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

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

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

Environment

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

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

Start at DifferentiationInterfaceZygoteExt.jl lines 64–65, where value_and_pullback processes the Zygote result; compare the sign/trunc MWE with the floor/ceil/round cases. Done means AutoZygote returns zero for the nothing-gradient cases without the iterate(::Nothing) MethodError, matching the issue’s expected result.