2  Auto Encoder

An encoder is a neural network that compresses high-dimensional input data into a lower-dimensional latent representation.

2.1 Architecture

1. Encoder: Maps input \(x \in \mathbb{R}^D\) to latent code \(z \in \mathbb{R}^d\) (compression).
2. Decoder: Reconstructs \(\hat{x}\) from \(z\) (reconstruction).

\[ \mathcal{L}_{\text{AE}} = \text{Reconstruction\_term} = \|x - \text{Decoder}(\text{Encoder}(x))\|^2 \]

Pytorch implementation: logic/model/autoencoder.py

2.2 Applications

• Feature extraction for clustering/visualization.
• Denoising (e.g., noisy Fashion-MNIST reconstruction).

2.3 Limitations

• Deterministic: No probabilistic latent space.
• No control over latent structure (e.g., disentanglement).