Today's trail

The success of convolutional neural networks is often attributed to locality and weight sharing. However, how these two properties separately shape learning, and how their effects depend on the spatial correlations of natural images, remain poorly understood. We address these…

Through a tangle of real-world interactions, from synthetic training pipelines to data shared on the open web, frontier LLMs absorb what their predecessors and competitors create. How well does each model play its role in this ecosystem, as a creator and as a solver? We…

Consensus is a fundamental problem in distributed computing and at the core of state machine replication (SMR). Despite decades of active human research, discovering practical low-latency solutions to the problem is still open, as it requires combining protocol knowledge,…

We analyze the problem of estimating univariate Gaussian mixture densities using the nonparametric maximum likelihood estimator (NPMLE) based on $n$ independent and identically distributed samples. We show that the unconstrained NPMLE achieves the minimax optimal rate…