Moderate deviation functions in convolutional neural networks

The paper presents new constructions of moderate deviation functions based on automorphisms and negation functions defined as in the symmetric interval [ − 1 , 1 ] . These constructions are then extended to a general closed interval [ 𝑎 , 𝑏 ] ⊂ ℝ . Consequently, all results formulated for [ − 1 , 1 ] can be transferred to arbitrary intervals, yielding symmetric, idempotent aggregation functions. The paper also introduces moderate deviation functions that are non-continuous or not strictly monotonic, giving rise to quantile-type operators. An illustrative example demonstrates how aggregation functions derived from these moderate deviation functions can replace standard methods in the fusion of features extracted by Convolutional Neural Networks. Experiments indicate that several of these constructions are effective alternatives that, when optimised by gradient descent, can enhance model performance without significant computational overhead.