Networked Information Aggregation for Binary Classification

A team of researchers from academia has published a theoretical analysis of networked binary classification on directed acyclic graphs (DAGs). In their model, each agent sees only a subset of feature columns from a shared dataset. Agents act sequentially: each receives prediction columns from its parents, augments its local features, fits a logistic predictor by minimizing binary cross-entropy (BCE), and forwards its prediction to downstream neighbors. The central question is whether this sequential distributed training achieves information aggregation—i.e., whether some agent attains small excess loss compared to the best logistic predictor trained on all features. Prior work by Kearns, Roth, and Ryu (SODA 2026) answered this for linear regression under squared loss, but their proof relied on quadratic structure that does not transfer to BCE with a logistic link.

The new analysis introduces a sequential logit-passing protocol and proves two main results. First, on depth-D paths, if every M consecutive agents collectively observe all features, the excess loss is bounded by O(M/√D). Second, they prove a lower bound of Ω(k/D), where k is the feature dimension, showing instances where performance degrades linearly with depth. Together, these bounds identify network depth as a fundamental bottleneck for information aggregation in logistic regression. The paper was accepted to the 43rd International Conference on Machine Learning (ICML 2026), signaling its theoretical significance for distributed machine learning systems.