Limitations of Neural Networks and methodological Alternatives

Neural Networks (NNs), particularly in their deep learning variants, have revolutionized pattern recognition and function approximation in high-dimensional spaces. They have emerged as powerful tools for solving problems involving non-linear relationships and unstructured data. From convolutional neural networks in computer vision to transformer architectures in natural language processing, they offer unparalleled capabilities. However, their application is not universally optimal. Their performance varies considerably depending on the structure of the input data, the size of the dataset, the interpretability requirements, and whether the problem is inferential, causal, or predictive in nature. This document presents a methodological critique of neural networks, identifies specific types of tasks where NNs fail, and recommends more suitable mathematical and statistical techniques.