Algebraically Stabilizing Blocks for Quantized and Finite-Precision Neural Networks

This paper proposes a construction of algebraically stabilizing blocks for quantized and finite-precision neural networks. The approach is based on linear transformations defined by integer-valued matrices satisfying a condition of the form Wk=I+μD, which specifies algebraically controlled k-step behavior and modular periodicity in the integer-valued setting. The proposed property is invariant under conjugation, allowing the stabilizing construction to be transferred across equivalent linear representations. The resulting module can be integrated locally into existing neural architectures without requiring the algebraic structure to be imposed globally. The theoretical results concern algebraic and modular stabilization of the linear block and do not constitute a general guarantee of classical spectral or asymptotic stability in real-valued space. The approach is evaluated experimentally under multi-component harmonic, impulsive, and noisy inputs in both floating-point and INT8-quantized settings. Across several experimental configurations, the proposed block reduces output energy, component-wise variation, selected amplitude-related measures, and finite-precision deviation relative to floating-point reference trajectories. Norm-matched control experiments further suggest that the observed effects are not attributable solely to a reduction in operator magnitude, but may also reflect structural properties of the algebraically constructed operator. The proposed construction is particularly relevant to neural systems operating under limited numerical precision, including FPGA-, ASIC-, and edge-oriented implementations. It provides a structural approach for incorporating formally specified algebraic properties into the design of neural-network architectures.