  Conventional Supervised Learning approaches focus on the mapping from input
features to output labels. After training, the learnt models alone are adapted
onto testing features to predict testing labels in isolation, with training
data wasted and their associations ignored. To take full advantage of the vast
number of training data and their associations, we propose a novel learning
paradigm called Memory-Associated Differential (MAD) Learning. We first
introduce an additional component called Memory to memorize all the training
data. Then we learn the differences of labels as well as the associations of
features in the combination of a differential equation and some sampling
methods. Finally, in the evaluating phase, we predict unknown labels by
inferencing from the memorized facts plus the learnt differences and
associations in a geometrically meaningful manner. We gently build this theory
in unary situations and apply it on Image Recognition, then extend it into Link
Prediction as a binary situation, in which our method outperforms strong
state-of-the-art baselines on three citation networks and ogbl-ddi dataset.
