Deep Learning 2.0.1: Mind and Cosmos - Towards Cosmos-Inspired Interpretable Neural Networks

The foundational dot product in deep learning, while ubiquitous, suffers from geometric limitations, conflating magnitude with direction and often obscuring complex data relationships. Conventional activation functions, introduced to imbue non-linearity, can further distort geometric fidelity. This paper introduces the ⵟ-product (Yat-product), a novel neural operator inspired by physical inverse-square laws, which intrinsically unifies vector alignment with spatial proximity to provide a geometrically richer measure of interaction. The ⵟ-product's inherent non-linearity and self-regulating properties form the basis of a new design philosophy, leading to Neural-Matter Networks (NMNs) that potentially obviate the need for separate activation and normalization layers to tap in the non-linearity. We demonstrate the efficacy of this approach through ⵟ-Conv in AetherResNet18 and ⵟ-Attention in AetherGPT, a GPT-2 style model. Experimental results show that these models achieve competitive or superior performance on benchmark datasets for image classification and language modeling, respectively, compared to standard architectures, despite their simplified design. This work suggests a path towards more interpretable, efficient, and geometrically faithful deep learning models by embedding non-linearity and regulation directly within the neural interaction mechanism.