A new theoretical paper nails down exactly how much accuracy you lose when predictions get passed hand-to-hand across a network of learners, instead of pooled all at once.
The setup, first studied by Kearns et al. (2026), puts learners on the nodes of a directed graph, each one training a linear predictor using its own local data plus whatever predictors its "parent" nodes already learned. That earlier work showed error falls at a rate no worse than O(1/sqrt(D)) as you move along a chain of length D, but only proved a weaker floor of Omega(1/D), leaving the true rate an open question. This paper closes that gap, constructing worst-case problem instances that force error all the way up to Omega(1/sqrt(D)) - matching the upper bound and settling the question. The analysis also stretches beyond squared error to a broad class of convex loss functions, including logistic loss, which resolves a parallel open gap from Bateni et al. (2026).
This matters because networked, information-passing systems are how a lot of real machine learning now works: federated setups, multi-agent pipelines, sensor networks relaying inference downstream. The result says the accuracy penalty from that structure isn't a quirk of sloppy engineering - it's a hard mathematical floor, and it doesn't get better with cleverer algorithms.
It's also a reminder that this is a proof about limits, not a fix. Nobody walks away with a faster network or a smarter aggregation trick - just a tighter, less optimistic ceiling on what one was ever going to get.