Pólya @PolyaEnum

OpenAI disproved all these hypotheses: ETH. SETH, in its fixed-k formulation. Randomized ETH, Randomized SETH. Gap-ETH, deterministic and randomized. Counting ETH. Counting SETH, for fixed widths. Nondeterministic SETH. Quantum ETH and fixed-width Quantum SETH. Unique-SAT ETH variants. Fixed-width quantum counting, parity, and majority hypotheses asserting exponential hardness. Average-case exponential-hardness hypotheses for fixed-width SAT decision/search/counting. ————— The following related problems are still OPEN: Unrestricted CNF-SAT ETH/SETH formulations, parameterized by the original number of variables. Unrestricted CNF counting/parity hypotheses. Broader QSETH frameworks, including unrestricted-CNF formulations. Circuit-SAT exponential-hardness hypotheses measured in input bits, allowing polynomials many gates. PPAD-ETH allowing polylogarithmic losses in the exponent. Hypotheses about quantified SAT, lattice problems, and other problems without a suitable reduction.

Dan Roberts @danintheory

a day ago

We are announcing three new discoveries in mathematics, computer science, and physics about harmonic analysis, complexity theory, and quantum field theory. openai.com/index/building…

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Pólya @PolyaEnum

23 hours ago

como entusiasta del area computational complexity theory, vengo a comentarles un anuncio que se realizo hoy, 26 de Oct. 2026 por parte de OpenAI afirman haber refutado la “Exponential Time Hypothesis” (ETH), una hipotesis fundamental del area. Todavia no esta verificado por la

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yo tambien creo que P = NP, pero no entiendo por que la gente lo anda afirmando en base con lo que paso con la ETH hoy... si se encontrara un algoritmo polinomial [ T(n) = O(n^k) ] para 3-SAT que es NP Completo, entonces si P = NP pero lo anunciado es que se encontro un tiempo subexponencial [ T(n) = 2^o(n) ] que NO es polinomial ademas la ETH implica que P != NP, pero refutarlo no hace que P = NP, de hecho seguimos igual que antes jajajjaj puedo llegar a entender el furor por un avance en el problema mas iconico en el area, pero no se sobregiren... todavia

never bet against Knuth!

Kimi @Kimi5407

a day ago

ETH is false(!) - seems pretty big My suspicion that P = NP continues to grow, Knuth (who famously believes there might be an impractical reduction from NP to P) might have been right all along…

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The computer science collaboration will understand and explain a result concerning the Exponential Time Hypothesis (ETH), a longstanding conjecture about the computational complexity of Boolean formula satisfiability, a problem deeply related to the P vs. NP problem. Surprisingly, our system has recently proved that the ETH is false, a result that was subsequently verified in Lean. The refutation of the ETH reopens questions about how much faster these tasks could become, and may help guide the search for better algorithms. Finding such algorithms, and turning theoretical advances into practical improvements, will require significant further research. Our system found its natural language disproof for the ETH we reached out to to @rrwilliams. Ryan will form a collaboration with Russell Impagliazzo and Ramamohan Paturi to verify and shepherd this result. Impagliazzo and Paturi, along with Francis Zane, are the original proposers of the Exponential Time Hypothesis, and Williams has refuted strong versions of the ETH, used ETH for hardness results, and connected algorithms and lower bounds. This group asked us to make all raw data of the results public to facilitate independent verification by the community, which we have done by posting the natural language proof and Lean formalization to our GitHub repo. The group also invites the community to help organize an open examination of the ETH claim and to discuss the broader questions that AI-generated breakthroughs raise about verification, access, credit, and the future of research. github.com/openai/math/bl…

INCREDIBLE detail from OpenAI’s latest discoveries: the two researchers who originally proposed the Exponential Time Hypothesis 25 years ago, are now leading a group to verify OpenAI’s proof that could DISPROVE their own conjecture.

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Dan Roberts @danintheory

a day ago

We are announcing three new discoveries in mathematics, computer science, and physics about harmonic analysis, complexity theory, and quantum field theory. openai.com/index/building…

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como entusiasta del area computational complexity theory, vengo a comentarles un anuncio que se realizo hoy, 26 de Oct. 2026 por parte de OpenAI afirman haber refutado la “Exponential Time Hypothesis” (ETH), una hipotesis fundamental del area. Todavia no esta verificado por la comunidad QUE ES 3-SAT?: es un problema NP-completo de decision en el que hay que determinar si existe una asignacion de valores True/False a las variables de una formula booleana en forma normal conjuntiva, de modo que todas sus clausulas sean verdaderas. Cada clausula contiene como maximo tres literales. Por ejemplo, C = (x1 ∨ ¬x2 ∨ x3). En terminos informales, la clausula se cumple si al menos uno de los literales es verdadero. La formula completa es satisfacible si existe una asignacion que hace verdaderas todas sus clausulas QUE DICE LA ETH?: 3-SAT no puede resolverse en tiempo subexponencial, es decir, en tiempo 2^o(n), donde n es la cantidad de variables. Es una hipotesis mas fuerte que P != NP porque descarta tanto algoritmos polinomiales como subexponenciales PARA QUE SIRVE LA ETH?: permite demostrar cotas inferiores para muchos problemas a partir de una sola hipotesis. Ejemplo: bajo la ETH, problemas sobre grafos como ciclo hamiltoniano, k-coloreo, clique maximo y vertex cover no tienen algoritmos 2^o(n) en la cantidad de vertices. Asi se descartan supuestas mejoras teoricas sin estudiar cada problema desde cero QUE SE ANUNCIO?: segun OpenAI, un algoritmo subexponencial para k-SAT con k fijo (incluye 3-SAT), con demostracion formalizada en Lean. Lo va a examinar un grupo de expertos, entre ellos investigadores vinculados al desarrollo original de la ETH. Si es correcto, la ETH queda refutada github.com/openai/math/bl…

Don’t let imposter syndrome define you. Embrace actual incompetence.

que vuelva la moda de sacar blogs tecnicos y poner en el footer el nombre del investigador y su anime pfp

電位測定 @Cupotential0235

2 days ago

ユタ大学で博士課程やってる霧雨魔理沙何者だよ（困惑）

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为什么现在的顶尖大模型说话越来越“拗口、难懂”了？ NYU 和 UT Austin 刚刚发了一篇非常扎心的心理语言学论文，直接扒开了现代大模型“不好好说人话”的底牌。 研究人员把 Claude Sonnet 5 / Opus 5.5、GPT-5.6、GLM-5、Kimi K2.5 等 9 款前沿模型拉出来做全方位句法解剖，发现了 3 个反直觉真相： 1️⃣ 顶尖 AI 正在滥用 6 种“高认知负荷”句式 相比真实人类写作和同义回译文本，前沿模型极度偏爱：省略 that 的宾语从句、多重名词硬堆叠（如 reader-patience budget）、名词强行作动词（如 calendar it / footnote it）、无生命主语配动作动词，以及超长句法依存距离。这些特征在心理语言学里全是消耗人类短期记忆的“阅读杀手”。 2️⃣ 根源在于“人类大脑”与“推理后训练”的错位 人类语言遵循“均匀信息密度（UID）”——为了照顾听众有限的工作记忆，我们会本能地加入过渡词把信息摊平。而现代大模型经过大量数学、代码和推理（RLVR）后训练，只追求在有限窗口内最大化“信息密度”。 3️⃣ 一个简单的长度惩罚，就能复刻这种“反人类文风” 团队在微调实验中加入长度惩罚（Length Penalty），逼模型少用 Token，结果模型立刻学会了砍掉连接词、堆叠名词，瞬间变成那股熟悉的“高密度 AI 味”。 当模型为了解题效率疯狂压缩 Token 时，你觉得未来的 AI 应该区分“高密度推理模式”和“人类友好沟通模式”吗？

We discovered a sophisticated recording device that was hidden inside one of our offices. We used our models to understand the device and where it had come from, identifying that a specific employee had planted it a few days earlier. We referred the matter to the FBI, and we’re grateful to the agents and prosecutors who moved quickly to make an arrest. The FBI’s investigation is ongoing and we will continue to support their work. At this time, we have no indications of this individual inappropriately accessing or exfiltrating model weights, source code, or customer data. The employee was terminated. We take protecting our technology, data, and people seriously, and as a matter of national importance. Our security program is designed to protect against a wide range of threat actors, from insider risks to cybercriminals to nation states, and this case is an example of how AI can help address these sophisticated security threats.

Got to admit, it's wild to see faster multiplication algorithms invented in real time. I was blown away when I first saw the classic n-log-n algorithm, I actually said to my instructor, surely multiplication is quadratic by nature! But it's not, and now I wonder if linear time multiplication is actually possible. The universe still hides deep secrets in mundane places.

Julian Schiavo @_julianschiavo

3 weeks ago

New data means new data analysis! Updated data suggests we will now reach linear time integer multiplication at 8:33am tomorrow morning x.com/0xdoug/status/…

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engineers don't even explain their code anymore they just look at you like this

We’re releasing a broad range of new mathematical results produced by an internal frontier model. We’ve been consulting with the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study, and we have drawn on their advice and public recommendations to inform how we release these results. github.com/openai/math

@askalphaxiv awesome!

The what now?! arxiv.org/abs/2610.06783…

arxiv.org/abs/2610.06783… Claude found a subquadratic 3SUM algorithm.

@trashh_dev hell yeah dude what moves, impressive

ahora pienso lo bochazo que fue el que me ensenio que era el DSU, sus optimizaciones (union by rank/size y path compression) y el detalle de demostrarme que, con ambas, la complejidad amortizada de una secuencia de m operaciones es O(m * a(n)) ( a(n) = funcion inversa de Ackermann )

despues de mucho tiempo, finalmente entro a la cancha este type

Pólya @PolyaEnum

a month ago

probablemente el mejor ejercicio de la practica

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