Latent-Space No-Arbitrage Geometry of Generative Models for Implied Volatility Surfaces

Generative models for implied volatility surfaces must produce outputs that satisfy static no-arbitrage constraints. We study these constraints in latent space. For a fixed generator, we assign each latent code a scalar margin determined by the no-arbitrage conditions of the generated surface. The codes with nonnegative margin form the admissible latent set. We establish conditions under which strictly admissible codes remain admissible under small perturbations and the boundary of the admissible set is characterized by zero margin. For regular boundary components, we formulate a level-set equation whose local dynamics are directed toward the zero-margin set. The analysis treats the generator as a map from latent variables to surfaces and is therefore not restricted to a particular architecture. It applies to variational autoencoders, generative adversarial networks, and other generative models with a deterministic realization map. Numerical tests recover known boundaries in analytic examples. Experiments with a variational autoencoder trained on Heston surfaces show that similar reconstruction errors can correspond to different admissible regions and that the latent prior may be concentrated inside such a region. The computed boundary can also be used to modify latent codes that generate violating surfaces.

Linguistic Distance Segregates Latent Representations in Automatic Speech Recognition Systems

While automatic speech recognition (ASR) models have achieved remarkable improvements in recent years, performance disparities persist across different speaker populations. One such disparity is for speakers whose first languages (L1) are from families distant from English. This paper investigates the relationship between first language background and English ASR performance. Through empirical analysis, we observe that the correlation between speakers' L1 distance and ASR error rates yields a systematic effect on English Speech, with its strength varying across datasets and models. This association is statistically significant in a follow-up analysis accounting for dataset-level variation in Tweedie mixed-effects models ($p<0.001$ across evaluated models). In addition, analysis of the latent space reveals a L1-based spatial segregation across deeper acoustic layers in the majority of evaluated architectures

Aristotelian Manifolds: Leveraging Platonic Perceptual Features for Backpropagation Free Rapid Concept Learning

This paper formalizes and systematically characterizes Aristotelian Manifolds, a generalized structural framework built upon the Platonic Representation Hypothesis. We position high-capacity foundation models as universal perceptual filters and conduct a comprehensive layer-wise investigation to map how knowledge is functionally synthesized within these latent subspaces. Across diverse architectural paradigms and multi-domain datasets, we rigorously chart the interplay between network depth, dimensionality reduction, and distance metrics. Our characterization reveals that semantic maturation does not follow a singular, monotonic path; instead, different data domains exhibit highly distinct geometric response profiles, characterized by intermediate mound-like peaks for specialized clinical modalities and sigmoidal plateaus for natural visual tasks. By profiling the exact coordinates where these manifolds achieve peak representational efficiency, we establish a predictable taxonomy for layer selection and feature compression. Ultimately, this systematic characterization demonstrates that mapping the internal geometry of frozen representations provides a robust, backpropagation-free, and interpretable framework for understanding and exploiting foundation model latent spaces.

How Molecular Generative Models Organize Molecular Identity

Generative models for matter are often evaluated as samplers over output representations, and their latent spaces are commonly used as proxies for navigating chemical space. Much less is known about how these models internally arrange discrete chemical identities within those representations. We study this arrangement by making molecular identity explicit and pulling it back through the generative process. Through these pullbacks we probe the regions that generate the same object, exposing the trained model's internal repertoire: a fixed partition that determines which objects (novel or not) the model can produce. Across three molecular generative architectures, we find that this repertoire is arranged into piecewise-constant regions separated by recurring coarse-to-fine boundaries. Its organization depends on the representation probed, the identity convention, decoder stochasticity, and the metric used to compare coordinates. During training, local chemical organization stabilizes while the number of distinct molecular identities represented within each neighborhood continues to change. Internal organization must therefore be characterized, rather than assumed, before a generative space can be treated as chemically navigable.

LatentFlow: Visual Analytics for Latent Space Analysis in Molecular Graph Neural Networks

Chemists and materials scientists increasingly use machine learning models, such as graph neural networks (GNNs), to predict properties of molecules and the outcomes of their reactions. Beyond predictive performance, understanding how these models organize chemical information internally in their latent spaces, i.e., the embeddings of the molecules, is critical. Analyzing latent spaces helps diagnose model behavior and assess whether the learned embeddings are organized in ways that reflect meaningful chemical relationships. Unfortunately, existing methods provide limited support for analyzing latent spaces across layers and across different model states (e.g., training epochs, model configurations, and input data), making it difficult to understand how these latent spaces evolve throughout a model or relate to chemical concepts. We present LatentFlow, a visual analytics system developed in collaboration with a domain expert for analyzing latent spaces in molecular GNNs. LatentFlow groups embeddings into clusters and supports exploration of latent spaces by tracking how these clusters change across layers and model states using a modified Sankey diagram. To support interpretation, LatentFlow links these clusters to representative molecules and their shared substructures, and it allows scientists to introduce their own domain knowledge and compare it with the patterns found in the latent spaces. We evaluate LatentFlow through two case studies. The results show that LatentFlow helps scientists understand how latent spaces evolve, identify meaningful molecular patterns, and better interpret model behavior.

On the Geometry of Learned Representations in Event-Based Multi-Modal Egomotion Estimation

Classical approaches to event-based egomotion estimation, including those adopted by the top-performing teams of the ELOPE challenge, rely on geometric optimization frameworks such as contrast maximization, homography estimation, or dense optical flow combined with analytic motion inversion. This work investigates the geometric structure that emerges inside a multi-modal network for egomotion estimation. Event tensors, inertial measurements, and range signals are fused through a cross-modal attention architecture and trained in a batch setting. We analyze the latent space geometry and attention dynamics, showing that (i) embeddings lie on low-dimensional manifolds aligned with motion variables, (ii) attention weights adapt with angular excitation and visual reliability, and (iii) the fused representation recovers classical observability cues. These results bridge analytical estimation theory and modern data-driven fusion.