Neural Network Alignment Determined by Data SNR and Sample Size

A new study from Umar and Laio investigates how data characteristics affect representational alignment in neural networks—the phenomenon where distinct networks develop structurally similar latent representations. Training ensembles of linear and nonlinear networks on regression and classification tasks with noise-perturbed datasets, the authors analytically derived alignment for a single-hidden-layer linear network and validated their findings on real-world data. They discovered that alignment varies monotonically with signal-to-noise ratio (SNR): cleaner data yields higher alignment. However, alignment changes non-monotonically with training sample size, reaching a minimum near the interpolation threshold (where model capacity matches data complexity). This pattern held across architectures, tasks, and data types.

Critically, the paper demonstrates that higher alignment does not imply better generalization—a counterintuitive finding for practitioners. The interpolation threshold, where alignment dips, is often associated with modern deep learning phenomena like double descent. This suggests that optimizing for alignment alone may be misleading; instead, understanding the interplay between data quantity, quality, and model capacity is essential. For professionals building production models, these insights imply that simply adding more noisy data or pursuing higher representation similarity may not improve performance. The research offers a theoretical foundation for designing robust training pipelines, especially in data-limited or high-noise domains like medical imaging or financial forecasting.