On Philomatics and Psychomatics for Combining Philosophy and Psychology with Mathematics

We propose the concepts of philomatics and psychomatics as hybrid combinations of philosophy and psychology with mathematics. We explain four motivations for this combination which are fulfilling the desire of analytical philosophy, proposing science of philosophy, justifying mathematical algorithms by philosophy, and abstraction in both philosophy and mathematics. We enumerate various examples for philomatics and psychomatics, some of which are explained in more depth. The first example is the analysis of relation between the context principle, semantic holism, and the usage theory of meaning with the attention mechanism in mathematics. The other example is on the relations of Plato's theory of forms in philosophy with the holographic principle in string theory, object-oriented programming, and machine learning. Finally, the relation between Wittgenstein's family resemblance and clustering in mathematics is explained. This paper opens the door of research for combining philosophy and psychology with mathematics

Learning Binary and Sparse Permutation-Invariant Representations for Fast and Memory Efficient Whole Slide Image Search

Learning suitable Whole slide images (WSIs) representations for efficient retrieval systems is a non-trivial task. The WSI embeddings obtained from current methods are in Euclidean space not ideal for efficient WSI retrieval. Furthermore, most of the current methods require high GPU memory due to the simultaneous processing of multiple sets of patches. To address these challenges, we propose a novel framework for learning binary and sparse WSI representations utilizing a deep generative modelling and the Fisher Vector. We introduce new loss functions for learning sparse and binary permutation-invariant WSI representations that employ instance-based training achieving better memory efficiency. The learned WSI representations are validated on The Cancer Genomic Atlas (TCGA) and Liver-Kidney-Stomach (LKS) datasets. The proposed method outperforms Yottixel (a recent search engine for histopathology images) both in terms of retrieval accuracy and speed. Further, we achieve competitive performance against SOTA on the public benchmark LKS dataset for WSI classification