Tootfinder

FACT: the Features At Convergence Theorem for neural networks
Enric Boix-Adsera, Neil Mallinar, James B. Simon, Mikhail Belkin
https://arxiv.org/abs/2507.05644

FACT: the Features At Convergence Theorem for neural networks
A central challenge in deep learning theory is to understand how neural networks learn and represent features. To this end, we prove the Features at Convergence Theorem (FACT), which gives a self-consistency equation that neural network weights satisfy at convergence when trained with nonzero weight decay. For each weight matrix $W$, this equation relates the "feature matrix" $W^\top W$ to the set of input vectors passed into the matrix during forward propagation and the loss gradients passed t…

The Proportional Fair Scheduler in Wavelength-Multiplexed Quantum Networks
Sanidhay Bhambay, Siddarth Koduru Joshi, Thirupathaiah Vasantam, Neil Walton
https://arxiv.org/abs/2507.13999

The Proportional Fair Scheduler in Wavelength-Multiplexed Quantum Networks
We address the problem of optimal pumping strategies in quantum networks. These networks enable secure communication by distributing entangled photon pairs to user (or node) pairs. Quantum Key Distribution (QKD) protocols, like BBM92, generate secret keys from entangled photons. While secure communication and error correction are essential for any quantum communication channel, resource contention, optimization, and fairness issues are critical for networks. In this article, we analyze the perf…