Non-Parametric Dual-Manifold Mapping via 8-Bit Bounded Transformation Matrices: Challenging FP-centric Hardware Paradigms in Low-Energy AI

Abstract

Modern deep learning hardware paradigms rely heavily on computationally expensive floating-point arithmetic (FP32, FP16, and FP8), requiring massive thermal and energetic overheads to maintain gradient-based optimization. This paper introduces a non-parametric, training-free computational framework for dual-manifold mapping that operates strictly within an 8-bit signed integer boundary and leverages simple bitwise and accumulation logic. By mapping a Spatial Manifold (N_spatial = 8192 neurons) and a Gabor-pooled Structural Manifold (N_structural = 4096 neurons) through an integer-based transformation matrix (Z-matrix), we eliminate the need for floating-point multipliers. Inference is achieved via cache-friendly pointer offsets and bitwise masks, accumulating directional sign-charges using fixed thresholds (theta_reject = 8.0, theta_cut = 2.0). Learning is executed through a localized, bounded update mechanism restricted strictly within [-127, 127], modulated by stochastic noise injection. Both architectures demonstrate extreme holographic resilience, preserving near-perfect reconstruction via a global scaling factor under 90% truncation sparsity and 20% random node destruction. By reducing core AI inference to 8-bit boundaries and boolean-like execution, this framework outlines a paradigm shift toward neuromorphic edge-computing, directly questioning the long-term necessity of dense, floating-point-centric GPU accelerators.