{"id":26685502,"url":"https://github.com/albanecoiffe/mlp_approximation_universelle","last_synced_at":"2025-03-26T10:16:33.616Z","repository":{"id":275823241,"uuid":"862371091","full_name":"albanecoiffe/MLP_approximation_universelle","owner":"albanecoiffe","description":"Étude de l'approximation universelle dans les réseaux de neurones.","archived":false,"fork":false,"pushed_at":"2025-02-04T18:40:41.000Z","size":309,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"main","last_synced_at":"2025-02-04T19:37:40.644Z","etag":null,"topics":["mlp","tensorflow"],"latest_commit_sha":null,"homepage":"","language":"HTML","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/albanecoiffe.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null}},"created_at":"2024-09-24T13:42:50.000Z","updated_at":"2025-02-04T18:40:45.000Z","dependencies_parsed_at":"2025-02-04T19:37:42.716Z","dependency_job_id":"6469161e-6fea-428d-a721-414bab817414","html_url":"https://github.com/albanecoiffe/MLP_approximation_universelle","commit_stats":null,"previous_names":["albanecoiffe/mlp_approximation_universelle"],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/albanecoiffe%2FMLP_approximation_universelle","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/albanecoiffe%2FMLP_approximation_universelle/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/albanecoiffe%2FMLP_approximation_universelle/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/albanecoiffe%2FMLP_approximation_universelle/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/albanecoiffe","download_url":"https://codeload.github.com/albanecoiffe/MLP_approximation_universelle/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":245632397,"owners_count":20647194,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["mlp","tensorflow"],"created_at":"2025-03-26T10:16:33.034Z","updated_at":"2025-03-26T10:16:33.595Z","avatar_url":"https://github.com/albanecoiffe.png","language":"HTML","funding_links":[],"categories":[],"sub_categories":[],"readme":"# 🌐 Study of Universal Approximation in Neural Networks\n\n[Notebook](https://albanecoiffe.github.io/MLP_approximation_universelle/)\n\n## 🧠 Objective\nThe goal of this lab is to study a fundamental property of static (non-recurrent) neural networks: the universal approximation theorem. This property states that neural networks, even with just one hidden layer, can approximate any continuous function given sufficient neurons.\n\nIn this lab, we train a Multi-Layer Perceptron (MLP) with a single hidden layer on a piecewise-defined function and analyze how well the network approximates it.\n\n## 📊 Lab Steps\n### 1. Data Generation\nThe function f(x) is defined as follows:      \n𝑓(𝑥)={     \nsin(𝜋𝑥) si 𝑥∈[−1,1[       \n0 si 𝑥∈[−2,−1]∪[1,2]       \n-Adding Gaussian noise (0,0.2) to the generated data.\n- Generating multiple training and test samples from this function.\n\n### 2. mplementing MLP with TensorFlow\n\n- Using a simple MLP with one hidden layer to approximate the generated function.\n- Exploring different architectures by varying the number of hidden neurons (e.g., 1, 3, 5, 7 neurons).      \n  \n### Recommendations\n- Analyzing results: Start with a small number of neurons and observe how the function approximation evolves.\n- Testing variations: Experiment with different hidden layer sizes to see how the approximation becomes more or less \"sparse\" depending on the model's capacity.\n- Evaluating performance: Assess the generalization of the model by testing it on a separate test set.      \n\n## 🛠️ Technologies Used\n- Python: Main programming language for implementation.\n- TensorFlow: Framework for building and training the MLP neural network.\n- NumPy: For generating and manipulating data.\n- Matplotlib: For visualizing function approximations.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Falbanecoiffe%2Fmlp_approximation_universelle","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Falbanecoiffe%2Fmlp_approximation_universelle","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Falbanecoiffe%2Fmlp_approximation_universelle/lists"}