Dietmar

@Mark-XP Here is a new, really nice program for to find the Multipliers of 3. It uses ONLY the Java Standard Bibliothek. So it runs on any compi. In detail you can check and test via this program, how a Neural Network works. And you see also, what happens, when you give to the program a number, which it was not trained for. Oh...looks not so good for SkyNet with Terminator Dietmar package multiof3; import java.util.Arrays; import java.util.Random; import java.util.Random; public class Multiof3 { private final int numInputNodes = 3; private final int numHiddenNodes = 2; private final int numOutputNodes = 1; private final double learningRate = 0.1; private final int numEpochs = 200000; private final double errorThreshold = 0.01; private double[][] inputToHiddenWeights; private double[][] hiddenToOutputWeights; private double[] hiddenBiases; private double[] outputBiases; public Multiof3() { Random random = new Random(); inputToHiddenWeights = new double[numInputNodes][numHiddenNodes]; hiddenToOutputWeights = new double[numHiddenNodes][numOutputNodes]; hiddenBiases = new double[numHiddenNodes]; outputBiases = new double[numOutputNodes]; for (int i = 0; i < numInputNodes; i++) { for (int j = 0; j < numHiddenNodes; j++) { inputToHiddenWeights[i][j] = random.nextDouble() - 0.5; } } for (int i = 0; i < numHiddenNodes; i++) { for (int j = 0; j < numOutputNodes; j++) { hiddenToOutputWeights[i][j] = random.nextDouble() - 0.5; } hiddenBiases[i] = random.nextDouble() - 0.5; } for (int i = 0; i < numOutputNodes; i++) { outputBiases[i] = random.nextDouble() - 0.5; } } public double sigmoid(double x) { return 1.0 / (1.0 + Math.exp(-x)); } public double sigmoidDerivative(double x) { return sigmoid(x) * (1 - sigmoid(x)); } public void train(double[][] trainingInputs, double[] trainingTargets) { for (int epoch = 1; epoch <= numEpochs; epoch++) { double totalError = 0.0; for (int i = 0; i < trainingInputs.length; i++) { double[] input = trainingInputs[i]; double target = trainingTargets[i]; // Forward propagation double[] hiddenOutputs = new double[numHiddenNodes]; for (int j = 0; j < numHiddenNodes; j++) { double weightedSum = 0.0; for (int k = 0; k < numInputNodes; k++) { weightedSum += inputToHiddenWeights[k][j] * input[k]; } hiddenOutputs[j] = sigmoid(weightedSum + hiddenBiases[j]); } double output = 0.0; for (int j = 0; j < numOutputNodes; j++) { double weightedSum = 0.0; for (int k = 0; k < numHiddenNodes; k++) { weightedSum += hiddenToOutputWeights[k][j] * hiddenOutputs[k]; } output = sigmoid(weightedSum + outputBiases[j]); } // Backward propagation double outputError = 0.5 * Math.pow(output - target, 2); // Mean squared error totalError += outputError; double outputDelta = (output - target) * sigmoidDerivative(output); for (int j = 0; j < numOutputNodes; j++) { outputBiases[j] -= learningRate * outputDelta; for (int k = 0; k < numHiddenNodes; k++) { hiddenToOutputWeights[k][j] -= learningRate * outputDelta * hiddenOutputs[k]; } } double[] hiddenDeltas = new double[numHiddenNodes]; for (int j = 0; j < numHiddenNodes; j++) { double weightedSum = 0.0; for (int k = 0; k < numOutputNodes; k++) { weightedSum += hiddenToOutputWeights[j][k] * outputDelta; } hiddenDeltas[j] = sigmoidDerivative(hiddenOutputs[j]) * weightedSum; } for (int j = 0; j < numHiddenNodes; j++) { hiddenBiases[j] -= learningRate * hiddenDeltas[j]; for (int k = 0; k < numInputNodes; k++) { inputToHiddenWeights[k][j] -= learningRate * hiddenDeltas[j] * input[k]; } } } totalError /= trainingInputs.length; if (epoch % 1000 == 0) { System.out.println("Epoch: " + epoch + ", Error: " + totalError); } if (totalError <= errorThreshold) { System.out.println("Training complete. Total error: " + totalError); break; } } } public double predict(double[] input) { double[] hiddenOutputs = new double[numHiddenNodes]; for (int j = 0; j < numHiddenNodes; j++) { double weightedSum = 0.0; for (int k = 0; k < numInputNodes; k++) { weightedSum += inputToHiddenWeights[k][j] * input[k]; } hiddenOutputs[j] = sigmoid(weightedSum + hiddenBiases[j]); } double output = 0.0; for (int j = 0; j < numOutputNodes; j++) { double weightedSum = 0.0; for (int k = 0; k < numHiddenNodes; k++) { weightedSum += hiddenToOutputWeights[k][j] * hiddenOutputs[k]; } output = sigmoid(weightedSum + outputBiases[j]); } return output; } public static void main(String[] args) { // Example usage of the neural network double[][] trainingInputs = {{0, 0, 0}, {0, 0, 1}, {0, 1, 0}, {0, 1, 1}, {1, 0, 0}, {1, 0, 1}, {1, 1, 0}, {1, 1, 1}}; double[] trainingTargets = {1, 0, 0, 1, 0, 0, 1, 0 }; Multiof3 nn = new Multiof3(); nn.train(trainingInputs, trainingTargets); System.out.println("Prediction for [0, 0, 0]: " + nn.predict(new double[]{0, 0, 0})); System.out.println("Prediction for [0, 0, 1]: " + nn.predict(new double[]{0, 0, 1})); System.out.println("Prediction for [0, 1, 0]: " + nn.predict(new double[]{0, 1, 0})); System.out.println("Prediction for [0, 1, 1]: " + nn.predict(new double[]{0, 1, 1})); System.out.println("Prediction for [1, 0, 0]: " + nn.predict(new double[]{1, 0, 0})); System.out.println("Prediction for [1, 0, 1]: " + nn.predict(new double[]{1, 0, 1})); System.out.println("Prediction for [1, 1, 0]: " + nn.predict(new double[]{1, 1, 0})); System.out.println("Prediction for [1, 1, 1]: " + nn.predict(new double[]{1, 1, 1})); } }

Even with 1000 of data, a Neural Network has BIG problems, to understand, if a given number is a Multiplier of 3 or not Dietmar package bine; import org.neuroph.core.data.DataSet; import org.neuroph.core.data.DataSetRow; import org.neuroph.nnet.MultiLayerPerceptron; import org.neuroph.util.TransferFunctionType; import java.util.Scanner; public class Bine { private static final int INPUT_SIZE = 20; private static final int OUTPUT_SIZE = 2; private static final String YES_LABEL = "y"; private static final String NO_LABEL = "n"; public static void main(String[] args) { int[] multiplesOfThree = generateMultiplesOfThree(1000); // Create training set DataSet trainingSet = new DataSet(INPUT_SIZE, OUTPUT_SIZE); for (int i = 0; i < INPUT_SIZE; i++) { String binaryInput = padZeros(Integer.toBinaryString(multiplesOfThree[i])); double[] inputArray = convertToDoubleArray(binaryInput); double[] outputArray = {1, 0}; // default output is "yes" as all multiples of 3 are "yes" // Add training set row DataSetRow trainingSetRow = new DataSetRow(inputArray, outputArray); trainingSet.add(trainingSetRow); } // Create neural network MultiLayerPerceptron neuralNetwork = new MultiLayerPerceptron(TransferFunctionType.SIGMOID, INPUT_SIZE, 20,20,20, OUTPUT_SIZE); neuralNetwork.learn(trainingSet); System.out.println("Multiplier of 3 Classifier"); System.out.println("Enter a number between 0 and 1048575 (or 'q' to quit): "); Scanner scanner = new Scanner(System.in); while (scanner.hasNext()) { String input = scanner.nextLine(); if (input.equalsIgnoreCase("q")) { break; } try { int number = Integer.parseInt(input); String binaryInput = padZeros(Integer.toBinaryString(number)); double[] inputArray = convertToDoubleArray(binaryInput); neuralNetwork.setInput(inputArray); neuralNetwork.calculate(); double[] outputArray = neuralNetwork.getOutput(); String prediction = outputArray[0] > outputArray[1] ? YES_LABEL : NO_LABEL; System.out.println("Input: " + number); System.out.println("Binary Input: " + binaryInput); System.out.println("Output: " + outputArray[0] + " " + outputArray[1]); System.out.println("Prediction: " + prediction); System.out.print("Is " + number + " a multiplier of 3? (Enter 'yes' or 'no'): "); String actualLabel = scanner.nextLine().toLowerCase(); // Update the training set with the actual label provided by the user double[] actualOutput = {0, 0}; if (actualLabel.equals(YES_LABEL)) { actualOutput[0] = 1; } else if (actualLabel.equals(NO_LABEL)) { actualOutput[1] = 1; } else { System.out.println("Invalid input. Please enter 'yes' or 'no'."); continue; } trainingSet.add(new DataSetRow(inputArray, actualOutput)); neuralNetwork.learn(trainingSet); System.out.println("Enter a number between 0 and 1048575 (or 'q' to quit): "); } catch (NumberFormatException e) { System.out.println("Invalid input. Please enter a valid number or 'q' to quit."); } } System.out.println("Exiting..."); } private static int[] generateMultiplesOfThree(int count) { int[] multiples = new int[count]; for (int i = 0; i < count; i++) { multiples[i] = i * 3; } return multiples; } private static String padZeros(String binaryString) { int padSize = INPUT_SIZE - binaryString.length(); StringBuilder stringBuilder = new StringBuilder(); for (int i = 0; i < padSize; i++) { stringBuilder.append("0"); } stringBuilder.append(binaryString); return stringBuilder.toString(); } private static double[] convertToDoubleArray(String binaryString) { double[] doubleArray = new double[binaryString.length()]; for (int i = 0; i < binaryString.length(); i++) { doubleArray[i] = Double.parseDouble(String.valueOf(binaryString.charAt(i))); } return doubleArray; } } run: Multiplier of 3 Classifier Enter a number between 0 and 1048575 (or 'q' to quit): 0 Input: 0 Binary Input: 00000000000000000000 Output: 0.9100712334367754 0.09189905889860366 Prediction: y Is 0 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 1 Input: 1 Binary Input: 00000000000000000001 Output: 0.9199956082571938 0.08266183058418203 Prediction: y Is 1 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 1 Input: 1 Binary Input: 00000000000000000001 Output: 0.3337935010084839 0.6956108756117879 Prediction: n Is 1 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 2 Input: 2 Binary Input: 00000000000000000010 Output: 0.9796338688814583 0.01525102284028862 Prediction: y Is 2 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 3 Input: 3 Binary Input: 00000000000000000011 Output: 0.8238038968341835 0.17195128283031036 Prediction: y Is 3 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 4 Input: 4 Binary Input: 00000000000000000100 Output: 0.9822951015347582 0.016470688185103253 Prediction: y Is 4 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 5 Input: 5 Binary Input: 00000000000000000101 Output: 0.001050534727176706 0.9987121963998032 Prediction: n Is 5 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 6 Input: 6 Binary Input: 00000000000000000110 Output: 0.839733051941253 0.163455141466426 Prediction: y Is 6 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 7 Input: 7 Binary Input: 00000000000000000111 Output: 0.9422758274098985 0.06609906216555786 Prediction: y Is 7 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 7 Input: 7 Binary Input: 00000000000000000111 Output: 0.1353661273127858 0.8479548991014965 Prediction: n Is 7 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 8 Input: 8 Binary Input: 00000000000000001000 Output: 0.9927541716568125 0.009574226211425924 Prediction: y Is 8 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 9 Input: 9 Binary Input: 00000000000000001001 Output: 0.974322603589938 0.02800165260840982 Prediction: y Is 9 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 10 Input: 10 Binary Input: 00000000000000001010 Output: 0.003214245556632083 0.9974629414600507 Prediction: n Is 10 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 11 Input: 11 Binary Input: 00000000000000001011 Output: 0.9538310639638198 0.049426501469771754 Prediction: y Is 11 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 12 Input: 12 Binary Input: 00000000000000001100 Output: 0.9305042545208035 0.06093073932423666 Prediction: y Is 12 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 13 Input: 13 Binary Input: 00000000000000001101 Output: 0.031104660029981284 0.967017516492239 Prediction: n Is 13 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 14 Input: 14 Binary Input: 00000000000000001110 Output: 0.7584994116416115 0.23504684198291034 Prediction: y Is 14 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 15 Input: 15 Binary Input: 00000000000000001111 Output: 0.8893613013013443 0.10890092946550244 Prediction: y Is 15 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 16 Input: 16 Binary Input: 00000000000000010000 Output: 0.9916013043686388 0.008933010479803792 Prediction: y Is 16 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 16 Input: 16 Binary Input: 00000000000000010000 Output: 0.35652098277360933 0.5526217281816489 Prediction: n Is 16 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 17 Input: 17 Binary Input: 00000000000000010001 Output: 0.48630373725336073 0.5024843160185609 Prediction: n Is 17 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 18 Input: 18 Binary Input: 00000000000000010010 Output: 0.9261826400724928 0.08958856435275989 Prediction: y Is 18 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 19 Input: 19 Binary Input: 00000000000000010011 Output: 0.8620823020896886 0.163939531835348 Prediction: y Is 19 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 20 Input: 20 Binary Input: 00000000000000010100 Output: 0.3351872280028068 0.6478808694200352 Prediction: n Is 20 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 21 Input: 21 Binary Input: 00000000000000010101 Output: 0.7904427907287952 0.23576855466040111 Prediction: y Is 21 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 22 Input: 22 Binary Input: 00000000000000010110 Output: 0.8170613517651504 0.20645015903126232 Prediction: y Is 22 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 22 Input: 22 Binary Input: 00000000000000010110 Output: 0.22787401245457897 0.7441538560501173 Prediction: n Is 22 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 23 Input: 23 Binary Input: 00000000000000010111 Output: 0.1339085286870765 0.8469448145925296 Prediction: n Is 23 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 24 Input: 24 Binary Input: 00000000000000011000 Output: 0.8874061486258907 0.11497359351313596 Prediction: y Is 24 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 25 Input: 25 Binary Input: 00000000000000011001 Output: 0.15755045584912372 0.8091783496834866 Prediction: n Is 25 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 26 Input: 26 Binary Input: 00000000000000011010 Output: 0.03925126560699438 0.9715306109005235 Prediction: n Is 26 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 27 Input: 27 Binary Input: 00000000000000011011 Output: 0.9559097639458656 0.05095360729159218 Prediction: y Is 27 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 28 Input: 28 Binary Input: 00000000000000011100 Output: 0.45200690232813 0.5357941076078971 Prediction: n Is 28 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 29 Input: 29 Binary Input: 00000000000000011101 Output: 0.12687961662377373 0.8584768579494491 Prediction: n Is 29 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 30 Input: 30 Binary Input: 00000000000000011110 Output: 0.9224716526513721 0.0858270690719063 Prediction: y Is 30 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 31 Input: 31 Binary Input: 00000000000000011111 Output: 0.49774812656404066 0.5025265565285598 Prediction: n Is 31 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 32 Input: 32 Binary Input: 00000000000000100000 Output: 0.9359186285571272 0.08614560640060934 Prediction: y Is 32 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 33 Input: 33 Binary Input: 00000000000000100001 Output: 0.9603041500915385 0.047485514235209095 Prediction: y Is 33 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 34 Input: 34 Binary Input: 00000000000000100010 Output: 0.9239103288560171 0.07854883505186429 Prediction: y Is 34 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 34 Input: 34 Binary Input: 00000000000000100010 Output: 0.19781752980316994 0.7858325722826717 Prediction: n Is 34 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 35 Input: 35 Binary Input: 00000000000000100011 Output: 0.28770592455358457 0.7156871726928946 Prediction: n Is 35 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 36 Input: 36 Binary Input: 00000000000000100100 Output: 0.9236156143759313 0.08846758473491223 Prediction: y Is 36 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 37 Input: 37 Binary Input: 00000000000000100101 Output: 0.23446107024438664 0.8250653732662508 Prediction: n Is 37 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 38 Input: 38 Binary Input: 00000000000000100110 Output: 0.051438331817040515 0.9437063918873614 Prediction: n Is 38 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 39 Input: 39 Binary Input: 00000000000000100111 Output: 0.9762792364704111 0.028936103018579736 Prediction: y Is 39 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 40 Input: 40 Binary Input: 00000000000000101000 Output: 0.1432548644088406 0.8355017022220126 Prediction: n Is 40 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 41 Input: 41 Binary Input: 00000000000000101001 Output: 0.17347697719232452 0.8178385982490991 Prediction: n Is 41 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 42 Input: 42 Binary Input: 00000000000000101010 Output: 0.9392881001757781 0.05788579216431461 Prediction: y Is 42 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 43 Input: 43 Binary Input: 00000000000000101011 Output: 0.29258802916394 0.6875516289760418 Prediction: n Is 43 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 44 Input: 44 Binary Input: 00000000000000101100 Output: 0.035499036517101325 0.9602535581278479 Prediction: n Is 44 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 45 Input: 45 Binary Input: 00000000000000101101 Output: 0.9760318272683148 0.029261784923761934 Prediction: y Is 45 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 46 Input: 46 Binary Input: 00000000000000101110 Output: 0.040685573799271714 0.9537492032509323 Prediction: n Is 46 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 47 Input: 47 Binary Input: 00000000000000101111 Output: 0.11327853160003044 0.883969734357003 Prediction: n Is 47 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 48 Input: 48 Binary Input: 00000000000000110000 Output: 0.6700494087039256 0.3574408802320197 Prediction: y Is 48 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 49 Input: 49 Binary Input: 00000000000000110001 Output: 0.6253087315720828 0.4108396596288409 Prediction: y Is 49 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 49 Input: 49 Binary Input: 00000000000000110001 Output: 0.12875234268833807 0.8717714013421612 Prediction: n Is 49 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 50 Input: 50 Binary Input: 00000000000000110010 Output: 0.6459714506419655 0.36180099233049323 Prediction: y Is 50 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 51 Input: 51 Binary Input: 00000000000000110011 Output: 0.16347818046005394 0.8312737613229517 Prediction: n Is 51 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 51 Input: 51 Binary Input: 00000000000000110011 Output: 0.9160031128700459 0.09356523417958804 Prediction: y Is 51 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 52 Input: 52 Binary Input: 00000000000000110100 Output: 0.8718983144433389 0.14481795320289975 Prediction: y Is 52 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 53 Input: 53 Binary Input: 00000000000000110101 Output: 0.03712895375449015 0.9615538502928446 Prediction: n Is 53 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 54 Input: 54 Binary Input: 00000000000000110110 Output: 0.34792203463078675 0.6476806112182635 Prediction: n Is 54 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 54 Input: 54 Binary Input: 00000000000000110110 Output: 0.9337528194925984 0.0734701302415432 Prediction: y Is 54 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 55 Input: 55 Binary Input: 00000000000000110111 Output: 0.8401025073226862 0.17624247029627635 Prediction: y Is 55 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 56 Input: 56 Binary Input: 00000000000000111000 Output: 0.4376921127204153 0.5288647412543214 Prediction: n Is 56 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 57 Input: 57 Binary Input: 00000000000000111001 Output: 0.35784229098837006 0.639184495428392 Prediction: n Is 57 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 58 Input: 58 Binary Input: 00000000000000111010 Output: 0.3275547600857225 0.6365719335860395 Prediction: n Is 58 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 59 Input: 59 Binary Input: 00000000000000111011 Output: 0.5212998937295816 0.46370447443571056 Prediction: y Is 59 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 60 Input: 60 Binary Input: 00000000000000111100 Output: 0.49494094163395463 0.515164077408551 Prediction: n Is 60 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 61 Input: 61 Binary Input: 00000000000000111101 Output: 0.12983194965647718 0.8751486276898385 Prediction: n Is 61 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 62 Input: 62 Binary Input: 00000000000000111110 Output: 0.1354627962453532 0.8508357725879964 Prediction: n Is 62 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 63 Input: 63 Binary Input: 00000000000000111111 Output: 0.8580775772153315 0.1548940737326462 Prediction: y Is 63 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 64 Input: 64 Binary Input: 00000000000001000000 Output: 0.6689906035307732 0.28523305336324334 Prediction: y Is 64 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 64 Input: 64 Binary Input: 00000000000001000000 Output: 0.09024607528015935 0.8855227387349809 Prediction: n Is 64 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 65 Input: 65 Binary Input: 00000000000001000001 Output: 0.0014028229343147122 0.9979661620811804 Prediction: n Is 65 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 66 Input: 66 Binary Input: 00000000000001000010 Output: 0.071277062085114 0.9316594962445945 Prediction: n Is 66 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 66 Input: 66 Binary Input: 00000000000001000010 Output: 0.7639158273279077 0.23643134493428689 Prediction: y Is 66 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 67 Input: 67 Binary Input: 00000000000001000011 Output: 0.32931192178485597 0.6249807256144181 Prediction: n Is 67 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 68 Input: 68 Binary Input: 00000000000001000100 Output: 0.0015278707240816741 0.997851621652362 Prediction: n Is 68 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 69 Input: 69 Binary Input: 00000000000001000101 Output: 0.004642258291229637 0.9960405384602112 Prediction: n Is 69 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 69 Input: 69 Binary Input: 00000000000001000101 Output: 0.05291105727425499 0.9650080807586029 Prediction: n Is 69 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 69 Input: 69 Binary Input: 00000000000001000101 Output: 0.6308213984022305 0.3873806565698832 Prediction: y Is 69 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 70 Input: 70 Binary Input: 00000000000001000110 Output: 0.11363700854908698 0.8758080479624577 Prediction: n Is 70 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 400000 Input: 400000 Binary Input: 01100001101010000000 Output: 0.4832064917528005 0.4811556109134067 Prediction: y Is 400000 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 400001 Input: 400001 Binary Input: 01100001101010000001 Output: 0.0036193370555938245 0.9946507642044927 Prediction: n Is 400001 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 400002 Input: 400002 Binary Input: 01100001101010000010 Output: 0.7446095173248048 0.23528279571892657 Prediction: y Is 400002 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 400003 Input: 400003 Binary Input: 01100001101010000011 Output: 0.05894585339564528 0.9372440386296929 Prediction: n Is 400003 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 400004 Input: 400004 Binary Input: 01100001101010000100 Output: 0.004140042080300098 0.9940283829617482 Prediction: n Is 400004 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 400005 Input: 400005 Binary Input: 01100001101010000101 Output: 0.14724910196008825 0.8341763303972134 Prediction: n Is 400005 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 400006 Input: 400006 Binary Input: 01100001101010000110 Output: 0.04719732699802866 0.9523921755461555 Prediction: n Is 400006 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 400007 Input: 400007 Binary Input: 01100001101010000111 Output: 0.08964804980246287 0.8901720297744107 Prediction: n Is 400007 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 400008 Input: 400008 Binary Input: 01100001101010001000 Output: 0.8926745955166815 0.09599591040932905 Prediction: y Is 400008 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 400009 Input: 400009 Binary Input: 01100001101010001001 Output: 0.08320620848618612 0.9122336408276123 Prediction: n Is 400009 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 900000 Input: 900000 Binary Input: 11011011101110100000 Output: 0.006660058988903214 0.9932227829445179 Prediction: n Is 900000 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 900000 Input: 900000 Binary Input: 11011011101110100000 Output: 0.9947426011094758 0.005870490518981226 Prediction: y Is 900000 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 900001 Input: 900001 Binary Input: 11011011101110100001 Output: 0.9945251541678684 0.006566273958997189 Prediction: y Is 900001 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 900002 Input: 900002 Binary Input: 11011011101110100010 Output: 0.005198558641792289 0.9947649705403714 Prediction: n Is 900002 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 900003 Input: 900003 Binary Input: 11011011101110100011 Output: 0.05779073219580073 0.9457906343599145 Prediction: n Is 900003 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 900003 Input: 900003 Binary Input: 11011011101110100011 Output: 0.9899582052817851 0.011386698089575481 Prediction: y Is 900003 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 900004 Input: 900004 Binary Input: 11011011101110100100 Output: 0.16576791749479478 0.8626139713512534 Prediction: n Is 900004 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 900005 Input: 900005 Binary Input: 11011011101110100101 Output: 0.9514640691115387 0.05356315464296517 Prediction: y Is 900005 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 900006 Input: 900006 Binary Input: 11011011101110100110 Output: 0.9553406282490174 0.052071081041834284 Prediction: y Is 900006 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 900007 Input: 900007 Binary Input: 11011011101110100111 Output: 0.019674569372234017 0.9831333704771245 Prediction: n Is 900007 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 900008 Input: 900008 Binary Input: 11011011101110101000 Output: 0.0757328021477335 0.9238494722865295 Prediction: n Is 900008 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 900009 Input: 900009 Binary Input: 11011011101110101001 Output: 0.9441941605886921 0.0629870673122703 Prediction: y Is 900009 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit): 1000000 Input: 1000000 Binary Input: 11110100001001000000 Output: 0.0035819148391924077 0.996487210875288 Prediction: n Is 1000000 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 1000001 Input: 1000001 Binary Input: 11110100001001000001 Output: 0.9204871456593733 0.08389017722343028 Prediction: y Is 1000001 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 1000001 Input: 1000001 Binary Input: 11110100001001000001 Output: 0.31750751148746975 0.6944189104683715 Prediction: n Is 1000001 a multiplier of 3? (Enter 'yes' or 'no'): n Enter a number between 0 and 1048575 (or 'q' to quit): 1000002 Input: 1000002 Binary Input: 11110100001001000010 Output: 0.5387750063738229 0.4577310559747821 Prediction: y Is 1000002 a multiplier of 3? (Enter 'yes' or 'no'): y Enter a number between 0 and 1048575 (or 'q' to quit):

@Mark-XP After hard work today, I make this program. May be, it has found something common in Primes! I make a hard train for this Network with the first 1000 primes. And now, it gives some correct answers for small and BIG primes Dietmar package bine; import org.neuroph.core.NeuralNetwork; import org.neuroph.core.data.DataSet; import org.neuroph.core.data.DataSetRow; import org.neuroph.nnet.MultiLayerPerceptron; import org.neuroph.util.TransferFunctionType; import java.util.Scanner; public class Bine { public static void main(String[] args) { // Generate and store the first 1000 prime numbers in an array int[] primeNumbers = generatePrimeNumbers(1000); // Create a multi-layer perceptron neural network with 10 input neurons, 10 hidden neurons, and 2 output neurons NeuralNetwork neuralNetwork = new MultiLayerPerceptron(TransferFunctionType.SIGMOID, 20, 20, 20, 2); // Create a training set to store input-output pairs for training the neural network DataSet trainingSet = new DataSet(20, 2); Scanner scanner = new Scanner(System.in); String inputStr; System.out.println("Prime Number Classifier"); System.out.println("Enter a number between 0 and 1048575 (or 'q' to quit): "); while (!(inputStr = scanner.nextLine()).equalsIgnoreCase("q")) { try { int input = Integer.parseInt(inputStr); // Convert the input number to binary representation String binaryInput = Integer.toBinaryString(input); binaryInput = String.format("%20s", binaryInput).replace(' ', '0'); System.out.println("Input: " + input); System.out.println("Binary Input: " + binaryInput); // Convert the binary input to an array of double values double[] inputArray = new double[20]; for (int i = 0; i < binaryInput.length(); i++) { inputArray[i] = Character.getNumericValue(binaryInput.charAt(i)); } // Fill remaining array elements with 0 for (int i = binaryInput.length(); i < 20; i++) { inputArray[i] = 0; } // Use the trained neural network to make a prediction neuralNetwork.setInput(inputArray); neuralNetwork.calculate(); double[] output = neuralNetwork.getOutput(); System.out.println("Output: " + output[0] + " " + output[1]); // Display the prediction String prediction = output[0] > output[1] ? "Prime" : "Not Prime"; System.out.println("Prediction: " + prediction); // Prompt for user input on whether the input number is actually prime or not System.out.print("Is it prime? (y/n): "); String isPrime = scanner.nextLine(); if (isPrime.equalsIgnoreCase("y")) { // Add the input-output pair to the training set as a prime number DataSetRow trainingSetRow = new DataSetRow(inputArray, new double[]{1, 0}); trainingSet.add(trainingSetRow); } else { // Add the input-output pair to the training set as a non-prime number DataSetRow trainingSetRow = new DataSetRow(inputArray, new double[]{0, 1}); trainingSet.add(trainingSetRow); } // Train the neural network with the updated training set neuralNetwork.learn(trainingSet); System.out.println("Enter a number between 0 and 1048575 (or 'q' to quit): "); } catch (NumberFormatException e) { System.out.println("Invalid input. Please enter a valid number between 0 and 1048575 (or 'q' to quit): "); } } // Save the trained neural network to a file neuralNetwork.save("trained_neural_network.nnet"); System.out.println("Trained neural network saved to file: trained_neural_network.nnet"); System.out.println("Program terminated."); } /** * Generates an array of prime numbers up to a specified limit. * * @param limit The upper limit for prime numbers generation. * @return An array of prime numbers. */ private static int[] generatePrimeNumbers(int limit) { int[] primes = new int[limit]; primes[0] = 2; int count = 1; int num = 3; while (count < limit) { boolean isPrime = true; for (int i = 2; i <= Math.sqrt(num); i++) { if (num % i == 0) { isPrime = false; break; } } if (isPrime) { primes[count] = num; count++; } num += 2; } return primes; } } run: Prime Number Classifier Enter a number between 0 and 1048575 (or 'q' to quit): 7919 Input: 7919 Binary Input: 00000001111011101111 Output: 0.5948178156516414 0.40897487989552267 Prediction: Prime Is it prime? (y/n): y Enter a number between 0 and 1048575 (or 'q' to quit): 7927 Input: 7927 Binary Input: 00000001111011110111 Output: 0.8982498273851647 0.09655551571874396 Prediction: Prime Is it prime? (y/n): y Enter a number between 0 and 1048575 (or 'q' to quit): 7907 Input: 7907 Binary Input: 00000001111011100011 Output: 0.9072894778480928 0.09231869767257159 Prediction: Prime Is it prime? (y/n): y Enter a number between 0 and 1048575 (or 'q' to quit): 7933 Input: 7933 Binary Input: 00000001111011111101 Output: 0.8989077406521399 0.09734911637879708 Prediction: Prime Is it prime? (y/n): y Enter a number between 0 and 1048575 (or 'q' to quit): 7937 Input: 7937 Binary Input: 00000001111100000001 Output: 0.9043350760591787 0.09614736963345205 Prediction: Prime Is it prime? (y/n): y Enter a number between 0 and 1048575 (or 'q' to quit): 1000 Input: 1000 Binary Input: 00000000001111101000 Output: 0.8899254682389591 0.10184634378010479 Prediction: Prime Is it prime? (y/n): n Enter a number between 0 and 1048575 (or 'q' to quit): 1000 Input: 1000 Binary Input: 00000000001111101000 Output: 0.1665975490914435 0.8151083424657837 Prediction: Not Prime Is it prime? (y/n): n Enter a number between 0 and 1048575 (or 'q' to quit): 2000 Input: 2000 Binary Input: 00000000011111010000 Output: 0.28750467198426777 0.6792374064713649 Prediction: Not Prime Is it prime? (y/n): n Enter a number between 0 and 1048575 (or 'q' to quit): 3000 Input: 3000 Binary Input: 00000000101110111000 Output: 0.20588325034563312 0.789819073942458 Prediction: Not Prime Is it prime? (y/n): n Enter a number between 0 and 1048575 (or 'q' to quit): 17389 Input: 17389 Binary Input: 00000100001111101101 Output: 0.12276962636373373 0.8798565969697876 Prediction: Not Prime Is it prime? (y/n): y Enter a number between 0 and 1048575 (or 'q' to quit): 17389 Input: 17389 Binary Input: 00000100001111101101 Output: 0.8110576316091068 0.2032560154260368 Prediction: Prime Is it prime? (y/n): y Enter a number between 0 and 1048575 (or 'q' to quit): 17393 Input: 17393 Binary Input: 00000100001111110001 Output: 0.43852962740457774 0.5431182165605312 Prediction: Not Prime Is it prime? (y/n): y Enter a number between 0 and 1048575 (or 'q' to quit): 17393 Input: 17393 Binary Input: 00000100001111110001 Output: 0.8034172912800364 0.20070059184113184 Prediction: Prime Is it prime? (y/n): y Enter a number between 0 and 1048575 (or 'q' to quit): 104723 Input: 104723 Binary Input: 00011001100100010011 Output: 0.9766085585945041 0.022881199994895813 Prediction: Prime Is it prime? (y/n): y Enter a number between 0 and 1048575 (or 'q' to quit): 104724 Input: 104724 Binary Input: 00011001100100010100 Output: 0.9411592225420404 0.05804579497623357 Prediction: Prime Is it prime? (y/n): n Enter a number between 0 and 1048575 (or 'q' to quit): 104724 Input: 104724 Binary Input: 00011001100100010100 Output: 0.21484292674011074 0.7599731192129849 Prediction: Not Prime Is it prime? (y/n): n Enter a number between 0 and 1048575 (or 'q' to quit): 17401 Input: 17401 Binary Input: 00000100001111111001 Output: 0.8248729136862214 0.19731821352791543 Prediction: Prime Is it prime? (y/n): y Enter a number between 0 and 1048575 (or 'q' to quit): 17402 Input: 17402 Binary Input: 00000100001111111010 Output: 0.25042646141880837 0.7694665916822424 Prediction: Not Prime Is it prime? (y/n): y Enter a number between 0 and 1048575 (or 'q' to quit): 17 Input: 17 Binary Input: 00000000000000010001 Output: 0.9147609290513441 0.07336348559716502 Prediction: Prime Is it prime? (y/n): y Enter a number between 0 and 1048575 (or 'q' to quit): 5 Input: 5 Binary Input: 00000000000000000101 Output: 0.9756104355881474 0.023320270188346374 Prediction: Prime Is it prime? (y/n): y Enter a number between 0 and 1048575 (or 'q' to quit): 1 Input: 1 Binary Input: 00000000000000000001 Output: 0.9532195348828819 0.04238520033787504 Prediction: Prime Is it prime? (y/n): y Enter a number between 0 and 1048575 (or 'q' to quit): 2 Input: 2 Binary Input: 00000000000000000010 Output: 0.6778584923010748 0.28103016635239125 Prediction: Prime Is it prime? (y/n): y Enter a number between 0 and 1048575 (or 'q' to quit): 0 Input: 0 Binary Input: 00000000000000000000 Output: 0.27281379291430097 0.6823362335383929 Prediction: Not Prime Is it prime? (y/n): y Enter a number between 0 and 1048575 (or 'q' to quit): 97 Input: 97 Binary Input: 00000000000001100001 Output: 0.995109554413573 0.005229627558735094 Prediction: Prime Is it prime? (y/n): y Enter a number between 0 and 1048575 (or 'q' to quit): 17401 Input: 17401 Binary Input: 00000100001111111001 Output: 0.9844012869157754 0.018723648793074754 Prediction: Prime Is it prime? (y/n): y Enter a number between 0 and 1048575 (or 'q' to quit): 17400 Input: 17400 Binary Input: 00000100001111111000 Output: 0.428308665635754 0.6069720955083222 Prediction: Not Prime Is it prime? (y/n): n Enter a number between 0 and 1048575 (or 'q' to quit): 17402 Input: 17402 Binary Input: 00000100001111111010 Output: 0.7872204761301146 0.240941722495304 Prediction: Prime Is it prime? (y/n): n

@Mark-XP I think, this is nearly best, what Neural Networks can offer for to find primes Dietmar package bine ; import org.neuroph.core.NeuralNetwork; import org.neuroph.core.data.DataSet; import org.neuroph.core.data.DataSetRow; import org.neuroph.nnet.MultiLayerPerceptron; import org.neuroph.util.TransferFunctionType; import java.io.FileWriter; import java.io.IOException; import java.util.Scanner; public class Bine { private static final String PRIME_FILE_PATH = "prime_numbers.txt"; private static final String NOT_PRIME_FILE_PATH = "not_prime_numbers.txt"; public static void main(String[] args) { // Create a multi-layer perceptron neural network with 10 input neurons, 10 hidden neurons, and 2 output neurons NeuralNetwork neuralNetwork = new MultiLayerPerceptron(TransferFunctionType.SIGMOID, 10, 10, 2); // Create a training set to store input-output pairs for training the neural network DataSet trainingSet = new DataSet(10, 2); Scanner scanner = new Scanner(System.in); String inputStr; System.out.println("Prime Number Classifier"); System.out.println("Enter a number between 0 and 1023 (or 'q' to quit): "); while (!(inputStr = scanner.nextLine()).equalsIgnoreCase("q")) { try { int input = Integer.parseInt(inputStr); // Convert the input number to binary representation String binaryInput = Integer.toBinaryString(input); binaryInput = String.format("%10s", binaryInput).replace(' ', '0'); System.out.println("Input: " + input); System.out.println("Binary Input: " + binaryInput); // Convert the binary input to an array of double values double[] inputArray = new double[10]; for (int i = 0; i < 10; i++) { inputArray[i] = Character.getNumericValue(binaryInput.charAt(i)); } // Use the trained neural network to make a prediction neuralNetwork.setInput(inputArray); neuralNetwork.calculate(); double[] output = neuralNetwork.getOutput(); System.out.println("Output: " + output[0] + " " + output[1]); // Display the prediction String prediction = output[0] > output[1] ? "Prime" : "Not Prime"; System.out.println("Prediction: " + prediction); // Prompt for user input on whether the input number is actually prime or not System.out.print("Is it prime? (y/n): "); String isPrime = scanner.nextLine(); if (isPrime.equalsIgnoreCase("y")) { // Add the input-output pair to the training set as a prime number DataSetRow trainingSetRow = new DataSetRow(inputArray, new double[]{1, 0}); trainingSet.add(trainingSetRow); writeToFile(PRIME_FILE_PATH, input); // Write the prime number to prime_numbers.txt } else { // Add the input-output pair to the training set as a non-prime number DataSetRow trainingSetRow = new DataSetRow(inputArray, new double[]{0, 1}); trainingSet.add(trainingSetRow); writeToFile(NOT_PRIME_FILE_PATH, input); // Write the non-prime number to not_prime_numbers.txt } // Train the neural network with the updated training set neuralNetwork.learn(trainingSet); System.out.println("Enter a number between 0 and 1023 (or 'q' to quit): "); } catch (NumberFormatException e) { System.out.println("Invalid input. Please enter a valid number between 0 and 1023 (or 'q' to quit): "); } } // Save the trained neural network to a file neuralNetwork.save("prime_number_classifier.nnet"); System.out.println("Neural network trained and saved successfully."); } private static void writeToFile(String filePath, int number) { try { FileWriter fileWriter = new FileWriter(filePath, true); fileWriter.write(number + "\n"); fileWriter.close(); } catch (IOException e) { System.out.println("Failed to write to file: " + e.getMessage()); } } }

@Mark-XP Yes. This I want to demonstrate first. Neural Networks are blind as much as possible in Mathematics. Today I make next try. More help is impossible for Neural Network. I give it 10 Input Neurons. In them I store numbers between 0 and 1023 in Binary form. Only I decide, if a number is prime or not. From this information, it should learn. For example, when the last digit is a "1", it cant be a prime (only 2). If this Network does not learn what primes are, then there is a brutal limitation in the "intelligence" of Neural Networks Dietmar

@Mark-XP new Prime Number program. This is nice Dietmar package primzahlerkennung; import org.neuroph.core.data.DataSet; import org.neuroph.core.data.DataSetRow; import org.neuroph.nnet.MultiLayerPerceptron; import org.neuroph.util.TransferFunctionType; import java.util.HashMap; import java.util.Random; import java.util.Scanner; public class PrimzahlErkennung { public static void main(String[] args) { int inputSize = 101; int outputSize = 1; MultiLayerPerceptron neuralNetwork = new MultiLayerPerceptron(TransferFunctionType.SIGMOID, inputSize, 10,10, outputSize); neuralNetwork.randomizeWeights(new Random()); Scanner scanner = new Scanner(System.in); HashMap<Integer, Boolean> results = new HashMap<>(); // store recognized numbers and their predicted primality DataSet trainingSet = new DataSet(inputSize, outputSize); // create a training set for updating the neural network boolean quit = false; // flag to determine when to quit the program while (!quit) { System.out.println("Bitte geben Sie eine Zahl zwischen 1 und 100 ein (oder 'q' zum Beenden oder 'liste' um die getesteten Zahlen anzuzeigen):"); String inputString = scanner.next(); if (inputString.equalsIgnoreCase("q")) { quit = true; // set flag to quit the loop continue; // continue to next iteration } else if (inputString.equalsIgnoreCase("liste")) { System.out.println("Die getesteten Zahlen sind:"); for (int num : results.keySet()) { System.out.println(num); } continue; // continue to next iteration } int input; try { input = Integer.parseInt(inputString); } catch (NumberFormatException e) { System.out.println("Ungültige Eingabe. Bitte eine Zahl zwischen 1 und 100 eingeben:"); continue; // continue to next iteration } while (input < 1 || input > 100) { System.out.println("Ungültige Eingabe. Bitte eine Zahl zwischen 1 und 100 eingeben:"); input = scanner.nextInt(); } if (results.containsKey(input)) { boolean isPrime = results.get(input); System.out.println("Ich denke, dass die eingegebene Zahl " + (isPrime ? "eine Primzahl ist." : "keine Primzahl ist.")); } else { double[] inputValues = new double[101]; for (int i = 0; i <= 100; i++) { inputValues[i] = (i == input) ? 1 : 0; } neuralNetwork.setInput(inputValues); neuralNetwork.calculate(); double[] output = neuralNetwork.getOutput(); boolean isPrime = output[0] > 0.5; String proposition = isPrime ? "eine Primzahl ist." : "keine Primzahl ist."; System.out.println("Ich denke, dass die eingegebene Zahl " + proposition); System.out.println("Ist " + input + " eine Primzahl? (y/n):"); String feedback = scanner.next(); while (!feedback.equalsIgnoreCase("y") && !feedback.equalsIgnoreCase("n")) { System.out.println("Ungültige Eingabe. Bitte 'y' oder 'n' eingeben:"); feedback = scanner.next(); } if (feedback.equalsIgnoreCase("y")) { trainingSet.add(new DataSetRow(inputValues, new double[]{1})); results.put(input, true); } else { trainingSet.add(new DataSetRow(inputValues, new double[]{0})); results.put(input, false); } neuralNetwork.learn(trainingSet); // update neural network with new training set } } System.out.println("Vielen Dank für die Nutzung der Primzahl-Erkennungs-Anwendung. Auf Wiedersehen!"); scanner.close(); } } run: Bitte geben Sie eine Zahl zwischen 1 und 100 ein (oder 'q' zum Beenden oder 'liste' um die getesteten Zahlen anzuzeigen): 1 Ich denke, dass die eingegebene Zahl eine Primzahl ist. Ist 1 eine Primzahl? (y/n): y Bitte geben Sie eine Zahl zwischen 1 und 100 ein (oder 'q' zum Beenden oder 'liste' um die getesteten Zahlen anzuzeigen): 2 Ich denke, dass die eingegebene Zahl eine Primzahl ist. Ist 2 eine Primzahl? (y/n): y Bitte geben Sie eine Zahl zwischen 1 und 100 ein (oder 'q' zum Beenden oder 'liste' um die getesteten Zahlen anzuzeigen): 3 Ich denke, dass die eingegebene Zahl eine Primzahl ist. Ist 3 eine Primzahl? (y/n): y Bitte geben Sie eine Zahl zwischen 1 und 100 ein (oder 'q' zum Beenden oder 'liste' um die getesteten Zahlen anzuzeigen): 4 Ich denke, dass die eingegebene Zahl eine Primzahl ist. Ist 4 eine Primzahl? (y/n): n Bitte geben Sie eine Zahl zwischen 1 und 100 ein (oder 'q' zum Beenden oder 'liste' um die getesteten Zahlen anzuzeigen): 5 Ich denke, dass die eingegebene Zahl eine Primzahl ist. Ist 5 eine Primzahl? (y/n): y Bitte geben Sie eine Zahl zwischen 1 und 100 ein (oder 'q' zum Beenden oder 'liste' um die getesteten Zahlen anzuzeigen): 4 Ich denke, dass die eingegebene Zahl keine Primzahl ist. Bitte geben Sie eine Zahl zwischen 1 und 100 ein (oder 'q' zum Beenden oder 'liste' um die getesteten Zahlen anzuzeigen): 6 Ich denke, dass die eingegebene Zahl eine Primzahl ist. Ist 6 eine Primzahl? (y/n): n Bitte geben Sie eine Zahl zwischen 1 und 100 ein (oder 'q' zum Beenden oder 'liste' um die getesteten Zahlen anzuzeigen): 7 Ich denke, dass die eingegebene Zahl eine Primzahl ist. Ist 7 eine Primzahl? (y/n): y Bitte geben Sie eine Zahl zwischen 1 und 100 ein (oder 'q' zum Beenden oder 'liste' um die getesteten Zahlen anzuzeigen): 8 Ich denke, dass die eingegebene Zahl eine Primzahl ist. Ist 8 eine Primzahl? (y/n): n Bitte geben Sie eine Zahl zwischen 1 und 100 ein (oder 'q' zum Beenden oder 'liste' um die getesteten Zahlen anzuzeigen): 8 Ich denke, dass die eingegebene Zahl keine Primzahl ist. Bitte geben Sie eine Zahl zwischen 1 und 100 ein (oder 'q' zum Beenden oder 'liste' um die getesteten Zahlen anzuzeigen): 9 Ich denke, dass die eingegebene Zahl eine Primzahl ist. Ist 9 eine Primzahl? (y/n): n Bitte geben Sie eine Zahl zwischen 1 und 100 ein (oder 'q' zum Beenden oder 'liste' um die getesteten Zahlen anzuzeigen): 10 Ich denke, dass die eingegebene Zahl eine Primzahl ist. Ist 10 eine Primzahl? (y/n): n Bitte geben Sie eine Zahl zwischen 1 und 100 ein (oder 'q' zum Beenden oder 'liste' um die getesteten Zahlen anzuzeigen): 11 Ich denke, dass die eingegebene Zahl eine Primzahl ist. Ist 11 eine Primzahl? (y/n): y Bitte geben Sie eine Zahl zwischen 1 und 100 ein (oder 'q' zum Beenden oder 'liste' um die getesteten Zahlen anzuzeigen): 12 Ich denke, dass die eingegebene Zahl keine Primzahl ist. Ist 12 eine Primzahl? (y/n): n Bitte geben Sie eine Zahl zwischen 1 und 100 ein (oder 'q' zum Beenden oder 'liste' um die getesteten Zahlen anzuzeigen): 12 Ich denke, dass die eingegebene Zahl keine Primzahl ist. Bitte geben Sie eine Zahl zwischen 1 und 100 ein (oder 'q' zum Beenden oder 'liste' um die getesteten Zahlen anzuzeigen): liste Die getesteten Zahlen sind: 1 2 3 4 5 6 7 8 9 10 11 12 Bitte geben Sie eine Zahl zwischen 1 und 100 ein (oder 'q' zum Beenden oder 'liste' um die getesteten Zahlen anzuzeigen):

Best, what you can find in Internet about Neural Network. Funny, this Network here "solves" any problem, because until now it has no Backpropagation. Means, it does not know, what it has to learn. And you can make a check, what happens to those two input values here. In my thinking, the output is any value between 0 and 1 for each Output Neuron. Should be equally(!) distributed Dietmar PS: I read, that a Neural Network can solve the same problems as a Turing Machine. But I think, that it is not true. I think, that it depends on at least 2 Hidden Layers. And for any tasks in Mathematics, Neural Networks are bad. They even cant find the Multipliers of 3 during looking for pattern in the integer Input Neurons values. I also make a try to find pattern in primes with a Neural Network. No pattern is found in primes by a Neural Network. They are blind. This is my definition of a real Intelligence: 1.) Find NEW patterns without any help. 2.) Can explain this new discovered pattern clear and easy to anyone. And sees the need of a prove for this pattern. Until now, no Ai can do this. So, SkyNet with Terminator has to wait for > 100 years.

@George King And here is the hacked version of acpi.sys 2003 5.2 bit32 against BSOD 0x7E(c0000005, ...) error in AcpiArbCrackPRT() when referencing null pointer Dietmar https://ufile.io/ibw0aaxu

@George King here is the original acpi.sys 5.2 bit32 with all the OS Fakes, build from my last Sources 2003 Dietmar https://ufile.io/p1lvafdp

@George King The from Sources 2003 build acpi.sys 5.2 bit32 is much more instable than the acpi.sys from Sources for XP SP1,2,3. So, after some talk in messages, I changed the Source Code from the acpi.sys for XP SP1, that now it supports to full(?) the acpi.sys 5.2 bit32 Dietmar PS: All acpi.sys contains now the OS fakes, that you mentioned.

@George King There has much more changed in Source Code. And also some new hacks. So, until now you can use only my acpi.sys which I send from here Dietmar

Hi, this browser is the only one, that works in April 2023 with ChatGPT under XP SP3 Dietmar https://ufile.io/d8bk1n0a

@George King The Source Code here in the beginning of the thread is build from @Mov AX, 0xDEAD . Some more I have, but not all. And the last hacks for AcpiArbCrackPRT() I think, he does not like. But they work Dietmar

@UsefulAGKHelper Here is brandnew acpi.sys for XP bit64, with hack against BSOD 0x7E(c0000005, ...) error in AcpiArbCrackPRT() when referencing null pointer Dietmar https://ufile.io/ehf890g3

@UsefulAGKHelper No, of course not;)). I love especially XP SP3. Very much I hope, that @Mov AX, 0xDEAD has some new ideas for XP, for example the lan i219 driver Dietmar

@d0minat0r Here is last acpi.sys for XP SP2 bit 64 good luck Dietmar https://ufile.io/t11kewkd

@Mark-XP Yes, neuroph is unstable. But the idea of neuroph is nice. So, I use it only for to test some concepts. I make 0 0 2 as input with 3 Neurons, for to run not in the Normalizations problem via Sigmoid. For me, the program works. And you can see, at which numbers of Neurons in Hidden Layers and at which numbers of Hidden Layers the program is overfitted. It then gives only answers as 0,00001 0,9999 even when this is wrong. But two bad things I noticed: Here, no output file was generated, outputfile works before in my Prime program. So I can use there a lot of Prime numbers for training. But the program is blind. I think, it is a fundamental problem of Neural Networks. A lot of problems from Mathematics they cant work well on. Take knowledge in Mathematics as IQ test, then ChatGPT and all other Neural Networks have an IQ = 0. And the even/odd program sometimes hangs up itself on the very first input Dietmar PS: Yesterday in the evening ChatGPT tolds me, that without mathematical formulas it can not decide, if a given number is a multiplier of 3. So, no SkyNet in this century.

This program learns the multipler of 2, nice . It then stores the learning in a file Dietmar package multi; import org.neuroph.core.data.DataSet; import org.neuroph.core.data.DataSetRow; import org.neuroph.nnet.MultiLayerPerceptron; import org.neuroph.nnet.learning.BackPropagation; import java.util.Scanner; public class Multi { public static void main(String[] args) { // create MultiLayerPerceptron neural network MultiLayerPerceptron neuralNet = new MultiLayerPerceptron(3, 4,4, 2); neuralNet.setLearningRule(new BackPropagation()); // create training set DataSet trainingSet = new DataSet(3, 2); trainingSet.add(new DataSetRow(new double[]{1, 2, 3}, new double[]{0, 1})); //odd trainingSet.add(new DataSetRow(new double[]{2, 2, 2}, new double[]{1, 0})); //even trainingSet.add(new DataSetRow(new double[]{4, 6, 0}, new double[]{1, 0})); //even trainingSet.add(new DataSetRow(new double[]{0, 0, 1}, new double[]{0, 1})); //odd Scanner scanner = new Scanner(System.in); while (true) { System.out.println("Enter a comma-separated list of 3 numbers or 'exit' to quit:"); String inputStr = scanner.nextLine(); if (inputStr.equals("exit")) { break; } String[] inputStrArray = inputStr.split(","); double[] input = new double[3]; for (int i = 0; i < 3; i++) { input[i] = Double.parseDouble(inputStrArray[i].trim()); } neuralNet.setInput(input); neuralNet.calculate(); double[] output = neuralNet.getOutput(); System.out.printf("Network prediction: %.2f odd, %.2f even%n", output[0], output[1]); if (output[0] > output[1]) { System.out.print("I think this is odd. Is that correct? (y/n) "); String answer = scanner.nextLine(); if (answer.equals("y")) { trainingSet.add(new DataSetRow(input, new double[]{1, 0})); //correcting as odd } else { trainingSet.add(new DataSetRow(input, new double[]{0, 1})); //correcting as even } } else { System.out.print("I think this is even. Is that correct? (y/n) "); String answer = scanner.nextLine(); if (answer.equals("y")) { trainingSet.add(new DataSetRow(input, new double[]{0, 1})); //correcting as even } else { trainingSet.add(new DataSetRow(input, new double[]{1, 0})); //correcting as odd } } // train neural network with updated training set neuralNet.learn(trainingSet); } // save trained neural network neuralNet.save("oddoreven.nnet"); } }

By the way, without counting numbers together (Quersumme) and without factors (n Modulo 3 = 0), ChatGPT cant see, if a number is a Multiplier of 3 or not. I make this test today evening. ChatGPT tells me, that it has no idea, how to find this out without any given formula. At once I understand the same crazy result by my Neural Network today by 100% Dietmar

Today I find by myself a very precise definition, what Intelligence really is: 1.) You find only by yourself a pattern. 2.) Then you can describe this pattern to somebody other. Very careful and exact. And why this pattern always works. Maximum, what any kind of Artificially Intelligence can do today, April 2023 is, to find a pattern. But not to describe it and why this works. Few months ago the Ai find a new, better way to multiply matritzes. But mathematics needs months for to understand, what the Ai is doing. Because the Ai understands nothing and so cant help them. Roentgen does not understand the nature of X-rays. Einstein understands his theory. Here, you can see the big big difference at once. SkyNet with terminator moves via this way soso much far away to future, I think >>40 years Dietmar

I make an interesting observation. Until now, I do not succeed to train an Neural Network, so that it can recognice the multiplers of 3. Hm, interesting: ChatGPT cant find until now all multiplieres of 7. So, some Mathematics seems to be a cool Intelligence Test for any Artificial Intelligence. Soon, I understand most pupils at school.. The task for the Ai was: I train with numbers to 1000. The multiplers of 2 she found all correct. But even with loong training, that 1002 is a multipler from 3, I gave up with 1005^^, oh my Dietmar PS: No tools like modulo 3 = 0 are allowed. Only the naked input data.

The Prime Program produces a file "input_log.txt". This file is stored. Now I write another program, for to put correct information about all no primes and primes into this file. It works. All the numbers in this file are now correct identified as primes or no prime from the prim program above. To teach the prim program, you have to answer with "0" for no prime and "1" for prime. Neural Networks can find pattern. I check with even and not even numbers, works. Here is the generator program for a filled "input_log.txt" until 1000 with correct information, cool Dietmar package generateinputlog; import java.io.BufferedWriter; import java.io.FileWriter; import java.io.IOException; public class GenerateInputLog { public static void main(String[] args) throws IOException { String logFileName = "input_log.txt"; BufferedWriter writer = new BufferedWriter(new FileWriter(logFileName)); for (int i = 0; i <= 1000; i++) { boolean isPrime = isPrime(i); int output = isPrime ? 1 : 0; writer.write(i + "," + output + "\n"); } writer.close(); } private static boolean isPrime(int num) { if (num <= 1) { return false; } for (int i = 2; i <= Math.sqrt(num); i++) { if (num % i == 0) { return false; } } return true; } }

@Mark-XP I write a new Prime Number program with Neuroph. It is the best until now. But it cant find primes. If there is anything, that Neural Networks can found, that it is a pattern. So, even with really BIG learning, no pattern can be found in Primes via a Neural network Dietmar package geradeungeradenetzwerk; import java.io.BufferedWriter; import java.io.FileWriter; import java.io.IOException; import java.nio.file.Files; import java.nio.file.Paths; import java.util.ArrayList; import java.util.HashMap; import java.util.List; import java.util.Map; import java.util.Scanner; import org.neuroph.core.NeuralNetwork; import org.neuroph.core.data.DataSet; import org.neuroph.core.data.DataSetRow; import org.neuroph.nnet.MultiLayerPerceptron; import org.neuroph.nnet.learning.BackPropagation; public class GeradeUngeradeNetzwerk { public static void main(String[] args) throws IOException { String logFileName = "input_log.txt"; Map<Integer, Double> userInputMap = new HashMap<>(); // Load input-output pairs from log file DataSet dataset = new DataSet(1, 1); if (Files.exists(Paths.get(logFileName))) { List<String> lines = Files.readAllLines(Paths.get(logFileName)); for (String line : lines) { String[] parts = line.split(","); int input = Integer.parseInt(parts[0]); double output = Double.parseDouble(parts[1]); double[] inputArr = new double[] { input }; double[] outputArr = new double[] { output }; dataset.add(new DataSetRow(inputArr, outputArr)); userInputMap.put(input, output); } } // Train neural network on input-output pairs MultiLayerPerceptron neuralNet = new MultiLayerPerceptron(1, 300, 300,300,300,300,300,300, 1); BackPropagation learningRule = neuralNet.getLearningRule(); learningRule.setMaxError(0.1); learningRule.setMaxIterations(1000); neuralNet.learn(dataset); // Use trained neural network to classify new integers as prime or not prime Scanner scanner = new Scanner(System.in); while (true) { System.out.print("Enter an integer (or 'exit' to quit): "); String inputStr = scanner.nextLine(); if (inputStr.equals("exit")) { break; } int input; try { input = Integer.parseInt(inputStr); } catch (NumberFormatException e) { System.out.println("Invalid input. Please enter an integer."); continue; } if(userInputMap.containsKey(input)){ double result = userInputMap.get(input); if (result >= 0.5) { System.out.println(input + " is prime (according to the neural network)"); } else { System.out.println(input + " is not prime (according to the neural network)"); } } else{ double[] inputArr = new double[] { input }; neuralNet.setInput(inputArr); neuralNet.calculate(); double[] output = neuralNet.getOutput(); double result = output[0]; if (result >= 0.5) { System.out.println(input + " is prime (according to the neural network)"); } else { System.out.println(input + " is not prime (according to the neural network)"); } // Ask user if result is correct and store input-output pair in log file System.out.print("Is this result correct? (y/n): "); String answer = scanner.nextLine().toLowerCase(); if (answer.equals("y")) { double[] outputArr = new double[]{result}; dataset.add(new DataSetRow(inputArr, outputArr)); BufferedWriter writer = new BufferedWriter(new FileWriter(logFileName, true)); writer.write(input + "," + result + "\n"); writer.close(); userInputMap.put(input, result); } else if (answer.equals("n")) { // Change output to the correct result and add input-output pair to log file System.out.print("What is the correct result? "); String correctResultStr = scanner.nextLine(); try { double correctResult = Double.parseDouble(correctResultStr); double[] outputArr = new double[]{correctResult}; dataset.add(new DataSetRow(inputArr, outputArr)); BufferedWriter writer = new BufferedWriter(new FileWriter(logFileName, true)); writer.write(input + "," + correctResult + "\n"); writer.close(); userInputMap.put(input, correctResult); } catch (NumberFormatException e) { System.out.println("Invalid input, the result was not recorded"); } } } }}}

@Mark-XP Here is a new version. It shows all my helpless (or the helpless of Ai). First I use the Input 0 0 0. Program calculates all Bias and Weights, so that it reaches about 0.5. Then, after 20 Iterations, the last Bias and Values are stored. Now, without any Backpropagation, I use this set of Bias and weights, for the new Input 0 0 1. And now, the crazy things happen: After each run, the output for the 0 0 0 is about 0.5. But the output for the 0 0 1 changes at lot with each run. ChatGPT tells me, to take the Middle of all the used Bias and Weights. But I think, this is helpless as much as possible. So, I have no idea to really train my Network for primes Dietmar package neuralnetwork; import java.util.Arrays; import java.util.concurrent.ThreadLocalRandom; import java.util.Scanner; public class NeuralNetwork { private int numInputNodes; private int numHiddenNodes1; private int numHiddenNodes2; private int numOutputNodes; private double[][] weights1; private double[][] weights2; private double[][] weights3; private double[] bias1; private double[] bias2; private double[] bias3; public NeuralNetwork(int numInputNodes, int numHiddenNodes1, int numHiddenNodes2, int numOutputNodes) { this.numInputNodes = numInputNodes; this.numHiddenNodes1 = numHiddenNodes1; this.numHiddenNodes2 = numHiddenNodes2; this.numOutputNodes = numOutputNodes; this.weights1 = new double[numInputNodes][numHiddenNodes1]; for (int i = 0; i < numInputNodes; i++) { for (int j = 0; j < numHiddenNodes1; j++) { this.weights1[i][j] = ThreadLocalRandom.current().nextDouble(-1, 1); } } this.weights2 = new double[numHiddenNodes1][numHiddenNodes2]; for (int i = 0; i < numHiddenNodes1; i++) { for (int j = 0; j < numHiddenNodes2; j++) { this.weights2[i][j] = ThreadLocalRandom.current().nextDouble(-1, 1); } } this.weights3 = new double[numHiddenNodes2][numOutputNodes]; for (int i = 0; i < numHiddenNodes2; i++) { for (int j = 0; j < numOutputNodes; j++) { this.weights3[i][j] = ThreadLocalRandom.current().nextDouble(-1, 1); } } this.bias1 = new double[numHiddenNodes1]; for (int i = 0; i < numHiddenNodes1; i++) { this.bias1[i] = ThreadLocalRandom.current().nextDouble(-1, 1); } this.bias2 = new double[numHiddenNodes2]; for (int i = 0; i < numHiddenNodes2; i++) { this.bias2[i] = ThreadLocalRandom.current().nextDouble(-1, 1); } this.bias3 = new double[numOutputNodes]; for (int i = 0; i < numOutputNodes; i++) { this.bias3[i] = ThreadLocalRandom.current().nextDouble(-1, 1); } } public double[] feedForward(double[] inputs) { double[] hidden1 = new double[numHiddenNodes1]; double[] hidden2 = new double[numHiddenNodes2]; double[] outputs = new double[numOutputNodes]; // Calculate outputs of hidden layer 1 for (int j = 0; j < numHiddenNodes1; j++) { double sum = 0; for (int i = 0; i < numInputNodes; i++) { sum += inputs[i] * weights1[i][j]; } sum += bias1[j]; hidden1[j] = Math.tanh(sum); } // Calculate outputs of hidden layer 2 for (int j = 0; j < numHiddenNodes2; j++) { double sum = 0; for (int i = 0; i < numHiddenNodes1; i++) { sum += hidden1[i] * weights2[i][j]; } sum += bias2[j]; hidden2[j] = Math.tanh(sum);; } // Calculate outputs for (int j = 0; j < numOutputNodes; j++) { double sum = 0; for (int i = 0; i < numHiddenNodes2; i++) { sum += hidden2[i] * weights3[i][j]; } sum += bias3[j]; outputs[j] = Math.tanh(sum);; } return outputs; } public void setWeights1(double[][] weights) { this.weights1 = weights; } public void setBias1(double[] bias) { this.bias1 = bias; } public void setWeights2(double[][] weights) { this.weights2 = weights; } public void setBias2(double[] bias) { this.bias2 = bias; } public void setWeights3(double[][] weights) { this.weights3 = weights; } public void setBias3(double[] bias) { this.bias3 = bias; } public double[][] getWeights1() { return this.weights1; } public double[][] getWeights2() { return this.weights2; } public double[][] getWeights3() { return this.weights3; } public double[] getBias1() { return this.bias1; } public double[] getBias2() { return this.bias2; } public double[] getBias3() { return this.bias3; } // Backward Propagation public void backPropagate(double[] inputs, double[] expectedOutputs, double learningRate) { // Feed forward to get outputs double[] hidden1 = new double[numHiddenNodes1]; double[] hidden2 = new double[numHiddenNodes2]; double[] outputs = feedForward(inputs); // Calculate error in output layer double[] outputErrors = new double[numOutputNodes]; for (int i = 0; i < numOutputNodes; i++) { outputErrors[i] = expectedOutputs[i] - outputs[i]; } // Calculate error in hidden layer 2 double[] hidden2Errors = new double[numHiddenNodes2]; for (int i = 0; i < numHiddenNodes2; i++) { double error = 0; for (int j = 0; j < numOutputNodes; j++) { error += outputErrors[j] * weights3[i][j]; } hidden2Errors[i] = (1 - Math.pow(Math.tanh(hidden2[i]), 2)) * error; } // Calculate error in hidden layer 1 double[] hidden1Errors = new double[numHiddenNodes1]; for (int i = 0; i < numHiddenNodes1; i++) { double error = 0; for (int j = 0; j < numHiddenNodes2; j++) { error += hidden2Errors[j] * weights2[i][j]; } hidden1Errors[i] = (1 - Math.pow(Math.tanh(hidden1[i]), 2)) * error; } // Update weights and biases in output layer for (int i = 0; i < numHiddenNodes2; i++) { for (int j = 0; j < numOutputNodes; j++) { double delta = outputErrors[j] * tanhDerivative(outputs[j]) * hidden2[i]; weights3[i][j] += learningRate * delta; } } for (int i = 0; i < numOutputNodes; i++) { bias3[i] += learningRate * outputErrors[i] * tanhDerivative(outputs[i]); } // Calculate error in hidden layer 1 for (int i = 0; i < numHiddenNodes1; i++) { double error = 0; for (int j = 0; j < numHiddenNodes2; j++) { error += hidden2Errors[j] * weights2[i][j]; } hidden1Errors[i] = error * tanhDerivative(hidden1[i]); } // Update weights and biases in hidden layer 2 for (int i = 0; i < numHiddenNodes1; i++) { for (int j = 0; j < numHiddenNodes2; j++) { double delta = hidden2Errors[j] * tanhDerivative(hidden2[j]) * hidden1[i]; weights2[i][j] += learningRate * delta; } } for (int i = 0; i < numHiddenNodes2; i++) { bias2[i] += learningRate * hidden2Errors[i] * tanhDerivative(hidden2[i]); } // Update weights and biases in hidden layer 1 for (int i = 0; i < numInputNodes; i++) { for (int j = 0; j < numHiddenNodes1; j++) { double delta = hidden1Errors[j] * tanhDerivative(hidden1[j]) * inputs[i]; weights1[i][j] += learningRate * delta; } } for (int i = 0; i < numHiddenNodes1; i++) { bias1[i] += learningRate * hidden1Errors[i] * tanhDerivative(hidden1[i]); } } // Helper method to calculate the derivative of the hyperbolic tangent function private double tanhDerivative(double x) { double tanh = Math.tanh(x); return 1 - tanh * tanh; } public static void main(String[] args) { NeuralNetwork nn = new NeuralNetwork(3, 4, 4, 1); double[] inputs = {0, 0, 0}; double[] expectedOutputs = {0.5}; for (int i = 0; i < 20; i++) { nn.backPropagate(inputs, expectedOutputs, 0.1); double[] outputs = nn.feedForward(inputs); System.out.println("\nIteration " + (i+1)); System.out.println("Weights1:"); System.out.println(Arrays.deepToString(nn.getWeights1())); System.out.println("Bias1:"); System.out.println(Arrays.toString(nn.getBias1())); System.out.println("Weights2:"); System.out.println(Arrays.deepToString(nn.getWeights2())); System.out.println("Bias2:"); System.out.println(Arrays.toString(nn.getBias2())); System.out.println("Weights3:"); System.out.println(Arrays.deepToString(nn.getWeights3())); System.out.println("Bias3:"); System.out.println(Arrays.toString(nn.getBias3())); System.out.println("Output:"); System.out.println(Arrays.toString(outputs)); try { Thread.sleep(1000); } catch (InterruptedException e) { e.printStackTrace(); } } Scanner scanner = new Scanner(System.in); System.out.println("\nEnter any key to continue:"); scanner.nextLine(); System.out.println("Initial weights and biases:"); System.out.println(Arrays.deepToString(nn.getWeights1())); System.out.println(Arrays.toString(nn.getBias1())); System.out.println(Arrays.deepToString(nn.getWeights2())); System.out.println(Arrays.toString(nn.getBias2())); System.out.println(Arrays.deepToString(nn.getWeights3())); System.out.println(Arrays.toString(nn.getBias3())); while (true) { System.out.println("\nEnter 'q' to quit or any other key to continue:"); String input = scanner.nextLine(); if (input.equals("q")) { break; } // Change weight and bias values nn.getWeights1()[1][2] += 0.5; nn.getBias2()[1] -= 0.5; nn.getWeights3()[0][0] *= 2; // Output modified weights and biases System.out.println("\nModified weights and biases:"); System.out.println(Arrays.deepToString(nn.getWeights1())); System.out.println(Arrays.toString(nn.getBias1())); System.out.println(Arrays.deepToString(nn.getWeights2())); System.out.println(Arrays.toString(nn.getBias2())); System.out.println(Arrays.deepToString(nn.getWeights3())); System.out.println(Arrays.toString(nn.getBias3())); // Feed-forward with new inputs using the last trained weights and biases double[] newInputs = {0, 0, 1}; nn.setWeights1(nn.getWeights1()); nn.setBias1(nn.getBias1()); nn.setWeights2(nn.getWeights2()); nn.setBias2(nn.getBias2()); nn.setWeights3(nn.getWeights3()); nn.setBias3(nn.getBias3()); double[] newOutputs = nn.feedForward(newInputs); System.out.println("New output:"); System.out.println(Arrays.toString(newOutputs)); try { Thread.sleep(1000); } catch (InterruptedException e) { e.printStackTrace(); } } } }

@Mark-XP I notice 2 things: Always the Wights and Bias are different, during different runs. And there appear Weights and Bias >1 and < -1 ??? Chatgpt tells, that this is normal. I would say, it is a big mistake. I really start to wonder, what an Ai is really learning. It can learn facts. But then? As long as there are 2 possible ways, with complete different Weights and Bias for to reach the same result, the Ai has no chance and takes randomally any way. Any "understanding" in such a situation is impossible, Dietmar PS: Those values >1 or <-1 are produced from the Backpropagate algorithmus, brr.. So I think, much more theoretical examination is necessary for Neural Networks.