{"id":10900,"date":"2026-03-04T07:02:37","date_gmt":"2026-03-04T07:02:37","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2026\/03\/04\/2603-02594\/"},"modified":"2026-03-04T07:02:37","modified_gmt":"2026-03-04T07:02:37","slug":"2603-02594","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2026\/03\/04\/2603-02594\/","title":{"rendered":"Low-Degree Method Fails to Predict Robust Subspace Recovery"},"content":{"rendered":"

Low-Degree Method Fails to Predict Robust Subspace Recovery
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arXiv:2603.02594v1 Announce Type: new
\nAbstract: 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 $k=n^{Omega(1)}$. Moreover, the low-degree moments match exactly up to degree $k=O(sqrt{log n\/loglog n})$. Our problem is a special case of the well-studied robust subspace recovery problem. The lower bounds suggest that there is no polynomial time algorithm for this problem. In contrast, we give a simple and robust polynomial time algorithm that solves the problem (and noisy variants of it), leveraging anti-concentration properties of the distribution. Our results suggest that the low-degree method and low-degree moments fail to capture algorithms based on anti-concentration, challenging their universality as a predictor of computational barriers.<\/div>\n

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\n He Jia, Aravindan Vijayaraghavan
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Low-Degree Method Fails to Predict Robust Subspace Recovery arXiv:2603.02594v1 Announce Type: new Abstract: 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 […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,1190,413,113,112],"tags":[1764,588,198],"class_list":["post-10900","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-cc","category-cs-ds","category-cs-lg","category-stat-ml","tag-degree","tag-low","tag-method"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/10900"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=10900"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/10900\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=10900"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=10900"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=10900"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}