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/*
Appellation: grad <mod>
Contrib: FL03 <jo3mccain@icloud.com>
*/
use crate::actions::grad::TensorGrad;
use crate::prelude::{ScalarExt, TensorExpr, TensorId, TensorResult};
use crate::TensorBase;
use acme::prelude::{Arithmetic, BinaryOp, Store, UnaryOp};
pub(crate) type Visited<K = TensorId> = std::collections::HashMap<K, bool>;
macro_rules! entry {
($ctx:expr, $entry:expr) => {
entry!($ctx, $entry, $entry.zeros_like())
};
($ctx:expr, $entry:expr, $default:expr) => {
$ctx.entry($entry.id()).or_insert($default)
};
}
impl<T> TensorBase<T>
where
T: ScalarExt,
{
/// toposort is a function which sorts the nodes of the op graph in topological order.
fn toposort(&self, reverse: bool) -> Vec<&TensorBase<T>> {
// Here, the sorted nodes are passed as an owned value rather than as a mutable reference to workaround some lifetime limitations.
fn walk<'a, T>(
scope: &'a TensorBase<T>,
nodes: Vec<&'a TensorBase<T>>,
visited: &mut Visited<TensorId>,
) -> (bool, Vec<&'a TensorBase<T>>) {
if let Some(&tg) = visited.get(&scope.id()) {
return (tg, nodes);
}
// track the gradient of the current node
let mut track = false;
// recursively call on the children nodes
let mut nodes = if scope.is_variable() {
// Do not call recursively on the "leaf" nodes.
track = true;
nodes
} else if let Some(op) = scope.op().op() {
match op {
TensorExpr::Binary(lhs, rhs, _kind) => {
let (tg, nodes) = walk(lhs, nodes, visited);
track |= tg;
let (tg, nodes) = walk(rhs, nodes, visited);
track |= tg;
nodes
}
TensorExpr::Unary(a, _kind) => {
let (tg, nodes) = walk(a, nodes, visited);
track |= tg;
nodes
}
_ => nodes,
}
} else {
nodes
};
visited.insert(scope.id(), track);
if track {
nodes.push(scope);
}
(track, nodes)
}
// walk through the dag
let (_tg, mut nodes) = walk(self, Vec::new(), &mut Visited::new());
// reverse the nodes; if needed
if reverse {
nodes.reverse();
}
// return the sorted nodes
nodes
}
/// Compute the gradient of the tensor
pub fn grad(&self) -> TensorResult<TensorGrad<T>> {
// get the sorted nodes
let sorted = self.toposort(true);
// initialize a new gradient store
let mut store = TensorGrad::new();
// insert the gradient w.r.t. the current node
store.insert(self.id(), self.ones_like());
for node in sorted.iter() {
if node.is_variable() {
continue;
}
// get the gradient of the node
let grad = store.remove(&node.id()).expect("Gradient not found");
// detach the gradient
let grad = grad.detach();
// handle the different types of operations
if let Some(op) = &*node.op {
match op {
TensorExpr::Binary(lhs, rhs, kind) => match kind {
BinaryOp::Arith(inner) => match inner {
Arithmetic::Add(_) => {
*entry!(store, lhs) += &grad;
*entry!(store, rhs) += &grad;
}
Arithmetic::Div(_) => {
*entry!(store, lhs) += &grad / rhs.as_ref();
*entry!(store, rhs) -= &grad * lhs.as_ref() / rhs.sqr();
}
Arithmetic::Mul(_) => {
*entry!(store, lhs) += &grad * rhs.as_ref();
*entry!(store, rhs) += &grad * lhs.as_ref();
}
Arithmetic::Sub(_) => {
*entry!(store, lhs) += &grad;
*entry!(store, rhs) -= &grad;
}
_ => todo!(),
},
_ => todo!(),
},
TensorExpr::BinaryScalar(lhs, rhs, kind) => match kind {
BinaryOp::Arith(inner) => match inner {
Arithmetic::Add(_) => {
*entry!(store, lhs) += &grad;
}
Arithmetic::Div(_) => {
*entry!(store, lhs) += &grad / *rhs;
}
Arithmetic::Mul(_) => {
*entry!(store, lhs) += &grad * *rhs;
}
Arithmetic::Pow(_) => {
*entry!(store, lhs) += &grad * *rhs * lhs.pow(*rhs - T::one());
}
Arithmetic::Sub(_) => {
*entry!(store, lhs) += &grad;
}
_ => todo!(),
},
_ => todo!(),
},
TensorExpr::Unary(val, kind) => match kind {
UnaryOp::Cos => {
*entry!(store, val) -= &grad * val.sin();
}
UnaryOp::Cosh => {
*entry!(store, val) += &grad * val.sinh();
}
UnaryOp::Exp => {
*entry!(store, val) += &grad * val.exp();
}
UnaryOp::Neg => {
*entry!(store, val) -= &grad;
}
UnaryOp::Recip => {
*entry!(store, val) -= &grad / val.sqr();
}
UnaryOp::Sin => {
*entry!(store, val) += &grad * val.cos();
}
UnaryOp::Sinh => {
*entry!(store, val) += &grad * val.cosh();
}
UnaryOp::Sqrt => {
*entry!(store, val) +=
&grad / (val.clone().sqrt() * T::from(2).unwrap());
}
UnaryOp::Tan => {
*entry!(store, val) += &grad / val.clone().cos().sqr();
}
_ => {}
},
TensorExpr::Sigmoid(val) => {
let tmp = val.detach();
*entry!(store, val) +=
&grad * tmp.sigmoid() * (tmp.ones_like() - tmp.sigmoid());
}
_ => {}
}
}
}
Ok(store)
}
}