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use super::*;
use crate::{shapes::*, tensor::*};
/// `log(softmax(t))` in numerically stable way across `Ax`. Does `t - logsumexp(t)` under the hood.
///
/// **Pytorch equivalent**: `t.log_softmax(Ax)`
///
/// Example:
/// ```rust
/// # use dfdx::prelude::*;
/// # let dev: Cpu = Default::default();
/// let t: Tensor<Rank3<2, 3, 5>, f32, _> = dev.zeros();
/// let _ = t.log_softmax::<Axis<2>>();
/// ```
///
/// Using multi axis log_softmax:
/// ```rust
/// # use dfdx::prelude::*;
/// # let dev: Cpu = Default::default();
/// # let t: Tensor<Rank3<2, 3, 5>, f32, _> = dev.zeros();
/// let _ = t.log_softmax::<Axes2<0, 2>>();
/// ```
pub fn log_softmax<Ax: Axes, S: Shape, E: Dtype, D: Device<E>, T: Tape<E, D>>(
t: Tensor<S, E, D, T>,
) -> Tensor<S, E, D, T>
where
S: ReduceShape<Ax>,
{
t.log_softmax::<Ax>()
}
impl<S: Shape, E: Dtype, D: Device<E>, T: Tape<E, D>> Tensor<S, E, D, T> {
/// See [log_softmax()]
pub fn log_softmax<Ax: Axes>(self) -> Self
where
S: ReduceShape<Ax>,
{
self.try_log_softmax::<Ax>().unwrap()
}
/// See [log_softmax()]
pub fn try_log_softmax<Ax: Axes>(self) -> Result<Self, D::Err>
where
S: ReduceShape<Ax>,
{
/*
# Notes on this reduction
log_softmax is equivalent to:
`t - t.logsumexp()`
logsumexp can be inlined to:
`t - ((t - t.max()).exp().sum().ln() + t.max())`
we can apply the subtraction in the following way:
`t - (t - t.max()).exp().sum().ln() - t.max()`
`t - t.max() - (t - t.max()).exp().sum().ln()`
Notice there is a repeated expression here of `t - t.max()`.
So we can re-use this calculation.
`tm - tm.exp().sum().ln()`
*/
let shape = *self.shape();
let (t, tape) = self.split_tape();
let max = t.clone().try_max::<_, Ax>()?;
let tm = {
// Do this calculation off of the tape
let keep_id = t.id;
let mut t = t.try_sub(max.try_broadcast_like::<_, Ax>(&shape)?)?;
t.id = keep_id;
t.put_tape(tape)
};
let logsumexp = tm.retaped::<T>().try_exp()?.try_sum::<_, Ax>()?.try_ln()?;
tm.try_sub(logsumexp.try_broadcast_like(&shape)?)
}
}
#[cfg(test)]
mod tests {
use crate::{shapes::*, tensor::*, tensor_ops::*, tests::*};
#[test]
fn test_log_softmax_equivalence() {
let dev: TestDevice = Default::default();
let t: Tensor<Rank4<8, 16, 32, 64>, TestDtype, _> = dev.sample_normal();
let p = t.leaky_trace().log_softmax::<Axis<3>>();
let p_truth = t.leaky_trace() - t.leaky_trace().logsumexp::<_, Axis<3>>().broadcast();
// we can't create an array as it will overflow the stack
for (p_i, pt_i) in p.as_vec().iter().zip(p_truth.as_vec().iter()) {
assert!((p_i - pt_i).abs() <= TestDtype::DEFAULT_TOLERANCE);
}
let g = p.square().mean().backward();
let g_truth = p_truth.square().mean().backward();
for (g_i, gt_i) in g
.get(&t)
.as_vec()
.iter()
.zip(g_truth.get(&t).as_vec().iter())
{
assert!((g_i - gt_i).abs() <= TestDtype::DEFAULT_TOLERANCE);
}
}
#[test]
fn test_log_softmax_1d() {
let dev: TestDevice = Default::default();
let a = dev
.tensor([-2.0, -1.0, 0.0, 1.0, 2.0])
.to_dtype::<TestDtype>();
let r = a.leaky_trace().log_softmax();
assert_close_to_literal!(
r,
[-4.4519143, -3.4519143, -2.4519143, -1.4519143, -0.4519143]
);
let g = r.mean().backward();
assert_close_to_literal!(
g.get(&a),
[
0.18834378,
0.16831508,
0.11387146,
-0.034121647,
-0.43640864,
]
);
}
#[test]
fn test_log_softmax_2d() {
let dev: TestDevice = Default::default();
let a = dev
.tensor([[-2.0, -1.0, 0.0], [1.0, 4.0, 7.0]])
.to_dtype::<TestDtype>();
let r = a.leaky_trace().log_softmax::<Axis<1>>();
assert_close_to_literal!(
r,
[
[-2.407606, -1.4076059, -0.40760595],
[-6.0509458, -3.0509458, -0.05094576],
]
);
let g = r.mean().backward();
assert_close_to_literal!(
g.get(&a),
[
[0.12165138, 0.044302434, -0.1659538],
[0.16548885, 0.14300959, -0.30849844],
]
);
}
}