A Comprehensive Analysis of Linear Algebra-Based Performance Modeling and Enterprise Invoice Processing
1. Goutam Gotur, The Oxford College of Engineering, Student, India
2. Dr Saravana Kumar, The Oxford College of Engineering, Professor, India
Hybrid artificial
intelligence architectures combining traditional computational methods with
neural network residuals represent a paradigm shift in addressing complex
real-world challenges. This report synthesizes two complementary approaches: (1) linear algebra-based digital system performance modeling that leverages
matrix-vector operations enhanced with neural network approximators, and (2) optical character recognition (OCR) integrated with large language models
(LLMs) for automated invoice processing in e-commerce environments. Both
methodologies exemplify the principle of interpretability-efficiency trade-offs
in modern AI systems. This work demonstrates how decomposing complex
problems into interpretable baselines with neural residuals yields superior
performance in accuracy, inference speed, and scalability compared to
monolithic deep learning approaches. The report presents mathematical
formulations, implementation strategies, empirical validation, and practical
deployment considerations across diverse application domains.
Hybrid AI systems Linear Algebra Neural Networks Large Language Models OCR Performance Modeling Automated data extraction E-commerce Interpretability Scalability
This report has
synthesized two complementary case studies in hybrid artificial intelligence
architectures: (1) linear algebra-based digital system performance modeling
with neural residuals, and (2) OCR-integrated large language models for
automated invoice processing in e-commerce. Both exemplify a powerful design
principle: decompose complex problems
into interpretable baselines plus learned residuals.
The hybrid
approach delivers substantial practical benefits :
·
Accuracy: Near
state-of-the-art performance (MSE 0.014 vs. 0.012 for pure NN, 75% error
reduction in invoice extraction)
·
Efficiency:
Dramatic reduction in computational cost and parameters (8.5k vs. 200k parameters
; 90% labor reduction)
·
Interpretability:
Baseline remains transparent, enabling diagnosis and debugging
·
Scalability:
Cost-efficient scaling to large workloads and datasets
The report has
provided mathematical foundations (error bounds, complexity analysis),
implementation guidance (algorithms, hyperparameters, deployment
architectures), and empirical validation across two distinct domains. These
elements collectively demonstrate the generality and robustness of the hybrid
decomposition principle.
1. Patel, D., & Pandit, H. B. (2024). Case study: Centralising diverse e-commerce invoices using invoice LLM model. Scientific Research Journal of Science, Engineering and Technology, 2(2), 79–82
2. Sankaran, A., Alashtiy, N. A., & Psarras, C. (2022). Benchmarking the linear algebra awareness of TensorFlow and PyTorch. RWTH Aachen University.
3. Pudukkottai, et al. (2021). Linear algebraic methods in neural networks. International Journal of Engineering Research & Technology, 12(1), 035
4. ] Baggag, A., & Saad, Y. (2023). Deep learning, transformers and graph neural networks: A linear algebra perspective. Qatar Computing Research Institute & University of Minnesota.
5. Desai, D., Jain, A., Naik, D., Panchal, N., & Sawant, D. (2021). Invoice processing using RPA & AI. SSRN Electronic Journal.
6. Baviskar, D., Ahirrao, S., Potdar, V., & Kotecha, K. (2021). Efficient automated processing of the unstructured documents using artificial intelligence: A systematic literature review and future directions. IEEE Access, 9, 72894–72936.
7. Saout, T., Lardeux, F., & Saubion, F. (2024). An overview of data extraction from invoices. IEEE Access.
8. Bardvall, M., & Hassle, I. (2024). Automating invoice recognition: A comparative study of large language models and OCR/ML technologies.
9. Daqqah, B. H. (2024). Leveraging large language models (LLMs) for automated extraction and processing of complex ordering forms. Doctoral Dissertation, Massachusetts Institute of Technology.
Goutam Parashuram Gotur handled the case study, including its design, execution, and analysis, while Dr. E. Saravana Kumar guided the case study by providing supervision, methodological direction, and critical insights. Both authors reviewed the manuscript thoroughly and approved the final version.
No external funding was received for this research.
This study employed a combination of computational and enterprise-level tools to support both the performance modeling and invoice processing methodologies. Linear algebra-based performance modeling was implemented using MATLAB and Python (NumPy, SciPy) libraries for mathematical formulation and complexity analysis. Neural network design and training were conducted using TensorFlow and PyTorch, ensuring reproducibility and scalability of the empirical validation. For enterprise invoice processing, Optical Character Recognition (OCR) was integrated through Tesseract OCR, while Large Language Models (LLMs) were utilized via the OpenAI API for entity extraction and semantic analysis. Data handling and preprocessing were managed using Pandas and SQL-based systems to ensure structured workflow integration. All software tools used in this study are either open-source or commercially available, and their versions are documented to maintain reproducibility.
The authors declare that there are no commercial or financial relationships that could be construed as a potential conflict of interest in the conduct of this research. The study was carried out solely for academic and scientific purposes, and no external funding or competing interests influenced the outcomes.
We gratefully acknowledge the contributions of the Department of Computer Science and Engineering at The Oxford College of Engineering. We thank colleagues and reviewers for valuable feedback that improved this manuscript.
The data supporting the findings of this study are available from the corresponding author upon reasonable request. Due to the inclusion of enterprise invoice records and proprietary case study materials, certain datasets cannot be publicly shared to protect confidentiality and organizational privacy. However, all mathematical formulations, performance modeling methodologies, and experimental frameworks described in the manuscript are fully reproducible based on the information provided.