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Traditional single-grid and pyramidal B-spline parameterizations used in deformable image registration require users to specify control point spacing configurations capable of accurately capturing both global and complex local deformations. In many cases, such grid configurations are non-obvious and largely selected based on user experience. Recent regularization methods imposing sparsity upon the B-spline coefficients throughout simultaneous multi-grid optimization, however, have provided a promising means of determining suitable configurations automatically. Unfortunately, imposing sparsity on over-parameterized B-spline models is computationally expensive and introduces additional difficulties such as undesirable local minima in the B-spline coefficient optimization process. To overcome these difficulties in determining B-spline grid configurations, this paper investigates the use of convolutional neural networks (CNNs) to learn and infer expressive sparse multi-grid configurations prior to B-spline coefficient optimization. Experimental results show that multi-grid configurations produced in this fashion using our CNN based approach provide registration quality comparable to L1-norm constrained over-parameterizations in terms of exactness, while exhibiting significantly reduced computational requirements.