On the Landscape of One-hidden-layer Sparse Networks and Beyond

Sparse neural networks have received increasing interests due to their small size compared to dense networks. Nevertheless, most existing works on neural network theory have focused on dense neural networks, and our understanding of sparse networks is very limited. In this paper, we study the loss landscape of one-hidden-layer sparse networks. We first consider sparse networks with linear activations. We show that sparse linear networks can have spurious strict minima, which is in sharp contrast to dense linear networks which do not even have spurious minima. Second, we show that spurious valleys can exist for wide sparse non-linear networks. This is different from wide dense networks which do not have spurious valleys under mild assumptions

Single-Curvature Sandwich Panels with Aluminum Foam Cores under Impulsive Loading

Single-curvature sandwich panels combine the advantages of the shell and sandwich structure and are therefore envisaged to possess good potential to resist blast and shock or impact loads. This study presents a comprehensive report on the dynamic response and shock resistance of single-curvature sandwich panels, comprising two aluminum alloy face-sheets and an aluminum foam core, subjected to air-blast loading, in terms of the experimental investigation and numerical simulation. The deformation modes, shock resistance capability, and energy absorption performance are studied, and the influences of specimen curvature, blast impulse, and geometrical configuration are discussed. Results indicate that the deformation/failure, deflection response, and energy absorption of curved sandwich panels are sensitive to the loading intensity and geometric configuration. These results are significant to guide the engineering applications of sandwich structures with metallic foam cores subjected to air-blast loading

Stochastic Distributed Optimization under Average Second-order Similarity: Algorithms and Analysis

We study finite-sum distributed optimization problems involving a master node and $n-1$ local nodes under the popular $\delta$-similarity and $\mu$-strong convexity conditions. We propose two new algorithms, SVRS and AccSVRS, motivated by previous works. The non-accelerated SVRS method combines the techniques of gradient sliding and variance reduction and achieves a better communication complexity of $\tilde{\mathcal{O}}(n {+} \sqrt{n}\delta/\mu)$ compared to existing non-accelerated algorithms. Applying the framework proposed in Katyusha X, we also develop a directly accelerated version named AccSVRS with the $\tilde{\mathcal{O}}(n {+} n^{3/4}\sqrt{\delta/\mu})$ communication complexity. In contrast to existing results, our complexity bounds are entirely smoothness-free and exhibit superiority in ill-conditioned cases. Furthermore, we establish a nearly matched lower bound to verify the tightness of our AccSVRS method.Comment: Camera-ready version for NeurIPS 202

Eulerian and Lagrangian transport by shallow-water breaking waves

This study examines the mass and Lagrangian transport, kinematic and dynamic characteristics of shallow-water breaking waves, focusing on the wave breaking, and jet impingement processes. A multiphase Navier–Stokes flow model has been developed to track the origin and trajectory for the jet and the splash-up using both a geometric piece-wise linear interface calculation volume-of-fluid (PLIC-VOF) and the Lagrangian particle tracking approaches. The model is first validated both quantitatively and qualitatively against the experimental data for the plunging jet and the splash-up during wave breaking, in which a good agreement is obtained. The mass transport and the origin of the jet and splash-up are studied using the new multi-component PLIC-VOF approach, and the different regions in the interior of the wave are tracked in an Eulerian way. Both horizontal and vertical drifts for the interior and surface particles are shown using the Lagrangian particles. The location and origin of the plunging jet can be clearly seen from the simulations. Various wave steepness and beach slopes have been investigated for different types of breakers. Furthermore, the detailed jet impingement, velocity, pressure, vorticity, and turbulence fields during wave breaking are discussed and presented, providing more detailed flow fields to gain further insight into the plunging jet and splash-up in shallow-water breaking waves