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ChainRulesTestUtils.jl helps you test ChainRulesCore.frule and ChainRulesCore.rrule methods, when adding rules for your functions in your own packages. For information about ChainRules, including how to write rules, refer to the general ChainRules Documentation:

Testing Method Table Sensibility

A basic feature of ChainRulesTestUtils is its ability to check that the method tables for rrule and frule remain sensible. This searches the method tables for methods that should not exist and when it fails tells you where they were defined. By calling test_method_tables ChainRulesTestUtils will check for things such as having attracted a rule to DataType rather than attaching it to a constructor. Basically all packages using ChainRulesTestUtils can use test_method_tables, as it is independent of what rules you have written.

Canonical example of testing frule and rrule

Let's suppose a custom transformation has been defined

function two2three(x1::Float64, x2::Float64)
    return 1.0, 2.0*x1, 3.0*x2

# output
two2three (generic function with 1 method)

along with the frule

using ChainRulesCore

function ChainRulesCore.frule((Δf, Δx1, Δx2), ::typeof(two2three), x1, x2)
    y = two2three(x1, x2)
    ∂y = Tangent{Tuple{Float64, Float64, Float64}}(ZeroTangent(), 2.0*Δx1, 3.0*Δx2)
    return y, ∂y
# output

and rrule which contains a mistake in the first cotangent

function ChainRulesCore.rrule(::typeof(two2three), x1, x2)
    y = two2three(x1, x2)
    function two2three_pullback(Ȳ)
        return (NoTangent(), 2.1*Ȳ[2], 3.0*Ȳ[3])
    return y, two2three_pullback
# output

The test_frule/test_rrule helper function compares the frule/rrule outputs to the gradients obtained by finite differencing. They can be used for any type and number of inputs and outputs.

Testing the frule

test_frule takes in the function f and the primal input x. The call will test the frule for function f at the point x in the domain. Keep this in mind when testing discontinuous rules for functions like ReLU, which should ideally be tested at both x being above and below zero.

julia> using ChainRulesTestUtils;

julia> test_frule(two2three, 3.33, -7.77);
Test Summary:                            | Pass  Total  Time
test_frule: two2three on Float64,Float64 |    6      6  2.7s

Testing the rrule

test_rrule takes in the function f, and primal inputs x. The call will test the rrule for function f at the point x, and similarly to frule some rules should be tested at multiple points in the domain.

julia> test_rrule(two2three, 3.33, -7.77);
test_rrule: two2three on Float64,Float64: Test Failed at /home/lior/.julia/dev/ChainRulesTestUtils/src/check_result.jl:24
  Expression: isapprox(actual, expected; kwargs...)
  Problem: cotangent for input 2, Float64
   Evaluated: isapprox(-4.032, -3.840000000001641; rtol = 1.0e-9, atol = 1.0e-9)

The output of the test indicates to us the cause of the failure under "Problem:" with the expected (rrule derived) and actual finite difference results. The Problem lies with the cotangent corresponding to input 2 of rrule, which is the first cotangent as expected.

Scalar example

For functions with a single argument and a single output, such as e.g. ReLU,

function relu(x::Real)
    return max(0, x)

# output
relu (generic function with 1 method)

with the frule and rrule defined with the help of @scalar_rule macro

@scalar_rule relu(x::Real) x <= 0 ? zero(x) : one(x)

# output

test_scalar function is provided to test both the frule and the rrule with a single call.

julia> test_scalar(relu, 0.5);
Test Summary:            | Pass  Total  Time
test_scalar: relu at 0.5 |   12     12  1.2s

julia> test_scalar(relu, -0.5);
Test Summary:             | Pass  Total  Time
test_scalar: relu at -0.5 |   12     12  0.0s

Testing constructors and functors (callable objects)

Testing constructor and functors works as you would expect. For struct Foo,

struct Foo
(f::Foo)(x) = return f.a + x
Base.length(::Foo) = 1
Base.iterate(f::Foo) = iterate(f.a)
Base.iterate(f::Foo, state) = iterate(f.a, state)

after defining the constructor and functor f/rules,

function ChainRulesCore.rrule(::Type{Foo}, val) # constructor rrule
    y = Foo(val)
    Foo_pb(ΔFoo) = (NoTangent(), unthunk(ΔFoo).a)
    return y, Foo_pb

function ChainRulesCore.rrule(foo::Foo, val) # functor rrule
    y = foo(val)
    function foo_pb(Δ)
        Δut = unthunk(Δ)
        return (Tangent{Foo}(;a=Δut), Δut)
    return y, foo_pb

both f/rrules can be tested by

test_rrule(Foo, rand()) # constructor

foo = Foo(rand())
test_rrule(foo, rand()) # functor

# it is also possible to provide tangents for `foo` explicitly
test_frule(foo ⊢ Tangent{Foo}(;a=rand()), rand())

Specifying Tangents

test_frule and test_rrule allow you to specify the tangents used for testing. By default, tangents will be automatically generated via FiniteDifferences.rand_tangent. To explicitly specify a tangent, pass in x ⊢ Δx, where x is the primal and Δx is the tangent, in the place of the primal inputs. (You can enter via \vdash + tab in the Julia REPL and supporting editors.) A special case of this is that if you specify it as x ⊢ NoTangent() then finite differencing will not be used on that input. Similarly, by setting the output_tangent keyword argument, you can specify the tangent for the primal output.

This can be useful when the default provided FiniteDifferences.rand_tangent doesn't produce the desired tangent for your type. For example, the default tangent for an Int is NoTangent(), which is correct e.g. when the Int represents a discrete integer like in indexing. But if you are testing something where the Int is actually a special case of a real number, then you would want to specify the tangent as a Float64.

Care must be taken when manually specifying tangents. In particular, when specifying the input tangents to test_frule and the output tangent to test_rrule. As these tangents are used to seed the derivative computation. Inserting inappropriate zeros can thus hide errors.

Testing higher order functions

Higher order functions, such as map, take a function (or a functor) f as an argument. f/rrules for these functions call back into AD to compute the f/rrule of f. To test these functions, we use a dummy AD system, which simply calls the appropriate rule for f directly. For this reason, when testing map(f, collection), the rules for f need to be defined. The RuleConfig for this dummy AD system is the default one, and does not need to be provided.

test_rrule(map, x->2x [1, 2, 3.]) # fails, because there is no rrule for x->2x

mydouble(x) = 2x
function ChainRulesCore.rrule(::typeof(mydouble), x)
    mydouble_pullback(ȳ) = (NoTangent(), ȳ)
    return mydouble(x), mydouble_pullback
test_rrule(map, mydouble, [1, 2, 3.]) # works

Testing AD systems

The gradients computed by AD systems can be also be tested using test_rrule. To do that, one needs to provide an rrule_f/frule_f keyword argument, as well as the RuleConfig used by the AD system. rrule_f is a function that wraps the gradient computation by an AD system in the same API as the rrule. RuleConfig is an object that determines which sets of rules are defined for an AD system. For example, let's say we have a complicated function

function complicated(x, y)
    return do(x + y) + some(x) * hard(y) + maths(x * y)

that we do not know an rrule for, and we want to check whether the gradients provided by the AD system are correct.

To test gradients computed by the AD system you need to provide a rrule_f function that acts like calling rrule but use AD rather than a defined rule. This has the exact same semantics as is required to overload ChainRulesCore.rrule_via_ad, thus almost all systems doing so should just overload that, and pass in that and the config, and then trigger test_rrule(MyADConfig, f, xs; rrule_f = ChainRulesCore.rrule_via_ad). See more info on rrule_via_ad and the rule configs in the ChainRules documentation. For some AD systems (e.g. Zygote) rrule_via_ad already exists. If it does not exist, see How to write rrule_via_ad function section below.

We use the test_rrule function to test the gradients using the config used by the AD system

config = MyAD.CustomRuleConfig()
test_rrule(config, complicated, 2.3, 6.1; rrule_f=rrule_via_ad)

by providing the rule config and specifying the rrule_via_ad as the rrule_f keyword argument.

How to write rrule_via_ad function

rrule_via_ad will use the AD system to compute gradients and will package them in the rrule-like API.

Let's say the AD package uses some custom differential types and does not provide a gradient w.r.t. the function itself. In order to make the pullback compatible with the rrule API we need to add a NoTangent() to represent the differential w.r.t. the function itself. We also need to transform the ChainRules differential types to the custom types (cr2custom) before feeding the Δ to the AD-generated pullback, and back to ChainRules differential types when returning from the rrule (custom2cr).

function rrule_via_ad(config::MyAD.CustomRuleConfig, f::Function, args...)
    y, ad_pullback = MyAD.pullback(f, args...)
    function rrulelike_pullback(Δ)
        diffs = custom2cr(ad_pullback(cr2custom(Δ)))
        return NoTangent(), diffs...
    return y, rrulelike_pullback

custom2cr(differential) = ...
cr2custom(differential) = ...

Custom finite differencing

If a package is using a custom finite differencing method of testing the frules and rrules, test_approx function provides a convenient way of comparing various types of differentials.

It is effectively (a, b) -> @test isapprox(a, b), but it preprocesses thunks and ChainRules differential types ZeroTangent(), NoTangent(), and Tangent, such that the error messages are helpful.

For example,

test_approx((@thunk 2*2.0), 4.1)

shows both the expression and the evaluated thunks

   Expression: isapprox(actual, expected; kwargs...)
   Evaluated: isapprox(4.0, 4.1)
ERROR: There was an error during testing

compared to

julia> @test isapprox(@thunk 2*2.0, 4.0)
Test Failed at REPL[52]:1
  Expression: isapprox(#= REPL[52]:1 =# @thunk((2 * 2.0, 4.0)))
   Evaluated: isapprox(Thunk(var"#24#25"()))
ERROR: There was an error during testing

which should have passed the test.

Inference tests

By default, all functions for testing rules check whether the output type (as well as that of the pullback for rrules) can be completely inferred, such that everything is type stable:

julia> function ChainRulesCore.rrule(::typeof(abs), x)
           abs_pullback(Δ) = (NoTangent(), x >= 0 ? Δ : big(-1.0) * Δ)
           return abs(x), abs_pullback

julia> test_rrule(abs, 1.)
test_rrule: abs on Float64: Error During Test at /home/runner/work/ChainRulesTestUtils.jl/ChainRulesTestUtils.jl/src/testers.jl:170
  Got exception outside of a @test
  return type Tuple{ChainRulesCore.NoTangent, Float64} does not match inferred return type Tuple{ChainRulesCore.NoTangent, Union{Float64, BigFloat}}

This can be disabled on a per-rule basis using the check_inferred keyword argument:

julia> test_rrule(abs, 1.; check_inferred=false)
Test Summary:              | Pass  Total
test_rrule: abs on Float64 |    5      5
Test.DefaultTestSet("test_rrule: abs on Float64", Any[], 5, false, false)

This behavior can also be overridden globally by setting the environment variable CHAINRULES_TEST_INFERRED before ChainRulesTestUtils is loaded or by changing ChainRulesTestUtils.TEST_INFERRED[] from inside Julia. ChainRulesTestUtils can detect whether a test is run as part of PkgEval and in this case disables inference tests automatically. Packages can use @maybe_inferred to get the same behavior for other inference tests.