diff --git a/Project.toml b/Project.toml
index 3c5d234a..d64f8d3e 100644
--- a/Project.toml
+++ b/Project.toml
@@ -19,6 +19,7 @@ SCS = "c946c3f1-0d1f-5ce8-9dea-7daa1f7e2d13"
[extras]
Flux = "587475ba-b771-5e3f-ad9e-33799f191a9c"
Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+JLD2 = "033835bb-8acc-5ee8-8aae-3f567f8a3819"
[targets]
-test = ["Test", "Flux"]
+test = ["Test", "Flux", "JLD2"]
diff --git a/examples/cars_workshop/.ipynb_checkpoints/4 visualverification-checkpoint.ipynb b/examples/cars_workshop/.ipynb_checkpoints/4 visualverification-checkpoint.ipynb
new file mode 100644
index 00000000..38bfeaa1
--- /dev/null
+++ b/examples/cars_workshop/.ipynb_checkpoints/4 visualverification-checkpoint.ipynb
@@ -0,0 +1,5655 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Two Dimensional Verification Example\n",
+ "\n",
+ "In this notebook, we use the `Network` and `Layer` API of NeuralVerification.jl to construct a neural network that maps two dimensional inputs to two dimensional outputs. We demonstrate how to define and verify a property on this network, and plot the output of the network at interesting moments throughout the problem."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 73,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "using NeuralVerification, LazySets, LinearAlgebra\n",
+ "# We also import several functions and types so we can \n",
+ "# avoid e.g. the verbose NeuralVerification.ReLU(), etc.\n",
+ "import NeuralVerification: Network, Layer, ReLU, Id, affine_map, forward_partition\n",
+ "\n",
+ "# Set up some plotting stuff for later.\n",
+ "using Plots, LaTeXStrings\n",
+ "default(size = (300,300), legend = :none)\n",
+ "function Plots.plot(V::Vector{<:AbstractPolytope}, args...)\n",
+ " p = plot()\n",
+ " for s in V\n",
+ " plot!(p, s, args...)\n",
+ " end\n",
+ " return p\n",
+ "end"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Layers\n",
+ "\n",
+ "Let's begin by constructing our network. A layer is defined by a set of weights $\\mathbf{W}$, a bias, $\\mathbf{b}$, and a nonlinear activation function, usually denoted $\\sigma$.\n",
+ "Here we define the input layer $L_1$ to be a ReLU layer expecting a 2D input. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 74,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Layer{ReLU,Float64}([1.0 0.5; 0.5 1.0], [0.0, -0.5], ReLU())"
+ ]
+ },
+ "execution_count": 74,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "W = [1.0 0.5;\n",
+ " 0.5 1.0]\n",
+ "\n",
+ "b = [0, -0.5]\n",
+ "\n",
+ "L₁ = Layer(W, b, ReLU())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We can apply our layer to an input $x$ by performing $\\sigma (Wx + b)$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 102,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "x: [2, -1] ⟶ ẑ: [1.5, -0.5] ⟶ z: [1.5, 0.0]\n"
+ ]
+ }
+ ],
+ "source": [
+ "let x = [2,-1], σ = L₁.activation\n",
+ " \n",
+ " ẑ = affine_map(L₁, x) # affine_map performs W*x + b\n",
+ " z = σ(ẑ)\n",
+ "\n",
+ " println(\"x: $x ⟶ ẑ: $ẑ ⟶ z: $z\")\n",
+ "end"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Networks \n",
+ "\n",
+ "A Network consists of a vector of these layers. Here we construct a network using $L_1$ and 6 more layers. The layers were initally created with random weights and biases, and then hard-coded here for repeatability. Note that the last layer is an identity layer."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 76,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "layers = [\n",
+ " L₁,\n",
+ " Layer([1.14327 0.1497; 0.0938726 1.02164], [0.427767, -0.441637], ReLU()), \n",
+ " Layer([1.03721 0.083906; 0.174684 1.13746], [-0.664744, 0.4121], ReLU()), \n",
+ " Layer([1.07418 0.155875; 0.147354 1.09946], [-1.20265, -0.566685], ReLU()), \n",
+ " Layer([1.08786 0.159884; 0.0990573 1.00572], [-0.559988, -0.301343], ReLU()),\n",
+ " Layer([1.18447 0.177153; 0.00392835 1.18098], [0.422727, 1.04569], ReLU()),\n",
+ " Layer([1.14041 0.182869; 0.186956 1.18623], [1.51287, 0.497855], Id()),\n",
+ " ]\n",
+ "\n",
+ "net = Network(layers);"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Sets\n",
+ "\n",
+ "Now we can consider an input/output property of interest. Normally, the inputs an outputs of the network would have some semantic meaning (controls, labels, etc.) which would inform these properties. In this case, since we don't have anything like that, we will choose our input and output sets to be two arbitrary hyperrectangles.\n",
+ "\n",
+ "$X = \\left\\{ x_1, x_2 \\mid 0 \\leq x_i \\leq 1 \\right\\}$\n",
+ "\n",
+ "$Y = \\left\\{ y_1, y_2 \\mid 2 \\leq y_i \\leq 4 \\right\\}$\n",
+ "\n",
+ "The verification problem consists of determining whether $f(X) \\subseteq Y$. Note that not all algorithms support all types of sets. The documentation contains a [table](https://sisl.github.io/NeuralVerification.jl/latest/problem/) listing input and output sets by algorithm."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 77,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n"
+ ]
+ },
+ "execution_count": 77,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "X = Hyperrectangle(low = [0, 0], high = [1, 1])\n",
+ "Y = Hyperrectangle(low = [2, 2], high = [4, 4]);\n",
+ "\n",
+ "plot(X, label = \"X\", legend = true)\n",
+ "plot!(Y, label = \"Y\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Reachability\n",
+ "\n",
+ "We can transform the input set according to each layer by applying the same transformation introduced earlier. However, the nonlinearity in the ReLU requires that the set be partitioned along the $x=0$ and $y=0$ axes and that each subset is treated independently. If the subset lies in the positive quadrant, it is unchanged. In the negative quadrants, the ReLU operation projects the set onto the axis (by setting the negative componets of points in the set to $0$).\n",
+ "\n",
+ "This is demonstrated in the cell below. We transform the set $X$ subject to $L_1$ (we use `affine_map` again as before, but this time must call `forward_partition` to perform the ReLU on a set)."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 68,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n"
+ ]
+ },
+ "execution_count": 68,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "Ẑ = affine_map(L₁, X)\n",
+ "Z = forward_partition(L₁.activation, Ẑ)\n",
+ "\n",
+ "\n",
+ "#### Just plotting stuff:\n",
+ "t1 = L\"\\mathcal{X}\"\n",
+ "t2 = L\"\\mathcal{X} \\mathrm{\\ and\\ } \\hat{\\mathcal{Z}}_1\"\n",
+ "t3 = L\"\\mathcal{X},\\ \\hat{\\mathcal{Z}}_1 \\mathrm{\\ and\\ } \\mathcal{Z}_1\"\n",
+ "\n",
+ "p1 = plot(X, fill = 0.7, xlim = (-0.3, 1.6), ylim = (-0.9 ,1.3), title = t1)\n",
+ "\n",
+ "p2 = deepcopy(p1)\n",
+ "plot!(p2, Ẑ, fill = 0.7, title = t2)\n",
+ "\n",
+ "p3 = deepcopy(p2)\n",
+ "hline!(p3, [0], line = (2, :black, :dash), fill = 0.7)\n",
+ "vline!(p3, [0], line = (2, :black, :dash), fill = 0.7)\n",
+ "plot!(p3, Z, line = (:green, 5), fill = (:green, 0.7), title = t3)\n",
+ "\n",
+ "plot(p1, p2, p3, size = (800, 250), layout = (1,3))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Solving a Problem\n",
+ "\n",
+ "Now that the network and property are both defined, we can construct a `Problem` object out of them. We use `ExactReach` to verify the property, which employs exact reachability techniques to calculate the true output set $f(X)$ and compare it to the desired output set $Y$. Since our network is small and simple, we can afford to do this, but in general, exact reachability is a computationaly expensive approach that scales poorly.\n",
+ "\n",
+ "\n",
+ "### ExactReach"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 78,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ ":violated"
+ ]
+ },
+ "execution_count": 78,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "prob = Problem(net, X, Y)\n",
+ "res = solve(ExactReach(), prob)\n",
+ "\n",
+ "# check the result\n",
+ "res.status"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We find that the property is violated. The full printout of `res` is avoided above because, in the case of a violated input-output relation, ExactReach returns the computed output set, which is quite long in this case. We plot the output set, as well as $\\mathcal Y$ below, to understand why the property does not hold."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 72,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n"
+ ]
+ },
+ "execution_count": 72,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "p1 = plot(X, title = L\"\\mathcal{X}\\mathrm{\\ and\\ }f(\\mathcal{X})\")\n",
+ "plot!(p1, res.reachable, line = (1, :black), fill = (0.7, :green))\n",
+ "\n",
+ "p2 = plot(X, title = L\"f(\\mathcal{X}) \\not\\subseteq \\mathcal{Y}\")\n",
+ "plot!(p2, Y)\n",
+ "plot!(p2, res.reachable, fill = (0.7, :green))\n",
+ "\n",
+ "plot(p1, p2, size = (600, 250))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### MaxSens\n",
+ "\n",
+ "We see that the desired output set does not contain the true output set, which is the definition of a violated property. However, we took a computationally expensive approach to reach this conclusion, as mentioned earlier. We have other reachability (and non-reachability) algorithms at our disposal as well, which trade off over-approximation with computational efficiency. Next, we will try the same thing again using the `MaxSens` algorithm, which first partitions the set into hyperrectangles at a specified resolution, and then propagates each of those through the network in a fast but approximate way. We can solve the problem with a number of different resolutions to observe the effect on accuracy."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 89,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "maxsens_results = [solve(MaxSens(resolution = r), prob) for r in reverse(0.1:0.1:0.9)];"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 90,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/svg+xml": [
+ "\n",
+ "\n"
+ ]
+ },
+ "execution_count": 90,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "p = []\n",
+ "\n",
+ "p1 = plot(X)\n",
+ "for i in 1:length(maxsens_results)\n",
+ " p2 = deepcopy(p1)\n",
+ " plot!(p2, Y)\n",
+ " plot!(p2, maxsens_results[i].reachable, line = (1, :black), \n",
+ " fill = (0.7, :green), titlefontsize = 12, \n",
+ " title = \"resolution = $(round(1.0 - 0.1*i, digits = 2))\")\n",
+ " push!(p, p2)\n",
+ "end\n",
+ "\n",
+ "plot(p..., size = (700,600))"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "@webio": {
+ "lastCommId": null,
+ "lastKernelId": null
+ },
+ "kernelspec": {
+ "display_name": "Julia 1.0.5",
+ "language": "julia",
+ "name": "julia-1.0"
+ },
+ "language_info": {
+ "file_extension": ".jl",
+ "mimetype": "application/julia",
+ "name": "julia",
+ "version": "1.0.1"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/examples/networks/R2_R2.nnet b/examples/networks/R2_R2.nnet
new file mode 100644
index 00000000..393e6a8b
--- /dev/null
+++ b/examples/networks/R2_R2.nnet
@@ -0,0 +1,15 @@
+2
+2,2,2
+0
+0
+0
+0
+0
+1,1
+-1,1
+-1
+-1
+1,0
+0,1
+0
+0
diff --git a/examples/networks/mnist_1000.nnet b/examples/networks/mnist_1000.nnet
new file mode 100644
index 00000000..87cbbda0
--- /dev/null
+++ b/examples/networks/mnist_1000.nnet
@@ -0,0 +1,128 @@
+// Neural Network File Format by Kyle Julian, Stanford 2016
+3,784,10,784,
+784,30,20,10,
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diff --git a/src/adversarial/neurify.jl b/src/adversarial/neurify.jl
index 4905149b..7bffd5dc 100644
--- a/src/adversarial/neurify.jl
+++ b/src/adversarial/neurify.jl
@@ -26,8 +26,19 @@ Sound but not complete.
"""
@with_kw struct Neurify
- max_iter::Int64 = 1000
+ max_iter::Int64 = 10
tree_search::Symbol = :DFS # only :DFS/:BFS allowed? If so, we should assert this.
+
+ # Becuase of over-approximation, a split may not bisect the input set.
+ # Therefore, the gradient remains unchanged (since input didn't change).
+ # And this node will be chosen to split forever.
+ # To prevent this, we split each node only once if the gradient of this node doesn't change.
+ # Each element in splits is a tuple (gradient_of_the_node, layer_index, node_index).
+
+ splits = Set() # To prevent infinity loop.
+
+ # But in some cases (which I don't have an example, just a sense),
+ # it can happen that a node indeed needs to be split twice with the same gradient.
end
struct SymbolicInterval{F<:AbstractPolytope}
@@ -41,74 +52,101 @@ SymbolicInterval(x::Matrix{Float64}, y::Matrix{Float64}) = SymbolicInterval(x, y
# Data to be passed during forward_layer
struct SymbolicIntervalGradient
sym::SymbolicInterval
- LΛ::Vector{Vector{Float64}}
+ LΛ::Vector{Vector{Float64}} # mask for computing gradient.
UΛ::Vector{Vector{Float64}}
+ r::Vector{Vector{Float64}} # range of a input interval (upper_bound - lower_bound)
end
function solve(solver::Neurify, problem::Problem)
+
+ while !isempty(solver.splits) pop!(solver.splits) end
problem = Problem(problem.network, convert(HPolytope, problem.input), convert(HPolytope, problem.output))
+
+ reach_lc = problem.input.constraints
+ output_lc = problem.output.constraints
+
+ n = size(reach_lc, 1)
+ m = size(reach_lc[1].a, 1)
+ model = Model(with_optimizer(GLPK.Optimizer))
+ @variable(model, x[1:m], base_name="x")
+ @constraint(model, [i in 1:n], reach_lc[i].a' * x <= reach_lc[i].b)
-reach = forward_network(solver, problem.network, problem.input)
- result = check_inclusion(reach.sym, problem.output, problem.network) # This called the check_inclusion function in ReluVal, because the constraints are Hyperrectangle
+ reach = forward_network(solver, problem.network, problem.input)
+ result, max_violation_con = check_inclusion(solver, reach.sym, problem.output, problem.network) # This calls the check_inclusion function in ReluVal, because the constraints are Hyperrectangle
result.status == :unknown || return result
- reach_list = SymbolicIntervalGradient[reach]
+
+ reach_list = [(reach, max_violation_con)]
+
for i in 2:solver.max_iter
length(reach_list) > 0 || return BasicResult(:holds)
- reach = pick_out!(reach_list, solver.tree_search)
- intervals = constraint_refinement(solver, problem.network, reach)
+ reach, max_violation_con = pick_out!(reach_list, solver.tree_search)
+ intervals = constraint_refinement(solver, problem.network, reach, max_violation_con)
for interval in intervals
reach = forward_network(solver, problem.network, interval)
- result = check_inclusion(reach.sym, problem.output, problem.network)
+ result, max_violation_con = check_inclusion(solver, reach.sym, problem.output, problem.network)
result.status == :violated && return result
- result.status == :holds || (push!(reach_list, reach))
+ result.status == :holds || (push!(reach_list, (reach, max_violation_con)))
end
end
return BasicResult(:unknown)
end
-function check_inclusion(reach::SymbolicInterval{HPolytope{N}}, output::AbstractPolytope, nnet::Network) where N
+function check_inclusion(solver, reach::SymbolicInterval{HPolytope{N}}, output::AbstractPolytope, nnet::Network) where N
# The output constraint is in the form A*x < b
- # We try to maximize output constraint to find a violated case, or to verify the inclusion,
- # suppose the output is [1, 0, -1] * x < 2, Then we are maximizing reach.Up[1] * 1 + reach.Low[3] * (-1)
-
+ # We try to maximize output constraint to find a violated case, or to verify the inclusion.
+ # Suppose the output is [1, 0, -1] * x < 2, Then we are maximizing reach.Up[1] * 1 + reach.Low[3] * (-1)
+
+ # return a result and the most violated constraint.
reach_lc = reach.interval.constraints
output_lc = output.constraints
-
n = size(reach_lc, 1)
m = size(reach_lc[1].a, 1)
model =Model(with_optimizer(GLPK.Optimizer))
@variable(model, x[1:m])
@constraint(model, [i in 1:n], reach_lc[i].a' * x <= reach_lc[i].b)
-
- for i in 1:size(output.constraints, 1)
+ max_violation = -1e9
+ max_violation_con = nothing
+ for i in 1:size(output_lc, 1)
obj = zeros(size(reach.Low, 2))
for j in 1:size(reach.Low, 1)
- if output.constraints[i].a[j] > 0
- obj += output.constraints[i].a[j] * reach.Up[j,:]
+ if output_lc[i].a[j] > 0
+ obj += output_lc[i].a[j] * reach.Up[j,:]
else
- obj += output.constraints[i].a[j] * reach.Low[j,:]
+ obj += output_lc[i].a[j] * reach.Low[j,:]
end
end
- @objective(model, Min, obj' * [x; [1]])
+ obj = transpose(obj)
+ @objective(model, Max, obj * [x; [1]])
optimize!(model)
- # println("termination_status")
- # println(termination_status(model))
- y = compute_output(nnet, value(x))
- if !∈(y, output)
+ if termination_status(model) == MOI.OPTIMAL
+ y = compute_output(nnet, value(x))
+ if !∈(y, output)
+ return CounterExampleResult(:violated, value(x)), nothing
+ end
+ if objective_value(model) > output_lc[i].b
+ if objective_value(model) - output_lc[i].b > max_violation
+ max_violation = objective_value(model) - output_lc[i].b
+ max_violation_con = output_lc[i].a
+ end
+ end
+ else
if ∈(value(x), reach.interval)
- return CounterExampleResult(:violated, value(x))
+ println("Not OPTIMAL, but x in the input set")
+ println("This is usually caused by open input set.")
+ println("Please check your input constraints.")
+ exit()
end
- end
- if objective_value(model) > output.constraints[i].b
- return BasicResult(:unknown)
+ println("No solution, please check the problem definition.")
+ exit()
end
end
- return BasicResult(:holds)
+ max_violation > 0 && return BasicResult(:unknown), max_violation_con
+ return BasicResult(:holds), nothing
end
-function constraint_refinement(solver::Neurify, nnet::Network, reach::SymbolicIntervalGradient)
- i, j, gradient = get_nodewise_gradient(nnet, reach.LΛ, reach.UΛ)
+function constraint_refinement(solver::Neurify, nnet::Network, reach::SymbolicIntervalGradient, max_violation_con::Vector{Float64})
+ i, j, influence = get_nodewise_influence(solver, nnet, reach, max_violation_con)
# We can generate three more constraints
# Symbolic representation of node i j is Low[i][j,:] and Up[i][j,:]
nnet_new = Network(nnet.layers[1:i])
@@ -126,27 +164,41 @@ function constraint_refinement(solver::Neurify, nnet::Network, reach::SymbolicIn
return intervals
end
-function get_nodewise_gradient(nnet::Network, LΛ::Vector{Vector{Float64}}, UΛ::Vector{Vector{Float64}})
+function get_nodewise_influence(solver::Neurify, nnet::Network, reach::SymbolicIntervalGradient, max_violation_con::Vector{Float64})
n_output = size(nnet.layers[end].weights, 1)
n_length = length(nnet.layers)
- LG = Matrix(1.0I, n_output, n_output)
- UG = Matrix(1.0I, n_output, n_output)
+ # We want to find the node with the largest influence
+ # Influence is defined as gradient * interval width
+ # The gradient is with respect to a loss defined by the most violated constraint.
+ LG = transpose(copy(max_violation_con))
+ UG = transpose(copy(max_violation_con))
max_tuple = (0, 0, 0.0)
for (k, layer) in enumerate(reverse(nnet.layers))
i = n_length - k + 1
- for j in size(layer.bias)
- if LΛ[i][j] ∈ (0.0, 1.0) && UΛ[i][j] ∈ (0.0, 1.0)
- max_gradient = max(abs(LG[j]), abs(UG[j]))
- if max_gradient > max_tuple[3]
- max_tuple = (i, j, max_gradient)
+ if layer.activation != Id()
+ # Only split Relu nodes
+ # A split over id node may not reduce over-approximation (the input set may not bisected).
+ for j in 1:size(layer.bias,1)
+ if (0 < reach.LΛ[i][j] < 1) && (0 < reach.UΛ[i][j] < 1)
+ max_gradient = max(abs(LG[j]), abs(UG[j]))
+ influence = max_gradient * reach.r[i][j]
+ if in((i,j, influence), solver.splits) # To prevent infinity loop
+ continue
+ end
+ # If we use > here, in the case that largest gradient is 0, this function will return (0, 0 ,0)
+ if influence >= max_tuple[3]
+ max_tuple = (i, j, influence)
+ end
end
end
end
+
i >= 1 || break
- LG_hat = max.(LG, 0.0) * Diagonal(LΛ[i]) + min.(LG, 0.0) * Diagonal(UΛ[i])
- UG_hat = min.(UG, 0.0) * Diagonal(LΛ[i]) + max.(UG, 0.0) * Diagonal(UΛ[i])
+ LG_hat = max.(LG, 0.0) * Diagonal(reach.LΛ[i]) + min.(LG, 0.0) * Diagonal(reach.UΛ[i])
+ UG_hat = min.(UG, 0.0) * Diagonal(reach.LΛ[i]) + max.(UG, 0.0) * Diagonal(reach.UΛ[i])
LG, UG = interval_map_right(layer.weights, LG_hat, UG_hat)
end
+ push!(solver.splits, max_tuple)
return max_tuple
end
@@ -160,7 +212,8 @@ function forward_linear(solver::Neurify, input::AbstractPolytope, layer::Layer)
sym = SymbolicInterval(hcat(W, b), hcat(W, b), input)
LΛ = Vector{Vector{Int64}}(undef, 0)
UΛ = Vector{Vector{Int64}}(undef, 0)
- return SymbolicIntervalGradient(sym, LΛ, UΛ)
+ r = Vector{Vector{Int64}}(undef, 0)
+ return SymbolicIntervalGradient(sym, LΛ, UΛ, r)
end
# Symbolic forward_linear
@@ -171,7 +224,7 @@ function forward_linear(solver::Neurify, input::SymbolicIntervalGradient, layer:
output_Up[:, end] += b
output_Low[:, end] += b
sym = SymbolicInterval(output_Low, output_Up, input.sym.interval)
- return SymbolicIntervalGradient(sym, input.LΛ, input.UΛ)
+ return SymbolicIntervalGradient(sym, input.LΛ, input.UΛ, input.r)
end
# Symbolic forward_act
@@ -179,6 +232,7 @@ function forward_act(input::SymbolicIntervalGradient, layer::Layer{ReLU})
n_node, n_input = size(input.sym.Up)
output_Low, output_Up = input.sym.Low[:, :], input.sym.Up[:, :]
mask_lower, mask_upper = zeros(Float64, n_node), ones(Float64, n_node)
+ interval_width = zeros(Float64, n_node)
for i in 1:n_node
if upper_bound(input.sym.Up[i, :], input.sym.interval) <= 0.0
# Update to zero
@@ -201,12 +255,14 @@ function forward_act(input::SymbolicIntervalGradient, layer::Layer{ReLU})
output_Up[i, end] -= up_low
output_Up[i, :] = up_slop * output_Up[i, :]
mask_lower[i], mask_upper[i] = low_slop, up_slop
+ interval_width[i] = up_up - low_low
end
end
sym = SymbolicInterval(output_Low, output_Up, input.sym.interval)
LΛ = push!(input.LΛ, mask_lower)
UΛ = push!(input.UΛ, mask_upper)
- return SymbolicIntervalGradient(sym, LΛ, UΛ)
+ r = push!(input.r, interval_width)
+ return SymbolicIntervalGradient(sym, LΛ, UΛ, r)
end
function forward_act(input::SymbolicIntervalGradient, layer::Layer{Id})
@@ -214,7 +270,8 @@ function forward_act(input::SymbolicIntervalGradient, layer::Layer{Id})
n_node = size(input.sym.Up, 1)
LΛ = push!(input.LΛ, ones(Float64, n_node))
UΛ = push!(input.UΛ, ones(Float64, n_node))
- return SymbolicIntervalGradient(sym, LΛ, UΛ)
+ r = push!(input.r, ones(Float64, n_node))
+ return SymbolicIntervalGradient(sym, LΛ, UΛ, r)
end
diff --git a/src/utils/util.jl b/src/utils/util.jl
index 9698b14a..b9bd496f 100644
--- a/src/utils/util.jl
+++ b/src/utils/util.jl
@@ -253,13 +253,13 @@ Inputs:
Outputs:
- `(lbound, ubound)` (after the mapping)
"""
-function interval_map(W::Matrix{N}, l::AbstractVecOrMat, u::AbstractVecOrMat) where N
+function interval_map(W::AbstractMatrix{N}, l::AbstractVecOrMat, u::AbstractVecOrMat) where N
l_new = max.(W, zero(N)) * l + min.(W, zero(N)) * u
u_new = max.(W, zero(N)) * u + min.(W, zero(N)) * l
return (l_new, u_new)
end
-function interval_map_right(W::Matrix{N}, l::AbstractVecOrMat, u::AbstractVecOrMat) where N
+function interval_map_right(W::AbstractMatrix{N}, l::AbstractVecOrMat, u::AbstractVecOrMat) where N
l_new = l * max.(W, zero(N)) + u * min.(W, zero(N))
u_new = u * max.(W, zero(N)) + l * min.(W, zero(N))
return (l_new, u_new)
diff --git a/test/MNIST_1000_data.jld2 b/test/MNIST_1000_data.jld2
new file mode 100644
index 00000000..d9806354
Binary files /dev/null and b/test/MNIST_1000_data.jld2 differ
diff --git a/test/mnist_1000.jl b/test/mnist_1000.jl
new file mode 100644
index 00000000..93e2d2ce
--- /dev/null
+++ b/test/mnist_1000.jl
@@ -0,0 +1,85 @@
+using LazySets, Test, LinearAlgebra, GLPKMathProgInterface
+using NeuralVerification
+import NeuralVerification: ReLU, Id
+using JLD2
+
+function test_solver(solver, test_selected)
+
+ # index of all violated cases in the first 1000 images.
+ violation_idx = [25, 142, 179, 183, 283, 285, 387, 392, 612, 647, 737]
+ # index of selected holding cases in the first 1000 images.
+ satisfied_idx = [10, 100, 200, 300, 400, 500 ,600, 700, 800, 900, 999, 213, 391, 660, 911]
+
+ if test_selected
+ test_idx = [violation_idx; satisfied_idx]
+ else
+ test_idx = 1:1000
+ end
+
+ @load "MNIST_1000_data.jld2" train_x train_y
+
+ net_file = "$(@__DIR__)/../examples/networks/mnist_1000.nnet"
+ mnist_net = read_nnet(net_file, last_layer_activation = Id())
+
+ for i = test_idx
+
+ input_center = reshape(train_x[:,:,i], 28*28)
+ label = train_y[i]
+ A = zeros(Float64, 10, 10)
+ A[diagind(A)] .= 1
+ A[:, label+1] = A[:, label+1] .- 1
+ A = A[1:end .!= label+1,:]
+
+ b = zeros(Float64, 9)
+
+ Y = HPolytope(A, b)
+ pred = argmax(NeuralVerification.compute_output(mnist_net, input_center))-1
+
+ if pred != label
+ continue
+ end
+
+ epsilon = 1.0/255.0
+ upper = input_center .+ epsilon
+ lower = input_center .- epsilon
+ clamp!(upper, 0.0, 1.0)
+ clamp!(lower, 0.0, 1.0)
+ X = Hyperrectangle(low=lower, high=upper)
+
+ problem_mnist = Problem(mnist_net, X, Y)
+
+ result = solve(solver, problem_mnist)
+
+ if result.status == :violated
+ @test i ∈ violation_idx
+ noisy = argmax(NeuralVerification.compute_output(mnist_net, result.counter_example))-1
+ @test noisy != pred
+ elseif result.status == :holds
+ @test !(i ∈ violation_idx)
+ else #result.status == :unknown
+
+ end
+ end
+end
+
+# if test_selected = true, only test selected index. Otherwise, test all 1000 images.
+test_selected = true
+
+# Please note the number of tests maybe different for different solvers.
+# Because the test cases depends on the result.
+
+if test_selected
+ @testset "MNIST selected, ReluVal" begin
+ test_solver(ReluVal(), test_selected)
+ end
+ @testset "MNIST selected, Neurify" begin
+ test_solver(Neurify(), test_selected)
+ end
+else
+ @testset "MNIST 1000, ReluVal" begin
+ test_solver(ReluVal(), test_selected)
+ end
+ @testset "MNIST 1000, Neurify" begin
+ test_solver(Neurify(), test_selected)
+ end
+end
\ No newline at end of file
diff --git a/test/runtests.jl b/test/runtests.jl
index 3c63c760..073b8fa9 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -4,4 +4,6 @@ include("inactive_relus.jl")
if Base.find_package("Flux") != nothing
include("flux.jl")
end
-include("complements.jl")
\ No newline at end of file
+include("complements.jl")
+include("splitting.jl")
+include("mnist_1000.jl")
\ No newline at end of file
diff --git a/test/splitting.jl b/test/splitting.jl
new file mode 100644
index 00000000..2c95f00c
--- /dev/null
+++ b/test/splitting.jl
@@ -0,0 +1,39 @@
+using LazySets, Test, LinearAlgebra
+using NeuralVerification
+import NeuralVerification: ReLU, Id
+
+@testset "Splitting Test" begin
+
+ net_file = "$(@__DIR__)/../examples/networks/R2_R2.nnet"
+ # This is a 3 layer simple network mapping from R2 to R2.
+
+ # y1 = x1 + x2 - 1
+ # y2 = -x1 + x2 - 1
+
+ # z1 = ReLU(y1)
+ # z2 = ReLU(y2)
+
+ # o1 = 1*z1 + 0*z2 + 0
+ # o2 = 0*z1 + 1*z2 + 0
+
+ net = read_nnet(net_file, last_layer_activation = Id())
+ A = [1. 0.; 0. 1.; -1. 0.; 0. -1.;]
+ b = [1.1, 1.1, 0.1, 0.1]
+ X = Hyperrectangle(low=[-1,-1], high=[1,1])
+ # The true output set is a union of two segments : (0,0)->(0,1) U (0,0)->(1,0)
+ Y = HPolytope(A, b) # Output constraints. Hyperrectangle: -0.1, -0.1, 1.1, 1.1
+ problem = Problem(net, X, Y)
+
+ @testset "Neurify" begin
+ solver = Neurify()
+ result = solve(solver, problem)
+ @test result.status == :holds
+ end
+
+ @testset "ReluVal" begin
+ solver = ReluVal()
+ result = solve(solver, problem)
+ @test result.status == :holds
+ end
+
+end
\ No newline at end of file