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David Harvey and Joris van der Hoeven's paper presenting a groundbreaking O(n log n) integer multiplication algorithm, breaking the long-standing complexity barrier for multiplying large integers.
A community research repository reports a sharper exponent bound for integer multiplication, achieving T(n)=O(n(log n)^(1-κ)) with κ=0.0023 under the OpenAI #109 framework, conditional on unverified hypotheses and not yet a complete Lean proof.
This paper theoretically and empirically explains why inference-time harnesses (scaffolds) outperform distilled student models: harnesses can compute closures that are NL-complete even from trivial AC0 primitives, a representational power no fixed-depth forward pass can replicate under standard complexity assumptions. The authors verify that enlarging the model, simplifying the task, or lengthening chain-of-thought can close this gap, including on competition math with agentic harnesses.
doubleAI claims, at a cost of $2000, to have solved the long-unsolved Longest Path problem in graph theory, with potential practical applications in error correction and accelerating calculations on quantum computers.
一篇技术评论文章，批评 OpenAI 在数学论文集中声称的更快快速傅里叶变换（FFT）算法，指出其改进微乎其微，更像是利用理论模型在硬件上并不实际可行的“恶意利用”，而非真正的突破。
An automated research run exploring integer multiplication algorithms with complexity below n log n, providing reproducible contributions, a repository contribution guide, and interactive visualization of ideas and pull requests.
This paper analyzes reasoning shortcuts in neurosymbolic systems through symmetry and automorphism groups, reveals flaws in a prior framework, proves complexity-theoretic results, and empirically validates the corrected theory on benchmarks like CLE4EVR and rsbench.
This paper studies instructional sequencing over prerequisite DAGs, proving that stochastic learning dynamics can be exactly reduced to a deterministic shortest-path problem, yet the optimal sequencing remains NP-hard in general, with polynomial-time cases under restricted transfer structures.
A Chinese professor has discovered a new deterministic shortest path algorithm that beats the 40-year-old sorting barrier by combining Dijkstra and Bellman-Ford with frontier reduction, achieving O(m log^(2/3) n) time on sparse graphs.
This article announces a free online course by Tim Roughgarden that covers fundamental concepts in computer science, including Turing machines, the halting problem, algorithmic efficiency, NP-completeness, and the P vs NP problem.
This paper establishes a theoretical connection between market competitiveness and the P versus NP problem, arguing that competitive markets exist if and only if P ≠ NP.
Computational complexity theorists argue that semiclassical gravity's non-linear dynamics would enable impossibly powerful computation, proving gravity must be quantized. The paper uses the Schrödinger-Newton equation to show that classical gravity coupled to quantum matter leads to computational contradictions.
This paper argues that under semiclassical gravity, a massive qubit can solve NP-complete problems in polynomial time via nonlinear dynamics, implying gravity must be quantized.
This paper introduces a quantitative notion of diversity of extensions in abstract argumentation based on symmetric difference, and provides a systematic complexity classification for related reasoning tasks.
A social media post explaining the P vs NP problem by comparing NP to a 'magical computer' that always finds the right path, referencing MIT's Introduction to Algorithms course.
This paper extends the study of computational hardness in learning robust classifiers, showing that efficient robust classification can be impossible even when unbounded robust classifiers exist, and establishing a win-win result: either an efficient robust classifier can be learned, or new cryptographic primitives can be constructed.