cost and a patchwork of group-specific implementations. We present bispectrum, an open-source, fully unit-tested PyTorch library that implements selective $G$-bispectra for seven different group actions, as differentiable modules that can be directly incorporated into machine learning pipelines and deep learning architectures. For finite groups $G$, selectivity reduces the computational cost from $O(|G|^2)$ to $O(|G|)$. For planar rotations, we leverage the disk bispectrum. For spherical 3D rotations, we introduce an augmented selective bispectrum at band-limit $L$ which reduces the cost from $O(L^3)$ to $Θ(L^2)$ coefficients. We profile the entire library (for which we implemented various compute optimizations), showing that it delivers near-exact $G$-invariance with its selective $G$-bispectra computed in sub-millisecond time on GPU (up to commonly used bandlimits). We evaluate the benefits of incorporating $G$-bispectra as pooling layers into deep learning architectures on three classical benchmark datasets --comparing against norm pooling, gated pooling, Fourier-ELU pooling, max pooling, and (non-equivariant) data-augmented convolutional baselines. Results show that $G$-bispectra consistently outperform alternatives in the low-data, moderate-capacity regime.

  PublisherDOI

• Projecting Latent RL Actions: Towards Generalizable and Scalable Graph Combinatorial Optimization

  HAL (Le Centre pour la Communication Scientifique Directe) · 2026-05-19

  preprintOpen access

  Graph combinatorial optimization (GCO) has attracted growing interest, as many NP-hard problems naturally admit graph formulations, yet their combinatorial explosion renders exact methods computationally intractable. Recent advances in Reinforcement Learning (RL) combined with Graph Neural Networks (GNNs) have significantly improved learning-based GCO solvers. However, existing approaches face limitations in both generalization across diverse graph instances and computational scalability as action spaces grow. To address both challenges, we introduce projection agents, a novel RL-GCO approach that operates directly in a continuous GNN-based action embedding space, predicting a desired latent action in a single forward pass and subsequently decoding it into a valid discrete action. Additionally, we enable fair comparison across RL methods through a shared embedding space for both observations and actions. Across diverse benchmarks, our approach achieves up to 16.2x faster inference and up to 40% better generalization than existing solutions using only simple nearest-neighbor decoding, while opening the door to strong RL performance in super-linear decision spaces with multiple interdependent variables. Finally, we release LaGCO-RL, a Python library that automates latent action-space construction and supports existing RL-GCO solutions, promoting reproducibility and adaptation to new GCO benchmarks.

  PublisherDOI

• bispectrum: Selective $G$-Bispectra Made Practical

  ArXiv.org · 2026-05-08

  articleOpen accessSenior author

  Many machine learning tasks are invariant under the action of a group $G$ of transformations: signal classification can be invariant under translations, image classification under 2D rotations, and spherical-image classification under 3D rotations. The $G$-bispectrum is a principled complete invariant of a signal (retaining all all signal's information up to the group action) with proven benefits in machine learning and as a pooling layer in deep networks. However, its deployment has been hampered by high computational cost and a patchwork of group-specific implementations. We present bispectrum, an open-source, fully unit-tested PyTorch library that implements selective $G$-bispectra for seven different group actions, as differentiable modules that can be directly incorporated into machine learning pipelines and deep learning architectures. For finite groups $G$, selectivity reduces the computational cost from $O(|G|^2)$ to $O(|G|)$. For planar rotations, we leverage the disk bispectrum. For spherical 3D rotations, we introduce an augmented selective bispectrum at band-limit $L$ which reduces the cost from $O(L^3)$ to $Θ(L^2)$ coefficients. We profile the entire library (for which we implemented various compute optimizations), showing that it delivers near-exact $G$-invariance with its selective $G$-bispectra computed in sub-millisecond time on GPU (up to commonly used bandlimits). We evaluate the benefits of incorporating $G$-bispectra as pooling layers into deep learning architectures on three classical benchmark datasets --comparing against norm pooling, gated pooling, Fourier-ELU pooling, max pooling, and (non-equivariant) data-augmented convolutional baselines. Results show that $G$-bispectra consistently outperform alternatives in the low-data, moderate-capacity regime.

  PublisherOA PDF

• Latent computing by biological neural networks: A dynamical systems framework

  ArXiv.org · 2025-02-20

  preprintOpen accessSenior author

  Although individual neurons and neural populations exhibit the phenomenon of representational drift, perceptual and behavioral outputs of many neural circuits can remain stable across time scales over which representational drift is substantial. These observations motivate a dynamical systems framework for neural network activity that focuses on the concept of \emph{latent processing units,} core elements for robust coding and computation embedded in collective neural dynamics. Our theoretical treatment of these latent processing units yields five key attributes of computing through neural network dynamics. First, neural computations that are low-dimensional can nevertheless generate high-dimensional neural dynamics. Second, the manifolds defined by neural dynamical trajectories exhibit an inherent coding redundancy as a direct consequence of the universal computing capabilities of the underlying dynamical system. Third, linear readouts or decoders of neural population activity can suffice to optimally subserve downstream circuits controlling behavioral outputs. Fourth, whereas recordings from thousands of neurons may suffice for near optimal decoding from instantaneous neural activity patterns, experimental access to millions of neurons may be necessary to predict neural ensemble dynamical trajectories across timescales of seconds. Fifth, despite the variable activity of single cells, neural networks can maintain stable representations of the variables computed by the latent processing units, thereby making computations robust to representational drift. Overall, our framework for latent computation provides an analytic description and empirically testable predictions regarding how large systems of neurons perform robust computations via their collective dynamics.

  PublisherOA PDFDOI

• Beyond Euclid: an illustrated guide to modern machine learning with geometric, topological, and algebraic structures

  Machine Learning Science and Technology · 2025-07-23 · 3 citations

  reviewOpen accessSenior author

  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 machine learning increasingly encounters richly structured data that is inherently non-Euclidean. This data can exhibit intricate geometric, topological and algebraic structure: from the geometry of the curvature of space-time, to topologically complex interactions between neurons in the brain, to the algebraic transformations describing symmetries of physical systems. Extracting knowledge from such non-Euclidean data necessitates a broader mathematical perspective. Echoing the 19th-century revolutions that gave rise to non-Euclidean geometry, an emerging line of research is redefining modern machine learning with non-Euclidean structures. Its goal: generalizing classical methods to unconventional data types with geometry, topology, and algebra. In this review, we provide an accessible gateway to this fast-growing field and propose a graphical taxonomy that integrates recent advances into an intuitive unified framework. We subsequently extract insights into current challenges and highlight exciting opportunities for future development in this field.

  PublisherDOI

• On the Approximation of the Riemannian Barycenter

  Lecture notes in computer science · 2025-10-19

  book-chapterOpen accessSenior author
  PublisherOA PDFDOI

• Learning from Landmarks, Curves, Surfaces, and Shapes in Geomstats

  ACM Transactions on Mathematical Software · 2025-12-12 · 1 citations

  articleSenior author

  We introduce the shape module of the Python package Geomstats to analyze shapes of objects represented as landmarks, curves, and surfaces across fields of natural sciences and engineering. The shape module first implements widely used shape spaces, such as the Kendall shape space, as well as elastic spaces of discrete curves and surfaces. The shape module further implements the abstract mathematical structures of group actions, fiber bundles, quotient spaces, and associated Riemannian metrics which allow users to build their own shape spaces. The Riemannian geometry tools enable users to compare, average, interpolate between shapes inside a given shape space. These essential operations can then be leveraged to perform statistics and machine learning on shape data. We present the object-oriented implementation of the shape module along with illustrative examples and show how it can be used to perform statistics and machine learning on shape spaces.

  PublisherDOI

• On the approximation of the Riemannian barycenter

  ArXiv.org · 2025-04-22

  preprintOpen accessSenior author

  We present a method to compute an approximate Riemannian barycenter of a collection of points lying on a Riemannian manifold. Our approach relies on the use of theoretically proven under- and overapproximations of the Riemannian distance function. We compare it to the exact computation of the Riemannian barycenter and to an approach that approximates the Riemannian logarithm using lifting maps. Experiments are conducted on the Stiefel manifold.

  PublisherOA PDFDOI

Frequent coauthors

• Xavier Pennec

  34 shared

• Frédéric Poitevin

  Stanford Medicine

  13 shared

• Susan Holmes

  Stanford University

  13 shared

• Nicolas Guigui

  ESPCI Paris

  12 shared

• Khanh Dao Duc

  University of British Columbia

  12 shared

• Axel Levy

  11 shared

• Mathilde Papillon

  10 shared

• Benjamin Charlier

  9 shared