The Learning with Errors (LWE) problem, a cornerstone of lattice-based cryptography, poses significant computational challenges believed to be intractable even for quantum computers. This paper introduces a novel approach utilizing machine learning techniques, specifically gradient descent, to address the LWE problem. By formulating LWE as an optimization problem, our method leverages gradient descent to iteratively approximate the secret vector. We present an efficient gradient descent algorithm designed to maintain numerical stability and ensure convergence. Experimental results demonstrate that our approach can successfully recover the secret vector in LWE instances, showcasing the potential of machine learning to tackle problems in post-quantum cryptography ( https://www.sciencedirect.com/topics/computer-science/learning , https://builtin.com/data-science/gradient-descent ).