In this short note we consider the gradient descent dynamics of deep scalar linear networks, $f(x) = \prod_{l=1}^L w_l x$, which enjoy exact time-course solutions for any integer depth. We show that even in this minimal model, the optimal depth-wise learning rate scaling depends on data, whereas data-agnostic scaling rules fail to transfer across depths. Under the data-dependent optimal scaling, the learning dynamics is independent of data and weakly dependent on depth, resulting in a constant linear convergence rate across all depths including infinity. We further show similar data-dependent effects in deep scalar linear networks with residual connections.
We address liquidity placement in the Bitcoin Lightning Network (LN): given a fixed budget, which channels should a node open to maximize its routing capacity? We cast this as a budget-constrained combinatorial optimization problem on graphs, selecting $k$ edge additions that max…
Molecular property prediction often relies on isolated data modalities, where continuous 3D graph neural networks (GNNs) struggle to efficiently capture long-range topological dependencies and exact macroscopic heuristics. In this work, we introduce a parameter-efficient Tri-Bran…
We introduce the Neuro-Bayesian-Symbolic Residual Attention Shallow Network (NBS-RASN), a hybrid neural architecture for explainable cybersecurity risk assessment in open-source ecosystems. Unlike deep models that trade interpretability for accuracy, our shallow network encodes d…
Learning-rate transfer can reduce the cost of training large language models: instead of sweeping learning rates at target scale, practitioners extrapolate from smaller runs. Existing approaches often assume that the optimal learning rate follows a log-linear scaling law in data…
Reliable and low-latency NR-V2X communications are essential for smart mobility in dense urban environments. However, limited Road-Side Unit (RSU) density, frequent non-line-of-sight conditions, and highly dynamic vehicular topologies often prevent many Connected and Automated Ve…
Deep learning models dependency on large-scale inertial datasets presents a significant bottleneck in inertial sensor-based classification tasks, such as human activity recognition and smartphone location recognition. In these domains, data collection requires massive recording c…