Exploring the latent space: compact representations with autoencoders

Abstract

This work analyzes how latent-space size and bottleneck structure affect reconstruction quality and downstream utility in convolutional autoencoders. We implement and evaluate four variants—standard (conv_ae), sparse (conv_sparse), denoising (conv_denoising) and variational (conv_vae)—on CIFAR-10 across five latent dimensions (16, 32, 64, 128, 256). Reconstructions are assessed with MSE, SSIM, PSNR, ERGAS and UQI; latent embeddings are evaluated with supervised classifiers (Logistic Regression, MLP, Random Forest, KNN) and unsupervised clustering (KMeans, GMM, HDBSCAN) using ARI and NMI. Results indi cate that conv_sparse attains the best perceptual reconstruction scores (e.g., MSE ≈ 0.0021, SSIM ≈ 0.89 at d = 256), conv_denoising yields the most discriminative embeddings for classification (best MLP accuracy ≈ 0.5471 at d = 256), and conv_vae underperforms at small d. Unsupervised clustering recovery is weak (ARI/NMI typically < 0.2), motivating future work on contrastive and clustering-aware objectives and modified VAE losses.