Low-Degree Method Fails to Predict Robust Subspace Recovery
The low-degree polynomial framework has been highly successful in predicting computational versus statistical gaps for high-dimensional problems in average-case analysis and machine learning. This success has led to the low-degree conjecture, which posits that this method captures the power and limitations of efficient algorithms for a wide class of high-dimensional statistical problems. We identify a natural and basic hypothesis testing problem in $\mathbb{R}^n$ which is polynomial time solvable, but for which the low-degree polynomial method fails to predict its computational tractability even up to degree $k=n^{Ω(1)}$. Moreover, the low-degree moments match exactly up to degree $k=O(\s...
| Authors | He Jia, Aravindan Vijayaraghavan |
|---|---|
| Primary category | stat.ML |
| Published | 3 March 2026 |
| Last updated at source | 3 March 2026 |
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