diff --git a/README.md b/README.md
index 876c49d403b0049e75c65e6420c57601fa447802..d5f4184630d6321b71d916400d61eae3faf439d4 100644
--- a/README.md
+++ b/README.md
@@ -1,92 +1,69 @@
-# Image classification
+## MOD 4.6 Deep Learning & Artificial Intelligence: an introduction 
 
+# TD1: Image Classification
 
+## Introduction
 
-## Getting started
+In this repository you'll find Python implementations of image classification programs featuring two successive models: the k-nearest neighbors (KNN) and neural networks (NN). The overarching objective of these solutions is to provide comprehensive insights into the process of constructing and evaluating image classification models using Python. Throughout the tutorial, you will delve into the step-by-step development of each model.
+The two models are tested on the image database CIFAR-10 which consists of 60 000 color images of size 32x32 divided into 10 classes (plane, car, bird, cat, ...).
 
-To make it easy for you to get started with GitLab, here's a list of recommended next steps.
+<div style="text-align:center;">
+  <img src="images/cifar.png" alt="Cifar database" width="300" height="200">
+</div>
 
-Already a pro? Just edit this README.md and make it your own. Want to make it easy? [Use the template at the bottom](#editing-this-readme)!
-
-## Add your files
-
-- [ ] [Create](https://docs.gitlab.com/ee/user/project/repository/web_editor.html#create-a-file) or [upload](https://docs.gitlab.com/ee/user/project/repository/web_editor.html#upload-a-file) files
-- [ ] [Add files using the command line](https://docs.gitlab.com/ee/gitlab-basics/add-file.html#add-a-file-using-the-command-line) or push an existing Git repository with the following command:
-
-```
-cd existing_repo
-git remote add origin https://gitlab.ec-lyon.fr/acavallo/image-classification.git
-git branch -M main
-git push -uf origin main
-```
-
-## Integrate with your tools
-
-- [ ] [Set up project integrations](https://gitlab.ec-lyon.fr/acavallo/image-classification/-/settings/integrations)
+## Description
 
-## Collaborate with your team
+### CIFAR Dataset
 
-- [ ] [Invite team members and collaborators](https://docs.gitlab.com/ee/user/project/members/)
-- [ ] [Create a new merge request](https://docs.gitlab.com/ee/user/project/merge_requests/creating_merge_requests.html)
-- [ ] [Automatically close issues from merge requests](https://docs.gitlab.com/ee/user/project/issues/managing_issues.html#closing-issues-automatically)
-- [ ] [Enable merge request approvals](https://docs.gitlab.com/ee/user/project/merge_requests/approvals/)
-- [ ] [Set auto-merge](https://docs.gitlab.com/ee/user/project/merge_requests/merge_when_pipeline_succeeds.html)
+1. The Python file named `read_cifar.py` is composed of:
 
-## Test and Deploy
+    - `read_cifar_batch(batch)`: takes the path of a single batch as a string and returns a matrix `batch_data` and a vector `batch_labels`.
 
-Use the built-in continuous integration in GitLab.
+    - `read_cifar(path)`: takes the path of the directory containing the six batches and returns a matrix `data` and a vector `labels`.
 
-- [ ] [Get started with GitLab CI/CD](https://docs.gitlab.com/ee/ci/quick_start/index.html)
-- [ ] [Analyze your code for known vulnerabilities with Static Application Security Testing(SAST)](https://docs.gitlab.com/ee/user/application_security/sast/)
-- [ ] [Deploy to Kubernetes, Amazon EC2, or Amazon ECS using Auto Deploy](https://docs.gitlab.com/ee/topics/autodevops/requirements.html)
-- [ ] [Use pull-based deployments for improved Kubernetes management](https://docs.gitlab.com/ee/user/clusters/agent/)
-- [ ] [Set up protected environments](https://docs.gitlab.com/ee/ci/environments/protected_environments.html)
+    - `split_dataset(data, labels, split_factor)`: randomly splits the dataset into a training set and a test set with a specified split factor.
 
-***
+### K-Nearest Neighbors
 
-# Editing this README
+3. The Python file named `knn.py` is composed of:
 
-When you're ready to make this README your own, just edit this file and use the handy template below (or feel free to structure it however you want - this is just a starting point!). Thank you to [makeareadme.com](https://www.makeareadme.com/) for this template.
+    - `distance_matrix(data_train, data_test)`: computes the L2 Euclidean distance matrix between the training data and the testing data.
 
-## Suggestions for a good README
-Every project is different, so consider which of these sections apply to yours. The sections used in the template are suggestions for most open source projects. Also keep in mind that while a README can be too long and detailed, too long is better than too short. If you think your README is too long, consider utilizing another form of documentation rather than cutting out information.
+    - `knn_predict(dists, labels_train, k)`: predicts the labels for the elements of `data_test` using k-nearest neighbors.
 
-## Name
-Choose a self-explaining name for your project.
+    - `evaluate_knn(dists, labels_train, labels_test, k)`: computes and returns the classification accuracy.
 
-## Description
-Let people know what your project can do specifically. Provide context and add a link to any reference visitors might be unfamiliar with. A list of Features or a Background subsection can also be added here. If there are alternatives to your project, this is a good place to list differentiating factors.
 
-## Badges
-On some READMEs, you may see small images that convey metadata, such as whether or not all the tests are passing for the project. You can use Shields to add some to your README. Many services also have instructions for adding a badge.
+### Artificial Neural Network (Multilayer Perceptron)
 
-## Visuals
-Depending on what you are making, it can be a good idea to include screenshots or even a video (you'll frequently see GIFs rather than actual videos). Tools like ttygif can help, but check out Asciinema for a more sophisticated method.
+4. The Python file named `mlp.py` is composed of:
+    
+    - `sigmoid(z)`: compute the sigmoid activation function
 
-## Installation
-Within a particular ecosystem, there may be a common way of installing things, such as using Yarn, NuGet, or Homebrew. However, consider the possibility that whoever is reading your README is a novice and would like more guidance. Listing specific steps helps remove ambiguity and gets people to using your project as quickly as possible. If it only runs in a specific context like a particular programming language version or operating system or has dependencies that have to be installed manually, also add a Requirements subsection.
+    - `learn_once_mse(w1, b1, w2, b2, data, targets, learning_rate)`: performs one gradient descent step using Mean Squared Error (MSE) loss.
 
-## Usage
-Use examples liberally, and show the expected output if you can. It's helpful to have inline the smallest example of usage that you can demonstrate, while providing links to more sophisticated examples if they are too long to reasonably include in the README.
+    - `one_hot(labels)`: converts labels into one-hot encoding.
 
-## Support
-Tell people where they can go to for help. It can be any combination of an issue tracker, a chat room, an email address, etc.
+    - `learn_once_cross_entropy(w1, b1, w2, b2, data, labels_train, learning_rate)`: performs one gradient descent step using binary cross-entropy loss.
 
-## Roadmap
-If you have ideas for releases in the future, it is a good idea to list them in the README.
+    - `train_mlp(w1, b1, w2, b2, data_train, labels_train, learning_rate, num_epoch)`: trains the MLP for a specified number of epochs and return the training accuracies.
 
-## Contributing
-State if you are open to contributions and what your requirements are for accepting them.
+    - `test_mlp(w1, b1, w2, b2, data_test, labels_test)`: tests the MLP on the test set and returns the final accuracy.
 
-For people who want to make changes to your project, it's helpful to have some documentation on how to get started. Perhaps there is a script that they should run or some environment variables that they need to set. Make these steps explicit. These instructions could also be useful to your future self.
+    - `run_mlp_training(data_train, labels_train, data_test, labels_test, d_h, learning_rate, num_epoch)`: trains an MLP classifier and returns training accuracies and testing accuracy.
 
-You can also document commands to lint the code or run tests. These steps help to ensure high code quality and reduce the likelihood that the changes inadvertently break something. Having instructions for running tests is especially helpful if it requires external setup, such as starting a Selenium server for testing in a browser.
 
-## Authors and acknowledgment
-Show your appreciation to those who have contributed to the project.
+5. In the `results` folder there are three plot images:
+   - `knn.png`: refers to the knn algorithm, it represents the plot of the accuracy evolution along increasing value of 'k' (from 1 to 20)
+   - `mlp.png`: refers to the MLP neural network, it represents the plot of the training accuracies evolution along 100 epochs 
+   - `loss.png`: refers to the MLP neural network, it represents the plot of the loss evolution along 100 epochs (further proof that the network works)
 
-## License
-For open source projects, say how it is licensed.
+## Usage
 
-## Project status
-If you have run out of energy or time for your project, put a note at the top of the README saying that development has slowed down or stopped completely. Someone may choose to fork your project or volunteer to step in as a maintainer or owner, allowing your project to keep going. You can also make an explicit request for maintainers.
+1. Clone the repository.
+    ```bash
+    git clone https://gitlab.ec-lyon.fr/acavallo/image-classification.git
+    ```
+2. Create a folder named data in which you move the downloaded cifar-10-batches-py folder. 
+3. run the desired model KNN or MLP NN by running the respective files `knn.py` et `mlp.py`.
+   - if you want to modify the hyperparameters just go for both files in the `main()` function and modify them as desired.
\ No newline at end of file
diff --git a/images/cifar.png b/images/cifar.png
new file mode 100644
index 0000000000000000000000000000000000000000..62d7188b90c46d95fdb68467c9c5e26b0d875fe1
Binary files /dev/null and b/images/cifar.png differ
diff --git a/knn.py b/knn.py
index 8f7755b712d4121e39a3df9b0c7ba888b14b2d8d..b2e8788af69e62d1588f6f784ed410efbede6c17 100644
--- a/knn.py
+++ b/knn.py
@@ -33,7 +33,7 @@ def knn_predict(dists, labels_train, k):
 
 def evaluate_knn(dists, labels_train, labels_test, k):
 
-    # We apply the knn algorithm and then we compare the predictionswith the labels
+    # We apply the knn algorithm and then we compare the prediction swith the labels
     predictions = knn_predict(dists, labels_train, k)
 
     return np.mean(predictions == labels_test)
diff --git a/mlp.py b/mlp.py
index c2f9b0eaa648e82416a4b628d492b462e812c98d..734a01e01363a0c9b87d655439b67898f95c93f7 100644
--- a/mlp.py
+++ b/mlp.py
@@ -1,18 +1,61 @@
-import numpy as np
 import matplotlib.pyplot as plt
 from read_cifar import *
-
-# Function to code a vector to one-hot encoding
-def one_hot(y):
-    one_hot_matrix = np.zeros((y.shape[0], max(y)+1))
-    for i in range(y.shape[0]):
-        one_hot_matrix[i, y[i]] = 1
-    return one_hot_matrix
+import numpy as np
 
 # Sigmoid activation function
 def sigmoid(z):
     return 1 / (1 + np.exp(-z))
 
+# Function to perform one gradient descent step with MSE loss
+def learn_once_mse(w1, b1, w2, b2, data, labels, learning_rate):
+
+    # Set input data, input dimension, hidden neurons, and output dimension
+    m = data.shape[0]
+
+    a0 = data
+    z1 = np.matmul(a0, w1) + b1
+    a1 = sigmoid(z1)
+    z2 = np.matmul(a1, w2) + b2
+    a2 = sigmoid(z2)
+
+    # Compute Mean Squared Error (MSE) loss
+    loss = np.mean(np.square(a2 - labels))
+
+    # Calculate gradients
+    d_a2 = 2 * (a2 - labels) / m
+    d_z2 = d_a2 * a2 * (1 - a2)
+    d_w2 = np.matmul(a1.T, d_z2)
+    d_b2 = np.sum(d_z2, axis=0)
+
+    d_a1 = np.matmul(d_z2, w2.T)
+    d_z1 = d_a1 * a1 * (1 - a1)
+    d_w1 = np.matmul(a0.T, d_z1)
+    d_b1 = np.sum(d_z1, axis=0)
+
+    # Update weights and biases
+    w1 -= learning_rate * d_w1
+    b1 -= learning_rate * d_b1
+    w2 -= learning_rate * d_w2
+    b2 -= learning_rate * d_b2
+
+    return w1, b1, w2, b2, loss
+
+'''
+Function to code a vector to one-hot encoding
+This function is general for any possible array, for a specific problem is better to use the number of possible classes to match 
+the dimension in the further computation, in case of not all the possible classes are present in the 'labels' array.
+For my algorithm it works well because I use the full training data in one step, so all the classes are surely present.
+'''
+def one_hot(labels):
+
+    #num_classes = 10
+    #one_hot_matrix = np.zeros((labels.shape[0], num_classes))
+
+    one_hot_matrix = np.zeros((labels.shape[0], max(labels)+1))
+    for i in range(labels.shape[0]):
+        one_hot_matrix[i, labels[i]] = 1
+    return one_hot_matrix
+
 # Function to perform one gradient descent step with Binary cross-entropy loss
 def learn_once_cross_entropy(w1, b1, w2, b2, data, labels, learning_rate):
     m = data.shape[0]  # Batch size
@@ -49,13 +92,11 @@ def learn_once_cross_entropy(w1, b1, w2, b2, data, labels, learning_rate):
 def train_mlp(w1, b1, w2, b2, data_train, labels_train, learning_rate, num_epochs):
 
     train_accuracies = []
-    losses=[]
     for epoch in range(num_epochs):
         print('EPOCH ' + str(epoch + 1))
         labels_coded = one_hot(labels_train)
         w1, b1, w2, b2, loss = learn_once_cross_entropy(w1, b1, w2, b2, data_train, labels_coded, learning_rate)
 
-    # Calculate training accuracy for this epoch
         a0 = data_train
         z1 = np.matmul(a0, w1) + b1
         a1 = sigmoid(z1)
@@ -63,12 +104,13 @@ def train_mlp(w1, b1, w2, b2, data_train, labels_train, learning_rate, num_epoch
         a2 = sigmoid(z2)
         predictions = np.argmax(a2, axis=1)
 
+        # Compute the training accuracy for this epoch
         accuracy = np.mean(predictions == labels_train)
         train_accuracies.append(accuracy)
-
+        print('Accuracy : ' + str(round(accuracy, 4)))
         print('Loss : '+ str(round(loss, 4)) + '\n')
 
-    return w1, b1, w2, b2, train_accuracies, losses
+    return w1, b1, w2, b2, train_accuracies
 
 # Function to test the MLP on a test set
 def test_mlp(w1, b1, w2, b2, data_test, labels_test):
@@ -97,12 +139,12 @@ def run_mlp_training(data_train, labels_train, data_test, labels_test, d_h, lear
     b2 = np.zeros((1, num_classes))
 
     # Train the MLP on the training data
-    w1, b1, w2, b2, train_accuracies, losses = train_mlp(w1, b1, w2, b2, data_train, labels_train, learning_rate, num_epochs)
+    w1, b1, w2, b2, train_accuracies = train_mlp(w1, b1, w2, b2, data_train, labels_train, learning_rate, num_epochs)
 
     # Test the MLP on the testing data
     test_accuracy = test_mlp(w1, b1, w2, b2, data_test, labels_test)
 
-    return train_accuracies, test_accuracy, losses
+    return train_accuracies, test_accuracy
 
 def main():
 
@@ -120,19 +162,19 @@ def main():
     data_train, data_test, labels_train, labels_test = split_dataset(data, labels, split_factor)
 
     # Run MLP training and testing
-    train_accuracies, test_accuracy, losses= run_mlp_training(data_train, labels_train, data_test, labels_test, d_h, learning_rate,
+    train_accuracies, test_accuracy= run_mlp_training(data_train, labels_train, data_test, labels_test, d_h, learning_rate,
                                                        num_epochs)
     # Test accuracy after 'num_epochs' epochs of training
     print('FINAL ACCURACY : ' + str(round(test_accuracy, 4)) + '\n')
 
     # Plot the training accuracy for each epoch
     x = range(1, num_epochs + 1)
-    plt.plot(x, losses)
+    plt.plot(x, train_accuracies)
     plt.xlabel('Epoch')
-    plt.ylabel('Training Loss')
-    plt.title('Training Loss vs. Epoch')
+    plt.ylabel('Training Accuracy')
+    plt.title('Training accuracy evolution')
     plt.grid()
-    plt.savefig('results/loss.png')
+    plt.savefig('results/mlp2.png')
     plt.show()
 
 if __name__ == "__main__":
diff --git a/read_cifar.py b/read_cifar.py
index 1e8d727b9cad306b8a15e59b29cbe48598027e79..1c9115027eb5f57553e404dde49b63b1c3fd964e 100644
--- a/read_cifar.py
+++ b/read_cifar.py
@@ -6,7 +6,6 @@ from sklearn.model_selection import train_test_split
 def read_cifar_batch(batch):
 
     with open(batch, 'rb') as file:
-
         dict = pickle.load(file, encoding='bytes')
         batch_data = dict[b'data']
         batch_labels = dict[b'labels']
diff --git a/results/mlp.png b/results/mlp.png
deleted file mode 100644
index e2e197c23034254cea0468048191f99bb0594821..0000000000000000000000000000000000000000
Binary files a/results/mlp.png and /dev/null differ