A repository for research-level works in the mathematical sciences and theoretical computer science.

[This is a guest post by Bryna Kra. This blog post was initially written in a different file format and converted using AI. — T.] For generations, mathematicians have treated the production o…

The paper provides data-dependent bounds on the test error of the Gibbs algorithm in the overparameterized interpolation regime, where low training errors are also obtained for impossible data, such a...

Joan Birman thought her major discoveries were behind her. Then came an email from a young neighbor — a girl who knew little but wanted to learn.

Contraction coefficients quantify the loss of distinguishability induced by a channel and provide a strong form of the data-processing inequality. While standard contraction coefficients ignore auxili...

Notes from the common room

OpenAI’s newest chatbot may be a whiz at math, but it seems to be lagging far behind humans in its academic rigor. Last week the company announced 10 more artificial-intelligence-generated math advan...

We present a polynomial-time quantum algorithm for the Dihedral Coset Problem (DCP). The algorithm is based on Regev's polynomial-time reduction of the Dihedral Subgroup Problem (DSP) to the modular ...

I have been thinking a lot about how social dynamics are going to shift in the new era of cognitive abundance. I don’t pretend to have any kind of crystal ball, but there are numerous histori…

Back into the swing of things in Maynooth, getting ready for the repeat examinations that start next month, I realized that I had forgotten to pass on an interesting paper that I found out about a few weeks ago but was reminded of while in London so I'm remedying my omission now. The title is The Coherence Principle: A Falsifiable Prior for Model Selection from the Grammar of Theories…

When checking that solutions to certain problems are correct, it turns out, you can’t get around the inherent complexity of the quantum world.

Non-local quantum computation (NLQC) studies how two collaborating players can implement channels on distributed systems using a single simultaneous round of quantum communication and shared entanglem...

Many moons ago I wrote a paper with a person called Antony J.M. Garrett with the title Bayesian Inductive Inference and the Anthropic Cosmological Principle (the full reference is A.J.M. Garrett and P. Coles, Comments on Astrophysics 17(1) 23-47 (1993). It got a few citations here and there, and has been discussed in a few books and other texts. In 1999, the journal…

Recent efforts to formulate quantum mechanics in a way that treats space and time on a more equal footing have led to a large variety of spacetime-oriented approaches. In this work we present a detail...