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Evidence record 18389 · automatically gathered

The Loss Does Not See the Basis, but Adam Does

Gradient descent on a factored model W = UV^top is implicitly biased toward low-rank solutions, while Adam, starting from the same small initialization, is not. We trace the difference to the gauge symmetry of the loss, its invariance under (U, V) mapsto (UQ, VQ). Gradient flow's low-rank mechanism is available to an optimizer only if that optimizer is gauge-equivariant, a condition necessary for the transfer but not sufficient for low-rank recovery. Gradient descent, momentum, "shared-scalar" A

Record details

Published: 4 August 2026
Source: HuggingFace Daily Papers
Category: Research
Topics: Bias & fairness
Retrieved: 12 August 2026

source-onlyevidence status

These records share source-supplied organisations, an exact publisher byline, automatic topics or regions. The reason is shown on every link; related does not mean supporting, agreeing with or verifying this record.

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How to cite this record

ethics.ai (4 August 2026), “The Loss Does Not See the Basis, but Adam Does,” evidence record 18389, https://ethics.ai/record/18389 (originally published by HuggingFace Daily Papers).

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