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Neural networks enjoy widespread use, but many aspects of their training,representation, and operation are poorly understood. In particular, our viewinto the training process is limited, with a single scalar loss being the mostcommon viewport into this high-dimensional, dynamic process. We propose a newwindow into training called Loss Change Allocation (LCA), in which credit forchanges to the network loss is conservatively partitioned to the parameters.This measurement is accomplished by decomposing the components of anapproximate path integral along the training trajectory using a Runge-Kuttaintegrator. This rich view shows which parameters are responsible fordecreasing or increasing the loss during training, or which parameters "help"or "hurt" the network's learning, respectively. LCA may be summed over trainingiterations and/or over neurons, channels, or layers for increasingly coarseviews. This new measurement device produces several insights into training. (1)We find that barely over 50% of parameters help during any given iteration. (2)Some entire layers hurt overall, moving on average against the traininggradient, a phenomenon we hypothesize may be due to phase lag in an oscillatorytraining process. (3) Finally, increments in learning proceed in a synchronizedmanner across layers, often peaking on identical iterations.

LCA: Loss Change Allocation for Neural Network Training