arXiv subjects

David Méndez

Publications and source records attributed to David Méndez.

9 recordsLinked to original sources

arXiv2026

Supervised Classification Heads as Semantic Prototypes: Unlocking Vision-Language Alignment via Weight Recycling

Vision-Language Models (VLMs) excel at tasks like zero-shot classification and cross-modal retrieval by mapping images and text to a shared space, but this requires expensive end-to-end training with massive paired datasets. Current post-hoc alignment methods reduce computational costs by connecting pretrained encoders through lightweight mappings, yet still demand substantial paired data. In this work, we investigate the potential of repurposing the classification heads of pretrained vision models as semantic prototypes. The recycling of these weights, typically discarded after pretraining, unlocks two distinct capabilities: it enables zero-shot alignment by using weights as semantic anchors, and serves as a robust data augmentation strategy by mixing these prototypes with real image-text pairs. We demonstrate that integrating our approach with several state-of-the-art post-hoc alignment techniques consistently boosts accuracy in cross-modal retrieval, zero- and few-shot classification tasks.

cs.CV↗

arXiv2025

CUBIC: Concept Embeddings for Unsupervised Bias Identification using VLMs

Deep vision models often rely on biases learned from spurious correlations in datasets. To identify these biases, methods that interpret high-level, human-understandable concepts are more effective than those relying primarily on low-level features like heatmaps. A major challenge for these concept-based methods is the lack of image annotations indicating potentially bias-inducing concepts, since creating such annotations requires detailed labeling for each dataset and concept, which is highly labor-intensive. We present CUBIC (Concept embeddings for Unsupervised Bias IdentifiCation), a novel method that automatically discovers interpretable concepts that may bias classifier behavior. Unlike existing approaches, CUBIC does not rely on predefined bias candidates or examples of model failures tied to specific biases, as such information is not always available. Instead, it leverages image-text latent space and linear classifier probes to examine how the latent representation of a superclass label$\unicode{x2014}$shared by all instances in the dataset$\unicode{x2014}$is influenced by the presence of a given concept. By measuring these shifts against the normal vector to the classifier's decision boundary, CUBIC identifies concepts that significantly influence model predictions. Our experiments demonstrate that CUBIC effectively uncovers previously unknown biases using Vision-Language Models (VLMs) without requiring the samples in the dataset where the classifier underperforms or prior knowledge of potential biases.

cs.CV↗

arXiv2022

The ring of stable homotopy classes of self-maps of $A_n^2$-polyhedra

We raise the problem of realisability of rings as $\{X,X\}$ the ring of stable homotopy classes of self-maps of a space $X$. By focusing on $A_n^2$-polyhedra, we show that the direct sum of three endomorphism rings of abelian groups, one of which must be free, is realisable as $\{X,X\}$ modulo the acyclic maps. We also show that $\mathbb{F}_p^3$ is not realisable in the setting of finite type $A_n^2$-polyhedra, for $p$ any prime.

math.AT↗

arXiv2021

A directed persistent homology theory for dissimilarity functions

We develop a theory of persistent homology for directed simplicial complexes which detects persistent directed cycles in odd dimensions. We relate directed persistent homology to classical persistent homology, prove some stability results, and discuss the computational challenges of our approach. Our directed persistent homology theory is motivated by homology with semiring coefficients: by explicitly removing additive inverses, we are able to detect directed cycles algebraically.

math.AT↗

arXiv2020

Colouring simplicial complexes via the Lechuga-Murillo's model

L. Lechuga and A. Murillo showed that a non-oriented, simple, connected, finite graph $G$ is $k$-colourable if and only if a certain pure Sullivan algebra associated to $G$ and $k$ is not elliptic. In this paper, we extend this result to simplicial complexes by means of several notions of colourings of these objects.

math.AT↗

arXiv2020

The group of self-homotopy equivalences of $A_n^2$-polyhedra

Let $X$ be a finite type $A_n^2$-polyhedron, $n \geq 2$. In this paper we study the quotient group $\mathcal{E}(X)/\mathcal{E}_*(X)$, where $\mathcal{E}(X)$ is the group of self-homotopy equivalences of $X$ and $\mathcal{E}_*(X)$ the subgroup of self-homotopy equivalences inducing the identity on the homology groups of $X$. We show that not every group can be realised as $\mathcal{E}(X)$ or $\mathcal{E}(X)/\mathcal{E}_*(X)$ for $X$ an $A_n^2$-polyhedron, $n\ge 3$, and specific results are obtained for $n=2$.

math.AT↗

arXiv2019

Realisability problem in arrow categories

In this paper we raise the realisability problem in arrow categories. Namely, for a fixed category $\mathcal{C}$ and for arbitrary groups $H\le G_1\times G_2$, is there an object $ϕ\colon A_1 \rightarrow A_2$ in $\operatorname{Arr}(\mathcal{C})$ such that $\operatorname{Aut}_{\operatorname{Arr}(\mathcal{C})}(ϕ) = H$, $\operatorname{Aut}_{\mathcal{C}}(A_1) = G_1$ and $\operatorname{Aut}_{\mathcal{C}}(A_2) = G_2$? We are interested in solving this problem when $\mathcal C =\mathcal{H}oTop_*$, the homotopy category of pointed topological spaces. To that purpose, we first settle that question in the positive when $\mathcal C = \mathcal{G}raphs$. Then, we construct an almost fully faithful functor from $\mathcal{G}raphs$ to $\operatorname{CDGA}$, the category of commutative differential graded algebras, that provides among other things, a positive answer to our question when $\mathcal C = \operatorname{CDGA}$ and, as long as we work with finite groups, when $\mathcal C =\mathcal{H}oTop_*$. Some results on representability of concrete categories are also obtained.

math.AT↗

arXiv2019

Representability of permutation representations on coalgebras and the isomorphism problem

Let $G$ be a group and let $ρ\colon G\to\operatorname{Sym}(V)$ be a permutation representation of $G$ on a set $V$. We prove that there is a faithful $G$-coalgebra $C$ such that $G$ arises as the image of the restriction of $\operatorname{Aut}(C)$ to $G(C)$, the set of grouplike elements of $C$. Furthermore, we show that $V$ can be regarded as a subset of $G(C)$ invariant through the $G$-action, and that the composition of the inclusion $G\hookrightarrow\operatorname{Aut}(C)$ with the restriction $\operatorname{Aut}(C)\to\operatorname{Sym}(V)$ is precisely $ρ$. We use these results to prove that isomorphism classes of certain families of groups can be distinguished through the coalgebras on which they act faithfully.

math.RT↗

arXiv2017

Homotopically rigid Sullivan algebras and Their applications

In this paper we construct an infinite family of homotopically rigid spaces. These examples are then used as building blocks to forge highly connected rational spaces with prescribed finite group of self-homotopy equivalences. They are also exploited to provide highly connected inflexible and strongly chiral manifolds.

math.AT↗