Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.lbfgs

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

AHoF O30 L-BFGS: limited-memory BFGS storing recent (s, y) pairs; the stored gradient change is y = g_{k+1} - g_k: gradient-change g-new g-old = g-new - g-old. Worked: 3-1=2. 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.lbfgs` prints this classification.

lbfgs/gradient-change :
  (x₁ x₂ : ℚ)
  → ℚ

lbfgs/change-example :
  → ℚ

lbfgs/no-change :
  → ℚ

lbfgs/gradient-change-unfold :
  (a b : ℚ)
  → dfp/step-vector a b = a - b

lbfgs/change-example-is-2 :
  → dfp/step-example = signed/from-nnrat 2

lbfgs/no-change-is-0 :
  → dfp/no-step = signed/from-nnrat 0