Deep Learning with Parametric Lenses
This provides a foundational theoretical framework for understanding and comparing machine learning algorithms, though it appears incremental in its practical impact.
The authors developed a categorical semantics framework using lenses, parametric maps, and reverse derivative categories to unify and explain various machine learning algorithms, including gradient descent methods, loss functions, and architectures, and demonstrated its practical application with a Python implementation.
We propose a categorical semantics for machine learning algorithms in terms of lenses, parametric maps, and reverse derivative categories. This foundation provides a powerful explanatory and unifying framework: it encompasses a variety of gradient descent algorithms such as ADAM, AdaGrad, and Nesterov momentum, as well as a variety of loss functions such as MSE and Softmax cross-entropy, and different architectures, shedding new light on their similarities and differences. Furthermore, our approach to learning has examples generalising beyond the familiar continuous domains (modelled in categories of smooth maps) and can be realised in the discrete setting of Boolean and polynomial circuits. We demonstrate the practical significance of our framework with an implementation in Python.