Unified CNNs and transformers underlying learning mechanism reveals multi-head attention modus vivendi

Abstract: Convolutional neural networks (CNNs) evaluate short-range correlations in input images which progress along the layers, whereas vision transformer (ViT) architectures evaluate long-range correlations, using repeated transformer encoders composed of fully connected layers. Both are designed to solve complex classification tasks but from different perspectives. This study demonstrates that CNNs and ViT architectures stem from a unified underlying learning mechanism, which quantitatively measures the single-nodal performance (SNP) of each node in feedforward (FF) and multi-head attention (MHA) sub-blocks. Each node identifies small clusters of possible output labels, with additional noise represented as labels outside these clusters. These features are progressively sharpened along the transformer encoders, enhancing the signal-to-noise ratio. This unified underlying learning mechanism leads to two main findings. First, it enables an efficient applied nodal diagonal connection (ANDC) pruning technique without affecting the accuracy. Second, based on the SNP, spontaneous symmetry breaking occurs among the MHA heads, such that each head focuses its attention on a subset of labels through cooperation among its SNPs. Consequently, each head becomes an expert in recognizing its designated labels, representing a quantitative MHA modus vivendi mechanism. This statistical mechanics inspired viewpoint enables to reveal macroscopic behavior of the entire network from the microscopic performance of each node. These results are based on a compact convolutional transformer architecture trained on the CIFAR-100 and Flowers-102 datasets and call for their extension to other architectures and applications, such as natural language processing.