arXiv subjects

Nina Miolane

Publications and source records attributed to Nina Miolane.

At least 19 recordsLinked to original sources

arXiv2026

Look Before You Lift: Visual and Quantitative Diagnostics for Topological Deep Learning

Topological deep learning (TDL) methods rely on lifting raw data into higher-order discrete domains such as simplicial complexes, cell complexes, and hypergraphs. In practice, this lifting step is often treated as a black box: practitioners select a lifting and then tune architectures, with limited visibility into whether the induced higher-order connectivity is meaningful for the downstream task. To address this missing diagnostic layer, we propose a visualization technique called TopoExplorer that leverages the strictly augmented Hasse graph form of topological datasets for exploratory data analysis. For the first time, practitioners can easily visualize the incidence- and adjacency-based neighborhoods that define the lifted dataset, as well as read off key graph metrics that describe its structural and feature landscape. Via an extensive set of experiments across many datasets and liftings, we show that several of these metrics correlate with downstream model performance, suggesting they can help inform TDL preprocessing design. Our perspective reframes the TDL workflow from lift-train to lift-look-design-train, enabling more principled, interpretable, and efficient model development. TopoExplorer is hosted at https://topoexplorer.pagekite.me, and its source code is available at github.com/geometric-intelligence/topoexplorer.

cs.LG↗

arXiv2026

Emergent topological structure in spontaneous brain-organoid activity

Neural activity is widely held to organize on low-dimensional structure embedded in a high-dimensional state space. Persistent homology reads such structure directly from the pattern of pairwise correlations, without assuming in advance which variables are relevant. We apply persistent homology to microelectrode-array (MEA) recordings of spontaneous activity from human (Lancaster) and mouse (Pa\c{s}ca) cortical organoids, spanning $26$--$234$ simultaneously sorted units, and ask whether topological data analysis resolves structure at the node counts that neural recordings actually deliver. Building weighted networks in correlation space and characterizing them by Vietoris--Rips filtration, we find that the first homology ($H_1$, loops) rises significantly above a rate- and population-preserving null in $14$ of $18$ datasets. This loop structure occupies a non-redundant core: it is robust to random removal of units yet disrupted by targeted removal of the units that carry it. Topological richness grows with network size, and second homology ($H_2$) emerges significantly above the null only in the larger networks. These results show that persistent homology resolves structured topology in neural recordings at the scale experiments actually deliver.

q-bio.NC↗

arXiv2026

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

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.

cs.AI↗

arXiv2026

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

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.

cs.LG↗

arXiv2026

bispectrum: Selective $G$-Bispectra Made Practical

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 $\Theta(L^2)$ 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.

cs.LG↗

arXiv2026

Sequential Group Composition: A Window into the Mechanics of Deep Learning

How do neural networks trained over sequences acquire the ability to perform structured operations, such as arithmetic, geometric, and algorithmic computation? To gain insight into this question, we introduce the sequential group composition task. In this task, networks receive a sequence of elements from a finite group encoded in a real vector space and must predict their cumulative product. This task can be order-sensitive and cannot be solved by a linear model. Our analysis isolates the roles of the group structure, encoding statistics, and sequence length in shaping learning. We prove that two-layer networks from vanishing initialization learn this task one irreducible representation of the group at a time in an order determined by the Fourier statistics of the encoding. To perfectly learn the task, these networks require a hidden width exponential in the sequence length $k$. In contrast, we construct deeper architectures that exploit associativity to dramatically improve this scaling: recurrent neural networks can compose elements sequentially in $k$ steps, while multilayer networks can compose adjacent pairs in parallel in $\log k$ layers. Overall, the sequential group composition task offers a tractable window into the mechanics of deep learning.

cs.LG↗

arXiv2025

Alternating Gradient Flows: A Theory of Feature Learning in Two-layer Neural Networks

What features neural networks learn, and how, remains an open question. In this paper, we introduce Alternating Gradient Flows (AGF), an algorithmic framework that describes the dynamics of feature learning in two-layer networks trained from small initialization. Prior works have shown that gradient flow in this regime exhibits a staircase-like loss curve, alternating between plateaus where neurons slowly align to useful directions and sharp drops where neurons rapidly grow in norm. AGF approximates this behavior as an alternating two-step process: maximizing a utility function over dormant neurons and minimizing a cost function over active ones. AGF begins with all neurons dormant. At each iteration, a dormant neuron activates, triggering the acquisition of a feature and a drop in the loss. AGF quantifies the order, timing, and magnitude of these drops, matching experiments across several commonly studied architectures. We show that AGF unifies and extends existing saddle-to-saddle analyses in fully connected linear networks and attention-only linear transformers, where the learned features are singular modes and principal components, respectively. In diagonal linear networks, we prove AGF converges to gradient flow in the limit of vanishing initialization. Applying AGF to quadratic networks trained to perform modular addition, we give the first complete characterization of the training dynamics, revealing that networks learn Fourier features in decreasing order of coefficient magnitude. Altogether, AGF offers a promising step towards understanding feature learning in neural networks.

cs.LG↗

arXiv2025

Selective Disk Bispectrum: A Complete and Rotation Invariant Image Descriptor

Rotation invariance is a fundamental requirement across many computer vision tasks. Historically, this inductive bias has been encoded through hand-crafted rotation-invariant representations. These are compact, interpretable, and fast to compute, but they come at the cost of descriptive power. More recently, architectures achieve inductive bias through learned representations. These are highly descriptive and achieve strong empirical performance, at the cost of efficiency and interpretability. In this work, we propose an alternative at the intersection of both paradigms. We introduce the selective disk bispectrum (SDB), a complex-valued rotation-invariant vector that preserves all information about the image except its orientation. Our key theoretical contributions are the selective disk bispectrum, its inversion, its (reduced) spatial and computational complexities (compared to the full disk bispectrum), and its expectation and variance under noise. Furthermore, we propose a numerical SDB approximation and provide theoretical guarantees for its accuracy and rotation invariance. Empirically, we validate SDB's invariance and robustness to noise classification tasks. We test our reconstruction algorithm on multi-reference alignment of rotated images.

eess.IV↗

arXiv2025

TopoTune : A Framework for Generalized Combinatorial Complex Neural Networks

Graph Neural Networks (GNNs) effectively learn from relational data by leveraging graph symmetries. However, many real-world systems -- such as biological or social networks -- feature multi-way interactions that GNNs fail to capture. Topological Deep Learning (TDL) addresses this by modeling and leveraging higher-order structures, with Combinatorial Complex Neural Networks (CCNNs) offering a general and expressive approach that has been shown to outperform GNNs. However, TDL lacks the principled and standardized frameworks that underpin GNN development, restricting its accessibility and applicability. To address this issue, we introduce Generalized CCNNs (GCCNs), a simple yet powerful family of TDL models that can be used to systematically transform any (graph) neural network into its TDL counterpart. We prove that GCCNs generalize and subsume CCNNs, while extensive experiments on a diverse class of GCCNs show that these architectures consistently match or outperform CCNNs, often with less model complexity. In an effort to accelerate and democratize TDL, we introduce TopoTune, a lightweight software for defining, building, and training GCCNs with unprecedented flexibility and ease.

cs.LG↗

arXiv2025

GraphUniverse: Synthetic Graph Generation for Evaluating Inductive Generalization

A fundamental challenge in graph learning is understanding how models generalize to new, unseen graphs. While synthetic benchmarks offer controlled settings for analysis, existing approaches are confined to single-graph, transductive settings where models train and test on the same graph structure. Addressing this gap, we introduce GraphUniverse, a framework for generating entire families of graphs to enable the first systematic evaluation of inductive generalization at scale. Our core innovation is the generation of graphs with persistent semantic communities, ensuring conceptual consistency while allowing fine-grained control over structural properties like homophily and degree distributions. This enables crucial but underexplored robustness tests, such as performance under controlled distribution shifts. Benchmarking a wide range of architectures -- from GNNs to graph transformers and topological architectures -- reveals that strong transductive performance is a poor predictor of inductive generalization. Furthermore, we find that robustness to distribution shift is highly sensitive not only to model architecture choice but also to the initial graph regime (e.g., high vs. low homophily). Beyond benchmarking, GraphUniverse's flexibility and scalability can facilitate the development of robust and truly generalizable architectures. The framework is open-source at https://github.com/LouisVanLangendonck/GraphUniverse.

cs.LG↗

arXiv2025

TopoBench: A Framework for Benchmarking Topological Deep Learning

This work introduces TopoBench, an open-source library designed to standardize benchmarking and accelerate research in topological deep learning (TDL). TopoBench decomposes TDL into a sequence of independent modules for data generation, loading, transforming and processing, as well as model training, optimization and evaluation. This modular organization provides flexibility for modifications and facilitates the adaptation and optimization of various TDL pipelines. A key feature of TopoBench is its support for transformations and lifting across topological domains. Mapping the topology and features of a graph to higher-order topological domains, such as simplicial and cell complexes, enables richer data representations and more fine-grained analyses. The applicability of TopoBench is demonstrated by benchmarking several TDL architectures across diverse tasks and datasets.

cs.LG↗

arXiv2025

Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures

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 nonEuclidean. 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.

cs.LG↗

arXiv2025

On the approximation of the Riemannian barycenter

We present a method for computing 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 over-approximations of the Riemannian distance function. We compare it to Riemannian steepest descent on the exact objective function of the Riemannian barycenter and to an approach that approximates the Riemannian logarithm using lifting maps. Experiments are conducted on the Stiefel manifold.

math.DG↗

arXiv2025

Dynamical phases of short-term memory mechanisms in RNNs

Short-term memory is essential for cognitive processing, yet our understanding of its neural mechanisms remains unclear. Neuroscience has long focused on how sequential activity patterns, where neurons fire one after another within large networks, can explain how information is maintained. While recurrent connections were shown to drive sequential dynamics, a mechanistic understanding of this process still remains unknown. In this work, we introduce two unique mechanisms that can support this form of short-term memory: slow-point manifolds generating direct sequences or limit cycles providing temporally localized approximations. Using analytical models, we identify fundamental properties that govern the selection of each mechanism. Precisely, on short-term memory tasks (delayed cue-discrimination tasks), we derive theoretical scaling laws for critical learning rates as a function of the delay period length, beyond which no learning is possible. We empirically verify these results by training and evaluating approximately 80,000 recurrent neural networks (RNNs), which are publicly available for further analysis. Overall, our work provides new insights into short-term memory mechanisms and proposes experimentally testable predictions for systems neuroscience.

q-bio.NC↗

arXiv2025

Unsupervised cell segmentation by fast Gaussian Processes

Cell boundary information is crucial for analyzing cell behaviors from time-lapse microscopy videos. Existing supervised cell segmentation tools, such as ImageJ, require tuning various parameters and rely on restrictive assumptions about the shape of the objects. While recent supervised segmentation tools based on convolutional neural networks enhance accuracy, they depend on high-quality labeled images, making them unsuitable for segmenting new types of objects not in the database. We developed a novel unsupervised cell segmentation algorithm based on fast Gaussian processes for noisy microscopy images without the need for parameter tuning or restrictive assumptions about the shape of the object. We derived robust thresholding criteria adaptive for heterogeneous images containing distinct brightness at different parts to separate objects from the background, and employed watershed segmentation to distinguish touching cell objects. Both simulated studies and real-data analysis of large microscopy images demonstrate the scalability and accuracy of our approach compared with the alternatives.

stat.AP↗

arXiv2025

HOPSE: Scalable Higher-Order Positional and Structural Encoder for Combinatorial Representations

While Graph Neural Networks (GNNs) have proven highly effective at modeling relational data, pairwise connections cannot fully capture multi-way relationships naturally present in complex real-world systems. In response to this, Topological Deep Learning (TDL) leverages more general combinatorial representations--such as simplicial or cellular complexes--to accommodate higher-order interactions. Existing TDL methods often extend GNNs through Higher-Order Message Passing (HOMP), but face critical scalability challenges due to the steep complexity overhead of propagating messages through combinatorial structures. To overcome this limitation, we propose HOPSE (Higher-Order Positional and Structural Encoder), a framework free of message passing layers that uses Hasse graph decompositions to derive efficient and expressive encodings over arbitrary higher-order domains. Notably, HOPSE scales linearly with the size of combinatorial representations while preserving the expressive power and permutation equivariance of the HOMP approaches. Experiments on molecular and topological benchmarks show that it matches or surpasses state-of-the-art performance while consistently achieving speedups over HOMP-based models, opening a new path for scalable TDL. The code is available at https://github.com/geometric-intelligence/topobench.git.

cs.LG↗

arXiv2025

Ordered Topological Deep Learning: a Network Modeling Case Study

Computer networks are the foundation of modern digital infrastructure, facilitating global communication and data exchange. As demand for reliable high-bandwidth connectivity grows, advanced network modeling techniques become increasingly essential to optimize performance and predict network behavior. Traditional modeling methods, such as packet-level simulators and queueing theory, have notable limitations --either being computationally expensive or relying on restrictive assumptions that reduce accuracy. In this context, the deep learning-based RouteNet family of models has recently redefined network modeling by showing an unprecedented cost-performance trade-off. In this work, we revisit RouteNet's sophisticated design and uncover its hidden connection to Topological Deep Learning (TDL), an emerging field that models higher-order interactions beyond standard graph-based methods. We demonstrate that, although originally formulated as a heterogeneous Graph Neural Network, RouteNet serves as the first instantiation of a new form of TDL. More specifically, this paper presents OrdGCCN, a novel TDL framework that introduces the notion of ordered neighbors in arbitrary discrete topological spaces, and shows that RouteNet's architecture can be naturally described as an ordered topological neural network. To the best of our knowledge, this marks the first successful real-world application of state-of-the-art TDL principles --which we confirm through extensive testbed experiments--, laying the foundation for the next generation of ordered TDL-driven applications.

cs.LG↗

arXiv2025

From superposition to sparse codes: interpretable representations in neural networks

Understanding how information is represented in neural networks is a fundamental challenge in both neuroscience and artificial intelligence. Despite their nonlinear architectures, recent evidence suggests that neural networks encode features in superposition, meaning that input concepts are linearly overlaid within the network's representations. We present a perspective that explains this phenomenon and provides a foundation for extracting interpretable representations from neural activations. Our theoretical framework consists of three steps: (1) Identifiability theory shows that neural networks trained for classification recover latent features up to a linear transformation. (2) Sparse coding methods can extract disentangled features from these representations by leveraging principles from compressed sensing. (3) Quantitative interpretability metrics provide a means to assess the success of these methods, ensuring that extracted features align with human-interpretable concepts. By bridging insights from theoretical neuroscience, representation learning, and interpretability research, we propose an emerging perspective on understanding neural representations in both artificial and biological systems. Our arguments have implications for neural coding theories, AI transparency, and the broader goal of making deep learning models more interpretable.

cs.LG↗