Title

A Linear Algebra–Based Mathematical Model of Digital System Performance Using Neural Networks as Predictive Approximators

Author

1. Goutam Gotur, Student, The Oxford College of Engineering, India
2. Chaitrashree S, Assistant Professor, The Oxford College of Engineering, India
3. Dr. Saravana Kumar, Assistant Professor, The Oxford College of Engineering, India

Abstract

Modern digital systems exhibit complex performance characteristics, throughput, and tail latency that depend nonlinearly on workload features and resource constraints. Traditional linear models 𝐴𝑥 provide computational efficiency and interpretability but systematically underfit nonlinear phenomena such as cache thrashing, queueing saturation, and inter-resource contention, while black-box neural networks achieve superior accuracy through universal approximation but sacrifice causal interpretability and increase inference latency. This paper develops a hybrid framework decomposing performance prediction into an interpretable linear baseline plus compact neural residual: 𝑦(𝑥) = 𝐴𝑥 + 𝑓 (𝑥; 𝜃), where matrix 𝐴 ∈ ℝ𝑚×𝑛 encodes resource-to-metric contributions and feedforward network 𝑓 (1-3 layers, 32-256 neurons) learns systematic residuals 𝑟(𝑥) = 𝑓(𝑥) − 𝐴𝑥. Construction employs ridge regression or sparse optimization for 𝐴, staged training alternating between baseline initialization and residual learning, and complexity analysis showing 𝑂(nnz(𝐴)) + 𝑂(∑𝑑ℓ−1𝑑ℓ) inference cost. Across CPU scheduling and bandwidth prediction case studies, the hybrid achieves near-black-box accuracy (MSE: 0.014, MAE: 0.05) with linear efficiency (8.5k parameters, 0.18 ms inference) versus linear-only (MSE: 0.045) or large NN (200k parameters, 1.8 ms), supported by theoretical error bounds ∥ 𝐸(𝑥) ∥≤∥𝑓(𝑥) − 𝐴𝑥 ∥ +𝜖 and ablation studies confirming optimal interpretability-accuracy trade-offs. The linear-neural hybrid resolves fundamental modeling trade-offs, providing production-ready performance prediction with guaranteed error decomposition, staged training algorithms, and deployment strategies including sparsity constraints and online adaptation.

Keywords

Conclusion

This work presents a complete hybrid linear-neural framework for modeling digital system performance. The approach systematically combines interpretable linear algebra with neural residual learning, achieving a principled balance between accuracy, computational efficiency, and model transparency. We established error bounds proving that prediction error decomposes into baseline bias plus neural approximation error, provided a practical multi-stage training algorithm, demonstrated competitive performance on synthetic benchmarks, and discussed deployment strategies including sparsity, quantization, and online adaptation. The hybrid model enables production systems to achieve near-NN accuracy with significantly reduced computational overhead and enhanced interpretability—critical requirements for operational performance prediction. Future work should explore transformer-based residual learners, multi-node distributed architectures, uncertainty-aware predictions via ensemble methods, and continuous online adaptation to evolving workload distributions.

Author Contrubution

Goutam Parashuram Gotur designed the hybrid framework, derived mathematical formulations, implemented training algorithms, conducted ablation studies, and drafted the manuscript. Chaitrashree S contributed to feature engineering, performed validation experiments, and provided critical feedback on theoretical guarantees and practical deployment considerations. Dr. E. Saravana Kumar (Project Guide) provided overall project supervision, methodological guidance, technical oversight of mathematical derivations and experimental validation, and critical review of the manuscript for publication readiness.

Funding

This research received no specific grant from any public, commercial, or not-for-profit funding agency.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Data Sharing Statement

The datasets analyzed for this study consist of synthetic digital system workload traces generated according to realistic performance modeling scenarios. Raw synthetic datasets and trained model checkpoints are available upon request from the corresponding author.

Software And Tools Use

Acknowledgements

The authors gratefully acknowledge the Department of Computer Science and Engineering at The Oxford College of Engineering for providing computational resources and laboratory facilities. We thank colleagues who provided valuable feedback on preliminary versions of this work.