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
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
|
use anyhow::{Context, Result};
use candle::{Device, Shape, Tensor, Var};
mod test_utils;
fn simple_grad(device: &Device) -> Result<()> {
let x = Var::new(&[3f32, 1., 4.], device)?;
let x = x.as_tensor();
let y = (((x * x)? + x * 5f64)? + 4f64)?;
let grads = y.backward()?;
let grad_x = grads.get(x).context("no grad for x")?;
assert_eq!(x.to_vec1::<f32>()?, [3., 1., 4.]);
// y = x^2 + 5.x + 4
assert_eq!(y.to_vec1::<f32>()?, [28., 10., 40.]);
// dy/dx = 2.x + 5
assert_eq!(grad_x.to_vec1::<f32>()?, [11., 7., 13.]);
Ok(())
}
fn sum_grad(device: &Device) -> Result<()> {
let x = Var::new(&[3f32, 1., 4.], device)?;
let x = x.as_tensor();
let y = (x.sqr()?.sum_keepdim(0)? * 2.)?;
let grads = y.backward()?;
let grad_x = grads.get(x).context("no grad for x")?;
assert_eq!(y.to_vec1::<f32>()?, [52.]);
// y = 2.x^2 so dy/dx = 4.x
assert_eq!(grad_x.to_vec1::<f32>()?, &[12., 4., 16.]);
// Same test as before but squeezing on the last dimension.
let y = (x.sqr()?.sum_keepdim(0)? * 2.)?.squeeze(0)?;
let grads = y.backward()?;
let grad_x = grads.get(x).context("no grad for x")?;
assert_eq!(y.to_scalar::<f32>()?, 52.);
// y = 2.x^2 so dy/dx = 4.x
assert_eq!(grad_x.to_vec1::<f32>()?, &[12., 4., 16.]);
Ok(())
}
fn matmul_grad(device: &Device) -> Result<()> {
let data: Vec<_> = (0..12).map(|i| i as f32).collect();
let x = Var::from_slice(&data, (2, 2, 3), device)?;
let data: Vec<_> = (0..12).map(|i| i as f32).collect();
let y = Var::from_slice(&data, (2, 3, 2), device)?;
let c = x.matmul(&y)?;
let grads = c.backward()?;
let grad_x = grads.get(&x).context("no grad for x")?;
let grad_y = grads.get(&y).context("no grad for y")?;
assert_eq!(grad_x.shape(), &Shape::from((2, 2, 3)));
assert_eq!(grad_y.shape(), &Shape::from((2, 3, 2)));
assert_eq!(
&*grad_x.to_vec3::<f32>()?,
&[
[[1., 5., 9.], [1., 5., 9.]],
[[13., 17., 21.], [13., 17., 21.]]
]
);
assert_eq!(
&*grad_y.to_vec3::<f32>()?,
&[
[[3., 3.], [5., 5.], [7., 7.]],
[[15., 15.], [17., 17.], [19., 19.]]
]
);
Ok(())
}
// The simplest gradient descent, using scalar variable.
fn grad_descent(device: &Device) -> Result<()> {
let x = Var::new(0f32, device)?;
let learning_rate = 0.1;
for _step in 0..100 {
let xt = x.as_tensor();
let c = ((xt - 4.2)? * (xt - 4.2)?)?;
let grads = c.backward()?;
let x_grad = grads.get(&x).context("no grad for x")?;
x.set(&(xt - x_grad * learning_rate)?)?
}
assert_eq!(x.to_scalar::<f32>()?, 4.199999);
Ok(())
}
fn unary_grad(device: &Device) -> Result<()> {
let x = Var::new(&[3f32, 1., 4., 0.15], device)?;
let x = x.as_tensor();
let y = (x.log()? + 1.)?;
let grads = y.backward()?;
let grad_x = grads.get(x).context("no grad for x")?;
assert_eq!(y.to_vec1::<f32>()?, [2.0986123, 1.0, 2.3862944, -0.89712]);
assert_eq!(grad_x.to_vec1::<f32>()?, [0.33333334, 1.0, 0.25, 6.6666665]);
let y = x.exp()?;
let grads = y.backward()?;
let grad_x = grads.get(x).context("no grad for x")?;
assert_eq!(
y.to_vec1::<f32>()?,
[20.085537, 2.7182817, 54.59815, 1.1618342]
);
assert_eq!(
grad_x.to_vec1::<f32>()?,
[20.085537, 2.7182817, 54.59815, 1.1618342]
);
let y = x.exp()?.sqr()?;
let grads = y.backward()?;
let grad_x = grads.get(x).context("no grad for x")?;
assert_eq!(
y.to_vec1::<f32>()?,
[403.4288, 7.3890557, 2980.9578, 1.3498588]
);
// exp(x)^2 = exp(2*x)
assert_eq!(
grad_x.to_vec1::<f32>()?,
[806.8576, 14.778111, 5961.9155, 2.6997175]
);
let y = x.sin()?;
let grads = y.backward()?;
let grad_x = grads.get(x).context("no grad for x")?;
assert_eq!(
test_utils::to_vec1_round(&y, 4)?,
[0.1411, 0.8415, -0.7568, 0.1494],
);
assert_eq!(
test_utils::to_vec1_round(grad_x, 4)?,
[-0.99, 0.5403, -0.6536, 0.9888],
);
let y = x.cos()?;
let grads = y.backward()?;
let grad_x = grads.get(x).context("no grad for x")?;
assert_eq!(
test_utils::to_vec1_round(&y, 4)?,
[-0.99, 0.5403, -0.6536, 0.9888],
);
assert_eq!(
test_utils::to_vec1_round(grad_x, 4)?,
[-0.1411, -0.8415, 0.7568, -0.1494],
);
let y = x.sqr()?;
let grads = y.backward()?;
let grad_x = grads.get(x).context("no grad for x")?;
assert_eq!(y.to_vec1::<f32>()?, [9.0, 1.0, 16.0, 0.0225]);
assert_eq!(grad_x.to_vec1::<f32>()?, [6.0, 2.0, 8.0, 0.3]);
let y = x.sqr()?.sqrt()?;
let grads = y.backward()?;
let grad_x = grads.get(x).context("no grad for x")?;
assert_eq!(y.to_vec1::<f32>()?, [3.0, 1.0, 4.0, 0.15]);
assert_eq!(grad_x.to_vec1::<f32>()?, [1.0, 1.0, 1.0, 1.0]);
let y = x.neg()?;
let grads = y.backward()?;
let grad_x = grads.get(x).context("no grad for x")?;
assert_eq!(y.to_vec1::<f32>()?, [-3.0, -1.0, -4.0, -0.15]);
assert_eq!(grad_x.to_vec1::<f32>()?, [-1.0, -1.0, -1.0, -1.0]);
let y = x.affine(0.2, 1.)?;
let grads = y.backward()?;
let grad_x = grads.get(x).context("no grad for x")?;
assert_eq!(y.to_vec1::<f32>()?, [1.6, 1.2, 1.8, 1.03]);
assert_eq!(grad_x.to_vec1::<f32>()?, [0.2, 0.2, 0.2, 0.2]);
let y = Tensor::new(1f32, device)?.broadcast_div(x)?;
let grads = y.backward()?;
let grad_x = grads.get(x).context("no grad for x")?;
assert_eq!(y.to_vec1::<f32>()?, [0.33333334, 1.0, 0.25, 6.6666665]);
assert_eq!(
grad_x.to_vec1::<f32>()?,
[-0.11111111, -1.0, -0.0625, -44.444443],
);
let y = x.broadcast_div(&Tensor::new(0.5f32, device)?)?;
let grads = y.backward()?;
let grad_x = grads.get(x).context("no grad for x")?;
assert_eq!(y.to_vec1::<f32>()?, [6., 2., 8., 0.3]);
assert_eq!(grad_x.to_vec1::<f32>()?, [2., 2., 2., 2.]);
Ok(())
}
test_device!(simple_grad, simple_grad_cpu, simple_grad_gpu);
test_device!(sum_grad, sum_grad_cpu, sum_grad_gpu);
test_device!(matmul_grad, matmul_grad_cpu, matmul_grad_gpu);
test_device!(grad_descent, grad_descent_cpu, grad_descent_gpu);
test_device!(unary_grad, unary_grad_cpu, unary_grad_gpu);
|
