JVP functions are forward-mode derivative functions. They take original
arguments and return original results and a differential function. Differential
functions take derivatives wrt arguments and return derivatives wrt results.
`JVPEmitter` is a cloner that emits JVP and differential functions at the same
time. In JVP functions, function applications are replaced with JVP function
applications. In differential functions, function applications are replaced
with differential function applications.
In JVP functions, each basic block takes a differential struct containing callee
differentials. These structs are consumed by differential functions.
Canonicalizes `differentiable_function` instructions by filling in missing
derivative function operands.
Derivative function emission rules, based on the original function value:
- `function_ref`: look up differentiability witness with the exact or a minimal
superset derivative configuration. Emit a `differentiability_witness_function`
for the derivative function.
- `witness_method`: emit a `witness_method` with the minimal superset derivative
configuration for the derivative function.
- `class_method`: emit a `class_method` with the minimal superset derivative
configuration for the derivative function.
If an *actual* emitted derivative function has a superset derivative
configuration versus the *desired* derivative configuration, create a "subset
parameters thunk" to thunk the actual derivative to the desired type.
For `differentiable_function` instructions formed from curry thunk applications:
clone the curry thunk (with type `(Self) -> (T, ...) -> U`) and create a new
version with type `(Self) -> @differentiable (T, ...) -> U`.
Progress towards TF-1211.
The differentiation transform does the following:
- Canonicalizes differentiability witnesses by filling in missing derivative
function entries.
- Canonicalizes `differentiable_function` instructions by filling in missing
derivative function operands.
- If necessary, performs automatic differentiation: generating derivative
functions for original functions.
- When encountering non-differentiability code, produces a diagnostic and
errors out.
Partially resolves TF-1211: add the main canonicalization loop.
To incrementally stage changes, derivative functions are currently created
with empty bodies that fatal error with a nice message.
Derivative emitters will be upstreamed separately.
