  We present analytical exploration of novel activation functions as
consequence of integration of several ideas leading to implementation and
subsequent use in habitability classification of exoplanets. Neural networks,
although a powerful engine in supervised methods, often require expensive
tuning efforts for optimized performance. Habitability classes are hard to
discriminate, especially when attributes used as hard markers of separation are
removed from the data set. The solution is approached from the point of
investigating analytical properties of the proposed activation functions. The
theory of ordinary differential equations and fixed point are exploited to
justify the "lack of tuning efforts" to achieve optimal performance compared to
traditional activation functions. Additionally, the relationship between the
proposed activation functions and the more popular ones is established through
extensive analytical and empirical evidence. Finally, the activation functions
have been implemented in plain vanilla feed-forward neural network to classify
exoplanets.
