Move the backprop bits to a separate file.

This commit is contained in:
laurent
2023-06-24 20:57:49 +01:00
parent 0988706c88
commit 213445c0e5
3 changed files with 299 additions and 287 deletions

290
src/backprop.rs Normal file
View File

@ -0,0 +1,290 @@
use crate::{op::Op, Error, Result, Tensor, TensorId};
use std::collections::HashMap;
impl Tensor {
/// Return all the nodes that lead to this value in a topologically sorted vec, the first
/// elements having dependencies on the latter ones, e.g. the first element if any is the
/// argument.
/// This assumes that the op graph is a DAG.
fn sorted_nodes(&self) -> Vec<&Tensor> {
// The vec of sorted nodes is passed as an owned value rather than a mutable reference
// to get around some lifetime limitations.
fn walk<'a>(
node: &'a Tensor,
nodes: Vec<&'a Tensor>,
already_seen: &mut HashMap<TensorId, bool>,
) -> (bool, Vec<&'a Tensor>) {
if let Some(&tg) = already_seen.get(&node.id()) {
return (tg, nodes);
}
let mut track_grad = false;
let mut nodes = if node.is_variable() {
// Do not call recursively on the "leaf" nodes.
track_grad = true;
nodes
} else if let Some(op) = node.op() {
match op {
Op::Add(lhs, rhs)
| Op::Mul(lhs, rhs)
| Op::Sub(lhs, rhs)
| Op::Div(lhs, rhs)
| Op::BroadcastAdd(lhs, rhs)
| Op::BroadcastMul(lhs, rhs)
| Op::BroadcastSub(lhs, rhs)
| Op::BroadcastDiv(lhs, rhs)
| Op::Embedding(lhs, rhs)
| Op::Matmul(lhs, rhs) => {
let (tg, nodes) = walk(lhs, nodes, already_seen);
track_grad |= tg;
let (tg, nodes) = walk(rhs, nodes, already_seen);
track_grad |= tg;
nodes
}
Op::Cat(args, _) => args.iter().fold(nodes, |nodes, arg| {
let (tg, nodes) = walk(arg, nodes, already_seen);
track_grad |= tg;
nodes
}),
Op::Affine { arg, mul, .. } => {
if *mul == 0. {
nodes
} else {
let (tg, nodes) = walk(arg, nodes, already_seen);
track_grad |= tg;
nodes
}
}
Op::Reshape(node)
| Op::Broadcast(node)
| Op::ToDType(node)
| Op::ToDevice(node)
| Op::Transpose(node, _, _)
| Op::Narrow(node, _, _, _)
| Op::Softmax(node, _)
| Op::Sqr(node)
| Op::Sqrt(node)
| Op::Gelu(node)
| Op::Exp(node)
| Op::Log(node)
| Op::Sin(node)
| Op::Cos(node)
| Op::Abs(node)
| Op::Neg(node) => {
let (tg, nodes) = walk(node, nodes, already_seen);
track_grad |= tg;
nodes
}
}
} else {
nodes
};
already_seen.insert(node.id(), track_grad);
if track_grad {
nodes.push(node);
}
(track_grad, nodes)
}
let (_tg, mut nodes) = walk(self, vec![], &mut HashMap::new());
nodes.reverse();
nodes
}
pub fn backward(&self) -> Result<GradStore> {
let sorted_nodes = self.sorted_nodes();
let mut grads = GradStore::new();
grads.insert(self, self.ones_like()?);
for node in sorted_nodes.iter() {
if node.is_variable() {
continue;
}
let grad = grads.remove(node).unwrap();
// TODO: We should perform all these operations in place (or at least not track the
// whole graph).
// The only drawback would be if we wanted to support grad of grad but this is out of
// scope.
if let Some(op) = node.op() {
match op {
Op::Add(lhs, rhs) => {
let lhs_sum_grad = grads.or_insert(lhs)?;
*lhs_sum_grad = lhs_sum_grad.add(&grad)?;
let rhs_sum_grad = grads.or_insert(rhs)?;
*rhs_sum_grad = rhs_sum_grad.add(&grad)?;
}
Op::Sub(lhs, rhs) => {
let lhs_sum_grad = grads.or_insert(lhs)?;
*lhs_sum_grad = lhs_sum_grad.add(&grad)?;
let rhs_sum_grad = grads.or_insert(rhs)?;
*rhs_sum_grad = rhs_sum_grad.sub(&grad)?;
}
Op::Mul(lhs, rhs) => {
let lhs_grad = grad.mul(rhs)?;
let lhs_sum_grad = grads.or_insert(lhs)?;
*lhs_sum_grad = lhs_sum_grad.add(&lhs_grad)?;
let rhs_grad = grad.mul(lhs)?;
let rhs_sum_grad = grads.or_insert(rhs)?;
*rhs_sum_grad = rhs_sum_grad.add(&rhs_grad)?;
}
Op::Div(lhs, rhs) => {
let lhs_grad = grad.div(rhs)?;
let lhs_sum_grad = grads.or_insert(lhs)?;
*lhs_sum_grad = lhs_sum_grad.add(&lhs_grad)?;
let rhs_grad = grad.mul(lhs)?.div(&rhs.sqr()?)?;
let rhs_sum_grad = grads.or_insert(rhs)?;
*rhs_sum_grad = rhs_sum_grad.add(&rhs_grad)?;
}
Op::BroadcastAdd(lhs, rhs) => {
let lhs_sum_grad = grads.or_insert(lhs)?;
*lhs_sum_grad = lhs_sum_grad.broadcast_add(&grad)?;
let rhs_sum_grad = grads.or_insert(rhs)?;
*rhs_sum_grad = rhs_sum_grad.broadcast_add(&grad)?;
}
Op::BroadcastSub(lhs, rhs) => {
let lhs_sum_grad = grads.or_insert(lhs)?;
*lhs_sum_grad = lhs_sum_grad.broadcast_add(&grad)?;
let rhs_sum_grad = grads.or_insert(rhs)?;
*rhs_sum_grad = rhs_sum_grad.broadcast_sub(&grad)?;
}
Op::BroadcastMul(lhs, rhs) => {
let lhs_grad = grad.broadcast_mul(rhs)?;
let lhs_sum_grad = grads.or_insert(lhs)?;
*lhs_sum_grad = lhs_sum_grad.broadcast_add(&lhs_grad)?;
let rhs_grad = grad.broadcast_mul(lhs)?;
let rhs_sum_grad = grads.or_insert(rhs)?;
*rhs_sum_grad = rhs_sum_grad.broadcast_add(&rhs_grad)?;
}
Op::BroadcastDiv(lhs, rhs) => {
let lhs_grad = grad.broadcast_div(rhs)?;
let lhs_sum_grad = grads.or_insert(lhs)?;
*lhs_sum_grad = lhs_sum_grad.broadcast_add(&lhs_grad)?;
let rhs_grad = grad.broadcast_mul(lhs)?.broadcast_div(&rhs.sqr()?)?;
let rhs_sum_grad = grads.or_insert(rhs)?;
*rhs_sum_grad = rhs_sum_grad.broadcast_add(&rhs_grad)?;
}
Op::Embedding(_lhs, _rhs) => {
return Err(Error::BackwardNotSupported { op: "embedding" })
}
Op::Matmul(lhs, rhs) => {
// Skipping checks, the op went ok, we can skip
// the matmul size checks for now.
let lhs_grad = grad.matmul(&rhs.t()?)?;
let lhs_sum_grad = grads.or_insert(lhs)?;
*lhs_sum_grad = lhs_sum_grad.add(&lhs_grad)?;
let rhs_grad = lhs.t()?.matmul(&grad)?;
let rhs_sum_grad = grads.or_insert(rhs)?;
*rhs_sum_grad = rhs_sum_grad.add(&rhs_grad)?;
}
Op::Cat(args, dim) => {
let mut start_idx = 0;
for arg in args {
let len = arg.dims()[*dim];
let arg_grad = grad.narrow(*dim, start_idx, len)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&arg_grad)?;
start_idx += len;
}
}
Op::Broadcast(_arg) => {
return Err(Error::BackwardNotSupported { op: "broadcast" })
}
Op::ToDType(arg) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&grad.to_dtype(node.dtype())?)?
}
Op::Affine { arg, mul, .. } => {
let arg_grad = grad.affine(*mul, 0.)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&arg_grad)?
}
Op::Log(arg) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&(&grad * *node)?)?
}
Op::Sin(arg) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&(&grad * arg.cos())?)?
}
Op::Cos(arg) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.sub(&(&grad * arg.sin())?)?
}
Op::Abs(_args) => return Err(Error::BackwardNotSupported { op: "abs" }),
Op::Exp(arg) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&(&grad / arg)?)?
}
Op::Neg(arg) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.sub(&grad)?
}
Op::Narrow(_arg, _, _, _) => {
return Err(Error::BackwardNotSupported { op: "narrow" })
}
Op::Softmax(_arg, _) => {
return Err(Error::BackwardNotSupported { op: "softmax" })
}
Op::Reshape(_arg) => return Err(Error::BackwardNotSupported { op: "reshape" }),
Op::Gelu(_) => return Err(Error::BackwardNotSupported { op: "gelu" }),
Op::Sqr(arg) => {
let arg_grad = arg.mul(&grad)?.affine(2., 0.)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&arg_grad)?
}
Op::Sqrt(arg) => {
let arg_grad = grad.div(arg)?.affine(0.5, 0.)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&arg_grad)?
}
Op::ToDevice(arg) => {
let sum_grad = grads.or_insert(arg)?;
let arg_grad = grad.to_device(&sum_grad.device())?;
*sum_grad = sum_grad.add(&arg_grad)?
}
Op::Transpose(arg, dim1, dim2) => {
let arg_grad = grad.transpose(*dim1, *dim2)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&arg_grad)?
}
};
}
}
Ok(grads)
}
}
pub struct GradStore(HashMap<TensorId, Tensor>);
impl GradStore {
fn new() -> Self {
GradStore(HashMap::new())
}
pub fn get_id(&self, id: TensorId) -> Option<&Tensor> {
self.0.get(&id)
}
pub fn get(&self, tensor: &Tensor) -> Option<&Tensor> {
self.0.get(&tensor.id())
}
pub fn remove(&mut self, tensor: &Tensor) -> Option<Tensor> {
self.0.remove(&tensor.id())
}
pub fn insert(&mut self, tensor: &Tensor, grad: Tensor) -> Option<Tensor> {
self.0.insert(tensor.id(), grad)
}
fn or_insert(&mut self, tensor: &Tensor) -> Result<&mut Tensor> {
use std::collections::hash_map::Entry;
let grad = match self.0.entry(tensor.id()) {
Entry::Occupied(entry) => entry.into_mut(),
Entry::Vacant(entry) => {
let grad = tensor.zeros_like()?;
entry.insert(grad)
}
};
Ok(grad)
}
}

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@ -1,3 +1,4 @@
mod backprop;
mod cpu_backend;
#[cfg(feature = "cuda")]
mod cuda_backend;

View File

@ -1,5 +1,4 @@
use crate::{op::Op, storage::Storage, DType, Device, Error, Result, Shape};
use std::collections::HashMap;
use std::sync::Arc;
/// Unique identifier for tensors.
@ -541,6 +540,14 @@ impl Tensor {
self.id
}
pub fn is_variable(&self) -> bool {
self.is_variable
}
pub(crate) fn op(&self) -> &Option<Op> {
&self.op
}
/// Returns a tensor that is a transposed version of the input, the two last dimensions of the
/// input are swapped.
pub fn t(&self) -> Result<Tensor> {
@ -819,256 +826,6 @@ impl Tensor {
}
Ok(from_storage(storage, shape, op, false))
}
/// Return all the nodes that lead to this value in a topologically sorted vec, the first
/// elements having dependencies on the latter ones, e.g. the first element if any is the
/// argument.
/// This assumes that the op graph is a DAG.
fn sorted_nodes(&self) -> Vec<&Tensor> {
// The vec of sorted nodes is passed as an owned value rather than a mutable reference
// to get around some lifetime limitations.
fn walk<'a>(
node: &'a Tensor,
nodes: Vec<&'a Tensor>,
already_seen: &mut HashMap<TensorId, bool>,
) -> (bool, Vec<&'a Tensor>) {
if let Some(&tg) = already_seen.get(&node.id) {
return (tg, nodes);
}
let mut track_grad = false;
let mut nodes = if node.is_variable {
// Do not call recursively on the "leaf" nodes.
track_grad = true;
nodes
} else if let Some(op) = &node.op {
match op {
Op::Add(lhs, rhs)
| Op::Mul(lhs, rhs)
| Op::Sub(lhs, rhs)
| Op::Div(lhs, rhs)
| Op::BroadcastAdd(lhs, rhs)
| Op::BroadcastMul(lhs, rhs)
| Op::BroadcastSub(lhs, rhs)
| Op::BroadcastDiv(lhs, rhs)
| Op::Embedding(lhs, rhs)
| Op::Matmul(lhs, rhs) => {
let (tg, nodes) = walk(lhs, nodes, already_seen);
track_grad |= tg;
let (tg, nodes) = walk(rhs, nodes, already_seen);
track_grad |= tg;
nodes
}
Op::Cat(args, _) => args.iter().fold(nodes, |nodes, arg| {
let (tg, nodes) = walk(arg, nodes, already_seen);
track_grad |= tg;
nodes
}),
Op::Affine { arg, mul, .. } => {
if *mul == 0. {
nodes
} else {
let (tg, nodes) = walk(arg, nodes, already_seen);
track_grad |= tg;
nodes
}
}
Op::Reshape(node)
| Op::Broadcast(node)
| Op::ToDType(node)
| Op::ToDevice(node)
| Op::Transpose(node, _, _)
| Op::Narrow(node, _, _, _)
| Op::Softmax(node, _)
| Op::Sqr(node)
| Op::Sqrt(node)
| Op::Gelu(node)
| Op::Exp(node)
| Op::Log(node)
| Op::Sin(node)
| Op::Cos(node)
| Op::Abs(node)
| Op::Neg(node) => {
let (tg, nodes) = walk(node, nodes, already_seen);
track_grad |= tg;
nodes
}
}
} else {
nodes
};
already_seen.insert(node.id, track_grad);
if track_grad {
nodes.push(node);
}
(track_grad, nodes)
}
let (_tg, mut nodes) = walk(self, vec![], &mut HashMap::new());
nodes.reverse();
nodes
}
pub fn backward(&self) -> Result<GradStore> {
let sorted_nodes = self.sorted_nodes();
let mut grads = GradStore::new();
grads.insert(self, self.ones_like()?);
for node in sorted_nodes.iter() {
if node.is_variable {
continue;
}
let grad = grads.remove(node).unwrap();
// TODO: We should perform all these operations in place (or at least not track the
// whole graph).
// The only drawback would be if we wanted to support grad of grad but this is out of
// scope.
if let Some(op) = &node.op {
match op {
Op::Add(lhs, rhs) => {
let lhs_sum_grad = grads.or_insert(lhs)?;
*lhs_sum_grad = lhs_sum_grad.add(&grad)?;
let rhs_sum_grad = grads.or_insert(rhs)?;
*rhs_sum_grad = rhs_sum_grad.add(&grad)?;
}
Op::Sub(lhs, rhs) => {
let lhs_sum_grad = grads.or_insert(lhs)?;
*lhs_sum_grad = lhs_sum_grad.add(&grad)?;
let rhs_sum_grad = grads.or_insert(rhs)?;
*rhs_sum_grad = rhs_sum_grad.sub(&grad)?;
}
Op::Mul(lhs, rhs) => {
let lhs_grad = grad.mul(rhs)?;
let lhs_sum_grad = grads.or_insert(lhs)?;
*lhs_sum_grad = lhs_sum_grad.add(&lhs_grad)?;
let rhs_grad = grad.mul(lhs)?;
let rhs_sum_grad = grads.or_insert(rhs)?;
*rhs_sum_grad = rhs_sum_grad.add(&rhs_grad)?;
}
Op::Div(lhs, rhs) => {
let lhs_grad = grad.div(rhs)?;
let lhs_sum_grad = grads.or_insert(lhs)?;
*lhs_sum_grad = lhs_sum_grad.add(&lhs_grad)?;
let rhs_grad = grad.mul(lhs)?.div(&rhs.sqr()?)?;
let rhs_sum_grad = grads.or_insert(rhs)?;
*rhs_sum_grad = rhs_sum_grad.add(&rhs_grad)?;
}
Op::BroadcastAdd(lhs, rhs) => {
let lhs_sum_grad = grads.or_insert(lhs)?;
*lhs_sum_grad = lhs_sum_grad.broadcast_add(&grad)?;
let rhs_sum_grad = grads.or_insert(rhs)?;
*rhs_sum_grad = rhs_sum_grad.broadcast_add(&grad)?;
}
Op::BroadcastSub(lhs, rhs) => {
let lhs_sum_grad = grads.or_insert(lhs)?;
*lhs_sum_grad = lhs_sum_grad.broadcast_add(&grad)?;
let rhs_sum_grad = grads.or_insert(rhs)?;
*rhs_sum_grad = rhs_sum_grad.broadcast_sub(&grad)?;
}
Op::BroadcastMul(lhs, rhs) => {
let lhs_grad = grad.broadcast_mul(rhs)?;
let lhs_sum_grad = grads.or_insert(lhs)?;
*lhs_sum_grad = lhs_sum_grad.broadcast_add(&lhs_grad)?;
let rhs_grad = grad.broadcast_mul(lhs)?;
let rhs_sum_grad = grads.or_insert(rhs)?;
*rhs_sum_grad = rhs_sum_grad.broadcast_add(&rhs_grad)?;
}
Op::BroadcastDiv(lhs, rhs) => {
let lhs_grad = grad.broadcast_div(rhs)?;
let lhs_sum_grad = grads.or_insert(lhs)?;
*lhs_sum_grad = lhs_sum_grad.broadcast_add(&lhs_grad)?;
let rhs_grad = grad.broadcast_mul(lhs)?.broadcast_div(&rhs.sqr()?)?;
let rhs_sum_grad = grads.or_insert(rhs)?;
*rhs_sum_grad = rhs_sum_grad.broadcast_add(&rhs_grad)?;
}
Op::Embedding(_lhs, _rhs) => {
return Err(Error::BackwardNotSupported { op: "embedding" })
}
Op::Matmul(lhs, rhs) => {
// Skipping checks, the op went ok, we can skip
// the matmul size checks for now.
let lhs_grad = grad.matmul(&rhs.t()?)?;
let lhs_sum_grad = grads.or_insert(lhs)?;
*lhs_sum_grad = lhs_sum_grad.add(&lhs_grad)?;
let rhs_grad = lhs.t()?.matmul(&grad)?;
let rhs_sum_grad = grads.or_insert(rhs)?;
*rhs_sum_grad = rhs_sum_grad.add(&rhs_grad)?;
}
Op::Cat(args, dim) => {
let mut start_idx = 0;
for arg in args {
let len = arg.dims()[*dim];
let arg_grad = grad.narrow(*dim, start_idx, len)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&arg_grad)?;
start_idx += len;
}
}
Op::Broadcast(_arg) => {
return Err(Error::BackwardNotSupported { op: "broadcast" })
}
Op::ToDType(arg) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&grad.to_dtype(node.dtype())?)?
}
Op::Affine { arg, mul, .. } => {
let arg_grad = grad.affine(*mul, 0.)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&arg_grad)?
}
Op::Log(arg) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&(&grad * *node)?)?
}
Op::Sin(arg) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&(&grad * arg.cos())?)?
}
Op::Cos(arg) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.sub(&(&grad * arg.sin())?)?
}
Op::Abs(_args) => return Err(Error::BackwardNotSupported { op: "abs" }),
Op::Exp(arg) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&(&grad / arg)?)?
}
Op::Neg(arg) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.sub(&grad)?
}
Op::Narrow(_arg, _, _, _) => {
return Err(Error::BackwardNotSupported { op: "narrow" })
}
Op::Softmax(_arg, _) => {
return Err(Error::BackwardNotSupported { op: "softmax" })
}
Op::Reshape(_arg) => return Err(Error::BackwardNotSupported { op: "reshape" }),
Op::Gelu(_) => return Err(Error::BackwardNotSupported { op: "gelu" }),
Op::Sqr(arg) => {
let arg_grad = arg.mul(&grad)?.affine(2., 0.)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&arg_grad)?
}
Op::Sqrt(arg) => {
let arg_grad = grad.div(arg)?.affine(0.5, 0.)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&arg_grad)?
}
Op::ToDevice(arg) => {
let sum_grad = grads.or_insert(arg)?;
let arg_grad = grad.to_device(&sum_grad.device())?;
*sum_grad = sum_grad.add(&arg_grad)?
}
Op::Transpose(arg, dim1, dim2) => {
let arg_grad = grad.transpose(*dim1, *dim2)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&arg_grad)?
}
};
}
}
Ok(grads)
}
}
macro_rules! bin_trait {
@ -1127,39 +884,3 @@ bin_trait!(Add, add, |_| 1., |v| v);
bin_trait!(Sub, sub, |_| 1., |v: f64| -v);
bin_trait!(Mul, mul, |v| v, |_| 0.);
bin_trait!(Div, div, |v| 1. / v, |_| 0.);
pub struct GradStore(HashMap<TensorId, Tensor>);
impl GradStore {
fn new() -> Self {
GradStore(HashMap::new())
}
pub fn get_id(&self, id: TensorId) -> Option<&Tensor> {
self.0.get(&id)
}
pub fn get(&self, tensor: &Tensor) -> Option<&Tensor> {
self.0.get(&tensor.id)
}
pub fn remove(&mut self, tensor: &Tensor) -> Option<Tensor> {
self.0.remove(&tensor.id)
}
pub fn insert(&mut self, tensor: &Tensor, grad: Tensor) -> Option<Tensor> {
self.0.insert(tensor.id, grad)
}
fn or_insert(&mut self, tensor: &Tensor) -> Result<&mut Tensor> {
use std::collections::hash_map::Entry;
let grad = match self.0.entry(tensor.id) {
Entry::Occupied(entry) => entry.into_mut(),
Entry::Vacant(entry) => {
let grad = tensor.zeros_like()?;
entry.insert(grad)
}
};
Ok(grad)
}
}