candle_core/backprop.rs
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/// Methods for backpropagation of gradients.
use crate::op::{BinaryOp, Op, ReduceOp, UnaryOp};
use crate::{Error, Result, Tensor, TensorId};
use std::collections::HashMap;
// arg has been reduced to node via reduce_dims, expand it back to arg.
// This has to handle keepdims.
fn broadcast_back(arg: &Tensor, node: &Tensor, reduced_dims: &[usize]) -> Result<Tensor> {
if arg.rank() == node.rank() {
// keepdim = true
node.broadcast_as(arg.shape())
} else {
// keepdim = false
// first expand the reduced dims.
node.reshape(reduced_dims)?.broadcast_as(arg.shape())
}
}
thread_local! {
static CANDLE_GRAD_DO_NOT_DETACH: bool = {
match std::env::var("CANDLE_GRAD_DO_NOT_DETACH") {
Ok(s) => {
!s.is_empty() && s != "0"
},
Err(_) => false,
}
}
}
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 node.dtype().is_int() {
nodes
} else if let Some(op) = node.op() {
match op {
Op::IndexAdd(t1, t2, t3, _)
| Op::ScatterAdd(t1, t2, t3, _)
| Op::CustomOp3(t1, t2, t3, _)
| Op::WhereCond(t1, t2, t3) => {
let (tg, nodes) = walk(t1, nodes, already_seen);
track_grad |= tg;
let (tg, nodes) = walk(t2, nodes, already_seen);
track_grad |= tg;
let (tg, nodes) = walk(t3, nodes, already_seen);
track_grad |= tg;
nodes
}
Op::Conv1D {
arg: lhs,
kernel: rhs,
..
}
| Op::ConvTranspose1D {
arg: lhs,
kernel: rhs,
..
}
| Op::Conv2D {
arg: lhs,
kernel: rhs,
..
}
| Op::ConvTranspose2D {
arg: lhs,
kernel: rhs,
..
}
| Op::CustomOp2(lhs, rhs, _)
| Op::Binary(lhs, rhs, _)
| Op::Gather(lhs, rhs, _)
| Op::IndexSelect(lhs, rhs, _)
| Op::Matmul(lhs, rhs)
| Op::SliceScatter0(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::Unary(_node, UnaryOp::Ceil)
| Op::Unary(_node, UnaryOp::Floor)
| Op::Unary(_node, UnaryOp::Round)
| Op::Unary(_node, UnaryOp::Sign) => nodes,
Op::Reshape(node)
| Op::UpsampleNearest1D { arg: node, .. }
| Op::UpsampleNearest2D { arg: node, .. }
| Op::AvgPool2D { arg: node, .. }
| Op::MaxPool2D { arg: node, .. }
| Op::Copy(node)
| Op::Broadcast(node)
| Op::Cmp(node, _)
| Op::Reduce(node, ReduceOp::Min | ReduceOp::Sum | ReduceOp::Max, _)
| Op::ToDevice(node)
| Op::Transpose(node, _, _)
| Op::Permute(node, _)
| Op::Narrow(node, _, _, _)
| Op::Unary(node, _)
| Op::Elu(node, _)
| Op::Powf(node, _)
| Op::CustomOp1(node, _) => {
let (tg, nodes) = walk(node, nodes, already_seen);
track_grad |= tg;
nodes
}
Op::ToDType(node) => {
if node.dtype().is_float() {
let (tg, nodes) = walk(node, nodes, already_seen);
track_grad |= tg;
nodes
} else {
nodes
}
}
Op::Reduce(_, ReduceOp::ArgMin | ReduceOp::ArgMax, _) => 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()?.contiguous()?);
for node in sorted_nodes.iter() {
if node.is_variable() {
continue;
}
let grad = grads
.remove(node)
.expect("candle internal error - grad not populated");
// https://github.com/huggingface/candle/issues/1241
// Ideally, we would make these operations in place where possible to ensure that we
// do not have to allocate too often. Here we just call `.detach` to avoid computing
// the backprop graph of the backprop itself. This would be an issue for second order
// derivatives but these are out of scope at the moment.
let do_not_detach = CANDLE_GRAD_DO_NOT_DETACH.with(|b| *b);
let grad = if do_not_detach { grad } else { grad.detach() };
if let Some(op) = node.op() {
match op {
Op::Binary(lhs, rhs, BinaryOp::Add) => {
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::Binary(lhs, rhs, BinaryOp::Sub) => {
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::Binary(lhs, rhs, BinaryOp::Mul) => {
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::Binary(lhs, rhs, BinaryOp::Div) => {
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.sub(&rhs_grad)?;
}
Op::Binary(lhs, rhs, BinaryOp::Minimum)
| Op::Binary(lhs, rhs, BinaryOp::Maximum) => {
let mask_lhs = node.eq(lhs)?.to_dtype(grad.dtype())?;
let mask_rhs = node.eq(rhs)?.to_dtype(grad.dtype())?;
// If both masks are 1 one the same point, we want to scale the
// gradient by 0.5 rather than 1.
let lhs_grad = mask_lhs.mul(&grad)?.div(&(&mask_rhs + 1.)?)?;
let lhs_sum_grad = grads.or_insert(lhs)?;
*lhs_sum_grad = lhs_sum_grad.add(&lhs_grad)?;
let rhs_grad = mask_rhs.mul(&grad)?.div(&(&mask_lhs + 1.)?)?;
let rhs_sum_grad = grads.or_insert(rhs)?;
*rhs_sum_grad = rhs_sum_grad.add(&rhs_grad)?;
}
Op::WhereCond(pred, t, f) => {
let zeros = grad.zeros_like()?;
let t_sum_grad = grads.or_insert(t)?;
let t_grad = pred.where_cond(&grad, &zeros)?;
*t_sum_grad = t_sum_grad.add(&t_grad)?;
let f_sum_grad = grads.or_insert(f)?;
let f_grad = pred.where_cond(&zeros, &grad)?;
*f_sum_grad = f_sum_grad.add(&f_grad)?;
}
Op::Conv1D {
arg,
kernel,
padding,
stride,
dilation,
} => {
// The output height for conv_transpose1d is:
// (l_in - 1) * stride - 2 * padding + dilation * (k_size - 1) + out_padding + 1
let grad_l_in = grad.dim(2)?;
let k_size = kernel.dim(2)?;
let out_size =
(grad_l_in - 1) * stride + dilation * (k_size - 1) + 1 - 2 * padding;
let out_padding = arg.dim(2)? - out_size;
let grad_arg = grad.conv_transpose1d(
kernel,
*padding,
out_padding,
*stride,
*dilation,
/* groups */ 1,
)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&grad_arg)?;
let grad_kernel = arg
.transpose(0, 1)?
.conv1d(&grad.transpose(0, 1)?, *padding, *dilation, *stride, 1)?
.transpose(0, 1)?;
let sum_grad = grads.or_insert(kernel)?;
let (_, _, k0) = kernel.dims3()?;
let (_, _, g_k0) = grad_kernel.dims3()?;
let grad_kernel = if g_k0 != k0 {
grad_kernel.narrow(2, 0, k0)?
} else {
grad_kernel
};
*sum_grad = sum_grad.add(&grad_kernel)?;
}
Op::Conv2D {
arg,
kernel,
padding,
stride,
dilation,
} => {
// The output height for conv_transpose2d is:
// (i_h - 1) * stride - 2 * padding + dilation * (k_h - 1) + out_padding + 1
let grad_h = grad.dim(2)?;
let k_h = kernel.dim(2)?;
let out_size =
(grad_h - 1) * stride + dilation * (k_h - 1) + 1 - 2 * padding;
let out_padding = arg.dim(2)? - out_size;
let grad_arg = grad.conv_transpose2d(
kernel,
*padding,
out_padding,
*stride,
*dilation,
)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&grad_arg)?;
let grad_kernel = arg
.transpose(0, 1)?
.conv2d(&grad.transpose(0, 1)?, *padding, *dilation, *stride, 1)?
.transpose(0, 1)?;
let sum_grad = grads.or_insert(kernel)?;
let (_, _, k0, k1) = kernel.dims4()?;
let (_, _, g_k0, g_k1) = grad_kernel.dims4()?;
let grad_kernel = if g_k0 != k0 || g_k1 != k1 {
grad_kernel.narrow(2, 0, k0)?.narrow(3, 0, k1)?
} else {
grad_kernel
};
*sum_grad = sum_grad.add(&grad_kernel)?;
}
Op::ConvTranspose1D { .. } => Err(Error::BackwardNotSupported {
op: "conv-transpose1d",
})?,
Op::ConvTranspose2D {
arg,
kernel,
padding,
stride,
dilation,
output_padding: _output_padding,
} => {
let grad_arg = grad.conv2d(kernel, *padding, *stride, *dilation, 1)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&grad_arg)?;
let grad_kernel = grad
.transpose(0, 1)?
.conv2d(&arg.transpose(0, 1)?, *padding, *dilation, *stride, 1)?
.transpose(0, 1)?;
let sum_grad = grads.or_insert(kernel)?;
let (_, _, k0, k1) = kernel.dims4()?;
let (_, _, g_k0, g_k1) = grad_kernel.dims4()?;
let grad_kernel = if g_k0 != k0 || g_k1 != k1 {
grad_kernel.narrow(2, 0, k0)?.narrow(3, 0, k1)?
} else {
grad_kernel
};
*sum_grad = sum_grad.add(&grad_kernel)?;
}
Op::AvgPool2D {
arg,
kernel_size,
stride,
} => {
if kernel_size != stride {
crate::bail!("backward not supported for avgpool2d if ksize {kernel_size:?} != stride {stride:?}")
}
let (_n, _c, h, w) = arg.dims4()?;
let grad_arg = grad.upsample_nearest2d(h, w)?;
let grad_arg =
(grad_arg * (1f64 / (kernel_size.0 * kernel_size.1) as f64))?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&grad_arg)?;
}
Op::MaxPool2D {
arg,
kernel_size,
stride,
} => {
if kernel_size != stride {
crate::bail!("backward not supported for maxpool2d if ksize {kernel_size:?} != stride {stride:?}")
}
let (_n, _c, h, w) = arg.dims4()?;
// For computing the max-pool gradient, we compute a mask where a 1 means
// that the element is the maximum, then we apply this mask to the
// upsampled gradient (taking into account that multiple max may exist so
// we scale the gradient for this case).
let node_upsampled = node.upsample_nearest2d(h, w)?;
let mask = arg.eq(&node_upsampled)?.to_dtype(arg.dtype())?;
let avg = mask.avg_pool2d_with_stride(*kernel_size, *stride)?;
let grad_arg = ((grad * avg)?.upsample_nearest2d(h, w)? * mask)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&grad_arg)?;
}
Op::UpsampleNearest1D { arg, target_size } => {
let (_n, c, size) = arg.dims3()?;
if target_size % size != 0 {
crate::bail!("backward not supported for non integer upscaling factors")
}
let scale = target_size / size;
let kernel = Tensor::ones((c, 1, scale), arg.dtype(), arg.device())?;
let conv_sum = grad.conv1d(&kernel, 0, scale, 1, c)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = conv_sum;
}
Op::UpsampleNearest2D {
arg,
target_h,
target_w,
} => {
let (_n, c, h, w) = arg.dims4()?;
if target_h % h != 0 || target_w % w != 0 {
crate::bail!("backward not supported for non integer upscaling factors")
}
let scale_h = target_h / h;
let scale_w = target_w / w;
if scale_h != scale_w {
crate::bail!("backward not supported for non uniform upscaling factors")
};
let kernel =
Tensor::ones((c, 1, scale_h, scale_w), arg.dtype(), arg.device())?;
let conv_sum = grad.conv2d(&kernel, 0, scale_h, 1, c)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = conv_sum;
}
Op::SliceScatter0(lhs, rhs, start_rhs) => {
let rhs_sum_grad = grads.or_insert(rhs)?;
let rhs_grad = grad.narrow(0, *start_rhs, rhs.dim(0)?)?;
*rhs_sum_grad = rhs_sum_grad.add(&rhs_grad)?;
let lhs_sum_grad = grads.or_insert(lhs)?;
let lhs_grad = grad.slice_scatter0(&rhs.zeros_like()?, *start_rhs)?;
*lhs_sum_grad = lhs_sum_grad.add(&lhs_grad)?
}
Op::Gather(arg, indexes, dim) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.scatter_add(indexes, &grad, *dim)?;
}
Op::ScatterAdd(init, indexes, src, dim) => {
let init_sum_grad = grads.or_insert(init)?;
*init_sum_grad = init_sum_grad.add(&grad)?;
let src_grad = grad.gather(indexes, *dim)?;
let src_sum_grad = grads.or_insert(src)?;
*src_sum_grad = src_sum_grad.add(&src_grad)?;
}
Op::IndexAdd(init, indexes, src, dim) => {
let init_sum_grad = grads.or_insert(init)?;
*init_sum_grad = init_sum_grad.add(&grad)?;
let src_grad = grad.index_select(indexes, *dim)?;
let src_sum_grad = grads.or_insert(src)?;
*src_sum_grad = src_sum_grad.add(&src_grad)?;
}
Op::IndexSelect(arg, indexes, dim) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.index_add(indexes, &grad, *dim)?;
}
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) => {
let arg_dims = arg.dims();
let node_dims = node.dims();
// The number of dims that have been inserted on the left.
let left_dims = node_dims.len() - arg_dims.len();
let mut sum_dims: Vec<usize> = (0..left_dims).collect();
for (dim, (node_dim, arg_dim)) in node_dims[left_dims..]
.iter()
.zip(arg_dims.iter())
.enumerate()
{
if node_dim != arg_dim {
sum_dims.push(dim + left_dims)
}
}
let mut arg_grad = grad.sum_keepdim(sum_dims.as_slice())?;
for _i in 0..left_dims {
arg_grad = arg_grad.squeeze(0)?
}
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&arg_grad.broadcast_as(sum_grad.dims())?)?;
}
Op::Reduce(arg, ReduceOp::Sum, reduced_dims) => {
let grad = broadcast_back(arg, &grad, reduced_dims)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&grad)?;
}
Op::Reduce(arg, ReduceOp::Max, reduced_dims) => {
let node = broadcast_back(arg, node, reduced_dims)?;
let grad = broadcast_back(arg, &grad, reduced_dims)?;
let grad = node.eq(arg)?.to_dtype(grad.dtype())?.mul(&grad)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&grad.broadcast_as(sum_grad.dims())?)?;
}
Op::Reduce(arg, ReduceOp::Min, reduced_dims) => {
let node = broadcast_back(arg, node, reduced_dims)?;
let grad = broadcast_back(arg, &grad, reduced_dims)?;
let grad = node.eq(arg)?.to_dtype(grad.dtype())?.mul(&grad)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&grad.broadcast_as(sum_grad.dims())?)?;
}
Op::ToDType(arg) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&grad.to_dtype(arg.dtype())?)?
}
Op::Copy(arg) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&grad)?
}
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::Unary(arg, UnaryOp::Log) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&(grad / arg)?)?
}
Op::Unary(arg, UnaryOp::Sin) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&(&grad * arg.cos())?)?
}
Op::Unary(arg, UnaryOp::Cos) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.sub(&(&grad * arg.sin())?)?
}
Op::Unary(arg, UnaryOp::Tanh) => {
let sum_grad = grads.or_insert(arg)?;
let minus_dtanh = (node.sqr()? - 1.)?;
*sum_grad = sum_grad.sub(&(&grad * &minus_dtanh)?)?
}
Op::Unary(arg, UnaryOp::Abs) => {
let sum_grad = grads.or_insert(arg)?;
let ones = arg.ones_like()?;
let abs_grad = arg.ge(&arg.zeros_like()?)?.where_cond(&ones, &ones.neg()?);
*sum_grad = sum_grad.add(&(&grad * abs_grad)?)?
}
Op::Unary(arg, UnaryOp::Exp) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&(&grad * *node)?)?
}
Op::Unary(arg, UnaryOp::Neg) => {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.sub(&grad)?
}
Op::Unary(arg, UnaryOp::Recip) => {
let sum_grad = grads.or_insert(arg)?;
let grad = (grad / arg.sqr()?)?;
*sum_grad = sum_grad.sub(&grad)?
}
&Op::Narrow(ref arg, dim, start_idx, len) => {
let arg_dims = arg.dims();
let left_pad = if start_idx == 0 {
None
} else {
let mut dims = arg_dims.to_vec();
dims[dim] = start_idx;
Some(Tensor::zeros(dims, grad.dtype(), grad.device())?)
};
let right_pad = arg_dims[dim] - start_idx - len;
let right_pad = if right_pad == 0 {
None
} else {
let mut dims = arg_dims.to_vec();
dims[dim] = right_pad;
Some(Tensor::zeros(dims, grad.dtype(), grad.device())?)
};
let arg_grad = match (left_pad, right_pad) {
(None, None) => grad,
(Some(l), None) => Tensor::cat(&[&l, &grad], dim)?,
(None, Some(r)) => Tensor::cat(&[&grad, &r], dim)?,
(Some(l), Some(r)) => Tensor::cat(&[&l, &grad, &r], dim)?,
};
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&arg_grad)?
}
Op::Unary(_, UnaryOp::Floor)
| Op::Unary(_, UnaryOp::Round)
| Op::Reduce(_, ReduceOp::ArgMin, _)
| Op::Reduce(_, ReduceOp::ArgMax, _)
| Op::Unary(_, UnaryOp::Sign)
| Op::Cmp(_, _) => {}
Op::Reshape(arg) => {
let arg_grad = grad.reshape(arg.dims())?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&arg_grad)?
}
Op::Unary(_, UnaryOp::Ceil) => Err(Error::BackwardNotSupported { op: "ceil" })?,
Op::Unary(arg, UnaryOp::Gelu) => {
let sum_grad = grads.or_insert(arg)?;
let cube = arg.powf(3.)?;
let tanh = (0.0356774 * &cube + (0.797885 * arg)?)?.tanh()?;
let gelu_grad = (((0.5 * &tanh)?
+ (0.0535161 * cube + (0.398942 * arg)?)? * (1. - tanh.powf(2.)?))?
+ 0.5)?;
*sum_grad = sum_grad.add(&(&grad * gelu_grad)?)?
}
Op::Unary(arg, UnaryOp::Erf) => {
let sum_grad = grads.or_insert(arg)?;
// d/dx erf(x) = 2/sqrt(pi) * e^(-x^2)
let erf_grad =
(2. / std::f64::consts::PI.sqrt()) * (arg.sqr()?.neg()?).exp()?;
*sum_grad = sum_grad.add(&(&grad * erf_grad)?)?
}
Op::Unary(arg, UnaryOp::GeluErf) => {
let sum_grad = grads.or_insert(arg)?;
// d/dx gelu_erf(x) = 0.5 + 0.398942 e^(-x^2/2) x + 0.5 erf(x/sqrt(2))
let neg_half_square = (arg.sqr()?.neg()? / 2.)?;
let scaled_exp_arg = (0.398942 * neg_half_square.exp()? * arg)?;
let arg_scaled_sqrt = (arg / 2f64.sqrt())?;
let erf_scaled_sqrt = (0.5 * arg_scaled_sqrt.erf()?)?;
let gelu_erf_grad = (0.5 + scaled_exp_arg + erf_scaled_sqrt)?;
*sum_grad = sum_grad.add(&(&grad * gelu_erf_grad)?)?;
}
Op::Unary(arg, UnaryOp::Relu) => {
let sum_grad = grads.or_insert(arg)?;
let relu_grad = arg.ge(&arg.zeros_like()?)?.to_dtype(arg.dtype())?;
*sum_grad = sum_grad.add(&(&grad * relu_grad)?)?
}
Op::Unary(arg, UnaryOp::Silu) => {
let sum_grad = grads.or_insert(arg)?;
// d/dx silu = sigmoid(x) * (1 + x * (1 - sigmoid(x))) = sigmoid(x) * (1 - node) + node
let sigmoid_arg = (arg.neg()?.exp()? + 1.)?.recip()?;
let silu_grad = &sigmoid_arg * (1. - *node) + *node;
*sum_grad = sum_grad.add(&(&grad * silu_grad)?)?
}
Op::Elu(arg, alpha) => {
// d/dx elu(x) = 1 for x > 0, alpha * e^x for x <= 0
let sum_grad = grads.or_insert(arg)?;
let zeros = arg.zeros_like()?;
let positive_mask = arg.gt(&zeros)?.to_dtype(arg.dtype())?;
let negative_mask = arg.le(&zeros)?.to_dtype(arg.dtype())?;
// node == alpha * (e^x - 1) for x <= 0, reuse it
let negative_exp_mask = (negative_mask * (*node + *alpha))?;
let combined_mask = (positive_mask + negative_exp_mask)?;
*sum_grad = sum_grad.add(&(grad * combined_mask)?)?
}
Op::Powf(arg, e) => {
let arg_grad = (&(grad * arg.powf(e - 1.)?)? * *e)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&arg_grad)?
}
Op::CustomOp1(arg, c) => {
if let Some(arg_grad) = c.bwd(arg, node, &grad)? {
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&arg_grad)?
}
}
Op::CustomOp2(arg1, arg2, c) => {
let (arg_grad1, arg_grad2) = c.bwd(arg1, arg2, node, &grad)?;
if let Some(arg_grad1) = arg_grad1 {
let sum_grad = grads.or_insert(arg1)?;
*sum_grad = sum_grad.add(&arg_grad1)?
}
if let Some(arg_grad2) = arg_grad2 {
let sum_grad = grads.or_insert(arg2)?;
*sum_grad = sum_grad.add(&arg_grad2)?
}
}
Op::CustomOp3(arg1, arg2, arg3, c) => {
let (arg_grad1, arg_grad2, arg_grad3) =
c.bwd(arg1, arg2, arg3, node, &grad)?;
if let Some(arg_grad1) = arg_grad1 {
let sum_grad = grads.or_insert(arg1)?;
*sum_grad = sum_grad.add(&arg_grad1)?
}
if let Some(arg_grad2) = arg_grad2 {
let sum_grad = grads.or_insert(arg2)?;
*sum_grad = sum_grad.add(&arg_grad2)?
}
if let Some(arg_grad3) = arg_grad3 {
let sum_grad = grads.or_insert(arg3)?;
*sum_grad = sum_grad.add(&arg_grad3)?
}
}
Op::Unary(arg, UnaryOp::Sqr) => {
let arg_grad = arg.mul(&grad)?.affine(2., 0.)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&arg_grad)?
}
Op::Unary(arg, UnaryOp::Sqrt) => {
let arg_grad = grad.div(node)?.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)?
}
Op::Permute(arg, dims) => {
let mut inv_dims = vec![0; dims.len()];
for (i, &dim_idx) in dims.iter().enumerate() {
inv_dims[dim_idx] = i
}
let arg_grad = grad.permute(inv_dims)?;
let sum_grad = grads.or_insert(arg)?;
*sum_grad = sum_grad.add(&arg_grad)?
}
};
}
}
Ok(grads)
}
}
/// A store for gradients, associating a tensor id to the corresponding gradient tensor, used for back propagation.
#[derive(Debug)]
pub struct GradStore(HashMap<TensorId, Tensor>);
impl GradStore {
/// Create a new gradient store
fn new() -> Self {
GradStore(HashMap::new())
}
/// Get the gradient tensor corresponding to the given tensor id
pub fn get_id(&self, id: TensorId) -> Option<&Tensor> {
self.0.get(&id)
}
/// Get the gradient tensor associated with the given tensor
pub fn get(&self, tensor: &Tensor) -> Option<&Tensor> {
self.0.get(&tensor.id())
}
/// Remove the gradient tensor associated with the given tensor, returning it if it exists
pub fn remove(&mut self, tensor: &Tensor) -> Option<Tensor> {
self.0.remove(&tensor.id())
}
/// Insert a gradient tensor associated with the given tensor, returning the previous gradient tensor if it existed
pub fn insert(&mut self, tensor: &Tensor, grad: Tensor) -> Option<Tensor> {
self.0.insert(tensor.id(), grad)
}
/// Get the gradient tensor associated with the given tensor, or, if it does not exist,
/// insert a tensor of zeroes, with the same shape and type as the given tensors and return it
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)
}
/// Get the tensor ids of the stored gradient tensors
pub fn get_ids(&self) -> impl Iterator<Item = &TensorId> {
self.0.keys()
}
}