NormFace: L2 Hypersphere Embedding for Face Verification

Thanks to the recent developments of Convolutional Neural Networks, the performance of face verification methods has increased rapidly. In a typical face verification method, feature normalization is a critical step for boosting performance. This motivates us to introduce and study the effect of normalization during training. But we find this is non-trivial, despite normalization being differentiable. We identify and study four issues related to normalization through mathematical analysis, which yields understanding and helps with parameter settings. Based on this analysis we propose two strategies for training using normalized features. The first is a modification of softmax loss, which optimizes cosine similarity instead of inner-product. The second is a reformulation of metric learning by introducing an agent vector for each class. We show that both strategies, and small variants, consistently improve performance by between 0.2% to 0.4% on the LFW dataset based on two models. This is significant because the performance of the two models on LFW dataset is close to saturation at over 98%. Codes and models are released on https://github.com/happynear/NormFaceComment: camera-ready versio

Dynamics of drop impact on solid surfaces: evolution of impact force and self-similar spreading

We investigate the dynamics of drop impacts on dry solid surfaces. By synchronising high-speed photography with fast force sensing, we simultaneously measure the temporal evolution of the shape and impact force of impacting drops over a wide range of Reynolds numbers (Re). At high Re, when inertia dominates the impact processes, we show that the early-time evolution of impact force follows a square-root scaling, quantitatively agreeing with a recent self-similar theory. This observation provides direct experimental evidence on the existence of upward propagating self-similar pressure fields during the initial impact of liquid drops at high Re. When viscous forces gradually set in with decreasing Re, we analyse the early-time scaling of the impact force of viscous drops using a perturbation method. The analysis quantitatively matches our experiments and successfully predicts the trends of the maximum impact force and the associated peak time with decreasing Re. Furthermore, we discuss the influence of viscoelasticity on the temporal signature of impact forces. Last but not least, we also investigate the spreading of liquid drops at high Re following the initial impact. Particularly, we find an exact parameter-free self-similar solution for the inertia-driven drop spreading, which quantitatively predicts the height of spreading drops at high Re. The limit of the self-similar approach for drop spreading is also discussed. As such, our study provides a quantitative understanding of the temporal evolution of impact forces across the inertial, viscous and viscoelastic regimes and sheds new light on the self-similar dynamics of drop impact processes.Comment: 24 pages, 9 figures, accepted by Journal of Fluid Mechanic

Monte Carlo Hamiltonian: Inverse Potential

The Monte Carlo Hamiltonian method developed recently allows to investigate ground state and low-lying excited states of a quantum system, using Monte Carlo algorithm with importance sampling. However, conventional MC algorithm has some difficulties when applying to inverse potentials. We propose to use effective potential and extrapolation method to solve the problem. We present examples from the hydrogen system.Comment: To appear in Communications in Theoretical Physic

Prediction-Based Task Assignment in Spatial Crowdsourcing (Technical Report)

Spatial crowdsourcing refers to a system that periodically assigns a number of location-based workers with spatial tasks nearby (e.g., taking photos or videos at some spatial locations). Previous works on the spatial crowdsourcing usually designed task assignment strategies that maximize some assignment scores, which are however only based on available workers/tasks in the system at the time point of assigning workers/tasks. These strategies may achieve local optimality, due to the neglect of future workers/tasks that may join the system. In contrast, in this paper, we aim to achieve "globally" optimal task assignments, by considering not only those present, but also future (via predictions), workers/tasks. Specifically, we formalize an important problem, namely prediction-based spatial crowdsourcing (PB-SC), which expects to obtain a "globally" optimal strategy for worker-and-task assignments, over both present and predicted task/worker locations, such that the total assignment quality score is maximized under the constraint of the traveling budget. In this paper, we design an effective grid-based prediction method to estimate spatial distributions of workers/tasks in the future, and then utilize the predicted ones in our procedure of task assignments. We prove that the PB-SC problem is NP-hard, and thus intractable. Therefore, we propose efficient approximate algorithms to tackle the PB-SC problem, including greedy and divide-and-conquer (D&C) approaches, which can efficiently assign workers to spatial tasks with high quality scores and low budget consumptions, by considering both current and future task/worker distributions. Through extensive experiments, we demonstrate the efficiency and effectiveness of our PB-SC processing approaches on real/synthetic data.Comment: 15 page