Learning Visual-Semantic Subspace Representations for Propositional Reasoning
<|reference_start|>Learning Visual-Semantic Subspace Representations for Propositional Reasoning: Learning representations that capture rich semantic relationships and accommodate propositional calculus poses a significant challenge. Existing approaches are either contrastive, lacking theoretical guarantees, or fall short in effectively representing the partial orders inherent to rich visual-semantic hierarchies. In this paper, we propose a novel approach for learning visual representations that not only conform to a specified semantic structure but also facilitate probabilistic propositional reasoning. Our approach is based on a new nuclear norm-based loss. We show that its minimum encodes the spectral geometry of the semantics in a subspace lattice, where logical propositions can be represented by projection operators.<|reference_end|>
@article{moreira2024learning,
    title={Learning Visual-Semantic Subspace Representations for Propositional
  Reasoning},
    author={Gabriel Moreira, Alexander Hauptmann, Manuel Marques, Jo~ao Paulo
  Costeira},
    journal={arXiv preprint arXiv:2405.16213},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.16213},
    primaryClass={cs.CV cs.LG}
}