PGELU: Metaverse-Driven Deep Learning Boosted by A Parametric GELU for Stable and Scalable Recognition of Emotions and 3D Objects

Metaverse applications necessitate advanced and versatile deep learning frameworks that can accommodate large-scale and continuously transforming data, such as three-dimensional objects, nuanced facial expressions, and interactive user inputs. In response to these stringent requirements, we introduce the Parametric Gaussian Error Linear Unit (PGELU), an enhancement of the well-established GELU activation function. Our refined approach embeds a trainable parameter that governs the non-linear characteristics of the activation, offering more precise control over gradient distribution. Through extensive empirical assessments on MNIST, AffectNet, and Objaverse, we demonstrate that PGELU achieves markedly faster convergence, heightened stability, and superior generalisation in comparison to ReLU, ELU, SiLU, and GELU. These advantages emerge from the function’s capacity to dynamically regulate gradient flow, thereby minimising neuron inactivation and preserving subtle variations within complex data distributions. Our investigations underscore PGELU’s potential to elevate classification accuracy and expedite convergence in digit recognition, facial emotion analysis, and three-dimensional object categorisation—key tasks within immersive virtual environments. By incorporating an adaptable activation mechanism, this study opens new pathways for constructing deeper and more resilient neural architectures, effectively accommodating the shifting demands of metaverse-oriented systems.