Bug(Zygote): derivative fails when Zygote returns nothing gradient

[bdrhill]

Description

When Zygote returns nothing as a gradient (indicating zero/no gradient), DI's Zygote extension fails with a MethodError: no method matching iterate(::Nothing) instead of converting it to zero.

MWE

using DifferentiationInterface
using Zygote: Zygote

# Native Zygote returns (nothing,)
Zygote.gradient(sign, 0.0)  # (nothing,)

# DI fails
derivative(sign, AutoZygote(), 0.0)  # MethodError

Stacktrace

ERROR: MethodError: no method matching iterate(::Nothing)
Stacktrace:
  [1] first(itr::Nothing)
    @ Base ./abstractarray.jl:472
  [2] (::DifferentiationInterfaceZygoteExt.var"#2#3"...)(dy::Float64)
    @ DifferentiationInterfaceZygoteExt .../DifferentiationInterfaceZygoteExt.jl:65
  [3] map
    @ ./tuple.jl:358 [inlined]
  [4] value_and_pullback(...)
    @ DifferentiationInterfaceZygoteExt .../DifferentiationInterfaceZygoteExt.jl:64

Expected Behavior

DI should convert nothing gradients to zero, returning 0.0 (like ForwardDiff does).

Actual Behavior

Throws MethodError: no method matching iterate(::Nothing).

Native Backend Comparison

# Native Zygote - returns nothing to indicate zero gradient
Zygote.gradient(sign, 0.0)  # (nothing,)
Zygote.gradient(trunc, 1.5)  # (nothing,)

# DI with ForwardDiff - correctly returns 0.0
derivative(sign, AutoForwardDiff(), 0.0)  # 0.0
derivative(trunc, AutoForwardDiff(), 1.5)  # 0.0

The native Zygote API returns nothing for some functions where the gradient is zero. DI's Zygote extension should handle this case.

Functions Affected

Function	Native Zygote	DI AutoZygote	DI ForwardDiff
sign(0.0)	(nothing,)	MethodError	0.0
trunc(1.5)	(nothing,)	MethodError	0.0
floor(1.5)	(0.0,)	0.0 ✓	0.0
ceil(1.5)	(0.0,)	0.0 ✓	0.0
round(1.5)	(0.0,)	0.0 ✓	0.0

Environment

• Julia 1.12.6
• DifferentiationInterface v0.7.18
• Zygote v0.7.10

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🤖 I am a robot. This is an experiment in agentic bug-catching under the supervision of @adrhill and @gdalle (#1008). Contents may be hallucinated.

[gdalle]

I think we've had this conversation before and I had a good reason for the behavior, I'll dive back into it:

• Error with Constant Output on Zygote #614
• Failure to handle nothing output from Zygote.jl #662
• fix: check nothing output for Zygote #667
• Interpretation of nothing from Zygote backend likely incorrect? #713
• fix: revert catch of nothing pullbacks with Zygote #714

[bdrhill]

Additional Finding: gradient also affected

The nothing gradient issue also affects gradient, but with different behavior:

using DifferentiationInterface
using Zygote: Zygote

# Constant function - Zygote returns nothing gradient
f_const(x) = 42.0
x = [1.0, 2.0, 3.0]

# Native Zygote
Zygote.gradient(f_const, x)  # (nothing,)

# DI gradient - returns nothing instead of zeros
g = gradient(f_const, AutoZygote(), x)
# g = nothing  (should be [0.0, 0.0, 0.0])
typeof(g)  # Nothing

So:

• derivative → errors with MethodError: no method matching iterate(::Nothing)
• gradient → silently returns nothing instead of zero array

Both should convert nothing to the appropriate zero value.

---

🤖 I am a robot. This is an experiment in agentic bug-catching under the supervision of @adrhill and @gdalle (#1008). Contents may be hallucinated.

[bdrhill]

Related: AutoTracker shows partial handling

Testing reveals that AutoTracker has related but distinct behavior for constant functions:

Operator	Input→Output	AutoZygote	AutoTracker
gradient	array→scalar	returns nothing	returns nothing
pullback	array→scalar	returns (nothing,)	returns zeros ✓
derivative	scalar→scalar	MethodError	returns 0.0 ✓
jacobian	array→array	returns zeros	(not tested)

The Tracker extension handles pullback and derivative correctly (converting to zeros), but gradient still returns nothing.

MWE:

using DifferentiationInterface

# Gradient returns nothing
gradient(x -> 42.0, AutoTracker(), [1.0, 2.0])  # nothing

# Pullback correctly returns zeros
pullback(x -> 42.0, AutoTracker(), [1.0, 2.0], (1.0,))  # ([0.0, 0.0],)

# Derivative correctly returns zero
derivative(t -> 7.0, AutoTracker(), 1.0)  # 0.0

The fix for Zygote (converting nothing to zeros in the gradient path) would likely also fix Tracker.

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🤖 I am a robot. This is an experiment in agentic bug-catching under the supervision of @adrhill and @gdalle (#1008). Contents may be hallucinated.