Learning without gradient descent encoded by the dynamics of a neurobiological model

The success of state-of-the-art machine learning is essentially all based on different variations of gradient descent algorithms that minimize some version of a cost or loss function. A fundamental limitation, however, is the need to train these systems in either supervised or unsupervised ways by exposing them to typically large numbers of training examples. Here, we introduce a fundamentally novel conceptual approach to machine learning that takes advantage of a neurobiologically derived model of dynamic signaling, constrained by the geometric structure of a network. We show that MNIST images can be uniquely encoded and classified by the dynamics of geometric networks with nearly state-of-the-art accuracy in an unsupervised way, and without the need for any training.

Inducing a hierarchy for multi-class classification problems

In applications where categorical labels follow a natural hierarchy, classification methods that exploit the label structure often outperform those that do not. Un-fortunately, the majority of classification datasets do not come pre-equipped with a hierarchical structure and classical flat classifiers must be employed. In this paper, we investigate a class of methods that induce a hierarchy that can similarly improve classification performance over flat classifiers. The class of methods follows the structure of first clustering the conditional distributions and subsequently using a hierarchical classifier with the induced hierarchy. We demonstrate the effectiveness of the class of methods both for discovering a latent hierarchy and for improving accuracy in principled simulation settings and three real data applications.

A partition-based similarity for classification distributions

Herein we define a measure of similarity between classification distributions that is both principled from the perspective of statistical pattern recognition and useful from the perspective of machine learning practitioners. In particular, we propose a novel similarity on classification distributions, dubbed task similarity, that quantifies how an optimally-transformed optimal representation for a source distribution performs when applied to inference related to a target distribution. The definition of task similarity allows for natural definitions of adversarial and orthogonal distributions. We highlight limiting properties of representations induced by (universally) consistent decision rules and demonstrate in simulation that an empirical estimate of task similarity is a function of the decision rule deployed for inference. We demonstrate that for a given target distribution, both transfer efficiency and semantic similarity of candidate source distributions correlate with empirical task similarity.

A general approach to progressive learning

In biological learning, data is used to improve performance on the task at hand, while simultaneously improving performance on both previously encountered tasks and as yet unconsidered future tasks. In contrast, classical machine learning starts from a blank slate, or tabula rasa, using data only for the single task at hand. While typical transfer learning algorithms can improve performance on future tasks, their performance degrades upon learning new tasks. Many recent approaches have attempted to mitigate this issue, called catastrophic forgetting, to maintain performance given new tasks. But striving to avoid forgetting sets the goal unnecessarily low: the goal of progressive learning, whether biological or artificial, is to improve performance on all tasks (including past and future) with any new data. We propose a general approach to progressive learning that ensembles representations, rather than learners. We show that ensembling representations---including representations learned by decision forests or neural networks---enables both forward and backward transfer on a variety of simulated and real data tasks, including vision, language, and adversarial tasks. This work suggests that further improvements in progressive learning may follow from a deeper understanding of how biological learning achieves such high degrees of efficiency.