Similarity Learning and Generalization with Limited Data: A Reservoir Computing Approach

We investigate the ways in which a machine learning architecture known as Reservoir Computing learns concepts such as “similar” and “different” and other relationships between image pairs and generalizes these concepts to previously unseen classes of data. We present two Reservoir Computing architectures, which loosely resemble neural dynamics, and show that a Reservoir Computer (RC) trained to identify relationships between image pairs drawn from a subset of training classes generalizes the learned relationships to substantially different classes unseen during training. We demonstrate our results on the simple MNIST handwritten digit database as well as a database of depth maps of visual scenes in videos taken from a moving camera. We consider image pair relationships such as images from the same class; images from the same class with one image superposed with noise, rotated 90°, blurred, or scaled; images from different classes. We observe that the reservoir acts as a nonlinear filter projecting the input into a higher dimensional space in which the relationships are separable; i.e., the reservoir system state trajectories display different dynamical patterns that reflect the corresponding input pair relationships. Thus, as opposed to training in the entire high-dimensional reservoir space, the RC only needs to learns characteristic features of these dynamical patterns, allowing it to perform well with very few training examples compared with conventional machine learning feed-forward techniques such as deep learning. In generalization tasks, we observe that RCs perform significantly better than state-of-the-art, feed-forward, pair-based architectures such as convolutional and deep Siamese Neural Networks (SNNs). We also show that RCs can not only generalize relationships, but also generalize combinations of relationships, providing robust and effective image pair classification. Our work helps bridge the gap between explainable machine learning with small datasets and biologically inspired analogy-based learning, pointing to new directions in the investigation of learning processes.