This paper discusses the limitations of kernel methods in learning complex functions and proposes deep architectures as a more efficient alternative. The authors argue that kernel machines, which are shallow architectures with a single layer of trainable coefficients, are inefficient in representing complex functions due to their shallow structure and local kernel limitations. They compare kernel methods with deep architectures, which can represent functions more efficiently and generalize beyond immediate neighbors. The paper highlights that deep architectures, composed of multiple layers of parameterized non-linear modules, can capture abstract representations and are more suitable for complex tasks like perception, reasoning, and language understanding. The authors also discuss the trade-off between depth and breadth in architectures, showing that deep architectures can represent functions more compactly and efficiently. They argue that kernel methods, while flexible, are limited by their local kernel assumptions and the curse of dimensionality, making them less effective for complex tasks. The paper concludes that deep architectures offer a promising path towards AI by enabling efficient learning of complex functions with minimal human intervention.This paper discusses the limitations of kernel methods in learning complex functions and proposes deep architectures as a more efficient alternative. The authors argue that kernel machines, which are shallow architectures with a single layer of trainable coefficients, are inefficient in representing complex functions due to their shallow structure and local kernel limitations. They compare kernel methods with deep architectures, which can represent functions more efficiently and generalize beyond immediate neighbors. The paper highlights that deep architectures, composed of multiple layers of parameterized non-linear modules, can capture abstract representations and are more suitable for complex tasks like perception, reasoning, and language understanding. The authors also discuss the trade-off between depth and breadth in architectures, showing that deep architectures can represent functions more compactly and efficiently. They argue that kernel methods, while flexible, are limited by their local kernel assumptions and the curse of dimensionality, making them less effective for complex tasks. The paper concludes that deep architectures offer a promising path towards AI by enabling efficient learning of complex functions with minimal human intervention.