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How Data Augmentation Shapes Neural Representations

NeurIPS 2026 · Label-efficient and robust learning › Recognition and long-tail · approach: Contrastive representation theory · 0 citations (OpenAlex)

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Uses Riemannian shape space (translation, scale, rotation, reflection invariant) to characterize how data augmentation strength and type move hidden representations along trajectories, and relates trajectory angles to ensemble gains on CIFAR-10.

Problem

Performance metrics alone obscure how data augmentation changes the geometry of learned hidden representations; it is unclear whether augmentation strengths trace structured paths and whether representational diversity predicts ensembling gains.

Approach

Embed hidden-layer representations of clean probe images into Riemannian shape space, where distance is invariant to translation, scale, rotation and reflection, and treat augmentation sweeps as geodesic trajectories whose angles and landmark displacements quantify representational change.

Key results

• Aligned shape distances show ordered trajectories for Gaussian noise and patch Gaussian augmentations, and ridge regression can predict held-out augmentation hyperparameters from aligned shapes, while unaligned distances show no such organization.
• Distance scales D_aug and D_seed separate around patch Gaussian s=0.2, giving a natural unit for augmentation strength relative to seed variation.
• Geodesic angles between augmentation trajectories (roughly 60 to 81 degrees) correlate with ensemble accuracy gains across pairs of augmentation methods.

Surprising findings

• Without orthogonal alignment, the organization of representations by augmentation strength disappears entirely, so Euclidean-style comparison misses the structure.

Limitations

• Limited to image classification, classical augmentations, and post-hoc analysis on a fixed set of test probe images.
• Riemannian shape distance is computationally expensive for high-dimensional convolutional representations, requiring PCA reduction.
• Only small architectures and CIFAR-10 studied; no larger models or learned augmentation policies.

Experimental setup

Datasets: CIFAR-10 ImageNet

Benchmarks: CIFAR-10

Metrics: Riemannian shape distance geodesic angle leave-one-out ridge regression R^2 / prediction accuracy of ensemble accuracy improvement D_aug vs D_seed

Baselines: linear CKA random seed variation

Builds on: Williams2021 metric spaces of representations Lange2023 representational trajectories Harvey normalized Bures similarity CKA

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