dfdx 0.13.0

Ergonomic auto differentiation in Rust, with pytorch like apis.
Documentation 
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

use crate::{
    shapes::{Axes, Dtype, ReduceShape, Shape},
    tensor::{HasErr, Tape, Tensor},
};

use super::{BroadcastTo, Device, MeanTo, TryAdd, TryDiv, TrySub};

/// Normalizes `t` to have mean `0.0` and stddev `1.0` along `Ax`. `epsilon` is used during stddev.
/// Computes `(t - t.mean(Ax)) / t.std(Ax, epsilon)`.
///
/// Normalizing a single axis:
/// ```rust
/// # use dfdx::prelude::*;
/// # let dev: Cpu = Default::default();
/// let t: Tensor<Rank2<2, 3>, f32, _> = dev.zeros();
/// let _ = t.normalize::<Axis<1>>(1e-5);
/// ```
pub fn normalize<Ax: Axes, S: Shape + ReduceShape<Ax>, E: Dtype, D: Device<E>, T: Tape<E, D>>(
    t: Tensor<S, E, D, T>,
    epsilon: impl Into<f64>,
) -> Tensor<S, E, D, T> {
    t.normalize::<Ax>(epsilon)
}

impl<S: Shape, E: Dtype, D: Device<E>, T: Tape<E, D>> Tensor<S, E, D, T> {
    /// See [normalize]
    pub fn normalize<Ax: Axes>(self, epsilon: impl Into<f64>) -> Self
    where
        S: ReduceShape<Ax>,
    {
        self.try_normalize::<Ax>(epsilon).unwrap()
    }

    /// See [normalize]
    pub fn try_normalize<Ax: Axes>(
        self,
        epsilon: impl Into<f64>,
    ) -> Result<Self, <Self as HasErr>::Err>
    where
        S: ReduceShape<Ax>,
    {
        let shape = self.shape;
        let mean = self.retaped::<T>().try_mean::<_, Ax>()?;
        let centered = self.try_sub(mean.try_broadcast_like(&shape)?)?;
        let std = centered
            .retaped::<T>()
            .try_square()?
            .try_mean::<_, Ax>()?
            .try_add(E::from_f64(epsilon.into()).unwrap())?
            .try_sqrt()?;
        centered.try_div(std.try_broadcast_like(&shape)?)
    }
}

#[cfg(test)]
mod tests {
    use crate::tests::*;
    use crate::{shapes::*, tensor::*, tensor_ops::*};

    #[test]
    fn test_1d_normalize_axis_last() {
        let dev: TestDevice = Default::default();
        let a = dev.tensor([-2.0, 0.0, 5.0]).to_dtype::<TestDtype>();
        let r = a.leaky_trace().normalize(1e-5);
        assert_close_to_literal!(&r, [-1.0190487, -0.3396829, 1.3587316]);
        // NOTE: .exp() so we can make sure normalize is using result grad properly
        let g = r.exp().mean().backward();
        assert_close_to_literal!(&g.get(&a), [0.033410847, -0.04677555, 0.013364702]);
    }

    #[test]
    fn test_2d_normalize_axis_last() {
        let dev: TestDevice = Default::default();
        let a = dev
            .tensor([[-2.0, 0.0, 5.0], [1.0, 2.0, 3.0]])
            .to_dtype::<TestDtype>();
        let r = a.leaky_trace().normalize::<Axis<1>>(1e-5);
        assert_close_to_literal!(
            r,
            [
                [-1.0190487, -0.3396829, 1.3587316],
                [-1.2247356, 0.0, 1.2247356],
            ]
        );
        let g = r.exp().mean().backward();
        assert_close_to_literal!(
            g.get(&a),
            [
                [0.016705424, -0.023387775, 0.006682351],
                [0.05773133, -0.11547226, 0.057740927],
            ]
        );
    }

    #[test]
    fn test_2d_normalize_axis_first() {
        let dev: TestDevice = Default::default();
        let a = dev
            .tensor([[-2.0, 0.0], [1.0, 2.0], [4.0, 5.0]])
            .to_dtype::<TestDtype>();
        let r = a.leaky_trace().normalize::<Axis<0>>(1e-5);
        assert_close_to_literal!(
            r,
            [
                [-1.2247438, -1.1355485],
                [0.0, -0.16222118],
                [1.2247438, 1.2977698],
            ]
        );
        let g = r.exp().mean().backward();
        assert_close_to_literal!(
            g.get(&a),
            [
                [0.019245632, 0.025835907],
                [-0.038491584, -0.043060362],
                [0.019245982, 0.01722446],
            ]
        );
    }

    #[test]
    fn test_3d_normalize_axis_last() {
        let dev: TestDevice = Default::default();
        let a: Tensor<Rank3<4, 2, 3>, TestDtype, _> = dev.ones();
        let r = a.leaky_trace().normalize::<Axis<2>>(1e-5);
        assert_close_to_literal!(r, [[[0.0; 3]; 2]; 4]);
        let g = r.exp().mean().backward();
        assert_close_to_literal!(g.get(&a), [[[0.0; 3]; 2]; 4]);
    }
}