Unveiling Neural Autoencoders Through Latent Vector Fields

Autoencoders and Their Latent Space

Neural networks are designed to learn compressed representations of high-dimensional data, and autoencoders (AEs) are a popular example of such models. These architectures consist of an encoder and a decoder that map input data into a low-dimensional latent space and then reconstruct it. This latent space makes patterns and features of the data more interpretable, enabling various downstream tasks. Autoencoders have widespread applications including image classification, generative modeling, and anomaly detection due to their ability to capture complex data distributions in a structured form.

Memorization Versus Generalization Challenge

A key challenge in neural models, especially autoencoders, is balancing memorization of training data with generalization to unseen data. Overfitting results in poor performance on new inputs, while excessive generalization might discard important details. Researchers seek to understand how these models encode knowledge internally in ways that can be revealed without direct access to input data. Insights into this balance can improve model design and training.

Limitations of Current Probing Techniques

Existing approaches focus mainly on performance metrics like reconstruction error or involve modifying the model or inputs to infer internal mechanisms. However, these methods often fail to explain how model architecture and training dynamics affect learning outcomes. There is a need for more intrinsic and interpretable techniques that go beyond conventional metrics and architectural tweaks.

Latent Vector Fields: Viewing Autoencoders as Dynamical Systems

Researchers from IST Austria and Sapienza University introduced a novel perspective by interpreting autoencoders as dynamical systems operating in latent space. By repeatedly applying the encoding-decoding function to a latent point, they form a latent vector field that reveals attractors—stable points where data representations converge. This field naturally exists in any autoencoder without requiring model changes or extra training. It provides visualization of data flow through the model and links to memorization and generalization. The method was validated on various datasets and foundation models, extending beyond synthetic benchmarks.

Iterative Mapping and Contraction Dynamics

The repeated encoder-decoder mapping is treated as a discrete differential equation, creating latent trajectories defined by residual vectors at each iteration. If the mapping is contractive—shrinking the space with each step—the system stabilizes at fixed points or attractors. Common design practices like weight decay, small bottleneck sizes, and augmentation-based training promote this contraction behavior. Thus, the latent vector field summarizes training dynamics and illustrates how models encode data.

Empirical Findings: Attractors Reflect Model Behavior

Experiments training convolutional autoencoders on MNIST, CIFAR10, and FashionMNIST showed that low-dimensional bottlenecks (2 to 16) yield high memorization coefficients (>0.8), while higher dimensions favor generalization with lower test errors. The number of attractors increases with training epochs, stabilizing over time. Testing a vision foundation model pretrained on Laion2B, attractors derived solely from Gaussian noise reconstructed data from six diverse datasets effectively. At 5% sparsity, reconstructions outperformed those from random orthogonal bases, with consistently lower mean squared error. This confirms attractors form a compact and robust dictionary of representations.

Implications for Model Interpretability

This research presents a powerful new tool to inspect how neural models store and utilize information. The latent vector fields and their attractors reveal a model's tendencies toward memorization or generalization, even without input data. Such insights can enhance the development of interpretable and robust AI by clarifying what models learn and how they behave during training and inference.

For full details, see the original research paper. All credit goes to the project researchers.