The brain performs unsupervised learning and (perhaps) simultaneous supervised learning. This raises the question as to whether a hybrid of supervised and unsupervised methods will produce better learning. Inspired by the rich space of Hebbian learning rules, we set out to directly learn the unsupervised learning rule on local information that best augments a supervised signal. We present the Hebbian-augmented training algorithm (HAT) for combining gradient-based learning with an unsupervised rule on pre-synpatic activity, post-synaptic activities, and current weights. We test HAT's effect on a simple problem (Fashion-MNIST) and find consistently higher performance than supervised learning alone. This finding provides empirical evidence that unsupervised learning on synaptic activities provides a strong signal that can be used to augment gradient-based methods.
    
     We further find that the meta-learned update rule is a time-varying function; thus, it is difficult to pinpoint an interpretable Hebbian update rule that aids in training.   We do find that the meta-learner eventually degenerates into a non-Hebbian rule that preserves important weights so as not to disturb the learner's convergence. The HAT algorithm demonstrates that local, unsupervised signals can provide performance-improving weight updates. Neural nets under HAT converge to better asymptotic losses as long as there is sufficient time (> 0.5 epochs) and a sufficient number of labels (> 20% of the data is labeled). The latter finding is surprising since the addition of an unsupervised learning algorithm depends on the presence of labels in order to deliver marginal benefits over gradient descent. The underlying form of the learned rule that makes HAT successful is still a mystery; we find that while the meta-learner may learn a useful update rule during training, the meta-learner does not converge to this useful rule in the long run and instead devolves into a linear function ConvergedRule. This converged function preserves fully-converged weights by reinforcing incoming weights for neurons with high activations.
Metalearning unsupervised update rules for neural networks improves performance and potentially demonstrates how neurons in the brain learn without access to global labels.
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