Ricardo Cruz

Jaime S. Cardoso, Ricardo Cruz, Tomé Albuquerque

In many real-world prediction tasks, class labels contain information about the relative order between labels that are not captured by commonly used loss functions such as multicategory cross-entropy. Recently, the preference for unimodal distributions in the output space has been incorporated into models and loss functions to account for such ordering information. However, current approaches rely on heuristics that lack a theoretical foundation. Here, we propose two new approaches to incorporate the preference for unimodal distributions into the predictive model. We analyse the set of unimodal distributions in the probability simplex and establish fundamental properties. We then propose a new architecture that imposes unimodal distributions and a new loss term that relies on the notion of projection in a set to promote unimodality. Experiments show the new architecture achieves top-2 performance, while the proposed new loss term is very competitive while maintaining high unimodality.

Ricardo P. M. Cruz, Rafael Cristino, Jaime S. Cardoso

Semantic segmentation consists of predicting a semantic label for each image pixel. While existing deep learning approaches achieve high accuracy, they often overlook the ordinal relationships between classes, which can provide critical domain knowledge (e.g., the pupil lies within the iris, and lane markings are part of the road). This paper introduces novel methods for spatial ordinal segmentation that explicitly incorporate these inter-class dependencies. By treating each pixel as part of a structured image space rather than as an independent observation, we propose two regularization terms and a new metric to enforce ordinal consistency between neighboring pixels. Two loss regularization terms and one metric are proposed for structural ordinal segmentation, which penalizes predictions of non-ordinal adjacent classes. Five biomedical datasets and multiple configurations of autonomous driving datasets demonstrate the efficacy of the proposed methods. Our approach achieves improvements in ordinal metrics and enhances generalization, with up to a 15.7% relative increase in the Dice coefficient. Importantly, these benefits come without additional inference time costs. This work highlights the significance of spatial ordinal relationships in semantic segmentation and provides a foundation for further exploration in structured image representations.

Rafael Morales, Noé Hernández, Ricardo Cruz et al.

Manuscript symbols can be stored, recognized and retrieved from an entropic digital memory that is associative and distributed but yet declarative; memory retrieval is a constructive operation, memory cues to objects not contained in the memory are rejected directly without search, and memory operations can be performed through parallel computations. Manuscript symbols, both letters and numerals, are represented in Associative Memory Registers that have an associated entropy. The memory recognition operation obeys an entropy trade-off between precision and recall, and the entropy level impacts on the quality of the objects recovered through the memory retrieval operation. The present proposal is contrasted in several dimensions with neural networks models of associative memory. We discuss the operational characteristics of the entropic associative memory for retrieving objects with both complete and incomplete information, such as severe occlusions. The experiments reported in this paper add evidence on the potential of this framework for developing practical applications and computational models of natural memory.