Function Approximations

A neural network that learns to approximate mathematical functions and images by training a small multilayer perceptron (MLP) to map inputs to outputs — with a live visualization that updates every epoch so you can watch the network learn in real time.

Example

python neuralnets/pipeline.py --image_path icons/Cupcake.png --epochs 200 --learning_rate 5e-3 --batch_size 64 --rgb

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What It Does

This app has two modes:

1. Function Mode

Given any mathematical function y = f(x), the network is trained to learn the mapping from x → y over the domain [-10, 10]. A live plot shows the network's prediction versus the true function at the end of every training epoch.

2. Image Mode

Given any image file, the network is trained to learn the mapping from pixel coordinates (x, y) → pixel color values. The network essentially learns to "memorize" the image as a continuous function. Supports both grayscale and RGB color modes, and a live preview updates every epoch showing the reconstructed image as training progresses.

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Architecture

The neural network (FunctionApproximator) is a simple 3-layer MLP defined in neuralnets/model.py:

• Input layer → 128 hidden units (ReLU)
• 128 hidden units → 128 hidden units (ReLU)
• 128 hidden units → Output layer

For function approximation, input size is 1 and output size is 1.
For image approximation, input size is 2 (x, y coordinates) and output size is 1 (grayscale) or 3 (RGB).

Training is handled via PyTorch Lightning with an Adam optimizer and MSE loss.

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Requirements

Install the dependencies before running:

pip install torch lightning numpy matplotlib sympy pillow

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Usage

Run pipeline.py from inside the neuralnets/ directory:

cd neuralnets
python pipeline.py [OPTIONS]

You must specify exactly one of --function or --image_path.

Options

Argument	Type	Default	Description
--function	str	None	Math function to approximate. Must be in the form "y=f(x)".
--image_path	str	None	Path to an image file to approximate.
--image_size	int	64	Width and height (in pixels) to resize the image to before training.
--rgb	flag	off	Use RGB (3-channel) output for image mode. Defaults to grayscale.
--epochs	int	100	Number of training epochs.
--batch_size	int	64	Batch size used during training.
--learning_rate	float	1e-3	Learning rate for the Adam optimizer.

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Project Structure

function_approximations/
├── neuralnets/
│   ├── model.py       # MLP model definition (FunctionApproximator)
│   └── pipeline.py    # Training pipeline, data loading, and live visualization
└── icons/             # Sample food emoji images to use as approximation targets