More Data Cannot Break a Symmetry: Identifiability by Design

Summary

The article demonstrates that symmetric stimulus designs (e.g., equally spaced colors) create a fundamental identifiability ceiling in unsupervised representation alignment that cannot be overcome. Neither additional data nor decoder reinitializations can surpass this limit. The study proposes a low-cost design-stage diagnostic to prevent such degenerate geometries before data collection begins.

Why it matters

The paper transforms a known invariant (Demetci et al., 2024) into a practical pre-experimental control with a single function call cost. This allows researchers to avoid months of failed alignment efforts. The finding that model separation and alignment recovery are fundamentally uncorrelated (r = −0.02) challenges a common assumption in representation learning benchmarks. If the symmetry argument generalizes beyond color to orientation, tone, or motion, it could reshape the design of psychophysical and neural decoding experiments.

Highlights

• A budget of 64 reinitializations fails to fix symmetric color designs, while an asymmetric cluster with the same N value is successfully recovered every time. This indicates that the failure is structural, not random.
• Selecting nine colors based solely on the diagnostic (without consulting learned representations) reduces catastrophic alignment errors in 93 model representations from 75% to 2%.
• The cheapest non-identity relabeling, i.e., the obvious degeneration diagnostic, misranks two published designs because it creates near-copy transpositions similar to dense sampling.

Critical take

The experimental demonstration is limited to the color space, where candidate geometries can be expressed in closed form. Generalization to orientation, tone, or motion is claimed as a risk but not tested. Therefore, the generalizability claim relies on analogy rather than evidence. Additionally, the striking improvement from 75% to 2% was measured while keeping all models, layers, N values, and decoders fixed. This leaves unclear how the diagnostic interacts with more realistic and heterogeneous experimental workflows.