cs.LGSep 13, 2026

SH-WRNN: Implicit Spherical Harmonics Weight Field Routing Neural Networks for Asymmetric Edge Intelligence

Authors: Zhibin Jiao, Xiangjing An

Organizations: Independent Researcher Team

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Abstract

Deep learning architectures remain rigidly built upon traditional fully connected layers. While networks scale up, few challenge this foundational root. In this work, we reshape this paradigm by transforming the core synapse weight matrix from static, discrete parameters into a differentiable, continuous field governed by spherical harmonics functions. We introduce the Implicit Spherical Harmonics Weight Field Routing Neural Network (SH-WRNN), which constrains weight matrices within a continuous parametric field instead of optimizing millions of localized discrete weights. When retrieving the weight matrix of the current layer, connection parameters are localized using latitude and longitude on a rectangular plane mapped from the continuous field. The latitudinal coordinate is specified by activated neurons from the previous layer, while the longitudinal coordinate is determined by keys generated from previous layer activations via matrix multiplication. By evaluating intersections on this map, the network dynamically extracts its connection weights on-the-fly. Empirical validation on MNIST demonstrates that under compact configurations of (32, 10, 10) and (32, 3, 10), SH-WRNN achieves robust accuracies of 91.05% and 81.54% within a single training epoch. Furthermore, we propose an asymmetric Surface Baking scheme. Upon convergence, the continuous weight field is baked once into a static parametric surface. By eliminating analytical spherical harmonics calculations during inference and reducing dynamic matrix extraction to high-speed localized memory slicing, this scheme achieves asymmetric algorithmic acceleration with negligible accuracy degradation. This paradigm shift bypasses GPU memory-bandwidth monopolies, opening a novel path to reshape the advantages of CPU computing. Code is available at https://github.com/jzb1111/SphericalHarmonyRoutedNeuralNetWork.

Figures & tables

Figure 1: The end-to-end cascading workflow of the SH-WRNN framework. Given a 28×2828\times 28 input, features are split into localized values (node activation levels) and initial position tracks (input layer activate nodes). During training , the 1st layer Spherical Harmony Engine stretches 16 global parameters to generate a continuous weight surface. During inference (The Asymmetric Surface Baking) , the continuous field is offline baked into a dense, non-parametric 2D rectangular map. The system routes the connections using two data-dependent steps: a matrix multiplication maps the values into longitudinal tracks (keys), while the input positions specify the latitudinal tracks. Under inference, the final discrete synapse weight matrix ( WW ) is dynamically extracted out of the baked rectangular map via ultra-fast bidirectional memory slicing ( gather row and gather col ), completely eliminating analytical formula overhead. The resulting connections cascade into the 2nd layer by passing forward the computed value output and activate node output seamlessly.
Network ProfileOperational ModeTest Accuracy (%)Total Inference Time (s)Speedup Factor
(32,10,10)(32,10,10) StructureContinuous Field (Train)91.05%36.40s1.00×1.00\times (Baseline)
 Baked Surface (Infer)91.01%9.20s�� 3.96 ×\times
(32,3,10)(32,3,10) StructureContinuous Field (Train)81.54%38.20s1.00×1.00\times (Baseline)
 Baked Surface (Infer)81.45%9.10s�� 4.20 ×\times
Table 1: Asymmetric Hardware Performance on 13th Gen Intel i5 CPU (Batch Size = 1)
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