Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.hypergradient-hg

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

AHoF O25 Hypergradient Descent: adapt the learning rate online by a hypergradient correction, updating rate-update rate adjustment = rate + adjustment. 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.hypergradient-hg` prints this classification.

hypergrad-ng/rate-update :
  (x₁ x₂ : ℚ)
  → ℚ

hypergrad-ng/update-example :
  → ℚ

hypergrad-ng/no-adjustment :
  → ℚ

hypergrad-ng/rate-update-unfold :
  (a b : ℚ)
  → game-ascent/ascent-step a b = a + b

hypergrad-ng/update-example-is-3 :
  → game-ascent/ascent-example = signed/from-nnrat 3

hypergrad-ng/no-adjustment-is-3 :
  → game-ascent/no-step = signed/from-nnrat 3