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}

Transformers have widely adopted attention networks for sequence mixing and MLPs for channel mixing, playing a pivotal role in achieving breakthroughs across domains. However, recent literature highlights issues with attention networks, including low inductive bias and quadratic complexity concerning input sequence length. State Space Models (SSMs) like S4 and others (Hippo, Global Convolutions, liquid S4, LRU, Mega, and Mamba), have emerged to address the above issues to help handle longer sequence lengths. Mamba, while being the state-of-the-art SSM, has a stability issue when scaled to large networks for computer vision datasets. We propose SiMBA, a new architecture that introduces Einstein FFT (EinFFT) for channel modeling by specific eigenvalue computations and uses the Mamba block for sequence modeling. Extensive performance studies across image and time-series benchmarks demonstrate that SiMBA outperforms existing SSMs, bridging the performance gap with state-of-the-art transformers. Notably, SiMBA establishes itself as the new state-of-the-art SSM on ImageNet and transfer learning benchmarks such as Stanford Car and Flower as well as task learning benchmarks as well as seven time series benchmark datasets.