The Infinite-Dimensional Mathematical Computation Framework: Dynamic Substitution of Infinity and Its Applications

This paper introduces a <b>novel infinite-dimensional mathematical framework</b> applied to <b>artificial intelligence optimization</b>. By implementing <b>trend computation and dynamic infinity substitution</b>, we propose an improved <b>gradient descent algorithm</b> that dynamically adjusts weight updates. Our <b>experimental study on neural networks</b> demonstrates that <b>trend-based optimization enhances training stability</b> by reducing oscillations in gradient updates. This approach has potential applications in <b>deep learning, reinforcement learning, and mathematical physics</b>.