Deriving Differential Target Propagation from Iterating Approximate Inverses
This work addresses the challenge of biologically plausible deep learning optimization for researchers in neural networks, offering an incremental improvement over existing target propagation methods.
The paper tackles the problem of making target propagation more biologically plausible and computationally efficient by deriving a differential form from iterating approximate inverses, showing it corresponds to approximate Gauss-Newton optimization without large matrix manipulations and that iterative procedures converge exponentially fast under certain conditions.
We show that a particular form of target propagation, i.e., relying on learned inverses of each layer, which is differential, i.e., where the target is a small perturbation of the forward propagation, gives rise to an update rule which corresponds to an approximate Gauss-Newton gradient-based optimization, without requiring the manipulation or inversion of large matrices. What is interesting is that this is more biologically plausible than back-propagation yet may turn out to implicitly provide a stronger optimization procedure. Extending difference target propagation, we consider several iterative calculations based on local auto-encoders at each layer in order to achieve more precise inversions for more accurate target propagation and we show that these iterative procedures converge exponentially fast if the auto-encoding function minus the identity function has a Lipschitz constant smaller than one, i.e., the auto-encoder is coarsely succeeding at performing an inversion. We also propose a way to normalize the changes at each layer to take into account the relative influence of each layer on the output, so that larger weight changes are done on more influential layers, like would happen in ordinary back-propagation with gradient descent.