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src/dense.jl

@@ -50,14 +50,41 @@ Defined by [ADTypes.jl](https://github.com/SciML/ADTypes.jl).
     AutoEnzyme(; mode=nothing, constant_function::Bool=false)
 
 The `constant_function` keyword argument (and type parameter) determines whether the function object itself should be considered constant or not during differentiation with Enzyme.jl.
-For simple functions, `constant_function` should usually be set to `false`, but in the case of closures or callable structs which contain differentiated data that can be treated as constant, `constant_function` should be set to `true` for increased performance.
+For simple functions, `constant_function` should usually be set to `false`, but in the case of closures or callable structs which contain differentiated data that can be treated as constant, `constant_function` should be set to `true` for increased performance (more details below).
 
 # Fields
 
   - `mode::M`: can be either
 
       + an object subtyping `EnzymeCore.Mode` (like `EnzymeCore.Forward` or `EnzymeCore.Reverse`) if a specific mode is required
       + `nothing` to choose the best mode automatically
+
+# Notes
+
+If `constant_function = true` but the enclosed data is not truly constant, then Enzyme.jl will not compute the correct derivative values.
+An example of such a function is:
+
+```julia
+cache = [0.0]
+function f(x)
+    cache[1] = x[1]^2
+    cache[1] + x[1]
+end
+```
+
+In this case, the enclosed cache is a function of the differentiated input, and thus its values are non-constant with respect to the input.
+Thus, in order to compute the correct derivative of the output, the derivative must propagate through the `cache` value, and said `cache` must not be treated as constant.
+
+Conversely, the following function can treat `parameter` as a constant, because `parameter` is never modified based on the input `x`:
+
+```julia
+parameter = [0.0]
+function f(x)
+    parameter[1] + x[1]
+end
+```
+
+In this case, `constant_function = true` would allow the chosen differentiation system to perform extra memory and compute optimizations, under the assumption that `parameter` is kept constant.
 """
 struct AutoEnzyme{M, constant_function} <: AbstractADType
     mode::M