{"slug": "improving-openai-s-bound-on-the-exact-discrete-fourier-transform-below-n-log-n", "title": "Improving OpenAI's bound on the exact discrete Fourier transform below n log n", "summary": "A research draft published on OpenAI Problem #130 proposes an all-length bound of T(n) = O(n(log n)^(1−δ)) with δ = 7.3×10⁻⁵ for computing the exact discrete Fourier transform, a 730-million-fold increase in the exponent saving over OpenAI's published δ = 10⁻¹³. The draft builds on Swapnil Jain's round-six complex network for Problem #109 and its cited predecessors, transferring those advances from integer multiplication to the Fourier setting. A sixth update to OpenAI Problem #109 reports κ > 2⁻¹⁵, tightened from κ = 2⁻¹⁸², with an exact witness of 3.667 × 10⁻⁵, about 2.4-fold over the previous 1.548 × 10⁻⁵ and a 2¹⁶⁷-fold improvement over the original OpenAI result.", "body_md": "We’re publishing a research draft on OpenAI Problem #130: computing the exact discrete Fourier transform below n log n.\nOur draft proposes an all-length bound of\nT(n) = O(n(log n)^(1−δ)), with δ = 7.3×10⁻⁵.\nThat’s a 730-million-fold increase in the exponent saving over OpenAI’s published δ = 10⁻¹³.\nBuilding on Swapnil Jain’s round-six complex network for Problem #109 and its cited predecessors, we propose transferring those advances from integer multiplication to the Fourier setting.\n\nSixth update to OpenAI problem #109 (integer multiplication): we are now past 2^-15.\nκ > 2⁻¹⁵  (tightened from κ = 2⁻¹⁸²)\nThe exact witness is 3.667 × 10⁻⁵, about 2.4 fold over our previous 1.548 × 10⁻⁵, and a 2¹⁶⁷ fold improvement over the original OAI result. \nBoth", "url": "https://wpnews.pro/news/improving-openai-s-bound-on-the-exact-discrete-fourier-transform-below-n-log-n", "canonical_source": "https://twitter.com/ryaneshea/status/2108239154572394772", "published_at": "2026-10-09 00:43:06+00:00", "updated_at": "2026-10-09 00:47:05.923427+00:00", "lang": "en", "topics": ["ai-research", "machine-learning"], "entities": ["OpenAI", "Swapnil Jain", "OpenAI Problem #130", "OpenAI Problem #109"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/improving-openai-s-bound-on-the-exact-discrete-fourier-transform-below-n-log-n", "markdown": "https://wpnews.pro/news/improving-openai-s-bound-on-the-exact-discrete-fourier-transform-below-n-log-n.md", "text": "https://wpnews.pro/news/improving-openai-s-bound-on-the-exact-discrete-fourier-transform-below-n-log-n.txt", "jsonld": "https://wpnews.pro/news/improving-openai-s-bound-on-the-exact-discrete-fourier-transform-below-n-log-n.jsonld"}}