topos 0.13.1

An autodiff compiler stack in Rust.
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

use smallvec::smallvec;

use crate::{Element, Recordable, Shape, Tensor};

use super::{Cotangents, Operation, Reads, binary};

/// The quotient of two values, with operands `[left, right]`.
///
/// The derivative with respect to the left operand is `1 / right`; with
/// respect to the right operand it is `-left / right^2`, which equals
/// `-output / right`, so `backward` reuses the node's own output the way
/// `Tanh` does. Gradients inherit the payload's division semantics near
/// zero.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub(crate) struct Div;

impl Div {
    /// Returns the arity: two operands.
    pub(crate) fn arity(&self) -> usize {
        2
    }

    /// Returns the read set of the derivative rule below.
    /// It reads the divisor and its own output.
    pub(crate) fn reads(&self) -> Reads {
        Reads {
            operands: [false, true],
            output: true,
        }
    }

    /// Infers the shape of the result, which both operands must share.
    pub(crate) fn infer_shape(&self, operands: &[Shape]) -> Shape {
        let (left, right) = binary(operands);
        assert_eq!(left, right, "division requires operands of equal shapes");
        left.clone()
    }
}

impl Div {
    pub(crate) fn forward<E: Element>(&self, operands: &[&Tensor<E>]) -> Tensor<E> {
        let (&left, &right) = binary(operands);
        left.clone() / right.clone()
    }
}

impl<Rule: Recordable> Operation<Rule> for Div {
    fn backward(&self, operands: &[&Rule], output: &Rule, gradient: &Rule) -> Cotangents<Rule> {
        let (_, &right) = binary(operands);
        smallvec![
            Some(gradient.clone() / right.clone()),
            Some(-(gradient.clone() * output.clone() / right.clone())),
        ]
    }
}