# MLP Regularization — MNIST

## Setup

A baseline multilayer perceptron (`Dense(500) → Dense(100) → Dense(10)`) compared against the same architecture with `Dropout(0.2)` added after each hidden layer.

## ⚠️ Two variables changed, not one

Before looking at the results: the baseline uses SGD at `lr=0.001`, while the dropout run uses SGD at `lr=0.01` — a 10x higher learning rate, in addition to Dropout being added. This means the comparison below shows what happened between two different configurations, not the isolated effect of Dropout. A rigorous ablation would hold the learning rate constant. This is flagged directly rather than presenting a confounded result as clean evidence for Dropout's effect.

## Training curves

**Baseline:**

![Baseline loss curve](images/mlp-baseline-loss.png)

**With Dropout (and higher learning rate):**

![Dropout loss curve](images/mlp-dropout-loss.png)

## Where each model gets it wrong

**Baseline misclassifications:**

![Baseline misclassified digits](images/mlp-baseline-misclassified.png)

**Dropout version misclassifications:**

![Dropout misclassified digits](images/mlp-dropout-misclassified.png)

## Results

| Model | Test loss |
|---|---|
| Baseline (no dropout, lr=0.001) | 0.279 |
| Dropout (0.2, lr=0.01) | 0.099 |

## Notebooks

- [`mnist-mlp-pred.ipynb`](../mnist-mlp-regularization/mnist-mlp-pred.ipynb)
- [`mnist-mlp-pred-dropout.ipynb`](../mnist-mlp-regularization/mnist-mlp-pred-dropout.ipynb)