Model-Theoretic Logic for Mathematical Theory of Semantic Information and Communication

In this paper, we propose an advancement to Tarskian model-theoretic semantics, leading to a unified quantitative theory of semantic information and communication. We start with description of inductive logic and probabilities, which serve as notable tools in development of the proposed theory. Then, we identify two disparate kinds of uncertainty in semantic communication, that of physical and content, present refined interpretations of semantic information measures, and conclude with proposing a new measure for semantic content-information and entropy. Our proposition standardizes semantic information across different universes and systems, hence bringing measurability and comparability into semantic communication. We then proceed with introducing conditional and mutual semantic cont-information measures and point out to their utility in formulating practical and optimizable lossless and lossy semantic compression objectives. Finally, we experimentally demonstrate the value of our theoretical propositions

CWCL: Cross-Modal Transfer with Continuously Weighted Contrastive Loss

This paper considers contrastive training for cross-modal 0-shot transfer wherein a pre-trained model in one modality is used for representation learning in another domain using pairwise data. The learnt models in the latter domain can then be used for a diverse set of tasks in a zero-shot way, similar to ``Contrastive Language-Image Pre-training (CLIP)'' and ``Locked-image Tuning (LiT)'' that have recently gained considerable attention. Most existing works for cross-modal representation alignment (including CLIP and LiT) use the standard contrastive training objective, which employs sets of positive and negative examples to align similar and repel dissimilar training data samples. However, similarity amongst training examples has a more continuous nature, thus calling for a more `non-binary' treatment. To address this, we propose a novel loss function called Continuously Weighted Contrastive Loss (CWCL) that employs a continuous measure of similarity. With CWCL, we seek to align the embedding space of one modality with another. Owing to the continuous nature of similarity in the proposed loss function, these models outperform existing methods for 0-shot transfer across multiple models, datasets and modalities. Particularly, we consider the modality pairs of image-text and speech-text and our models achieve 5-8% (absolute) improvement over previous state-of-the-art methods in 0-shot image classification and 20-30% (absolute) improvement in 0-shot speech-to-intent classification and keyword classification.Comment: Accepted to Neural Information Processing Systems (NeurIPS) 2023 conferenc