lamp-core

Implements reverse mode automatic differentiaton

The main types in this package are lamp.autograd.Variable and lamp.autograd.Op. The computational graph built by this package consists of vertices representing values (as lamp.autograd.Variable) and vertices representing operations (as lamp.autograd.Op).

Variables contain the value of a R^n^ => R^m^ function. Variables may also contain the partial derivative of their argument with respect to a single scalar. A Variable whose value is a scalar (m=1) can trigger the computation of partial derivatives of all the intermediate upstream Variables. Computing partial derivatives with respect to non-scalar variables is not supported.

A constant Variable may be created with the const or param factory method in this package. const may be used for constants which do not need their partial derivatives to be computed. param on the other hand create Variables which will fill in their partial derivatives. Further variables may be created by the methods in this class, eventually expressing more complex R^n^ => R^m^ functions. ===Example===

lamp.Scope.root{ implicit scope =>
 // x is constant (depends on no other variables) and won't compute a partial derivative
 val x = lamp.autograd.const(STen.eye(3, STenOptions.d))
 // y is constant but will compute a partial derivative
 val y = lamp.autograd.param(STen.ones(List(3,3), STenOptions.d))

 // z is a Variable with x and y dependencies
 val z = x+y

 // w is a Variable with z as a direct and x, y as transient dependencies
 val w = z.sum
 // w is a scalar (number of elements is 1), thus we can call backprop() on it.
 // calling backprop will fill out the partial derivatives of the upstream variables
 w.backprop()

 // partialDerivative is empty since we created `x` with `const`
 assert(x.partialDerivative.isEmpty)

 // `y`'s partial derivatie is defined and is computed
 // it holds `y`'s partial derivative with respect to `w`, the scalar which we called backprop() on
 assert(y.partialDerivative.isDefined)

}

This package may be used to compute the derivative of any function, provided the function can be composed out of the provided methods. A particular use case is gradient based optimization.

Provides building blocks for neural networks

Notable types:

• nn.GenericModule is an abstraction on parametric functions
• nn.Optimizer is an abstraction of gradient based optimizers
• nn.LossFunction is an abstraction of loss functions, see the companion object for the implemented losses
• nn.SupervisedModel combines a module with a loss

Optimizers:

• nn.AdamW
• nn.SGDW
• nn.RAdam
• nn.Yogi

Modules facilitating composing other modules:

• nn.Sequential composes a homogenous list of modules (analogous to List)
• nn.sequence composes a heterogeneous list of modules (analogous to tuples)
• nn.EitherModule composes two modules in a scala.Either

Examples of neural network building blocks, layers etc:

• nn.Linear implements W X + b with parameters W and b and input X
• nn.BatchNorm, nn.LayerNorm implement batch and layer normalization
• nn.MLP is a factory of a multilayer perceptron architecture