  This work addresses flexibility in deep learning by means of transductive
reasoning. For adaptation to new data and tasks, e.g., in continual learning,
existing methods typically involve tuning learnable parameters or 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
method which leverages a memory module for solving dense prediction tasks. At
inference, hidden representations in memory are being searched to find
corresponding patterns. In contrast to other methods that rely on continuous
training of learnable parameters, PARMESAN learns via memory consolidation
simply by modifying stored contents. Our method is compatible with commonly
used architectures and canonically transfers to 1D, 2D, and 3D grid-based data.
The capabilities of our approach are demonstrated at the complex task of
continual learning. PARMESAN learns by 3-4 orders of magnitude faster than
established baselines while being on par in terms of predictive performance,
hardware-efficiency, and knowledge retention.
