Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.nn-verification

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/nn_verification.clj1 definitions, 4 theorems

AHoF V47 Neural Network Verification: certify that a network's output stays within a safety bound over an input region; a concrete output is safe when it is within the safety bound: safe? output bound = decide (output <= bound). Proved native and axiom-free (decision, two positive instances, at-most certificate, negative instance). Requires audit/decide-nnrat-at-most, nnrat/at-most, nnrat/decide-at-most-true-sound (all in the D63 checkpoint). Scope (measured by the kernel): this module has 4 worked instances (statements about specific values). None of its theorems is a guarantee about the algorithm for all inputs; `lein verify rainbow.algorithms.proofs.ahof.nn-verification` prints this classification.

nnverify/safe? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

nnverify/output-within-bound-safe :
  → lis/extends? 1/2 3/4 = data/true

nnverify/boundary-safe :
  → lis/extends? 1/2 1/2 = data/true

nnverify/safety-certificate :
  → 1/2 ≤ 3/4

nnverify/output-over-bound-unsafe :
  → lis/extends? 3/4 1/2 = data/false