arXiv subjects

João Paulo Costeira

Publications and source records attributed to João Paulo Costeira.

10 recordsLinked to original sources

arXiv2026

Native Hierarchical and Compositional Representations with Subspace Embeddings

Traditional embeddings represent datapoints as vectors, which makes similarity easy to compute but limits how well they capture hierarchies and compositionality. We propose a fundamentally different approach: representing concepts as linear subspaces. By spanning multiple dimensions, subspaces can model broader concepts with higher-dimensional regions and nest more specific concepts within them. This geometry naturally captures generality through dimension, hierarchy through inclusion, and enables an emergent structure for composition via linear algebraic operations. To make this paradigm trainable, we introduce a differentiable subspace parameterization via soft projection matrices, allowing the effective dimension of each subspace to be learned. Our method not only achieves state-of-the-art performance on hierarchical and natural language inference benchmarks but also provides a geometrically-grounded model of entailment. Further, we demonstrate that while standard vector embeddings degrade to near-random performance on negated queries, subspace embeddings natively capture logical composition without explicit supervision, while preserving compatibility with efficient Euclidean vector search.

cs.LG↗

arXiv2026

Spectral Guidance for Flexible and Efficient Control of Diffusion Models

We introduce Spectral Guidance, a framework for controlling diffusion models by leveraging the intrinsic geometry of the generative process. As data is progressively corrupted by noise, only a small number of features remain informative for control. We characterize them as the singular functions of a conditional expectation operator and show that they can be learned via a self-supervised objective. Once recovered, this basis enables the projection of arbitrary guidance signals, such as labels, CLIP embeddings, or masks, directly onto the sampling trajectory. This approach allows for stable, high-fidelity control without retraining or denoiser backpropagation during sampling. Empirically, we improve conditional accuracy on CIFAR-10 by 37 percentage points over the strongest training-free baseline while offering $4\times$ faster sampling. Moreover, the same representations that support label and CLIP guidance also enable spatial control, such as mask-based guidance, without auxiliary models. Finally, our framework reveals a phase transition in the generative process, pinpointing the optimal time window for effective guidance.

cs.LG↗

arXiv2025

Learning Visual-Semantic Subspace Representations

Learning image representations that capture rich semantic relationships remains a significant challenge. Existing approaches are either contrastive, lacking robust theoretical guarantees, or struggle to effectively represent the partial orders inherent to structured visual-semantic data. In this paper, we introduce a nuclear norm-based loss function, grounded in the same information theoretic principles that have proved effective in self-supervised learning. We present a theoretical characterization of this loss, demonstrating that, in addition to promoting class orthogonality, it encodes the spectral geometry of the data within a subspace lattice. This geometric representation allows us to associate logical propositions with subspaces, ensuring that our learned representations adhere to a predefined symbolic structure.

cs.CV↗

arXiv2024

Rotation Averaging: A Primal-Dual Method and Closed-Forms in Cycle Graphs

A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In addition to being an integral part of bundle adjustment and structure-from-motion, the problem of synchronizing rotations also finds applications in visual simultaneous localization and mapping, where it is used as an initialization for iterative solvers, and camera network calibration. Nevertheless, this optimization problem is both non-convex and high-dimensional. In this paper, we address it from a maximum likelihood estimation standpoint and make a twofold contribution. Firstly, we set forth a novel primal-dual method, motivated by the widely accepted spectral initialization. Further, we characterize stationary points of rotation averaging in cycle graphs topologies and contextualize this result within spectral graph theory. We benchmark the proposed method in multiple settings and certify our solution via duality theory, achieving a significant gain in precision and performance.

cs.CV↗

arXiv2024

VICAN: Very Efficient Calibration Algorithm for Large Camera Networks

The precise estimation of camera poses within large camera networks is a foundational problem in computer vision and robotics, with broad applications spanning autonomous navigation, surveillance, and augmented reality. In this paper, we introduce a novel methodology that extends state-of-the-art Pose Graph Optimization (PGO) techniques. Departing from the conventional PGO paradigm, which primarily relies on camera-camera edges, our approach centers on the introduction of a dynamic element - any rigid object free to move in the scene - whose pose can be reliably inferred from a single image. Specifically, we consider the bipartite graph encompassing cameras, object poses evolving dynamically, and camera-object relative transformations at each time step. This shift not only offers a solution to the challenges encountered in directly estimating relative poses between cameras, particularly in adverse environments, but also leverages the inclusion of numerous object poses to ameliorate and integrate errors, resulting in accurate camera pose estimates. Though our framework retains compatibility with traditional PGO solvers, its efficacy benefits from a custom-tailored optimization scheme. To this end, we introduce an iterative primal-dual algorithm, capable of handling large graphs. Empirical benchmarks, conducted on a new dataset of simulated indoor environments, substantiate the efficacy and efficiency of our approach.

cs.CV↗

arXiv2023

2D Image head pose estimation via latent space regression under occlusion settings

Head orientation is a challenging Computer Vision problem that has been extensively researched having a wide variety of applications. However, current state-of-the-art systems still underperform in the presence of occlusions and are unreliable for many task applications in such scenarios. This work proposes a novel deep learning approach for the problem of head pose estimation under occlusions. The strategy is based on latent space regression as a fundamental key to better structure the problem for occluded scenarios. Our model surpasses several state-of-the-art methodologies for occluded HPE, and achieves similar accuracy for non-occluded scenarios. We demonstrate the usefulness of the proposed approach with: (i) two synthetically occluded versions of the BIWI and AFLW2000 datasets, (ii) real-life occlusions of the Pandora dataset, and (iii) a real-life application to human-robot interaction scenarios where face occlusions often occur. Specifically, the autonomous feeding from a robotic arm.

cs.CV↗

arXiv2023

Hyperbolic vs Euclidean Embeddings in Few-Shot Learning: Two Sides of the Same Coin

Recent research in representation learning has shown that hierarchical data lends itself to low-dimensional and highly informative representations in hyperbolic space. However, even if hyperbolic embeddings have gathered attention in image recognition, their optimization is prone to numerical hurdles. Further, it remains unclear which applications stand to benefit the most from the implicit bias imposed by hyperbolicity, when compared to traditional Euclidean features. In this paper, we focus on prototypical hyperbolic neural networks. In particular, the tendency of hyperbolic embeddings to converge to the boundary of the Poincaré ball in high dimensions and the effect this has on few-shot classification. We show that the best few-shot results are attained for hyperbolic embeddings at a common hyperbolic radius. In contrast to prior benchmark results, we demonstrate that better performance can be achieved by a fixed-radius encoder equipped with the Euclidean metric, regardless of the embedding dimension.

cs.CV↗

arXiv2021

Rotation Averaging in a Split Second: A Primal-Dual Method and a Closed-Form for Cycle Graphs

A cornerstone of geometric reconstruction, rotation averaging seeks the set of absolute rotations that optimally explains a set of measured relative orientations between them. In spite of being an integral part of bundle adjustment and structure-from-motion, averaging rotations is both a non-convex and high-dimensional optimization problem. In this paper, we address it from a maximum likelihood estimation standpoint and make a twofold contribution. Firstly, we set forth a novel initialization-free primal-dual method which we show empirically to converge to the global optimum. Further, we derive what is to our knowledge, the first optimal closed-form solution for rotation averaging in cycle graphs and contextualize this result within spectral graph theory. Our proposed methods achieve a significant gain both in precision and performance.

cs.CV↗

arXiv2017

LocDyn: Robust Distributed Localization for Mobile Underwater Networks

How to self-localize large teams of underwater nodes using only noisy range measurements? How to do it in a distributed way, and incorporating dynamics into the problem? How to reject outliers and produce trustworthy position estimates? The stringent acoustic communication channel and the accuracy needs of our geophysical survey application demand faster and more accurate localization methods. We approach dynamic localization as a MAP estimation problem where the prior encodes dynamics, and we devise a convex relaxation method that takes advantage of previous estimates at each measurement acquisition step; The algorithm converges at an optimal rate for first order methods. LocDyn is distributed: there is no fusion center responsible for processing acquired data and the same simple computations are performed for each node. LocDyn is accurate: experiments attest to a smaller positioning error than a comparable Kalman filter. LocDyn is robust: it rejects outlier noise, while the comparing methods succumb in terms of positioning error.

cs.MA↗

arXiv2016

Asymmetric Peer Influence in Smartphone Adoption in a Large Mobile Network

Understanding adoption patterns of smartphones is of vital importance to telecommunication managers in today's highly dynamic mobile markets. In this paper, we leverage the network structure and specific position of each individual in the social network to account for and measure the potential heterogeneous role of peer influence in the adoption of the iPhone 3G. We introduce the idea of core/periphery as a meso-level organizational principle to study the social network, which complements the use of centrality measures derived from either global network properties (macro-level) or from each individual's local social neighbourhood (micro-level). Using millions of call detailed records from a mobile network operator in one country for a period of eleven months, we identify overlapping social communities as well as core and periphery individuals in the network. Our empirical analysis shows that core users exert more influence on periphery users than vice versa. Our findings provide important insights to help identify influential members in the social network, which is potentially useful to design optimal targeting strategies to improve current network-based marketing practices.

cs.SI↗