Alison Pouplin

Paul Scherer, Alison Pouplin, Alice Del Vecchio et al.

Active learning (AL) is a sub-field of ML focused on the development of methods to iteratively and economically acquire data by strategically querying new data points that are the most useful for a particular task. Here, we introduce PyRelationAL, an open source library for AL research. We describe a modular toolkit based around a two step design methodology for composing pool-based active learning strategies applicable to both single-acquisition and batch-acquisition strategies. This framework allows for the mathematical and practical specification of a broad number of existing and novel strategies under a consistent programming model and abstraction. Furthermore, we incorporate datasets and active learning tasks applicable to them to simplify comparative evaluation and benchmarking, along with an initial group of benchmarks across datasets included in this library. The toolkit is compatible with existing ML frameworks. PyRelationAL is maintained using modern software engineering practices -- with an inclusive contributor code of conduct -- to promote long term library quality and utilisation. PyRelationAL is available under a permissive Apache licence on PyPi and at https://github.com/RelationRx/pyrelational.

Alison Pouplin, Hrittik Roy, Sidak Pal Singh et al. · eth-zurich

One of the main challenges in modern deep learning is to understand why such over-parameterized models perform so well when trained on finite data. A way to analyze this generalization concept is through the properties of the associated loss landscape. In this work, we consider the loss landscape as an embedded Riemannian manifold and show that the differential geometric properties of the manifold can be used when analyzing the generalization abilities of a deep net. In particular, we focus on the scalar curvature, which can be computed analytically for our manifold, and show connections to several settings that potentially imply generalization.

Alison Pouplin, David Eklund, Carl Henrik Ek et al.

Riemannian geometry provides us with powerful tools to explore the latent space of generative models while preserving the underlying structure of the data. The latent space can be equipped it with a Riemannian metric, pulled back from the data manifold. With this metric, we can systematically navigate the space relying on geodesics defined as the shortest curves between two points. Generative models are often stochastic, causing the data space, the Riemannian metric, and the geodesics, to be stochastic as well. Stochastic objects are at best impractical, and at worst impossible, to manipulate. A common solution is to approximate the stochastic pullback metric by its expectation. But the geodesics derived from this expected Riemannian metric do not correspond to the expected length-minimising curves. In this work, we propose another metric whose geodesics explicitly minimise the expected length of the pullback metric. We show this metric defines a Finsler metric, and we compare it with the expected Riemannian metric. In high dimensions, we prove that both metrics converge to each other at a rate of $O\left(\frac{1}{D}\right)$. This convergence implies that the established expected Riemannian metric is an accurate approximation of the theoretically more grounded Finsler metric. This provides justification for using the expected Riemannian metric for practical implementations.

Rafał Karczewski, Markus Heinonen, Alison Pouplin et al.

We present a novel geometric perspective on the latent space of diffusion models. We first show that the standard pullback approach, utilizing the deterministic probability flow ODE decoder, is fundamentally flawed. It provably forces geodesics to decode as straight segments in data space, effectively ignoring any intrinsic data geometry beyond the ambient Euclidean space. Complementing this view, diffusion also admits a stochastic decoder via the reverse SDE, which enables an information geometric treatment with the Fisher-Rao metric. However, a choice of $x_T$ as the latent representation collapses this metric due to memorylessness. We address this by introducing a latent spacetime $z=(x_t,t)$ that indexes the family of denoising distributions $p(x_0 | x_t)$ across all noise scales, yielding a nontrivial geometric structure. We prove these distributions form an exponential family and derive simulation-free estimators for curve lengths, enabling efficient geodesic computation. The resulting structure induces a principled Diffusion Edit Distance, where geodesics trace minimal sequences of noise and denoise edits between data. We also demonstrate benefits for transition path sampling in molecular systems, including constrained variants such as low-variance transitions and region avoidance. Code is available at: https://github.com/rafalkarczewski/spacetime-geometry

Olga Zaghen, Floor Eijkelboom, Alison Pouplin et al.

We present Riemannian Gaussian Variational Flow Matching (RG-VFM), a geometric extension of Variational Flow Matching (VFM) for generative modeling on manifolds. In Euclidean space, predicting endpoints (VFM), velocities (FM), or noise (diffusion) are largely equivalent due to affine interpolations. On curved manifolds this equivalence breaks down, and we hypothesize that endpoint prediction provides a stronger learning signal by directly minimizing geodesic distances. Building on this insight, we derive a variational flow matching objective based on Riemannian Gaussian distributions, applicable to manifolds with closed-form geodesics. We formally analyze its relationship to Riemannian Flow Matching (RFM), exposing that the RFM objective lacks a curvature-dependent penalty - encoded via Jacobi fields - that is naturally present in RG-VFM. Experiments on synthetic spherical and hyperbolic benchmarks, as well as real-world tasks in material and protein generation, demonstrate that RG-VFM more effectively captures manifold structure and improves downstream performance over Euclidean and velocity-based baselines.

Georgios Arvanitidis, Miguel González-Duque, Alison Pouplin et al.

Latent space geometry has shown itself to provide a rich and rigorous framework for interacting with the latent variables of deep generative models. The existing theory, however, relies on the decoder being a Gaussian distribution as its simple reparametrization allows us to interpret the generating process as a random projection of a deterministic manifold. Consequently, this approach breaks down when applied to decoders that are not as easily reparametrized. We here propose to use the Fisher-Rao metric associated with the space of decoder distributions as a reference metric, which we pull back to the latent space. We show that we can achieve meaningful latent geometries for a wide range of decoder distributions for which the previous theory was not applicable, opening the door to `black box' latent geometries.

Dimitris Kalatzis, Johan Ziruo Ye, Alison Pouplin et al.

We present a framework for learning probability distributions on topologically non-trivial manifolds, utilizing normalizing flows. Current methods focus on manifolds that are homeomorphic to Euclidean space, enforce strong structural priors on the learned models or use operations that do not easily scale to high dimensions. In contrast, our method learns distributions on a data manifold by "gluing" together multiple local models, thus defining an open cover of the data manifold. We demonstrate the efficiency of our approach on synthetic data of known manifolds, as well as higher dimensional manifolds of unknown topology, where our method exhibits better sample efficiency and competitive or superior performance against baselines in a number of tasks.

Antonia Creswell, Alison Pouplin, Anil A Bharath

We propose a novel deep learning model for classifying medical images in the setting where there is a large amount of unlabelled medical data available, but labelled data is in limited supply. We consider the specific case of classifying skin lesions as either malignant or benign. In this setting, the proposed approach -- the semi-supervised, denoising adversarial autoencoder -- is able to utilise vast amounts of unlabelled data to learn a representation for skin lesions, and small amounts of labelled data to assign class labels based on the learned representation. We analyse the contributions of both the adversarial and denoising components of the model and find that the combination yields superior classification performance in the setting of limited labelled training data.