Alejandro Ascarate

Alejandro Ascarate, Leo Lebrat, Rodrigo Santa Cruz et al.

Variational autoencoders (VAE) encode data into lower-dimensional latent vectors before decoding those vectors back to data. Once trained, one can hope to detect out-of-distribution (abnormal) latent vectors, but several issues arise when the latent space is high dimensional. This includes an exponential growth of the hypervolume with the dimension, which severely affects the generative capacity of the VAE. In this paper, we draw insights from high dimensional statistics: in these regimes, the latent vectors of a standard VAE are distributed on the `equators' of a hypersphere, challenging the detection of anomalies. We propose to formulate the latent variables of a VAE using hyperspherical coordinates, which allows compressing the latent vectors towards a given direction on the hypersphere, thereby allowing for a more expressive approximate posterior. We show that this improves both the fully unconditional-OOD and conditional-OOD anomaly detection ability of the VAE, achieving the best performance on the datasets we considered, outperforming existing methods. For the unconditional-OOD and conditional-OOD modalities, respectively, these are: i) detecting unusual landscape from the Mars Rover camera and unusual Galaxies from ground based imagery (complex, real world datasets); ii) standard benchmarks like Cifar10 and subsets of ImageNet as the in-distribution (ID) class.

Alejandro Ascarate, Leo Lebrat, Rodrigo Santa Cruz et al.

Many practical anomalies are not merely rare inputs, but violations of semantic constraints: objects co-occur in structured ways, actions imply preconditions, and events satisfy temporal or relational regularities. We study anomaly detection in this setting, where constraints are given as logical rules over learned visual concepts, but real rule violations are rare or absent during training. We propose a neural rule evaluator that compiles each constraint into a directed acyclic graph and learns feature-aware subtree MLP gates for its internal logical operators. Each gate maps child features and edge-level negations to a parent representation and a rule-satisfaction probability, with intermediate supervision obtained from exact Boolean propagation over ground-truth concept labels. The key difficulty is that same-image training data often provide insufficient coverage of informative truth configurations and also allow shortcut solutions. To address this, we introduce chimera training: an operand-level counterfactual construction at the feature level. Instead of mixing input images, we concatenate subtree features from different samples; each operand keeps the hard truth label of the sample it came from, and the chimera target is obtained by applying the node's logical operator to those inherited labels. This supplies supervised logical counterexamples without requiring real anomalous images. Across CLEVRER, OpenImages, and VidOR, the resulting evaluator improves rule-level anomaly AUROC over independent-events and same-image semantic-training baselines, especially for compositional and relational rules. The method yields both scalar anomaly scores and rule-level attributions.

Alejandro Ascarate, Leo Lebrat, Rodrigo Santa Cruz et al.

Within-dataset class-split evaluation is widely used as a proxy for fully unconditional out-of-distribution anomaly detection. We show that this protocol can become ill-posed when the held-out anomaly class overlaps the normal mixture in representation space. In this regime, anomaly scores may collapse toward chance or even invert, and the preferred score direction can depend on the unknown anomaly class. We introduce a simple training-free diagnostic, neighborhood class leakage, and show that it predicts score-direction instability across Fashion-MNIST, CIFAR-10, and Imagenette, in both pixel and VAE latent spaces. Our results suggest that class-split AD benchmarks should be treated as geometry-dependent stress tests rather than unconditional evidence of anomaly-detection ability.

Alejandro Ascarate, Leo Lebrat, Rodrigo Santa Cruz et al.

We study autoencoder and variational-autoencoder latent spaces through the lens of spin-glass theory. The paper has two components. First, we formalize a latent-space spin-glass dictionary: for a fixed decoder, the reconstruction term together with a hyperspherical coordinates prior induces a Hamiltonian on the latent sphere, where latent coordinates play the role of continuous spins and the prior acts as an external magnetic field. This allows us to import operational spin-glass diagnostics -- overlap distributions, susceptibility, and block-spin coarse-graining -- to detect ordered, disordered, and edge-of-stability phases in trained latent representations. Second, we show that deliberately driving the latent system toward the edge-of-stability of the topological trivialization regime has concrete downstream consequences. In generation, hyperspherical compression improves the reconstruction-generation trade-off on CIFAR-10 and CelebA64, yielding lower self-FID while preserving or improving reconstruction. In anomaly detection, the same semi-ordered latent geometry improves both fully unsupervised and conditional OOD detection, including real-world Mars Rover and Galaxy Zoo datasets, as well as CIFAR-10/100 and Imagenette-based OOD benchmarks. We therefore advocate a phase-aware evaluation paradigm for AEs/VAEs, in which spin-glass observables complement standard ML metrics and expose the latent regimes that underlie downstream success or failure in many cases.

Alejandro Ascarate, Leo Lebrat, Rodrigo Santa Cruz et al.

Variational autoencoders (VAE) encode data into lower-dimensional latent vectors before decoding those vectors back to data. Once trained, decoding a random latent vector from the prior usually does not produce meaningful data, at least when the latent space has more than a dozen dimensions. In this paper, we investigate this issue by drawing insight from high dimensional statistics: in these regimes, the latent vectors of a standard VAE are by construction distributed uniformly on a hypersphere. We propose to formulate the latent variables of a VAE using hyperspherical coordinates, which allows compressing the latent vectors towards an island on the hypersphere, thereby reducing the latent sparsity and we show that this improves the generation ability of the VAE. We propose a new parameterization of the latent space with limited computational overhead.