refactor: use direct reduction for global pooling

src/layers/pooling.jl

@@ -13,7 +13,8 @@ end
 
 struct GlobalPoolMode <: AbstractPoolMode end
 
-(::GlobalPoolMode)(x) = PoolDims(x, size(x)[1:(end - 2)])
+# XXX: Use PoolDims once EnzymeJAX supports stablehlo.reduce_window adjoint
+(::GlobalPoolMode)() = GlobalPoolMode()
 
 @concrete struct AdaptivePoolMode <: AbstractPoolMode
     out_size <: Tuple{Vararg{IntegerType}}
@@ -33,15 +34,23 @@ symbol_to_pool_mode(::StaticSymbol{:adaptive}) = AdaptivePoolMode
 abstract type AbstractPoolOp end
 
 struct MaxPoolOp <: AbstractPoolOp end
+
 (m::MaxPoolOp)(x, pdims) = maxpool(x, pdims)
+function (m::MaxPoolOp)(x, ::GlobalPoolMode)
+    return maximum(x; dims=1:(ndims(x) - 2), init=eltype(x)(-Inf))
+end
 
 struct MeanPoolOp <: AbstractPoolOp end
+
 (m::MeanPoolOp)(x, pdims) = meanpool(x, pdims)
+(m::MeanPoolOp)(x, ::GlobalPoolMode) = mean(x; dims=1:(ndims(x) - 2))
 
 @concrete struct LpPoolOp <: AbstractPoolOp
     p
 end
+
 (m::LpPoolOp)(x, pdims) = lpnormpool(x, pdims; m.p)
+(m::LpPoolOp)(x, ::GlobalPoolMode) = lpnormpool(x, PoolDims(x, size(x)[1:(end - 2)]); m.p)
 
 symbol_to_pool_op(::StaticSymbol{:max}, _) = MaxPoolOp()
 symbol_to_pool_op(::StaticSymbol{:mean}, _) = MeanPoolOp()