Vijay S. Agneeswaran

Badri N. Patro, Vijay S. Agneeswaran

The field of artificial intelligence has undergone a revolution from foundational Transformer architectures to reasoning-capable systems approaching human-level performance. We present LLMOrbit, a comprehensive circular taxonomy navigating the landscape of large language models spanning 2019-2025. This survey examines over 50 models across 15 organizations through eight interconnected orbital dimensions, documenting architectural innovations, training methodologies, and efficiency patterns defining modern LLMs, generative AI, and agentic systems. We identify three critical crises: (1) data scarcity (9-27T tokens depleted by 2026-2028), (2) exponential cost growth ($3M to $300M+ in 5 years), and (3) unsustainable energy consumption (22x increase), establishing the scaling wall limiting brute-force approaches. Our analysis reveals six paradigms breaking this wall: (1) test-time compute (o1, DeepSeek-R1 achieve GPT-4 performance with 10x inference compute), (2) quantization (4-8x compression), (3) distributed edge computing (10x cost reduction), (4) model merging, (5) efficient training (ORPO reduces memory 50%), and (6) small specialized models (Phi-4 14B matches larger models). Three paradigm shifts emerge: (1) post-training gains (RLHF, GRPO, pure RL contribute substantially, DeepSeek-R1 achieving 79.8% MATH), (2) efficiency revolution (MoE routing 18x efficiency, Multi-head Latent Attention 8x KV cache compression enables GPT-4-level performance at <$0.30/M tokens), and (3) democratization (open-source Llama 3 88.6% MMLU surpasses GPT-4 86.4%). We provide insights into techniques (RLHF, PPO, DPO, GRPO, ORPO), trace evolution from passive generation to tool-using agents (ReAct, RAG, multi-agent systems), and analyze post-training innovations.

Badri N. Patro, Vijay S. Agneeswaran

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. The project page is available on this website ~\url{https://github.com/badripatro/Simba}.

Badri N. Patro, Vijay S. Agneeswaran

State space models (SSMs) achieve linear-time complexity but struggle with multi-channel physiological signals due to three limitations: fixed kernels cannot capture multi-scale temporal dynamics (motor preparation over hundreds of milliseconds vs. execution transients in tens of milliseconds), Markovian state updates restrict global context for periodic oscillations, and channel-independent processing ignores spatial electrode topology. We introduce NAKUL, extending SSMs for medical signal analysis through three contributions: (1) Dynamic Kernel Generation-parallel SSM branches with varying kernel sizes (3, 5, 7, 11 timesteps) are weighted by a meta-network that analyzes input statistics, enabling adaptive temporal scale selection; (2) Spectral Context Modeling-FFT-based operations with learnable Gaussian frequency band filters capture global periodic patterns in $O(N \log N)$ complexity; (3) Graph-Guided Spatial Attention-fixed electrode topology provides spatial biases to multi-head attention for principled cross-channel interaction. On BCI Competition IV-2a motor imagery (our primary benchmark), NAKUL achieves 91.7$\pm$0.6\% accuracy, matching EEG-Conformer (92.1$\pm$0.7\%) while using 28\% fewer parameters (2.5M vs 3.5M) and 2.0$\times$ faster inference (4.3ms vs 8.7ms). The model generalizes to EEG emotion recognition (83.6\%), multimodal EEG-fMRI (91.4\%), and medical imaging (92.8\% on ultrasound), demonstrating architectural versatility. Ablations show dynamic kernels contribute +2.6\% and exhibit interpretable scale selection patterns correlated with known neural dynamics.

Badri N. Patro, Vijay S. Agneeswaran

Vision State Space Models (SSMs) like Vim, VMamba, and SiMBA rely on complex scanning strategies to adapt sequential SSMs to process 2D images, introducing computational overhead and architectural complexity. We propose HAMSA, a scanning-free SSM operating directly in the spectral domain. HAMSA introduces three key innovations: (1) simplified kernel parameterization-a single Gaussian-initialized complex kernel replacing traditional (A, B, C) matrices, eliminating discretization instabilities; (2) SpectralPulseNet (SPN)-an input-dependent frequency gating mechanism enabling adaptive spectral modulation; and (3) Spectral Adaptive Gating Unit (SAGU)-magnitude-based gating for stable gradient flow in the frequency domain. By leveraging FFT-based convolution, HAMSA eliminates sequential scanning while achieving O(L log L) complexity with superior simplicity and efficiency. On ImageNet-1K, HAMSA reaches 85.7% top-1 accuracy (state-of-the-art among SSMs), with 2.2 X faster inference than transformers (4.2ms vs 9.2ms for DeiT-S) and 1.4-1.9X speedup over scanning-based SSMs, while using less memory (2.1GB vs 3.2-4.5GB) and energy (12.5J vs 18-25J). HAMSA demonstrates strong generalization across transfer learning and dense prediction tasks.

Badri N. Patro, Suhas Ranganath, Vinay P. Namboodiri et al.

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}