Samanta: Hierarchical Selective State Space Models (HS-SSM) with Multi-Rank Funnel Topology for Efficient Autonomous Sequence Modeling

Abstract: In this paper, we introduce Samanta, powered by the HS-SSM (Hierarchical Selective State Space Model) framework—a fundamental architectural class designed to eliminate spatial rank redundancy and multi-scale representation limits in sequential and continuous dynamical systems. Unlike traditional homogeneous state vector approaches or temporal multi-scale SSMs, HS-SSM constructs a multi-rank spatial funnel topology that splits the global state space into a hierarchical bus (\Sigma h_t) consisting of K dynamic tracks with strictly monotonically decreasing ranks (N_0 > N_1 > ... > N_{K-1}), while maintaining an O(1) state cache memory footprint with respect to context length n. The proposed formalism supports a hybrid precision continuum (ranging from FP8, FP16, BF16 up to FP32) and independent spectral layer scaling (L_{FFT}), establishing a rigorous mathematical framework for scaling autonomous systems without computational complexity blowup or marginalization