Hangyu Zhou, Constantine Dovrolis, Stephen Mussmann · 2026 · arXiv
DOI: 10.48550/arXiv.2610.28555 · open-access PDF
Pembelajaran statistik dalam dimensi tinggi menderita kutukan dimensionalitas. Untungnya, banyak fungsi yang menarik praktis komposisi jarang, yang berarti mereka mengakui komposisi fungsi lokal, masing-masing tergantung pada hanya beberapa variabel, memungkinkan kompleksitas sampel untuk bergantung pada arity lokal daripada dimensi lingkungan. Namun menyadari manfaat ini membutuhkan eksploitasi struktur komposisi tersembunyi, yang teori tidak menetapkan untuk pelatihan berbasis gradient praktis. Kami mempelajari kesenjangan ini dengan CSFRBench, benchmark terkontrol yang menyembunyikan komputasi komposisi target selama
Machine translation (Meta M2M100); the English original follows.
Statistical learning in high dimensions suffers from the curse of dimensionality. Fortunately, many functions of practical interest are compositionally sparse, meaning they admit a composition of local functions, each depending on only a few variables, allowing sample complexity to depend on local arity rather than ambient dimension. Yet realizing this benefit requires exploiting hidden compositional structure, which theory does not establish for practical gradient-based training. We study this gap with CSFRBench, a controlled benchmark that hides the target's compositional computation during
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