May came with 3 new papers on property testing algorithms — or inspired by them.

**Interactive Proofs for General Distribution Properties**, by Tal Herman and Guy Rothblum (ECCC). Following a fruitful line of work (including by the authors themselves: see, e.g., this previous monthly post), this paper considers interactive proofs for distribution testing: Merlin and Arthur have data over a universe of size \(n\), Arthur wants to test properties of that data (probability distribution), but he has *much* less data (samples) than Merlin.

As it turns out, as long as the property he’s interested in can be checked efficiently (computationally: via a small-depth circuit), then Arthur can do it with strongly sublinear sample complexity: he needs only \(n^{1-\Omega(1)}\) samples, even for tolerant testing! And all that’s needed is a small number of rounds of interaction with Merlin. And even more, all (honest) parties can do that via a computationally efficient protocol…

**Oracle-Checker Scheme for Evaluating a Generative Large Language Model**, by Yueling Jenny Zeng, Li-C. Wang, and Thomas Ibbetson (arXiv). This paper draws inspiration from property testing and program checking (*à la* Blum, Luby, and Rubinfeld) to check the output of large language models (LLMs): specifically, for the task of entity extraction: the authors formalize how to view entity extraction as a homomorphism, and then assess empirically what using a property tester for linearity leads to. Overall, it sounds like an interesting (and somewhat unexpected?) use of property testing for LLM trustworthiness assessment!

**Property testing in graphical models: testing small separation numbers**, by Luc Devroye, Gábor Lugosi, and Piotr Zwiernik (arXiv). Here too, ideas from property testing are used, this time in the context of high-dimensional (Gaussian) graphical models. This paper focuses on testing properties of the structure of the graphical model: given query access to the covariance matrix $\latex \Sigma$ consistent with some underlying graph structure \(G\), can we test whether this structure is a tree? Is it has small separation number?

The focus differs a little from the classical setting of property testing, in that there is no distance parameter and the goal is to get an exact decision algorithm (adaptive, but with unbounded query complexity: rejecting graphs that are far from the property as a function of the unknown distance parameter, and always accepting graphs with the property). But besides this small variation, great to see more uses of property testing in the wild!