Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.natural-gradient-ng

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

AHoF D50 Natural Gradient: precondition the gradient by the inverse Fisher metric and step; the parameter update descends update theta step = theta - step. Worked: 4-1=3. Values proved by signed cross-product equivalence. Proved native and axiom-free. Requires signed/subtract, 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.natural-gradient-ng` prints this classification.

nat-grad/update :
  (x₁ x₂ : ℚ)
  → ℚ

nat-grad/update-example :
  → ℚ

nat-grad/no-update :
  → ℚ

nat-grad/update-unfold :
  (a b : ℚ)
  → nat-grad/update a b = a - b

nat-grad/update-example-is-3 :
  → bfgs/change-example = signed/from-nnrat 3

nat-grad/no-update-is-0 :
  → dfp/no-step = signed/from-nnrat 0