/// <summary>
/// Given the symbolic output we check which columns are completely zero,
/// which effectively implies that the corresponding variables do not participate
/// in the Jacobian.
/// </summary>
/// <param name="output"></param>
public static void ReportSparsity(LPSTerm[] output)
{
var matrix = LPSTerm.UnderlyingMatrix(output);
Vector<double> zeros = DenseVector.Create(output.Length,0.0);
// int sparse_count = 0;
List<Tuple<int, double>> stats = new List<Tuple<int, double>>();
for (int i=0; i < matrix.ColumnCount; i++)
{
var col = matrix.Column(i);
stats.Add(new Tuple<int, double>(i, col.Maximum()));
}
stats.Sort(delegate(Tuple<int,double> t1, Tuple<int,double> t2)
{
return t1.Item2.CompareTo(t2.Item2);
});
foreach (var s in stats)
{
Console.WriteLine(s.Item2);
}
}
/// <summary>
/// Generate symbolic inputs and (potentially) a term for the epsilon of the objective.
/// </summary>
public static Tuple<LPSTerm[],LPSTerm> GenSymbolicInputs(int inputDimension)
{
LPSTerm[] inputs = null;
LPSTerm epsilon = null;
LPSTerm.ResetVariableFactory(inputDimension + 1);
var all = LPSTerm.FreshVariables(inputDimension+1);
epsilon = all[inputDimension];
inputs = new LPSTerm[inputDimension];
Array.Copy(all, inputs, inputDimension);
return new Tuple<LPSTerm[], LPSTerm>(inputs, epsilon);
}
public void AddConstraint(LPSConstraint ct)
{
int ctid = ct_cnt;
solver_.AddRow("constraint" + ct_cnt, out ctid);
Vector <double> coefficients = ct.Term.GetCoefficients();
int totalvars = LPSTerm.TotalVarCount();
for (int j = 0; j < totalvars; j++)
{
// Due to the way MSF works, if we are adding a 0 coefficient
// this amounts to actually removing it. However, the coefficient
// is not there to start with, hence let's not add it, at all!
if (coefficients[j] != 0)
{
solver_.SetCoefficient(ctid, vars_[j], coefficients[j]);
}
}
switch (ct.Inequality)
{
case InequalityType.LT:
solver_.SetUpperBound(ctid, -ct.Term.Intercept); // - RobustnessOptions.StrictInequalityLambda * Math.Abs(ct.Term.Intercept));
break;
case InequalityType.LE:
solver_.SetUpperBound(ctid, -ct.Term.Intercept);
break;
case InequalityType.GT:
solver_.SetLowerBound(ctid, -ct.Term.Intercept); // + RobustnessOptions.StrictInequalityLambda * Math.Abs(ct.Term.Intercept));
break;
case InequalityType.GE:
solver_.SetLowerBound(ctid, -ct.Term.Intercept);
break;
case InequalityType.EQ:
// solver_.SetValue(ctid, -ct.Term.Intercept); WRONG
solver_.SetBounds(ctid, -ct.Term.Intercept, -ct.Term.Intercept);
break;
default:
break;
}
ct_cnt++;
}
public LPSolver(
int input_dimension,
int total_constraint_count,
double[] origin, // Just the image, not the epsilon
double originbound // Bounding rectangle
)
{
solver_ = new GurobiSolver();
input_dimension_ = input_dimension;
int varCount = LPSTerm.TotalVarCount();
Console.WriteLine("Number of variables: " + varCount);
vars_ = new int[varCount];
for (int i = 0; i < varCount; i++)
{
int vid;
solver_.AddVariable("x" + i, out vid);
solver_.SetIntegrality(vid, RobustnessOptions.Integrality);
if (i < origin.Length)
{
double lb = Math.Max(Utils.RobustnessOptions.MinValue, origin[i] - originbound);
double ub = Math.Min(Utils.RobustnessOptions.MaxValue, origin[i] + originbound);
if (lb <= ub)
{
// Tighter bounds for the image variables!
solver_.SetBounds(vid, lb, ub);
}
else
{
// Bound validation failed, very weird. Oh well just don't use the bounds.
// The programmer got the Min/Max values wrong.
solver_.SetBounds(vid, origin[i] - originbound, origin[i] + originbound);
}
}
else
{
solver_.SetBounds(vid, Utils.RobustnessOptions.MinValue, Utils.RobustnessOptions.MaxValue);
}
vars_[i] = vid;
}
}
public void AddConstraints(LPSConstraints constraints, Nullable <LPSObjective> objective)
{
// Constraints
int numConstraints = constraints.Count;
int tmp = 0;
Console.WriteLine("LP constraints: " + numConstraints);
int varCount = LPSTerm.TotalVarCount();
foreach (LPSConstraint ct in constraints)
{
AddConstraint(ct);
tmp++;
// Console.Write("\rAdding LP constraints: {0:0.000}%", (double)tmp * 100.0 / numConstraints);
}
Console.WriteLine();
if (objective.HasValue)
{
int objid;
solver_.AddRow("Objective", out objid);
for (int j = 0; j < varCount; j++)
{
solver_.SetCoefficient(objid, vars_[j], objective.Value.term.GetCoefficient(j));
// objConstr += objective.Value.term.GetCoefficient(j) * vars[j];
}
switch (objective.Value.type)
{
case LPSObjectiveType.Max:
solver_.AddGoal(objid, 10, false);
objective_id = objid;
break;
case LPSObjectiveType.Min:
solver_.AddGoal(objid, 10, true);
objective_id = objid;
break;
}
}
}
/// <summary>
/// Synthesize a counterexample from an existing labelled image.
/// </summary>
/// <param name="options"></param>
/// <param name="nn">The model.</param>
/// <param name="imageLab">The image and labeling information from the network.</param>
/// <param name="instr"></param>
/// <param name="realLabel">The label of the image from the training set.</param>
/// <param name="rowSize"></param>
/// <param name="colSize"></param>
/// <param name="isColor"></param>
/// <returns>NULL if we were not able to synthesize a counterexample, otherwise some information about it.</returns>
public static Nullable<LabelWithConfidence> SynthesizeCounterexample
( NeuralNet nn
, LPSTerm[] inputs // Symbolic inputs (cropped)
, LPSTerm epsilon // Epsilon variable
, LabelWithConfidence imageLab // Original image classification info (uncropped)
, NNInstrumentation instr
, int realLabel // Ground truth for this image (from training set)
, int rowSize // Original (uncropped) row size
, int colSize // Original (uncropped) col size
, bool isColor)
{
int origLabel = imageLab.actualLabel;
int targetLabel = imageLab.secBestLabel;
int input_dimension_pre_crop = nn.InputDimensionPreCrop;
int input_dimension_post_crop = nn.InputDimensionPostCrop;
double[] orig_image = imageLab.datum;
double[] orig_image_crop = nn.CropMaybe(DenseVector.OfArray(orig_image)).ToArray();
if (realLabel != origLabel)
{
Console.WriteLine("This image is misclassifed already! Skipping.");
return null;
}
if (RobustnessOptions.IgnoreLowConfidence && imageLab.softMaxValue < RobustnessOptions.LowConfidenceThreshold)
{
Console.WriteLine("This image is misclassifed with low confidence! Skipping.");
return null;
}
// Fast path:
// DiffInfo diff_info;
/* *********************
* DV: Commenting out the fast path for now (but we are still keeping the Dictionary, for debugging)
* *********************
if (diffDict.TryGetValue(new Tuple<int,int>(origLabel,targetLabel),out diff_info))
{
Console.WriteLine("Got a hit in the difference cache!");
Vector<double> diff_counterexample = diff_info.diff;
Vector<double> cand = DenseVector.OfArray(orig_image) + diff_counterexample;
Console.WriteLine("oooooooooooooooo Checking with the fast path!");
double[] cand_arr_crop = nn.CropMaybe(cand).ToArray();
if (RobustnessOptions.QuantizationSafety)
{
Utils.UArray.InPlaceRoundDoubleArray(cand_arr_crop);
}
LabelWithConfidence candLab = Utils.ULabel.LabelWithConfidence(nn, cand_arr_crop,false); // Already cropped, don't crop!
if (candLab.actualLabel != origLabel)
{
Console.WriteLine("=> Real counterexample (from fast path)!");
diff_info.number++;
return candLab;
}
Console.WriteLine("xxxx Fast path failed, continuing with symbolic interpreter ...");
// otherwise continue with the slow path ...
}
***********************/
var state = new LPSState(instr, orig_image_crop);
int nomodelcount = 0;
double[] newImageUnrounded;
NOMODELLOOP:
if (nomodelcount++ > 0) return null;
state.ClearConstraints();
LPSTerm[] output = nn.EvaluateNNSymbolicPostCrop(state, inputs);
// Just some tracing ...
// ReportSparsity(output);
LPSConstraints currentCts = state.CurrentCts;
LPSConstraints deferredCts = state.DeferredCts;
// Conjoin the label formula
currentCts.And(NNetFormulas.LabelFormula(output, targetLabel, RobustnessOptions.LabelConfidenceDiff));
// If we are just looking for bounds, then the variables themselves will contain "origin" bounds
if (RobustnessOptions.DoOptimization)
{
NNETObjectives.AddEpsilonBounds(currentCts, inputs, epsilon, orig_image_crop);
}
// Ensure that at least *one* entry is different by at least 1.0
if (RobustnessOptions.QuantizationSafety)
{
NNETObjectives.AddQuantizationSafety(currentCts, inputs, orig_image_crop);
}
// Create objective
Nullable<LPSObjective> objective = null;
if (RobustnessOptions.DoOptimization)
{
switch (RobustnessOptions.ObjectiveKind)
{
case LPSObjectiveKind.MinLinf:
objective = NNETObjectives.MinLInf(currentCts, inputs, epsilon, orig_image_crop);
break;
case LPSObjectiveKind.MaxConf:
objective = NNETObjectives.MaxConf(output, origLabel, targetLabel);
break;
default:
break;
}
}
if (!RobustnessOptions.CEGAR)
{
currentCts.And(deferredCts);
deferredCts = new LPSConstraints();
}
// CEGAR loop header
LabelWithConfidence newLab;
Console.WriteLine(
"Current constraints: {0}, deferred: {1}",
currentCts.Count,
deferredCts.Count);
LPSolver lps = new LPSolver(
input_dimension_post_crop,
currentCts.Count + deferredCts.Count,
orig_image_crop,
RobustnessOptions.Epsilon);
lps.AddConstraints(currentCts, objective);
int cegar_iterations = 0;
while (true)
{
if (cegar_iterations++ > RobustnessOptions.CEGARGiveUpIterations)
{
Console.WriteLine("xxxxxxxxxxxxxxxx Giving up CEGAR, could not find model!");
goto NOMODELLOOP;
}
var newImage = lps.SolveLowLevelLP();
currentCts = new LPSConstraints();
if (newImage == null)
{
Console.WriteLine("xxxxxxxxxxxxxxxx No model!");
goto NOMODELLOOP;
}
Console.WriteLine("oooooooooooooooo Found model!");
newImageUnrounded = new double[newImage.Length];
Array.Copy(newImage, newImageUnrounded, newImage.Length);
if (RobustnessOptions.QuantizationSafety)
{
Utils.UArray.InPlaceRoundDoubleArray(newImage);
}
int samcount = Utils.UArray.ComputeRoundIdenticals(orig_image_crop, newImage);
Console.WriteLine("Synthesized image has {0} identical inputs (after rounding) to original (cropped)", samcount);
// Now, try to label the new example
newLab = Utils.ULabel.LabelWithConfidence(nn, newImage,false); // Already cropped, don't crop!
if (newLab.actualLabel != targetLabel)
{
if (newLab.actualLabel == realLabel)
{
// Here the synthesized image is not really a counterexample.
// This could be due to either (a) quantization errors or (b) CEGAR
// underapproximation. But the only thing we can try and do here is
// add mor constraints and try to resolve.
if (RobustnessOptions.CEGAR)
Console.WriteLine("Not really a counterexample, going round CEGAR loop.");
int added = 0;
// new_image_plus_eps = newImage : 0.0
// so that the length matches the coefficients of each constraint ...
double[] newimage_plus_eps = new double[newImage.Length+1];
Array.Copy(newImageUnrounded,newimage_plus_eps,newImage.Length);
newimage_plus_eps[newImage.Length] = 0.0;
Vector<double> newImageVec_eps = DenseVector.OfArray(newimage_plus_eps);
var denumerator = deferredCts.GetEnumerator();
Parallel.For(0, deferredCts.Count, i =>
{
LPSConstraint curr_deferred;
if (added > 699) return;
lock (lockObj)
{
denumerator.MoveNext();
curr_deferred = (LPSConstraint)denumerator.Current;
if (curr_deferred.Added == true) return;
}
bool sat = Satisfiable(curr_deferred, newImageVec_eps);
lock (lockObj)
{
if (!sat)
{
lps.AddConstraint(curr_deferred);
// currentCts.And(curr_deferred.Term, curr_deferred.Inequality);
curr_deferred.Added = true;
added++;
}
}
});
Console.WriteLine();
Console.WriteLine("Added {0} constraints for CEGAR", added);
if (added == 0)
{
Console.WriteLine("=> CEGAR cannot improve things.");
goto NOMODELLOOP;
// return null;
}
// lps.AddConstraints(currentCts, null);
continue;
}
else
{
Console.WriteLine("=> Real counterexample! (Although with different label than expected)");
break;
}
}
else
{
Console.WriteLine("=> Real counterexample! (New image has second-best label");
break;
}
}
if (RobustnessOptions.DisplaySynthesizedImagesAndPause)
{
Utils.UDraw.DisplayImageAndPause(Utils.UArray.ToIntArray(imageLab.datum), rowSize, colSize, isColor);
Utils.UDraw.DisplayImageAndPause(Utils.UArray.ToIntArray(newLab.datum), rowSize, colSize, isColor);
}
/* NB: Uncrop the image in newLab */
newLab.datum = nn.UnCropMaybe(DenseVector.OfArray(orig_image), DenseVector.OfArray(newLab.datum)).ToArray();
double[] tmp = nn.UnCropMaybe(DenseVector.OfArray(orig_image), DenseVector.OfArray(newImageUnrounded)).ToArray();
Vector<double> diff_val = DenseVector.OfArray(tmp) - DenseVector.OfArray(orig_image);
var key = new Tuple<int, int>(origLabel, newLab.actualLabel);
DiffInfo dinfo;
if (diffDict.TryGetValue(key, out dinfo))
{
dinfo.number++;
}
else
{
dinfo = new DiffInfo();
dinfo.diff = diff_val;
dinfo.number = 1;
diffDict.Add(new Tuple<int, int>(origLabel, newLab.actualLabel), dinfo);
}
return newLab;
}
