modular task-level program learned on the fly to solve specific task geometric subroutine conclusions data and feedback algorithmic subroutine task # actions geometric subroutine algorithmic subroutine figure learned program relying on both geomet ric primit ives (patt ern recognit ionint uit ionand algorithmic primitives (reasoningsearchmemorybeyond backpropagation and differentiable layers if machine-learning models become more like programsthen they will mostly no longer be differentiable--these programs will still use continuous geometric layers as subroutineswhich will be differentiablebut the model as whole won' be as resultusing backpropagation to adjust weight values in fixedhardcoded network can' be the method of choice for training models in the future--at leastit can' be the entire story we need to figure out how to train non-differentiable systems efficiently current approaches include genetic algorithmsevolution strategiescertain reinforcement-learning methodsand alternating direction method of multipliers (admmnaturallygradient descent isn' going anywheregradient information will always be useful for optimizing differentiable parametric functions but our models will become increasingly more ambitious than mere differentiable parametric functionsand thus their automatic development (the learning in machine learningwill require more than backpropagation in additionbackpropagation is end to endwhich is great thing for learning good chained transformations but is computationally inefficient because it doesn' fully take advantage of the modularity of deep networks to make something more efficientthere' one universal recipeintroduce modularity and hierarchy so we can make backpropagation more efficient by introducing decoupled training modules with synchronization mechanism between themorganized in hierarchical fashion this strategy is somewhat reflected in deepmind' recent work on synthetic gradients expect more along these lines in the near future can imagine future where models that are globally non-differentiable (but feature differentiable partsare trained-grown--using an efficient search process that doesn' use gradientswhereas the differentiable parts are trained even faster by taking advantage of gradients using more efficient version of backpropagation automated machine learning in the futuremodel architectures will be learned rather than be handcrafted by engineer-artisans learning architectures goes hand in hand with the use of richer sets of primitives and program-like machine-learning models licensed to