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2 Commits
master ... b1c95d4819

Author SHA1 Message Date
TreetopFlyer
b1c95d4819 move padding into learn/label 2021-07-29 20:53:31 -04:00
TreetopFlyer
94c7abdda5 remove old files 2021-07-29 20:47:17 -04:00
7 changed files with 20 additions and 951 deletions
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717
index.html
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@ -1,717 +0,0 @@
<script>
/* Vector Library */
/*
Works with n-dimensional vectors: represented as arrays of numbers
*/
var V = {};
V.Subtract = function(inV1, inV2)
{
var out = [];
for(var i=0; i<inV1.length; i++)
{
out[i] = inV1[i] - inV2[i];
}
return out;
};
V.Add = function(inV1, inV2)
{
var out = [];
for(var i=0; i<inV1.length; i++)
{
out[i] = inV1[i] + inV2[i];
}
return out;
};
V.Distance = function(inV1, inV2)
{
return V.Length(V.Subtract(inV1, inV2))
};
V.Dot = function(inV1, inV2)
{
var out = 0;
for(var i=0; i<inV1.length; i++)
{
out += inV1[i] * inV2[i];
}
return out;
};
V.Multiply = function(inV1, inV2)
{
var out = [];
for(var i=0; i<inV1.length; i++)
{
out[i] = inV1[i] * inV2[i];
}
return out;
};
V.Length = function(inV1)
{
return Math.sqrt(V.Dot(inV1, inV1));
};
V.Scale = function(inV1, inScalar)
{
var out = [];
for(var i=0; i<inV1.length; i++)
{
out[i] = inV1[i] * inScalar;
}
return out;
};
V.Normalize = function(inV1)
{
return V.Scale(inV1, 1/V.Length(inV1));
};
V.Clone = function(inV1)
{
var out = [];
var i;
for(i=0; i<inV1.length; i++)
{
out[i] = inV1[i];
}
return out;
};
var M = {};
/**************************
M A T R I X
*/
// transform inC with inM
// returns the transformed inC
M.Transform = function(inM, inC)
{
var outM = [];
var outV = [];
var i, j;
for(i=0; i<inC.length; i++)
{
outV = [];
for(j=0; j<inM.length; j++)
{
outV[j] = V.Dot(inM[j], inC[i]);
}
outM.push(outV);
}
return outM;
};
// flip rows for columns in inM
// returns the modified Matrix
M.Transpose = function(inM)
{
var dimensions = inM[0].length;
var i, j;
var outM = [];
var outV = [];
for(i=0; i<dimensions; i++)
{
outV = [];
for(j=0; j<inM.length; j++)
{
//the Ith componenth of the Jth member
outV[j] = inM[j][i];
}
outM.push(outV);
}
return outM;
}
// returns a matrix that is the result of the outer product of inV1 and inV2
// where the Nth member of outM is a copy of V1, scaled by the Nth component of V2
M.Outer = function(inV1, inV2)
{
var outM = [];
var i;
for(i=0; i<inV2.length; i++)
{
outM.push(V.Scale(inV1, inV2[i]));
}
return outM;
};
/**************************
B A T C H
*/
//smash the members of inM with a softmax
M.Sigmoid = function(inM)
{
var i, j;
var outM = [];
var outV = [];
for(i=0; i<inM.length; i++)
{
outV = [];
for(j=0; j<inM[i].length; j++)
{
outV[j] = 1/(1 + Math.pow(Math.E, -inM[i][j]));
}
outM.push(outV);
}
return outM;
};
// return the derivatives of the members of inM (that have been run through the softmax)
M.Derivative = function(inM)
{
var i, j;
var component;
var outM = [];
var outV = [];
for(i=0; i<inM.length; i++)
{
outV = [];
for(j=0; j<inM[i].length; j++)
{
component = inM[i][j];
outV[j] = component*(1 - component);
}
outM.push(outV);
}
return outM;
};
// batch multiply these pairs of vectors
M.Multiply = function(inCloud1, inCloud2)
{
var i;
var outM = [];
for(i=0; i<inCloud1.length; i++)
{
outM.push(V.Multiply(inCloud1[i], inCloud2[i]));
};
return outM;
};
// batch add
M.Add = function(inCloud1, inCloud2)
{
var outM = [];
var i;
for(i=0; i<inCloud1.length; i++)
{
outM.push(V.Add(inCloud1[i], inCloud2[i]));
}
return outM;
};
M.Subtract = function(inCloud1, inCloud2)
{
var outM = [];
var i;
for(i=0; i<inCloud1.length; i++)
{
outM.push(V.Subtract(inCloud1[i], inCloud2[i]));
}
return outM;
};
M.Scale = function(inCloud1, inScalar)
{
var outM = [];
var i;
for(i=0; i<inCloud1.length; i++)
{
outM.push(V.Scale(inCloud1[i], inScalar));
}
return outM;
};
M.Clone = function(inM)
{
var i;
var outM;
var outV;
outM =[];
for(i=0; i<inM.length; i++)
{
outM.push(V.Clone(inM[i]));
}
return outM;
};
/**************************
B O U N D S
*/
// return the bounding box of inM as a two-member Matrix
M.Bounds = function(inM)
{
var dimensions = inM[0].length;
var i, j;
var min = [];
var max = [];
for(i=0; i<dimensions; i++)
{
min[i] = 9999999;
max[i] = -999999;
}
for(i=0; i<inM.length; i++)
{
for(j=0; j<dimensions; j++)
{
if(inM[i][j] < min[j])
{
min[j] = inM[i][j];
}
if(inM[i][j] > max[j])
{
max[j] = inM[i][j];
}
}
}
return [min, max];
};
// find the local coordinates for all the members of inM, within the bounding box inB
// returns a new Matrix of relative vectors
M.GlobalToLocal = function(inM, inB)
{
var dimensions = inB[0].length;
var i, j;
var outM = [];
var outV = [];
var size;
var min;
var denominator;
for(i=0; i<inM.length; i++)
{
outV = [];
for(j=0; j<dimensions; j++)
{
denominator = inB[1][j] - inB[0][j];
if(denominator == 0)
{
outV[j] = inB[1][j];// if min and max are the same, just output max
}
else
{
outV[j] = (inM[i][j] - inB[0][j])/denominator;
}
}
outM.push(outV);
}
return outM;
};
// find the global coordinates for all the members of inM, within the bounding box inB
// returns a new Matrix of global vectors
M.LocalToGlobal = function(inM, inB)
{
var dimensions = inB[0].length;
var i, j;
var outM = [];
var outV = [];
var size;
var min;
for(i=0; i<inM.length; i++)
{
outV = [];
for(j=0; j<dimensions; j++)
{
outV[j] = inB[0][j] + inM[i][j] * (inB[1][j] - inB[0][j]);
}
outM.push(outV);
}
return outM;
};
/**************************
C L O U D
*/
// return some number of points from inM as a new Matrix
M.Reduce = function(inM, inCount)
{
var largeGroupSize;
var largeGroupCount;
var smallGroupSize;
var outM = [];
largeGroupSize = Math.floor(inM.length/inM);
smallGroupSize = inM.length%inCount
for(i=0; i<inM-1; i++)
{
index = i*largeGroupSize + Math.floor(Math.random()*largeGroupSize);
outM.push( V.Clone(inM[index]) );
}
if(smallGroupSize != 0)
{
index = i*largeGroupSize + Math.floor(Math.random()*smallGroupSize)
outM.push( V.Clone(inM[index]) );
}
return outM;
};
// return a Matrix of length inCount, where all the members fall within the circle paramemters, including a bias
M.Circle = function(inCenter, inRadius, inBias, inCount)
{
var i, j;
var vector;
var length;
var outM = [];
for(i=0; i<inCount; i++)
{
//generate a random vector
vector = [];
for(j=0; j<inCenter.length; j++)
{
vector[j] = (Math.random() - 0.5);
}
//normalize the vector
vector = V.Scale(vector, 1/V.Length(vector));
//set a random length (with a bias)
length = Math.pow(Math.random(), Math.log(inBias)/Math.log(0.5))*inRadius;
vector = V.Scale(vector, length);
//move the vector to the center
vector = V.Add(vector, inCenter);
outM.push(vector);
}
return outM;
};
// return a Matrix of length inCount, where all the members fall within inBounds
M.Box = function(inBounds, inCount)
{
var vector;
var dimensions = inBounds[0].length;
var i, j;
var min, max;
var outM = [];
for(i=0; i<inCount; i++)
{
vector = [];
for(j=0; j<dimensions; j++)
{
min = inBounds[0][j];
max = inBounds[1][j];
vector[j] = min + Math.random()*(max - min);
}
outM.push(vector);
}
return outM;
};
//combine all the matricies in inList into one long Matrix
M.Combine = function(inList)
{
var i, j;
var outM = [];
for(i=0; i<inList.length; i++)
{
for(j=0; j<inList[i].length; j++)
{
outM.push(V.Clone(inList[i][j]));
}
}
return outM;
};
/*
PLEASE NOTE: These padding routines are unique to this library in that they
actually modify the input object(s) rather than returning modified copies!
*/
// add a new component (set to '1') to each member of inM
M.Pad = function(inM)
{
var i;
for(i=0; i<inM.length; i++)
{
inM[i].push(1);
}
return inM;
};
// remove the last component of each memeber of inM
M.Unpad = function(inM)
{
var i;
for(i=0; i<inM.length; i++)
{
inM[i].pop();
}
return inM;
};
// set the last component of each member of inM to 1
M.Repad = function(inM)
{
var i;
var last = inM[0].length-1;
for(i=0; i<inM.length; i++)
{
inM[i][last] = 1;
}
return inM;
};
</script>
<script>
var NN = {};
NN.TrainingSet = {};
NN.TrainingSet.Instances = [];
NN.TrainingSet.Create = function()
{
var obj = {};
obj.Input = [];
obj.Output = [];
obj.Order = [];
NN.TrainingSet.Instances.push(obj);
return obj;
};
NN.TrainingSet.AddPoint = function(inTrainingSet, inType, inData)
{
inTrainingSet.Input.push(inData);
inTrainingSet.Output.push(inType);
inTrainingSet.Order.push(inTrainingSet.Order.length);
};
NN.TrainingSet.AddCloud = function(inTrainingSet, inLabel, inCloud)
{
var i;
for(i=0; i<inCloud.length; i++)
{
NN.TrainingSet.AddPoint(inTrainingSet, inLabel, inCloud[i]);
}
};
NN.TrainingSet.Randomize = function(inTrainingSet)
{
var newOrder = [];
var selection;
while(inTrainingSet.Order.length != 0)
{
selection = Math.floor(inTrainingSet.Order.length * Math.random());
inTrainingSet.Order.splice(selection, 1);
newOrder.push(selection);
}
inTrainingSet.Order = newOrder;
};
NN.Layer = {};
NN.Layer.Create = function(sizeIn, sizeOut)
{
var i;
var min = [];
var max = [];
var obj = {};
sizeIn++;
obj.Forward = {};
for(i=0; i<sizeIn; i++)
{
min.push(-1);
max.push(1);
}
obj.Forward.Matrix = M.Box([min, max], sizeOut);
obj.Forward.StageInput = [];
obj.Forward.StageAffine = [];
obj.Forward.StageSigmoid = [];
obj.Forward.StageDerivative = [];
obj.Backward = {};
obj.Backward.Matrix = M.Transpose(obj.Forward.Matrix);
obj.Backward.StageInput = [];
obj.Backward.StageDerivative = [];
obj.Backward.StageAffine = [];
return obj;
};
NN.Layer.Forward = function(inLayer, inInput)
{
inLayer.Forward.StageInput = M.Pad(inInput); // Pad the input
inLayer.Forward.StageAffine = M.Transform(inLayer.Forward.Matrix, inLayer.Forward.StageInput);
inLayer.Forward.StageSigmoid = M.Sigmoid(inLayer.Forward.StageAffine);
return inLayer.Forward.StageSigmoid;
};
NN.Layer.Error = function(inLayer, inTarget)
{
return M.Subtract(inLayer.Forward.StageSigmoid, inTarget);
};
NN.Layer.Backward = function(inLayer, inInput)
{
/* We need the derivative of the forward pass, but only during the backward pass.
That's why-- even though it "belongs" to the forward pass-- it is being calculated here. */
inLayer.Forward.StageDerivative = M.Derivative(inLayer.Forward.StageSigmoid);
/* This transpose matrix is for sending the error back to a previous layer.
And again, even though it is derived directly from the forward matrix, it is only needed during the backward pass so we calculate it here.*/
inLayer.Backward.Matrix = M.Transpose(inLayer.Forward.Matrix);
/* When the error vector arrives at a layer, it always needs to be multiplied (read 'supressed') by the derivative of
what the layer output earlier during the forward pass.
So despite its name, Backward.StageDerivative contains the result of this *multiplication* and not some new derivative calculation.*/
inLayer.Backward.StageInput = inInput;
inLayer.Backward.StageDerivative = M.Multiply(inLayer.Backward.StageInput, inLayer.Forward.StageDerivative);
inLayer.Backward.StageAffine = M.Transform(inLayer.Backward.Matrix, inLayer.Backward.StageDerivative);
return M.Unpad(inLayer.Backward.StageAffine);// Unpad the output
};
NN.Layer.Adjust = function(inLayer, inLearningRate)
{
var deltas;
var vector;
var scalar;
var i, j;
for(i=0; i<inLayer.Forward.StageInput.length; i++)
{
deltas = M.Outer(inLayer.Forward.StageInput[i], inLayer.Backward.StageDerivative[i]);
deltas = M.Scale(deltas, inLearningRate);
inLayer.Forward.Matrix = M.Subtract(inLayer.Forward.Matrix, deltas);
}
};
NN.Layer.Stochastic = function(inLayer, inTrainingSet, inIterations)
{
/* this method is ONLY for testing individual layers, and does not translate to network-level training */
var i, j;
var current;
var error;
for(i=0; i<inIterations; i++)
{
NN.TrainingSet.Randomize(inTrainingSet);
for(j=0; j<inTrainingSet.Order.length; j++)
{
current = inTrainingSet.Order[j];
NN.Layer.Forward(inLayer, [inTrainingSet.Input[current]]);
error = M.Subtract(inLayer.Forward.StageSigmoid, [inTrainingSet.Output[current]]);
NN.Layer.Backward(inLayer, error);
NN.Layer.Adjust(inLayer, 0.1);
}
}
};
NN.Network = {};
NN.Network.Instances = [];
NN.Network.Create = function()
{
var obj = {};
var i;
obj.Layers = [];
obj.LearningRate = 0.1;
obj.Error = [];
for(i=0; i<arguments.length-1; i++)
{
obj.Layers.push(NN.Layer.Create(arguments[i], arguments[i+1]));
}
NN.Network.Instances.push(obj);
return obj;
};
NN.Network.Observe = function(inNetwork, inBatch)
{
var input = M.Clone(inBatch);
var i;
for(i=0; i<inNetwork.Layers.length; i++)
{
input = NN.Layer.Forward(inNetwork.Layers[i], input);
}
return inNetwork.Layers[inNetwork.Layers.length-1].Forward.StageSigmoid;
};
NN.Network.Error = function(inNetwork, inTraining)
{
return M.Subtract(inNetwork.Layers[inNetwork.Layers.length-1].Forward.StageSigmoid, inTraining);
};
NN.Network.Learn = function(inNetwork, inError)
{
var input = inError;
var i;
for(i=inNetwork.Layers.length-1; i>=0; i--)
{
input = NN.Layer.Backward(inNetwork.Layers[i], input);
NN.Layer.Adjust(inNetwork.Layers[i], inNetwork.LearningRate);
}
};
NN.Network.Batch = function(inNetwork, inTrainingSet, inIterations)
{
var i;
for(i=0; i<inIterations; i++)
{
NN.Network.Observe(inNetwork, inTrainingSet.Input);
inNetwork.Error = NN.Network.Error(inNetwork, inTrainingSet.Output)
NN.Network.Learn(inNetwork, inNetwork.Error);
}
};
NN.Network.Stochastic = function(inNetwork, inTrainingSet, inIterations)
{
var i, j;
var current;
for(i=0; i<inIterations; i++)
{
NN.TrainingSet.Randomize(inTrainingSet);
for(j=0; j<inTrainingSet.Order.length; j++)
{
current = inTrainingSet.Order[j];
NN.Network.Observe(inNetwork, [inTrainingSet.Input[current]]);
inNetwork.Error = NN.Network.Error(inNetwork, [inTrainingSet.Output[current]]);
NN.Network.Learn(inNetwork, inNetwork.Error);
}
}
};
</script>
<script>
let matrix1 = [
[-0.43662948305036675, -0.368590640707799, -0.23227179558890843],
[-0.004292653969505622, 0.38670055222186317, -0.2478421495365568],
[0.738181366836224, 0.3389203747353555, 0.4920200816404332]
];
let matrix2 = [
[0.7098703863463034, 0.35485944251238033, 0.7642849892333241, 0.03046174288491077],
[-0.30655426258144347, 0.45509633551425077, -0.5013795222004322, -0.3421292736637427]
];
let input = [
[ 0.1, 0.05],
[ 0.0, -0.06],
[ 0.99, 0.85],
[ 1.2, 1.05]
];
let output = [
[1, 0],
[1, 0],
[0, 1],
[0, 1]
];
let nn1 = NN.Network.Create(2, 3, 2);
nn1.Layers[0].Forward.Matrix = matrix1;
nn1.Layers[1].Forward.Matrix = matrix2;
nn1.LearningRate = 0.1;
//let logLayers = inNN => inNN.Layers.forEach(L=>console.log(L.Forward.Matrix));
NN.Network.Batch(nn1, {Input:input, Output:output}, 1000);
console.log(NN.Network.Observe(nn1, input));
</script>

11
index.js Normal file
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@ -0,0 +1,11 @@
import { Build, Learn, Label } from "./nn.ts";
const inputs = [[0.10, 0.50], [0.00, 0.06], [0.99, 0.85], [0.80, 0.95]];
const labels = [[ 0, 1 ], [ 0, 1 ], [ 1, 0 ], [ 1, 0 ]];
const layers = Build(2, 5, 2);
const errors = Learn(inputs, layers, labels, 1000, 0.1);
const output = Label(inputs, layers);
console.log("error after training:", errors);
console.log("re-classified inputs:", output);

3
m.ts
View File

@ -31,7 +31,8 @@ const Methods = {
Box: (inV1:Cloud.V, inV2:Cloud.V, inCount:number):Cloud.M=> Methods.Iterate.Loop(inV1.length, inCount, i=> inV1[i]+(inV2[i]-inV1[i])*Math.random()),
Transpose: (inCloud:Cloud.M):Cloud.M=> Methods.Iterate.Loop(inCloud.length, inCloud[0].length, (i, row)=> inCloud[i][row]),
Outer: (inV1:Cloud.V, inV2:Cloud.V):Cloud.M=> Methods.Iterate.Loop(inV1.length, inV2.length, (i, row)=> inV1[i]*inV2[row]),
Clone: (inCloud:Cloud.M):Cloud.M=> Methods.Iterate.Edit(inCloud, i=> i)
Clone: (inCloud:Cloud.M):Cloud.M=> Methods.Iterate.Edit(inCloud, i=> i),
Padded: (inCloud:Cloud.M):Cloud.M=> inCloud.map((row:Cloud.V)=> [...row, 1])
},
Mutate:
{

14
methods.md
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@ -1,14 +0,0 @@
box(boundingBox, count) // done
transpose(inMatrix) // done
outer(inv1, inv2) // done
clone(inCloud) // done
pad(inCloud) // done
unpad(inCloud) // done
transform(inCloud, inMatrix) // done
sigmoid(inCloud) // 1/(1+e^x) // done
derivative(inCloud) // x*(1-x) // done
scale(inCloud1, inV) // done
subtract(inCloud1, inCloud2) // done
multiply(inCloud1, inCloud2) // done

5
nn.test.js
View File

@ -17,8 +17,9 @@ Deno.test("NN.Split", ()=>
assert(input);
assert(output);
assertEquals(input.length, output.length, "data split into equal input and output");
console.log(output);
assertEquals(input[0].length, 3, "padded input");
assertEquals(input[0].length, 2, "unpadded input");
assertEquals(output[0].length, 2, "unpadded output");
});
@ -27,7 +28,7 @@ Deno.test("NN.Build", ()=>
layers = Build(2, 5, 2);
assertEquals(layers.length, 2, "correct number of matrices");
assertEquals(layers[0][0].length, input[0].length, "input: padded input");
assertEquals(layers[0][0].length, input[0].length+1, "input: padded input");
assertEquals(layers[0].length, 5, "input: unpadded output");
assertEquals(layers[1][0].length, 6, "hidden: padded input");

10
nn.ts
View File

@ -40,10 +40,8 @@ const Split = (inTrainingSet:Cloud.M, inHeaderLabel:Cloud.V, inHeaderKeep:Cloud.
}
inTrainingSet.forEach((row:Cloud.V):void =>
{
let vectorData = [ ...inHeaderKeep.map((i:number)=>row[i]), 1];
let vectorLabel = inHeaderLabel.map((i:number)=>row[i])
data.push( vectorData );
label.push( vectorLabel );
data.push( inHeaderKeep.map((i:number)=>row[i]) );
label.push( inHeaderLabel.map((i:number)=>row[i]) );
});
return [ data, label ];
};
@ -60,7 +58,7 @@ const Build = (...inLayers:Array<number>):N =>
};
const Label = (inData:Cloud.M, inLayers:N):Cloud.M =>
{
let stages:N = Forward(inData, inLayers);
let stages:N = Forward(M.Create.Padded(inData), inLayers);
return stages[stages.length-1];
};
const Learn = (inData:Cloud.M, inLayers:N, inLabels:Cloud.M, inIterations:number, inRate:number):Cloud.M =>
@ -68,7 +66,7 @@ const Learn = (inData:Cloud.M, inLayers:N, inLabels:Cloud.M, inIterations:number
let stages:N = [];
for(let i=0; i<inIterations; i++)
{
stages = Forward(inData, inLayers);
stages = Forward(M.Create.Padded(inData), inLayers);
Backward(stages, inLayers, inLabels, inRate);
}
return M.Batch.Subtract(stages[stages.length-1], inLabels);

211
nn_old.js
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@ -1,211 +0,0 @@
var NN = {};
NN.TrainingSet = {};
NN.TrainingSet.Instances = [];
NN.TrainingSet.Create = function()
{
var obj = {};
obj.Input = [];
obj.Output = [];
obj.Order = [];
NN.TrainingSet.Instances.push(obj);
return obj;
};
NN.TrainingSet.AddPoint = function(inTrainingSet, inType, inData)
{
inTrainingSet.Input.push(inData);
inTrainingSet.Output.push(inType);
inTrainingSet.Order.push(inTrainingSet.Order.length);
};
NN.TrainingSet.AddCloud = function(inTrainingSet, inLabel, inCloud)
{
var i;
for(i=0; i<inCloud.length; i++)
{
NN.TrainingSet.AddPoint(inTrainingSet, inLabel, inCloud[i]);
}
};
NN.TrainingSet.Randomize = function(inTrainingSet)
{
var newOrder = [];
var selection;
while(inTrainingSet.Order.length != 0)
{
selection = Math.floor(inTrainingSet.Order.length * Math.random());
inTrainingSet.Order.splice(selection, 1);
newOrder.push(selection);
}
inTrainingSet.Order = newOrder;
};
NN.Layer = {};
NN.Layer.Create = function(sizeIn, sizeOut)
{
var i;
var min = [];
var max = [];
var obj = {};
sizeIn++;
obj.Forward = {};
for(i=0; i<sizeIn; i++)
{
min.push(-1);
max.push(1);
}
obj.Forward.Matrix = M.Box([min, max], sizeOut);
obj.Forward.StageInput = [];
obj.Forward.StageAffine = [];
obj.Forward.StageSigmoid = [];
obj.Forward.StageDerivative = [];
obj.Backward = {};
obj.Backward.Matrix = M.Transpose(obj.Forward.Matrix);
obj.Backward.StageInput = [];
obj.Backward.StageDerivative = [];
obj.Backward.StageAffine = [];
return obj;
};
NN.Layer.Forward = function(inLayer, inInput)
{
inLayer.Forward.StageInput = M.Pad(inInput); // Pad the input
inLayer.Forward.StageAffine = M.Transform(inLayer.Forward.Matrix, inLayer.Forward.StageInput);
inLayer.Forward.StageSigmoid = M.Sigmoid(inLayer.Forward.StageAffine);
return inLayer.Forward.StageSigmoid;
};
NN.Layer.Error = function(inLayer, inTarget)
{
return M.Subtract(inLayer.Forward.StageSigmoid, inTarget);
};
NN.Layer.Backward = function(inLayer, inInput)
{
/* We need the derivative of the forward pass, but only during the backward pass.
That's why-- even though it "belongs" to the forward pass-- it is being calculated here. */
inLayer.Forward.StageDerivative = M.Derivative(inLayer.Forward.StageSigmoid);
/* This transpose matrix is for sending the error back to a previous layer.
And again, even though it is derived directly from the forward matrix, it is only needed during the backward pass so we calculate it here.*/
inLayer.Backward.Matrix = M.Transpose(inLayer.Forward.Matrix);
/* When the error vector arrives at a layer, it always needs to be multiplied (read 'supressed') by the derivative of
what the layer output earlier during the forward pass.
So despite its name, Backward.StageDerivative contains the result of this *multiplication* and not some new derivative calculation.*/
inLayer.Backward.StageInput = inInput;
inLayer.Backward.StageDerivative = M.Multiply(inLayer.Backward.StageInput, inLayer.Forward.StageDerivative);
inLayer.Backward.StageAffine = M.Transform(inLayer.Backward.Matrix, inLayer.Backward.StageDerivative);
return M.Unpad(inLayer.Backward.StageAffine);// Unpad the output
};
NN.Layer.Adjust = function(inLayer, inLearningRate)
{
var deltas;
var vector;
var scalar;
var i, j;
for(i=0; i<inLayer.Forward.StageInput.length; i++)
{
deltas = M.Outer(inLayer.Forward.StageInput[i], inLayer.Backward.StageDerivative[i]);
deltas = M.Scale(deltas, inLearningRate);
inLayer.Forward.Matrix = M.Subtract(inLayer.Forward.Matrix, deltas);
}
};
NN.Layer.Stochastic = function(inLayer, inTrainingSet, inIterations)
{
/* this method is ONLY for testing individual layers, and does not translate to network-level training */
var i, j;
var current;
var error;
for(i=0; i<inIterations; i++)
{
NN.TrainingSet.Randomize(inTrainingSet);
for(j=0; j<inTrainingSet.Order.length; j++)
{
current = inTrainingSet.Order[j];
NN.Layer.Forward(inLayer, [inTrainingSet.Input[current]]);
error = M.Subtract(inLayer.Forward.StageSigmoid, [inTrainingSet.Output[current]]);
NN.Layer.Backward(inLayer, error);
NN.Layer.Adjust(inLayer, 0.1);
}
}
};
NN.Network = {};
NN.Network.Instances = [];
NN.Network.Create = function()
{
var obj = {};
var i;
obj.Layers = [];
obj.LearningRate = 0.8;
obj.Error = [];
for(i=0; i<arguments.length-1; i++)
{
obj.Layers.push(NN.Layer.Create(arguments[i], arguments[i+1]));
}
NN.Network.Instances.push(obj);
return obj;
};
NN.Network.Observe = function(inNetwork, inBatch)
{
var input = M.Clone(inBatch);
var i;
for(i=0; i<inNetwork.Layers.length; i++)
{
input = NN.Layer.Forward(inNetwork.Layers[i], input);
}
return inNetwork.Layers[inNetwork.Layers.length-1].Forward.StageSigmoid;
};
NN.Network.Error = function(inNetwork, inTraining)
{
return M.Subtract(inNetwork.Layers[inNetwork.Layers.length-1].Forward.StageSigmoid, inTraining);
};
NN.Network.Learn = function(inNetwork, inError)
{
var input = inError;
var i;
for(i=inNetwork.Layers.length-1; i>=0; i--)
{
input = NN.Layer.Backward(inNetwork.Layers[i], input);
NN.Layer.Adjust(inNetwork.Layers[i], inNetwork.LearningRate);
}
};
NN.Network.Batch = function(inNetwork, inTrainingSet, inIterations)
{
var i;
for(i=0; i<inIterations; i++)
{
NN.Network.Observe(inNetwork, inTrainingSet.Input);
inNetwork.Error = NN.Network.Error(inNetwork, inTrainingSet.Output)
NN.Network.Learn(inNetwork, inNetwork.Error);
}
};
NN.Network.Stochastic = function(inNetwork, inTrainingSet, inIterations)
{
var i, j;
var current;
for(i=0; i<inIterations; i++)
{
NN.TrainingSet.Randomize(inTrainingSet);
for(j=0; j<inTrainingSet.Order.length; j++)
{
current = inTrainingSet.Order[j];
NN.Network.Observe(inNetwork, [inTrainingSet.Input[current]]);
inNetwork.Error = NN.Network.Error(inNetwork, [inTrainingSet.Output[current]]);
NN.Network.Learn(inNetwork, inNetwork.Error);
}
}
};