mathconstruct: Challenging LLM Reasoning with Constructive Proofs https://arxiv.org/abs/2502.10197
arXiv.org
MathConstruct: Challenging LLM Reasoning with Constructive Proofs
While Large Language Models (LLMs) demonstrate impressive performance in mathematics, existing math benchmarks come with significant limitations. Many focus on problems with fixed ground-truth...
BaxBench: Can LLMs Generate Secure and Correct Backends? https://baxbench.com/
Baxbench
BaxBench: Can LLMs Generate Secure and Correct Backends?
We introduce a novel benchmark to evaluate LLMs on secure and correct code generation, showing that even flagship LLMs are not ready for coding automation, frequently generating insecure or incorrect code.
STP: Self-play LLM Theorem Provers with Iterative Conjecturing and Proving https://arxiv.org/abs/2502.00212
arXiv.org
STP: Self-play LLM Theorem Provers with Iterative Conjecturing and Proving
A fundamental challenge in formal theorem proving by LLMs is the lack of high-quality training data. Although reinforcement learning or expert iteration partially mitigates this issue by...
LIMO: Less is More for Reasoning https://arxiv.org/abs/2502.03387
arXiv.org
LIMO: Less is More for Reasoning
We present a fundamental discovery that challenges our understanding of how complex reasoning emerges in large language models. While conventional wisdom suggests that sophisticated reasoning...
Universal Quantum Computation with the S3 Quantum Double: A Pedagogical Exposition https://arxiv.org/abs/2502.14974
arXiv.org
Universal Quantum Computation with the $S_3$ Quantum Double: A...
Non-Abelian topological order (TO) enables topologically protected quantum computation with its anyonic quasiparticles. Recently, TO with $S_3$ gauge symmetry was identified as a sweet spot --...
Detecting emergent 1-form symmetries with quantum error correction https://arxiv.org/abs/2502.17572
arXiv.org
Detecting emergent 1-form symmetries with quantum error correction
Higher-from symmetries act on sub-dimensional spatial manifolds of a quantum system and they can emerge as an exact symmetry at low energies even when they are explicitly broken at the microscopic...
Hardware-efficient quantum error correction via concatenated bosonic qubits https://www.nature.com/articles/s41586-025-08642-7
Nature
Hardware-efficient quantum error correction via concatenated bosonic qubits
Nature - Bosonic qubits can be engineered to feature intrinsic protection against certain kinds of errors, which makes quantum error correction across many bosonic qubits possible with less overhead.
LLM Processes: Numerical Predictive Distributions Conditioned on Natural Language https://arxiv.org/abs/2405.12856
arXiv.org
LLM Processes: Numerical Predictive Distributions Conditioned on...
Machine learning practitioners often face significant challenges in formally integrating their prior knowledge and beliefs into predictive models, limiting the potential for nuanced and...
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GitHub
GitHub - LadybirdBrowser/ladybird: Truly independent web browser
Truly independent web browser. Contribute to LadybirdBrowser/ladybird development by creating an account on GitHub.
The three-dimensional Kakeya conjecture, after Wang and Zahl
https://terrytao.wordpress.com/2025/02/25/the-three-dimensional-kakeya-conjecture-after-wang-and-zahl
via @cme_channel
https://terrytao.wordpress.com/2025/02/25/the-three-dimensional-kakeya-conjecture-after-wang-and-zahl
via @cme_channel
What's new
The three-dimensional Kakeya conjecture, after Wang and Zahl
There has been some spectacular progress in geometric measure theory: Hong Wang and Joshua Zahl have just released a preprint that resolves the three-dimensional case of the infamous Kakeya set con…
Comment on "InAs-Al hybrid devices passing the topological gap protocol", Microsoft Quantum, Phys. Rev. B 107, 245423 (2023) https://arxiv.org/abs/2502.19560
arXiv.org
Comment on "InAs-Al hybrid devices passing the topological gap...
The topological gap protocol (TGP) is presented as "a series of stringent experimental tests" for the presence of topological superconductivity and associated Majorana bound states. Here, we show...
Forwarded from сладко стянул
Zagier, D. (1990). How Often Should You Beat Your Kids? Mathematics Magazine, 63(2), 89–92. https://doi.org/10.1080/0025570X.1990.11977493
<...>
We, however, maintain that only the most degenerate parent would play against a two-year-old for money, and that our concern must therefore be, not by how much you can expect to win, but with what probability you will win at all. Our principal result is that this probability tends asymptotically to 85.4% (more precisely: to 1/2 + 1/sqrt(8)) as n tends to infinity. This shows with what unerring instinct Levasseur's mother selected the game — the high 85% loss rate will instill in the young progeny a due respect for the immense superiority of their parents, while the 15% win rate will maintain their interest and prevent them from succumbing to feelings of hopelessness and frustration.
<...>
<...>
We, however, maintain that only the most degenerate parent would play against a two-year-old for money, and that our concern must therefore be, not by how much you can expect to win, but with what probability you will win at all. Our principal result is that this probability tends asymptotically to 85.4% (more precisely: to 1/2 + 1/sqrt(8)) as n tends to infinity. This shows with what unerring instinct Levasseur's mother selected the game — the high 85% loss rate will instill in the young progeny a due respect for the immense superiority of their parents, while the 15% win rate will maintain their interest and prevent them from succumbing to feelings of hopelessness and frustration.
<...>
Taylor & Francis
How Often Should You Beat Your Kids?
Published in Mathematics Magazine (Vol. 63, No. 2, 1990)
Proving Olympiad Inequalities by Synergizing LLMs and Symbolic Reasoning https://arxiv.org/abs/2502.13834
arXiv.org
Proving Olympiad Inequalities by Synergizing LLMs and Symbolic Reasoning
Large language models (LLMs) can prove mathematical theorems formally by generating proof steps (\textit{a.k.a.} tactics) within a proof system. However, the space of possible tactics is vast and...
Anomalies of Coset Non-Invertible Symmetries https://arxiv.org/abs/2503.00105
arXiv.org
Anomalies of Coset Non-Invertible Symmetries
Anomalies of global symmetries provide important information on the quantum dynamics. We show the dynamical constraints can be organized into three classes: genuine anomalies, fractional...
Warning Signs of a Possible Collapse of Contemporary Mathematics https://web.math.princeton.edu/~nelson/papers/warn.pdf
Enforced Gaplessness from States with Exponentially Decaying Correlations https://arxiv.org/abs/2503.01977
arXiv.org
Enforced Gaplessness from States with Exponentially Decaying Correlations
It is well known that an exponentially localized Hamiltonian must be gapless if its ground state has algebraic correlations. We show that even certain exponentially decaying correlations can imply...