We analyze fundamental mathematical mechanisms of AI and ML models and study various methods to improve their performance based on the theoretical analysis results. Accordingly, we analyze their latent weaknesses in detail and study various methods to improve these weaknesses in terms to effectiveness, computational efficiency, and stability.

The optimization algorithm is one of the most important elements constitute to AI and ML models. In particular, we develop various optimization algorithms to train large-scale machine learning models effectively and verify their convergence, stability, and validity theoretically.

Many real-world problems are difficult to solve within polynomial time using traditional algorithms or require excessively high computational costs. In such cases, it is reasonable to utilize methods that explore approximate optimal solutions using various AI-based numerical methods, such as nature-inspired AI algorithms. Accordingly, we study various numerical algorithms to effectively solve high-dimensional global optimization and NP-hard problems by utilizing nature-inspired AI algorithms.

We conduct numerous studies to enhance the performance of AI & ML application models by addressing vulnerabilities found in their mathematical mechanisms and structures.