  Transformers have revolutionized image modeling tasks with adaptations like
DeIT, Swin, SVT, Biformer, STVit, and FDVIT. However, these models often face
challenges with inductive bias and high quadratic complexity, making them less
efficient for high-resolution images. State space models (SSMs) such as Mamba,
V-Mamba, ViM, and SiMBA offer an alternative to handle high resolution images
in computer vision tasks. These SSMs encounter two major issues. First, they
become unstable when scaled to large network sizes. Second, although they
efficiently capture global information in images, they inherently struggle with
handling local information. To address these challenges, we introduce Heracles,
a novel SSM that integrates a local SSM, a global SSM, and an attention-based
token interaction module. Heracles leverages a Hartely kernel-based state space
model for global image information, a localized convolutional network for local
details, and attention mechanisms in deeper layers for token interactions. Our
extensive experiments demonstrate that Heracles-C-small achieves
state-of-the-art performance on the ImageNet dataset with 84.5\% top-1
accuracy. Heracles-C-Large and Heracles-C-Huge further improve accuracy to
85.9\% and 86.4\%, respectively. Additionally, Heracles excels in transfer
learning tasks on datasets such as CIFAR-10, CIFAR-100, Oxford Flowers, and
Stanford Cars, and in instance segmentation on the MSCOCO dataset. Heracles
also proves its versatility by achieving state-of-the-art results on seven
time-series datasets, showcasing its ability to generalize across domains with
spectral data, capturing both local and global information. The project page is
available at this link.\url{https://github.com/badripatro/heracles}
