Anatilik Space Topology and Its Application in Artificial Intelligence: A Dynamic Activation Paradigm for Deep Learning

The development of artificial intelligence (AI) and deep learning has been largely influenced by innovations in mathematical modeling, particularly regarding neural network architectures and their activation functions. Traditional activation functions, such as ReLU, sigmoid, and tanh, have been pivotal in shaping the learning capacity of neural networks. However, these fixed activations present limitations in terms of flexibility and adaptability to complex, non-stationary data patterns. This paper introduces a novel approach—Anatilik Space Topology—which enables dynamic, continuous, and learnable transitions between different activation functions within a neural network. By framing activation function selection as a topological problem, we open the door to more expressive, adaptive, and robust deep learning paradigms.The author acknowledges the use of OpenAI’s language model for assistance in drafting certain sections of this workl<br>