From d1b25fbde6b01529fd1bcfdd5778b6cb378eb865 Mon Sep 17 00:00:00 2001 From: ericmarin Date: Tue, 31 Mar 2026 11:14:57 +0200 Subject: added ONNX Add and ONNX Sub --- proof.md | 28 ++++++++++++++++++++++++++++ 1 file changed, 28 insertions(+) (limited to 'proof.md') diff --git a/proof.md b/proof.md index 7fb6413..a376bb9 100644 --- a/proof.md +++ b/proof.md @@ -46,6 +46,34 @@ Equal to Gemm with ![alpha=1](https://latex.codecogs.com/svg.image?\inline&space ### Reshape Just identity mapping. +### Add +ONNX Add node is defined as: +![C = A + B](https://latex.codecogs.com/svg.image?&space;C=A+B) + +The translation defines the interactions: +![Add(c_i, b_i) ~ a_i](https://latex.codecogs.com/svg.image?Add(c_i,b_i)\sim&space;a_i) + +By definition this interaction is equal to: +![c_i = a_i + b_i](https://latex.codecogs.com/svg.image?c_i=a_i+b_i) + +By grouping the operations we get: +![C = A + B](https://latex.codecogs.com/svg.image?C=A+B) + +### Sub +ONNX Sub node is defined as: +![C = A - B](https://latex.codecogs.com/svg.image?C=A-B) + +The translation defines the interactions: +![Add(c_i, neg_b_i) ~ a_i](https://latex.codecogs.com/svg.image?Add(c_i,neg_i)\sim&space;a_i) +![Mul(neg_b_i, Concrete(-1)) ~ b_i](https://latex.codecogs.com/svg.image?Mul(neg_i,Concrete(-1))\sim&space;b_i) + +By definition this interaction is equal to: +![c_i = a_i + neg_b_i](https://latex.codecogs.com/svg.image?c_i=a_i+neg_i) +![neg_b_i = -1 * b_i](https://latex.codecogs.com/svg.image?neg_i=-1*b_i) + +By grouping the operations we get: +![C = A - B](https://latex.codecogs.com/svg.image?C=A-B) + ## Soundness of Interaction Rules ### Materialize The Materialize agent transforms a Linear agent into a tree of explicit mathematical operations -- cgit v1.2.3