Researcher profile

Asael Fabian Martínez

Asael Fabian Martínez contributes to research discovery and scholarly infrastructure.

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Published work

3 published item(s)

preprint2026arXiv

Inducing Spatial Locality in Vision Transformers through the Training Protocol

We investigate whether the training protocol can induce spatial locality in the early layers of a Vision Transformer (ViT) trained from scratch, without large-scale pretraining. Keeping the architecture and optimization procedure fixed, we compare a Baseline protocol with a Modern protocol (AutoAugment/ColorJitter, CutMix, and Label Smoothing) on CIFAR-10, CIFAR-100, and Tiny-ImageNet, characterizing each attention head via Mean Attention Distance (MAD) and normalized entropy. Across all three datasets, the Modern protocol produces more local and more concentrated attention in early layers; on CIFAR-100, the minimum MAD drops from 0.316 (Baseline) to 0.008 (Modern). To identify the source of this effect, we conduct an ablation study on CIFAR-100 by adding or removing each component individually. The results identify CutMix as the determining component within our experiments: all conditions with CutMix exhibit MAD 0.024, while all conditions without CutMix remain at MAD 0.210. AutoAugment and Label Smoothing show no independent effect on locality. Taken together, these findings suggest that the pressure to classify from partial image regions, induced by CutMix, can promote the emergence of local attention in Vision Transformers.

preprint2022arXiv

Bayesian estimation of topological features of persistence diagrams

Persistent homology is a common technique in topological data analysis providing geometrical and topological information about the sample space. All this information, known as topological features, is summarized in persistence diagrams, and the main interest is in identifying the most persisting ones since they correspond to the Betti number values. Given the randomness inherent in the sampling process, and the complex structure of the space where persistence diagrams take values, estimation of Betti numbers is not straightforward. The approach followed in this work makes use of features' lifetimes and provides a full Bayesian clustering model, based on random partitions, in order to estimate Betti numbers. A simulation study is also presented.

preprint2022arXiv

Clustering constrained on linear networks

An unsupervised classification method for point events occurring on a network of lines is proposed. The idea relies on the distributional flexibility and practicality of random partition models to discover the clustering structure featuring observations from a particular phenomenon taking place on a given set of edges. By incorporating the spatial effect in the random partition distribution, induced by a Dirichlet process, one is able to control the distance between edges and events, thus leading to an appealing clustering method. A Gibbs sampler algorithm is proposed and evaluated with a sensitivity analysis. The proposal is motivated and illustrated by the analysis of crime and violence patterns in Mexico City.