New metric exposes hidden weakness in neural network representations undetected by standard measures

Existing methods for analyzing how neural networks organize information have a critical blind spot: they can confirm that two representations look similar, but they cannot tell whether that structure will actually hold up under stress. A new study from researchers on arXiv introduces geometric stability as a previously overlooked dimension of representation quality, along with a metric called Shesha designed to measure it.

The limitation of current approaches#

Standard techniques like representational similarity analysis, centered kernel alignment (CKA), and Procrustes distance focus on alignment between spaces — whether one network's internal geometry resembles another's. But this tells only part of the story. These rotation-invariant metrics ignore a crucial property: whether a representation's learned structure survives when models are actually manipulated in practice.

In real-world applications, researchers and engineers interact with neural network representations through probing, patching, and steering, all of which operate on specific coordinate dimensions. A representation might have the same geometric alignment as another after being rotated, yet this rotation could destroy the very structure that makes the representation useful for downstream tasks. Traditional metrics cannot detect this vulnerability.

How Shesha measures what others miss#

Shesha quantifies geometric stability by computing dissimilarity matrices from complementary random halves of a model's feature dimensions and measuring how well they correlate. This approach is intentionally rotation-non-invariant — meaning it will detect when feature coordinates are rearranged, even if the underlying spectrum remains unchanged.

The researchers demonstrate a striking double dissociation that isolates the mechanism:

• Removing the top principal component collapses CKA scores while Shesha remains robust
• Rotating a representation into its eigenbasis (which preserves both spectrum and CKA exactly) causes Shesha to collapse

This proves the two metrics measure genuinely different properties.

Empirical findings across multiple domains#

Testing across 2,463 encoder configurations spanning seven different domains, the study found that CKA and Shesha are but (correlation: −0.47). This pattern held consistently whether looking at vision models, language encoders, or other architectures.