docs for nothing behavior and for walking a tree with keypath (#191)

* cl/zero

* Update docs/src/index.md

Co-authored-by: Michael Abbott <[email protected]>

---------

Co-authored-by: Michael Abbott <[email protected]>

Author: CarloLucibello

docs/src/index.md

@@ -311,8 +311,50 @@ julia> trainables(model)
  Float32[-0.8764882 0.40812716 0.1919528; -0.9123545 -0.4462516 0.6751252]
  Float32[0.0, 0.0]
 
-julia> l2reg(model) = sum([sum(abs2,p) for p in trainables(model)]);
+julia> l2reg(model) = sum([sum(abs2, p) for p in trainables(model)]);
 
 julia> g = gradient(l2reg, model)[1];
 ```
 Notice that the `BatchNorm` layer has two trainable parameters, `γ` and `β`, which are included in the list, while the `μ ` and `σ²` buffers are not.
+
+Sometimes one wants to iterate over all trainable parameters in a model and the corresponding parameters of a matched structure such a gradient or the moving average of the model. 
+This can be done using `trainables(model, path=true)`. For instance, here is how to update the parameters
+of a moving average model with the parameters of the model:
+
+```julia
+for (kp, p_avg) in trainables(model_avg, path=true)
+    p = getkeypath(model, kp)  
+    p_avg .= 0.99 .* p_avg .+ 0.01 .* p
+end
+```
+
+## Incomplete or nothing gradients
+
+If the gradient is not available for some parameters, or branches of the model, 
+`update` will not take an optimisation step for those parameters.
+This is the case when the gradient is `nothing` or a subtype of `ChainRules.AbstractZero`.
+
+For stateful optimisers, skipping an update it is generaly not the same as updating with a zero gradient.
+For example, in the case of Adam, the momentum and variance are updated even if the gradient is zero:
+
+```julia-repl
+julia> x = (a = ones(2), b = ones(2));
+(a = [1.0, 1.0], b = [1.0, 1.0])
+
+julia> opt_state = Optimisers.setup(Adam(0.1), x)
+(a = Leaf(Adam(0.1, (0.9, 0.999), 1.0e-8), ([0.0, 0.0], [0.0, 0.0], (0.9, 0.999))), b = Leaf(Adam(0.1, (0.9, 0.999), 1.0e-8), ([0.0, 0.0], [0.0, 0.0], (0.9, 0.999))))
+
+julia> g = (; a = ones(2), b = ones(2)); # First an update with a non-zero gradient to increase the momentum and variance
+
+julia> Optimisers.update!(opt_state, x, g);
+
+julia> opt_state # the state in `a` and `b` are the same
+(a = Leaf(Adam(0.1, (0.9, 0.999), 1.0e-8), ([0.1, 0.1], [0.001, 0.001], (0.81, 0.998001))), b = Leaf(Adam(0.1, (0.9, 0.999), 1.0e-8), ([0.1, 0.1], [0.001, 0.001], (0.81, 0.998001))))
+
+julia> g = (; a = zeros(2), b = nothing); # Now an update with a zero gradient for a and no gradient for b
+
+julia> Optimisers.update!(opt_state, x, g);
+
+julia> opt_state # the state in `a` and `b` differ
+(a = Leaf(Adam(0.1, (0.9, 0.999), 1.0e-8), ([0.09, 0.09], [0.000999, 0.000999], (0.729, 0.997003))), b = Leaf(Adam(0.1, (0.9, 0.999), 1.0e-8), ([0.1, 0.1], [0.001, 0.001], (0.81, 0.998001))))
+```

src/interface.jl

@@ -103,13 +103,21 @@ end
 subtract!(x, x̄) = maywrite(x) ? (x .= x .- x̄) : eltype(x).(x .- x̄)
 subtract!(x, x̄::Zero) = x
 
+# If we get Zero from AD on a leaf we skip the optimizer step. See
+# https://github.com/FluxML/Optimisers.jl/issues/140
 _grads!(dict::IdDict, ℓ::Leaf, x, ::Zero...) = nothing
+
 function _grads!(dict::IdDict, ℓ::Leaf, x, x̄s...)
   x̄s₀ = get(dict, ℓ, map(_ -> ZeroTangent(), x̄s))
   dict[ℓ] = map(+, x̄s, x̄s₀)  # adding Zero should be free. Lazy accumulation broadcasted(+, x̄, x̄₀) also possible.
   nothing
 end
+
+# If we get Zero from AD in correspondence of a non-leaf node
+# we end the recursion. The optimizer step won't be taken.
+# https://github.com/FluxML/Optimisers.jl/issues/140
 _grads!(dict::IdDict, t, x, ::Zero...) = nothing
+
 function _grads!(dict::IdDict, tree, x, x̄s...)
   # The only reason _grads! takes model is that functor(typeof(x), base(x̄)) may differ from 
   # functor(typeof(tree), base(x̄)), for things like Transpose