Hybrid Dual-Path Linear Transformations for Efficient Transformer Architectures

Abstract: Standard Transformer architectures rely heavily on dense linear transformations, treating feature projection as a monolithic, full-rank operation. We argue that this formulation is inefficient and lacks the structural inductive bias necessary for distinguishing between local feature preservation and global context integration. To address this, we introduce the Hybrid Dual-Path Linear (HDPL) operator, which decomposes the affine transformation into two topologically distinct pathways: a sparse block-diagonal component for high-rank local processing, and a low-rank Variational Autoencoder (VAE) bottleneck for global context regularization. By "surgically" replacing specific projections (Query, Key, Value, Gate, Up) with HDPL operators while retaining standard dense layers for aggregation (Output, Down), we achieve a superior balance of efficiency and representational power. Experiments on the FineWeb-Edu dataset demonstrate that the HDPL architecture outperforms a standard Llama-style baseline, reducing validation loss while simultaneously reducing parameter count by 6.8%. Beyond immediate performance gains, we discuss how the explicit materialization of a probabilistic latent space within the Transformer backbone serves as a vital architectural affordance, offering new pathways for inference-time or hypernetwork induced control, continual adaptation, interpretability, and cross-model or cross-modal synchronization. The code is available at https://github.com/VladimerKhasia/HDPL