diff --git a/CMakeLists.txt b/CMakeLists.txt
index 461b2a6..e759032 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -3,5 +3,5 @@ project(c_net C)
 
 set(CMAKE_C_STANDARD 11)
 
-add_executable(c_net main.c matrix.c image.c neuronal_network.c util.c util.h)
+add_executable(c_net main.c matrix.c image.c neuronal_network.c util.c util.h neural_net.c neural_net.h)
 target_link_libraries(c_net m)
diff --git a/image.c b/image.c
index 11d7340..c262fbf 100644
--- a/image.c
+++ b/image.c
@@ -68,8 +68,8 @@ Image * load_pgm_image(char * image_file_string){
 Image** import_images(char* image_file_string, char* label_file_string, int* _number_imported, int count) {
     printf("Loading Images\n");
     // create file pointer for the image and label data
-    FILE* image_file = fopen(image_file_string, "r");
-    FILE* label_file = fopen(label_file_string, "r");
+    FILE* image_file = fopen(image_file_string, "rb");
+    FILE* label_file = fopen(label_file_string, "rb");
 
     // check if the file could be opened
     if(image_file == NULL || label_file == NULL) {
@@ -159,6 +159,17 @@ Image** import_images(char* image_file_string, char* label_file_string, int* _nu
     return images;
 }
 
+Matrix* create_one_hot_result(Image* image){
+    if(image->label < 0 || image->label > 9){
+        printf("create_one_hot_result should only be used on correctly labeled images\n");
+        exit(1);
+    }
+
+    Matrix* result = matrix_create(10, 1);
+    result->numbers[image->label][0] = 1;
+    return result;
+}
+
 void img_print (Image* img) {
 
     //print the image
diff --git a/image.h b/image.h
index 6d3caeb..78dff98 100644
--- a/image.h
+++ b/image.h
@@ -1,8 +1,6 @@
 #pragma once
 #include "matrix.h"
 
-#include "matrix.h"
-
 typedef struct {
     Matrix* pixel_values;
     char label;
@@ -27,6 +25,7 @@ static const int MAGIC_NUMBER_IMAGES = 2051;
  */
 Image ** import_images(char* image_file_string, char* label_file_string, int* number_imported, int count);
 Image * load_pgm_image(char * image_file_string);
+Matrix* create_one_hot_result(Image* image);
 void img_print (Image* image);
 void img_visualize(Image*image);
 void img_free (Image* image);
\ No newline at end of file
diff --git a/main.c b/main.c
index 309e363..da6ef80 100644
--- a/main.c
+++ b/main.c
@@ -2,25 +2,36 @@
 
 #include "matrix.h"
 #include "image.h"
-#include "neuronal_network.h"
+
+#include "neural_net.h"
 
 int main() {
-    Image** images = import_images("../data/train-images.idx3-ubyte", "../data/train-labels.idx1-ubyte", NULL, 60000);
-//    img_visualize(images[4]);
-
-    Neural_Network* nn = new_network(28*28, 16, 10, 0.5);
-    randomize_network(nn, 20);
-//    save_network(nn);
-
-//    Neural_Network* nn = load_network("../networks/test1.txt");
-
-
-    for (int i = 0; i < 10000; ++i) {
-        train_network(nn, images[i], images[i]->label);
-    }
-
-    measure_network_accuracy(nn, images, 100);
-
-
-
+//    Image** images = import_images("../data/train-images.idx3-ubyte", "../data/train-labels.idx1-ubyte", NULL, 60000);
+////    img_visualize(images[4]);
+//
+//    Neural_Network* nn = new_network(28*28, 16, 10, 0.5);
+//    randomize_network(nn, 20);
+////    save_network(nn);
+//
+////    Neural_Network* nn = load_network("../networks/test1.txt");
+//
+//
+//    for (int i = 0; i < 10000; ++i) {
+//        train_network(nn, images[i], images[i]->label);
+//    }
+//
+//    measure_network_accuracy(nn, images, 100);
+//    Matrix *m = matrix_create(2, 1);
+//    m->numbers[0][0] = 1;
+//    m->numbers[1][0] = 1;
+//    Neural_Network * net = create_network(3, 2, 3, 1);
+//    feedforward(net, m);
+//
+//    int pause;
+    int imported_count = 0;
+    Image** images = import_images("../data/train-images.idx3-ubyte", "../data/train-labels.idx1-ubyte", &imported_count, 60000);
+    matrix_save(images[0]->pixel_values, "image1.txt");
+    matrix_save(images[1]->pixel_values, "images2.txt");
+    Neural_Network * net = create_network(3, 28*28, 30, 10);
+    train_network_with_batches(net, images, imported_count, 1, 10, 3);
 }
\ No newline at end of file
diff --git a/neural_net.c b/neural_net.c
new file mode 100644
index 0000000..5368f96
--- /dev/null
+++ b/neural_net.c
@@ -0,0 +1,218 @@
+//
+// Created by jakob on 22.09.2023.
+//
+#include <stdarg.h>
+#include <stdlib.h>
+#include "neural_net.h"
+#include <math.h>
+#include "image.h"
+
+void evaluate(Neural_Network * network, Image** images, int imageCount){
+    int numCorrect = 0;
+    for(int i = 0; i <= imageCount; i++){
+        Matrix * input = matrix_flatten(images[i]->pixel_values, 0);
+        Matrix * res = feedforward(network, input);
+        char result = (char)matrix_argmax(res);
+        if(result == images[i]->label){
+            numCorrect++;
+        }
+        matrix_free(input);
+        matrix_free(res);
+    }
+    printf("%d/%d", numCorrect, imageCount);
+}
+
+double sigmoid(double input) {
+    return 1.0 / (1 + exp(-1 * input));
+}
+
+double sigmoid_prime(double input){
+    return sigmoid(input)*(1- sigmoid(input));
+}
+
+void back_prop(Neural_Network * network, Image* training_sample, Matrix ** weights_delta, Matrix ** biases_delta){
+    //all Matrix** are external, to avoid repeated memory allocation and deallocation.
+    for(int i = 0; i < network->layer_count - 1; i++){
+        matrix_fill(weights_delta[i], 0);
+        matrix_fill(biases_delta[i], 0);
+    }
+
+    Matrix * desired_result = create_one_hot_result(training_sample); //freed in line 47
+
+
+    //feedforward######################################
+    //input_activation
+    Matrix * current_activation = matrix_flatten(training_sample->pixel_values, 0);//freed by freeing layer_activation
+
+    Matrix ** layer_activations = malloc(sizeof(Matrix*) * network->layer_count); //freed at end
+    Matrix ** layer_activations_wo_sigmoid = malloc(sizeof(Matrix*) * network->layer_count - 1);//freed at end
+    layer_activations[0] = current_activation;
+
+    for(int i = 0; i < network->layer_count-1; i++){
+        Matrix * dot_result = dot(network->weights[i], current_activation);//freed 3 lines below
+        Matrix * addition_result = add(dot_result, network->biases[i]); //freed by freeing layer activations wo sigmoid
+        matrix_free(dot_result);
+        layer_activations_wo_sigmoid[i] = addition_result;
+        current_activation = apply(sigmoid, addition_result);
+        layer_activations[i+1] = current_activation; //freed by freeing layer activations
+        dot_result = NULL;
+    }
+
+    //backward pass####################################
+    //calculate delta for last layer;
+    //bias
+    Matrix * subtraction_result = subtract(layer_activations[network->layer_count-1], desired_result);
+    Matrix * delta = apply(sigmoid_prime, subtraction_result);
+    matrix_free(subtraction_result);
+    biases_delta[network->layer_count-1] = delta;
+
+    //weights
+    Matrix * transposed = transpose(layer_activations[network->layer_count-2]);
+    weights_delta[network->layer_count-1] = dot(delta, transposed);
+    matrix_free(transposed);
+    transposed = NULL;
+
+    for(int layer = network->layer_count-3; layer >= 0; layer--){
+        Matrix * activation_wo_sigmoid = layer_activations_wo_sigmoid[layer];
+        Matrix * derivative = apply(sigmoid_prime, activation_wo_sigmoid);
+        Matrix * transposed_layer_weight = transpose(network->weights[layer + 1]);
+        Matrix * dot_result = dot(transposed_layer_weight, delta);
+        matrix_free(transposed_layer_weight);
+        delta = multiply(dot_result, derivative);
+
+        biases_delta[layer] = delta;
+        Matrix * transposed_activation = transpose(layer_activations[layer]);
+        weights_delta[layer] = dot(delta, transposed_activation);
+        matrix_free(transposed_activation);
+    }
+
+    matrix_free(desired_result);
+
+    //free layer_activations
+    for(int i = 0; i < network->layer_count; i++){
+        matrix_free(layer_activations[i]);
+    }
+    free(layer_activations);
+
+    //free layer_activations wo sigmoid
+    for(int i = 0; i < network->layer_count - 1; i++){
+        matrix_free(layer_activations_wo_sigmoid[i]);
+    }
+    free(layer_activations_wo_sigmoid);
+
+
+}
+
+void update_batch(Neural_Network * network, Image** training_data, int batch_start, int batch_end, double learning_rate){
+    Matrix** weights_delta = malloc(sizeof(Matrix*)*network->layer_count - 1);
+    Matrix** biases_delta = malloc(sizeof(Matrix*)*network->layer_count - 1);
+    Matrix** sum_weights_delta = malloc(sizeof(Matrix*)*network->layer_count - 1);
+    Matrix** sum_biases_delta = malloc(sizeof(Matrix*)*network->layer_count - 1);
+
+    for(int i = 0; i < network->layer_count - 1; i++){
+        weights_delta[i] = matrix_create(network->weights[i]->rows, network->weights[i]->columns);
+        biases_delta[i] = matrix_create(network->biases[i]->rows, network->biases[i]->columns);
+        sum_weights_delta[i] = matrix_create(network->weights[i]->rows, network->weights[i]->columns);
+        sum_biases_delta[i] = matrix_create(network->biases[i]->rows, network->biases[i]->columns);
+    }
+
+    for(int i = batch_start; i <= batch_end; i++){
+        back_prop(network, training_data[i], weights_delta, biases_delta);
+        for(int j = 0; j < network->layer_count-1; j++){
+            Matrix * sum_weights_free = sum_weights_delta[j];
+            sum_weights_delta[j] = add(sum_weights_delta[j], weights_delta[j]);
+            matrix_free(sum_weights_free);
+
+            Matrix * sum_biases_free = sum_biases_delta[j];
+            sum_biases_delta[j] = add(sum_biases_delta[j], biases_delta[j]);
+            matrix_free(sum_biases_free);
+        }
+    }
+
+    //change network
+    double scaling_factor = learning_rate/(batch_end-batch_start);
+    for(int i = 0; i < network->layer_count-1; i++){
+        //update weights
+        Matrix * weight_change = scale(sum_weights_delta[i], scaling_factor);
+        matrix_free(sum_weights_delta[i]);
+        Matrix * new_weights = subtract(network->weights[i], weight_change);
+        matrix_free(network->weights[i]);
+        network->weights[i] = new_weights;
+
+        //update biases
+        Matrix * bias_change = scale(sum_biases_delta[i], scaling_factor);
+        matrix_free(sum_biases_delta[i]);
+        Matrix * new_biases = subtract(network->biases[i], bias_change);
+        matrix_free(network->biases[i]);
+        network->biases[i] = new_biases;
+    }
+    //TODO: update mini batch
+
+
+}
+
+void train_network_with_batches(Neural_Network * network, Image** training_data, int image_count, int epochs, int batch_size, double learning_rate){
+    for(int i = 0; i < epochs;  i++){
+        for(int j = 0; j < image_count/batch_size; j++){
+            int batch_start = j*batch_size;
+            int batch_end = j*batch_size + batch_size - 1;
+            update_batch(network, training_data, batch_start, batch_end, learning_rate);
+        }
+        evaluate(network, training_data, 1000);
+    }
+}
+
+
+Neural_Network* create_network(int layer_count,...){
+    Neural_Network * network = malloc(sizeof(Neural_Network));
+    network->layer_count = layer_count;
+    network->sizes = malloc(sizeof(int) * layer_count);
+    network->weights = malloc(sizeof(Matrix*)*(layer_count-1));
+    network->biases = malloc(sizeof(Matrix*)*(layer_count-1));
+
+    //read sizes
+    va_list layer_sizes;
+    va_start(layer_sizes, layer_count);
+    for(int i = 0; i < layer_count; i++){
+        network->sizes[i] = va_arg(layer_sizes, int);
+    }
+    va_end(layer_sizes);
+
+    //init weights
+    for(int i = 0; i < layer_count-1; i++){
+        network->weights[i] = matrix_create(network->sizes[i+1], network->sizes[i]);
+        matrix_randomize(network->weights[i], network->sizes[i]);
+    }
+
+    //init biases
+    for(int i = 0; i < layer_count-1; i++){
+        network->biases[i] = matrix_create(network->sizes[i+1], 1);
+        matrix_randomize(network->biases[i], network->sizes[i]);
+    }
+
+    return network;
+}
+
+
+
+//given an input "activations" it returns the matrix that the network would output
+Matrix * feedforward(Neural_Network * net, Matrix * activations){
+
+    Matrix * current_layer_activation = activations;
+
+    //next_layer_activation = sigmoid(dot(layer_weights, layer_activations)+layer_biases);
+    for(int i = 0; i < net->layer_count - 1; i++){
+        Matrix * dot_result = dot(net->weights[i], current_layer_activation);
+        Matrix * addition_result = add(dot_result, net->biases[i]);
+        Matrix * sigmoid_result = apply(sigmoid, addition_result);
+
+        current_layer_activation = sigmoid_result;
+        matrix_free(dot_result);
+        matrix_free(addition_result);
+    }
+    return current_layer_activation;
+}
+
+
+
+
diff --git a/neural_net.h b/neural_net.h
new file mode 100644
index 0000000..45a9779
--- /dev/null
+++ b/neural_net.h
@@ -0,0 +1,22 @@
+//
+// Created by jakob on 22.09.2023.
+//
+
+#include "matrix.h"
+#include "image.h"
+
+#ifndef C_NET_NEURAL_NET_H
+#define C_NET_NEURAL_NET_H
+
+#endif //C_NET_NEURAL_NET_H
+
+typedef struct {
+    int layer_count;
+    int* sizes;
+    Matrix ** weights;
+    Matrix ** biases;
+} Neural_Network;
+
+Neural_Network* create_network(int layer_count,...);
+Matrix * feedforward(Neural_Network * net, Matrix * activations);
+void train_network_with_batches(Neural_Network * network, Image** training_data, int image_count, int epochs, int batch_size, double learning_rate);
diff --git a/neuronal_network.c b/neuronal_network.c
index a970cec..862ddb3 100644
--- a/neuronal_network.c
+++ b/neuronal_network.c
@@ -343,9 +343,9 @@ Matrix * backPropagation(double learning_rate, Matrix* weights, Matrix* biases,
 
 //void batch_train_network(Neural_Network* network, Image** images, int size);
 
-double sigmoid(double input) {
-    return 1.0 / (1 + exp(-1 * input));
-}
+//double sigmoid(double input) {
+//    return 1.0 / (1 + exp(-1 * input));
+//}
 
 double sigmoid_derivative(double x) {
     return x * (1.0 - x);