  This study leverages the data representation capability of fuzzy based
membership-mappings for practical secure distributed deep learning using fully
homomorphic encryption. The impracticality issue of secure machine (deep)
learning with fully homomorphic encrypted data, arising from large
computational overhead, is addressed via applying fuzzy attributes. Fuzzy
attributes are induced by globally convergent and robust variational
membership-mappings based local deep models. Fuzzy attributes combine the local
deep models in a robust and flexible manner such that the global model can be
evaluated homomorphically in an efficient manner using a boolean circuit
composed of bootstrapped binary gates. The proposed method, while preserving
privacy in a distributed learning scenario, remains accurate, practical, and
scalable. The method is evaluated through numerous experiments including
demonstrations through MNIST dataset and Freiburg Groceries Dataset. Further, a
biomedical application related to mental stress detection on individuals is
considered.
