Noisy Gaussian NN – Robustness to Label Noise

Overview

This project explores how a simple 1-hidden-layer neural network handles increasing label noise when fitting a Gaussian curve.
We test three noise levels (σ = 0.05, 0.1, 0.2) to see when the network smooths effectively and when it starts to underfit.

Dataset

Synthetic dataset: Gaussian curve (y = exp(-x^2))
Noise added directly to labels using torch.normal
200 evenly spaced x points in [-2, 2]

Model

Architecture: 1 hidden layer, 50 neurons, ReLU activation
Loss: MSELoss
Optimizer: Adam (lr=0.01)
Training: 2000 epochs

Results

Low noise: NN fits curve smoothly.
Medium noise: Slight underfitting.
High noise: Curve shape lost, noise dominates.

Key Insight

More noise ≠ better regularization.
Too much noise can destroy the signal beyond recovery.

Files

GaussianApproximation.ipynb – Full experiment, plots, and analysis
README.md – This file

License

MIT License – free to use, modify, and distribute with attribution.