In this work we address flexibility in deep learning by means of transductive reasoning. For adaptation to new tasks or new data, existing methods typically involve tuning of learnable parameters or even complete re-training from scratch, rendering such approaches unflexible in practice. We argue that the notion of separating computation from memory by the means of transduction can act as a stepping stone for solving these issues. We therefore propose PARMESAN (parameter-free memory search and transduction), a scalable transduction method which leverages a memory module for solving dense prediction tasks. At inference, hidden representations in memory are being searched to find corresponding examples. In contrast to other methods, PARMESAN learns without the requirement for any continuous training or fine-tuning of learnable parameters simply by modifying the memory content. Our method is compatible with commonly used neural architectures and canonically transfers to 1D, 2D, and 3D grid-based data. We demonstrate the capabilities of our approach at complex tasks such as continual and few-shot learning. PARMESAN learns up to 370 times faster than common baselines while being on par in terms of predictive performance, knowledge retention, and data-efficiency.

Mathematics is a highly specialized domain with its own unique set of challenges that has seen limited study in natural language processing. However, mathematics is used in a wide variety of fields and multidisciplinary research in many different domains often relies on an understanding of mathematical concepts. To aid researchers coming from other fields, we develop a prototype system for searching for and defining mathematical concepts in context, focusing on the field of category theory. This system, Parmesan, depends on natural language processing components including concept extraction, relation extraction, definition extraction, and entity linking. In developing this system, we show that existing techniques cannot be applied directly to the category theory domain, and suggest hybrid techniques that do perform well, though we expect the system to evolve over time. We also provide two cleaned mathematical corpora that power the prototype system, which are based on journal articles and wiki pages, respectively. The corpora have been annotated with dependency trees, lemmas, and part-of-speech tags.