  The brain modifies its synaptic strengths during learning in order to better
adapt to its environment. However, the underlying plasticity rules that govern
learning are unknown. Many proposals have been suggested, including Hebbian
mechanisms, explicit error backpropagation, and a variety of alternatives. It
is an open question as to what specific experimental measurements would need to
be made to determine whether any given learning rule is operative in a real
biological system. In this work, we take a "virtual experimental" approach to
this problem. Simulating idealized neuroscience experiments with artificial
neural networks, we generate a large-scale dataset of learning trajectories of
aggregate statistics measured in a variety of neural network architectures,
loss functions, learning rule hyperparameters, and parameter initializations.
We then take a discriminative approach, training linear and simple non-linear
classifiers to identify learning rules from features based on these
observables. We show that different classes of learning rules can be separated
solely on the basis of aggregate statistics of the weights, activations, or
instantaneous layer-wise activity changes, and that these results generalize to
limited access to the trajectory and held-out architectures and learning
curricula. We identify the statistics of each observable that are most relevant
for rule identification, finding that statistics from network activities across
training are more robust to unit undersampling and measurement noise than those
obtained from the synaptic strengths. Our results suggest that activation
patterns, available from electrophysiological recordings of post-synaptic
activities on the order of several hundred units, frequently measured at wider
intervals over the course of learning, may provide a good basis on which to
identify learning rules.
