Equinox: neural networks in JAX via callable PyTrees and filtered transformations

JAX and PyTorch are two popular Python autodifferentiation frameworks. JAX is based around pure functions and functional programming. PyTorch has popularised the use of an object-oriented (OO) class-based syntax for defining parameterised functions, such as neural networks. That this seems like a fundamental difference means current libraries for building parameterised functions in JAX have either rejected the OO approach entirely (Stax) or have introduced OO-to-functional transformations, multiple new abstractions, and been limited in the extent to which they integrate with JAX (Flax, Haiku, Objax). Either way this OO/functional difference has been a source of tension. Here, we introduce `Equinox', a small neural network library showing how a PyTorch-like class-based approach may be admitted without sacrificing JAX-like functional programming. We provide two main ideas. One: parameterised functions are themselves represented as `PyTrees', which means that the parameterisation of a function is transparent to the JAX framework. Two: we filter a PyTree to isolate just those components that should be treated when transforming (`jit', `grad' or `vmap'-ing) a higher-order function of a parameterised function -- such as a loss function applied to a model. Overall Equinox resolves the above tension without introducing any new programmatic abstractions: only PyTrees and transformations, just as with regular JAX. Equinox is available at \url{https://github.com/patrick-kidger/equinox}.