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
151
152
153

use crate::prelude::*;
use rand::{distributions::Distribution, Rng};

/// A linear transformation of the form `xW + b`, where `W` is a matrix, `x` is a vector or matrix,
/// and `b` is a vector. If `x` is a matrix this does matrix multiplication.
///
/// Implements [Module] for both vectors of size `[I]` and batches of vectors of size `[B, I]`.
/// Implements [Randomize] to set weight & bias to random numbers drawn from a distribution.
///
/// Example usage:
/// `Linear<5, 2>` can act on vectors with 5 elements, and results in vectors with 2 elements.
/// ```
/// # use dfdx::prelude::*;
/// let model: Linear<5, 2> = Default::default();
/// assert_eq!(model.weight.data(), &[[0.0; 2]; 5]);
/// assert_eq!(model.bias.data(), &[0.0; 2]);
/// let x: Tensor1D<5> = Default::default();
/// let y: Tensor1D<2> = model.forward(x);
/// ```
#[derive(Default, Debug, Clone)]
pub struct Linear<const I: usize, const O: usize> {
    pub weight: Tensor2D<I, O, NoTape>,
    pub bias: Tensor1D<O, NoTape>,
}

impl<const I: usize, const O: usize> CanUpdateWithGradients for Linear<I, O> {
    fn update<G: GradientProvider>(&mut self, grads: &mut G) {
        self.weight.update(grads);
        self.bias.update(grads);
    }
}

impl<const I: usize, const O: usize> Randomize<f32> for Linear<I, O> {
    fn randomize<R: Rng, D: Distribution<f32>>(&mut self, rng: &mut R, dist: &D) {
        self.weight.randomize(rng, dist);
        self.bias.randomize(rng, dist);
    }
}

impl<const I: usize, const O: usize, H: TapeHolder> Module<Tensor1D<I, H>> for Linear<I, O> {
    type Output = Tensor1D<O, H>;

    /// 1d forward
    fn forward(&self, x: Tensor1D<I, H>) -> Self::Output {
        add(&self.bias, vecmat_mul(x, &self.weight))
    }
}

impl<const B: usize, const I: usize, const O: usize, H: TapeHolder> Module<Tensor2D<B, I, H>>
    for Linear<I, O>
{
    type Output = Tensor2D<B, O, H>;

    /// Batched 2d forward
    fn forward(&self, x: Tensor2D<B, I, H>) -> Self::Output {
        broadcast_outer_add(matmul(x, &self.weight), &self.bias)
    }
}

#[cfg(test)]
mod tests {
    use super::*;

    const W: [[f32; 2]; 5] = [
        [-0.34588930, 0.11733949],
        [-0.30371523, 0.14059687],
        [-0.37120569, -0.10670426],
        [0.14303583, -0.09373143],
        [-0.02689660, 0.18974298],
    ];
    const B: [f32; 2] = [0.37653649, -0.29071701];

    #[test]
    fn test_forward_1d() {
        let model: Linear<5, 2> = Linear {
            weight: Tensor2D::new(W),
            bias: Tensor1D::new(B),
        };

        let x = Tensor1D::new([-0.88080013, 2.41853333, 2.24783349, 0.05652110, 2.03129911]);
        let y = model.forward(x.trace());
        assert_eq!(y.data(), &[-0.93430865, 0.08624211]);

        let loss = y.square().mean();
        let gradients = loss.backward();
        assert_eq!(
            gradients.ref_gradient(&model.weight),
            &[
                [0.82293916, -0.07596206],
                [-2.25965667, 0.20857942],
                [-2.10017037, 0.19385791],
                [-0.05280815, 0.004874499],
                [-1.89786029, 0.17518352]
            ]
        );
        assert_eq!(
            gradients.ref_gradient(&model.bias),
            &[-0.93430865, 0.08624211]
        );
    }

    #[test]
    fn test_forward_2d() {
        let model: Linear<5, 2> = Linear {
            weight: Tensor2D::new(W),
            bias: Tensor1D::new(B),
        };

        let x = Tensor2D::new([
            [-1.94686651, 1.46117854, -1.66989815, 1.40886295, 1.34256434],
            [
                -1.33998311,
                3.05106783,
                -0.17936817,
                -0.04943254,
                -0.80527049,
            ],
            [
                -0.82914120,
                0.07691376,
                -0.26538327,
                0.90017676,
                -1.87904549,
            ],
        ]);
        let y = model.forward(x.trace());
        assert_eq!(
            y.data(),
            &[
                [1.39143777, -0.012851536],
                [-0.005462587, -0.14800104],
                [0.9177769, -0.7897872]
            ]
        );

        let loss = y.square().mean();
        let gradients = loss.backward();
        assert_eq!(
            gradients.ref_gradient(&model.weight),
            &[
                [-1.15419686, 0.29272807],
                [0.69568729, -0.17702839],
                [-0.85538071, 0.08586791],
                [0.92892551, -0.24057935],
                [0.04931633, 0.52865762]
            ]
        );
        assert_eq!(
            gradients.ref_gradient(&model.bias),
            &[0.76791739, -0.31687993]
        );
    }
}