1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150

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],
            ]
        );
    }
}