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@document.meta
title: Neural Network Equivalence
description: WIP tool to prove NNEQ using Interaction Nets as pre-processor fo my Batchelor's Thesis
authors: ericmarin
categories: research
created: 2026-03-14T09:21:24
updated: 2026-03-21T11:53:27
version: 1.1.1
@end
* TODO
- (?) Scalability: Added cache for already processed NN. Inpla is the bottleneck but now I removed most of the limits.
- (x) Soundness of translated NN: {:proof.norg:}[PROOF]
- (x) Compatibility with other types of NN: Added support for ONNX format. For now only GEMM and ReLU operations are implemented.
- ( ) Comparison with other tool ({https://github.com/NeuralNetworkVerification/Marabou}[Marabou], {https://github.com/guykatzz/ReluplexCav2017}[Reluplex])
- ( ) Add Range agent to enable ReLU optimization
* Agents
** Built-in
- Eraser: delete other agents recursively
- Dup: duplicates other agents recursively
** Implemented
- Linear(x, float q, float r): represent "q*x + r"
- Concrete(float k): represent a concrete value k
- Symbolic(id): represent the variable id
- Add(out, b): represent the addition (has various steps AddCheckLinear/AddCheckConcrete)
- Mul(out, b): represent the multiplication (has various steps MulCheckLinear/MulCheckConcrete)
- ReLU(out): represent "IF x > 0 THEN x ELSE 0"
- Materialize(out): transforms a Linear packet into a final representation of TermAdd/TermMul
* Rules
** Add
Linear(x, float q, float r) >< Add(out, b) => b ~ AddCheckLinear(out, x, q, r);
Concrete(float k) >< Add(out, b)
| k == 0 => out ~ b
| _ => b ~ AddCheckConcrete(out, k);
Linear(y, float s, float t) >< AddCheckLinear(out, x, float q, float r)
| (q == 0) && (r == 0) && (s == 0) && (t == 0) => out ~ Concrete(0), x ~ Eraser, y ~ Eraser
| (s == 0) && (t == 0) => out ~ Linear(x, q, r), y ~ Eraser
| (q == 0) && (r == 0) => out ~ (*L)Linear(y, s, t), x ~ Eraser
| _ => Linear(x, q, r) ~ Materialize(out_x), (*L)Linear(y, s, t) ~ Materialize(out_y), out ~ Linear(TermAdd(out_x, out_y), 1, 0);
Concrete(float j) >< AddCheckLinear(out, x, float q, float r) => out ~ Linear(x, q, r + j);
Linear(y, float s, float t) >< AddCheckConcrete(out, float k) => out ~ Linear(y, s, t + k);
Concrete(float j) >< AddCheckConcrete(out, float k)
| j == 0 => out ~ Concrete(k)
| _ => out ~ Concrete(k + j);
** Mul
Linear(x, float q, float r) >< Mul(out, b) => b ~ MulCheckLinear(out, x, q, r);
Concrete(float k) >< Mul(out, b)
| k == 0 => b ~ Eraser, out ~ (*L)Concrete(0)
| k == 1 => out ~ b
| _ => b ~ MulCheckConcrete(out, k);
Linear(y, float s, float t) >< MulCheckLinear(out, x, float q, float r)
| ((q == 0) && (r == 0)) || ((s == 0) && (t == 0)) => out ~ Concrete(0), x ~ Eraser, y ~ Eraser
| _ => Linear(x, q, r) ~ Materialize(out_x), (*L)Linear(y, s, t) ~ Materialize(out_y), out ~ Linear(TermMul(out_x, out_y), 1, 0);
Concrete(float j) >< MulCheckLinear(out, x, float q, float r) => out ~ Linear(x, q * j, r * j);
Linear(y, float s, float t) >< MulCheckConcrete(out, float k) => out ~ Linear(y, s * k, t * k);
Concrete(float j) >< MulCheckConcrete(out, float k)
| j == 0 => out ~ Concrete(0)
| j == 1 => out ~ Concrete(k)
| _ => out ~ Concrete(k * j);
** ReLU
Linear(x, float q, float r) >< ReLU(out) => (*L)Linear(x, q, r) ~ Materialize(out_x), out ~ Linear(TermReLU(out_x), 1, 0);
Concrete(float k) >< ReLU(out)
| k > 0 => out ~ (*L)Concrete(k)
| _ => out ~ Concrete(0);
** Materialize
Linear(x, float q, float r) >< Materialize(out)
| (q == 0) => out ~ Concrete(r), x ~ Eraser
| (q == 1) && (r == 0) => out ~ x
| (q == 1) && (r != 0) => out ~ TermAdd(x, Concrete(r))
| (q != 0) && (r == 0) => out ~ TermMul(Concrete(q), x)
| _ => out ~ TermAdd(TermMul(Concrete(q), x), Concrete(r));
Concrete(float k) >< Materialize(out) => out ~ (*L)Concrete(k);
|
