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A law of adversarial risk, interpolation, and label noise

ICLR 2023 · Label-efficient and robust learning › Noisy labels · approach: Instance-dependent noise modeling · 0 citations (OpenAlex)

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Interpolate uniformly noisy labelsAny classifier on a compact input subset C · Compact input subset Cadversarial risk: lower bound: \frac14 \mu(\mathcal C)Helped
Interpolate uniformly noisy labelsAny classifier on a compactly supported distribution · Support of μadversarial risk: lower bound: \frac14Helped
Interpolate up to ⌊1.01^d⌋ noisy samples with a classifier that otherwise uses the ground-truth thresholdConstructed classifier on the sphere · Uniform distribution on sphere S^(d−1)adversarial risk: o_d(1)No clear effect
Use uniform label noise instead of noise confined to the long tailInterpolators on the long-tailed interval mixture · Long-tailed mixture of A+B intervalsadversarial risk: O_{\rho} \left( \frac{ A}{B} \right) -> \Omega_{\rho} \left( 1 \right)Hurt
Use the T-shaped hypothesis class rather than the threshold classInterpolating classifiers on the constructed distribution · Distribution on [0,W] × {0}adversarial risk: \mathcal{O}\br{\rho} -> \Omega\br{1}Hurt
Train on uniform label noise rather than human-generated label noise at the same reported noise rateResNet34 · CIFAR-10/100-nadversarial errorHurt
Train on human-generated labels rather than clean labelsResNet34 · CIFAR-10/100-nadversarial errorNo clear effect
Increase the uniform-noise sample size and adversarial radius relative to poisoningUniform-noise adversary versus Poisoner · General distribution with Ω(1) poisoning riskadversarial risk: \Runif_{2\rho, T, \eta} \geq \frac12 \Rpoison_{\rho , N}Helped

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