Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.reverse-mode-ad

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/reverse_mode_ad.clj3 definitions, 3 theorems

AHoF O5 Reverse-Mode Auto-Diff: backpropagate adjoints, accumulating each node's adjoint as the sum of its downstream contributions: adjoint-accumulate a b = a + b. Worked: 1+2=3. Values proved by signed cross-product equivalence. Proved native and axiom-free. Requires signed/add, signed/from-nnrat, signed/equivalent (all in the D63 checkpoint). Scope (measured by the kernel): this module has 2 worked instances (statements about specific values) and 1 definitional unfoldings (true by unfolding a definition). None of its theorems is a guarantee about the algorithm for all inputs; `lein verify rainbow.algorithms.proofs.ahof.reverse-mode-ad` prints this classification.

rev-ad/adjoint-accumulate :
  (x₁ x₂ : ℚ)
  → ℚ

rev-ad/accumulate-example :
  → ℚ

rev-ad/single-contribution :
  → ℚ

rev-ad/adjoint-accumulate-unfold :
  (a b : ℚ)
  → game-ascent/ascent-step a b = a + b

rev-ad/accumulate-example-is-3 :
  → rev-ad/accumulate-example = signed/from-nnrat 3

rev-ad/single-contribution-is-3 :
  → game-ascent/no-step = signed/from-nnrat 3