A construction for circulant type dropout designs.

Dropout is used in deep learning to prevent overlearning. It is a method of learning by invalidating nodes randomly for each layer in the multi-layer neural network. Let V 1 , V 2 , ... , V n be mutually disjoint node sets (layers). A multi-layer neural network can be regarded as a union of the complete bipartite graphs K | V i | , | V i + 1 | on two consecutive node sets V i and V i + 1 for i = 1 , 2 , ... , n - 1 . The dropout method deletes a random sample of activations (nodes) to zero during the training process. A random sample of nodes also causes irregular frequencies of dropout edges. A dropout design is a combinatorial design on dropout nodes from each layer which balances frequencies of selected edges. The block set of a dropout design is B = { { C 1 | C 2 | ... | C n } | C i ⊆ V i , C i ≠ ∅ , 1 ≤ i ≤ n } having a balancing condition in consecutive t sub-blocks C i , C i + 1 , ... , C i + t - 1 , see [3]. If | V i | and | C i | are constants for 1 ≤ i ≤ n , then the dropout design is called uniform. If a uniform dropout design satisfies the circulant property, then the design can be extended to a design with as many layers as you need. In this paper, we describe a construction for uniform dropout designs of circulant type by using affine geometries. [ABSTRACT FROM AUTHOR]