Addressing Overfitting in Autoencoders

Autoencoders are a type of neural network with a fundamental architecture designed to learn compressed representations by minimizing reconstruction error. The basic autoencoder aims to make the output $x'$ as close as possible to the input $x$ , formally $x' = g(f(x)) \approx x$ , where $f$ is the encoder and $g$ is the decoder. While powerful, this simple objective can lead to a significant problem: overfitting.

Overfitting occurs when a model learns the training data too well, capturing noise and specific details rather than the underlying patterns. In the context of autoencoders, this often manifests in the network learning an approximate identity function. If the autoencoder, particularly the encoder $f$ and decoder $g$ , possesses sufficient capacity (e.g., many parameters through deep or wide layers) relative to the complexity of the data, it can simply learn to pass the input through the bottleneck layer with minimal information loss, effectively memorizing the training examples.

Consider an autoencoder with a bottleneck dimension equal to or greater than the input dimension. Without any constraints, the network could theoretically learn to copy the input directly to the output, achieving near-perfect reconstruction on the training data. Even with an undercomplete bottleneck (latent dimension < input dimension), if the network capacity is high, it might still find complex mappings that reproduce the training data accurately but fail to generalize to unseen examples. The resulting latent representation, while allowing for good reconstruction of familiar inputs, might not capture the essential, generalizable features of the data distribution. Instead, it might embed noise or idiosyncrasies specific to the training set.

This leads to poor performance on new, unseen data. The reconstruction error on a validation or test set might be significantly higher than on the training set, or the learned latent features might prove useless for downstream tasks like classification or clustering.

Illustration of overfitting during autoencoder training. While training loss continuously decreases, validation loss starts to increase after a certain point, indicating the model is memorizing training data rather than generalizing.

To prevent the autoencoder from merely learning the identity function and to encourage the discovery of more meaningful representations, we need to introduce additional constraints or penalties into the learning process. This is the core idea behind regularization. Regularization techniques modify the autoencoder's objective function or training process to discourage overly complex solutions and promote desirable properties in the learned latent code $z = f(x)$ . These properties might include sparsity (activating only a few neurons), robustness to noise, or smoothness (small changes in input lead to small changes in representation).

By applying regularization, we guide the autoencoder to learn representations that not only reconstruct the input well but also capture the underlying structure of the data in a more generalizable manner. The following sections examine specific regularization strategies, starting with Sparse Autoencoders, Denoising Autoencoders, and Contractive Autoencoders, each designed to combat overfitting and improve the quality of the learned features.

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References

Deep Learning, Ian Goodfellow, Yoshua Bengio, and Aaron Courville, 2016 (MIT Press) - Comprehensive coverage of deep learning, including dedicated chapters on regularization techniques to combat overfitting and the architecture and applications of autoencoders.
Extracting and Composing Robust Features with Denoising Autoencoders, Pascal Vincent, Hugo Larochelle, Isabelle Lajoie, Yoshua Bengio, Pierre-Antoine Manzagol, 2008 Proceedings of the 25th International Conference on Machine Learning (ICML) (ACM) DOI: 10.1145/1390156.1390294 - Introduces Denoising Autoencoders, a regularization technique designed to learn robust feature representations by training the autoencoder to reconstruct the original input from a corrupted version.
UFLDL Tutorial: Sparse Autoencoders, Andrew Ng, 2011 (Stanford University) - Explains the concept and implementation of Sparse Autoencoders, a regularization method that encourages a sparse representation in the latent layer to prevent overfitting and learn more meaningful features.
Contractive Auto-Encoders: Explicit Invariance Through Penalizing Local Contractions, Salah Rifai, Pascal Vincent, Xavier Muller, Xavier Glorot, Yoshua Bengio, 2011 Proceedings of the 28th International Conference on Machine Learning (ICML) (JMLR Workshop and Conference Proceedings) - Introduces Contractive Autoencoders, a regularization technique that encourages the learned representation to be robust to small perturbations of the input by penalizing large derivatives of the encoding function.