Signal-to-Noise Ratio and Sample Size Govern Representational Alignment in Neural Networks

• URL: http://arxiv.org/abs/2605.26973v1
• Date: Tue, 26 May 2026 12:58:48 GMT
• Title: Signal-to-Noise Ratio and Sample Size Govern Representational Alignment in Neural Networks
• Abstract summary: We train an ensemble of networks on regression and classification tasks using training sets by independent realizations of a noise process.<n>We show that the signal-to-noise ratio (SNR) and the training sample size influence the alignment.<n>Across linear and nonlinear networks, regression and classification tasks, and both synthetic and real-world data, we consistently observe that alignment varies monotonically with SNR.
• Score: 48.553902624178995
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural networks are known to develop latent representations that are $aligned$, namely structurally similar across networks trained with different architectures, training protocols, or training datasets. We study this phenomenon in a controlled setting, where we train an ensemble of networks on regression and classification tasks using training sets perturbed by independent realizations of a noise process. We show that the signal-to-noise ratio (SNR) and the training sample size influence the alignment in qualitatively similar ways in networks trained on real-world datasets and in an extremely simple $linear$ network with a single hidden layer, for which the alignment can be estimated analytically. Across linear and nonlinear networks, regression and classification tasks, and both synthetic and real-world data, we consistently observe that alignment varies monotonically with SNR but non-monotonically with training sample size. In particular, the alignment is minimized near the interpolation threshold, and a stronger alignment does not necessarily correspond to better generalization error. These findings reveal a non-trivial dependence of alignment on data quality and quantity, decoupled from generalization performance.

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