Analysis of the divide-and-conquer method for electronic structure calculations

We study the accuracy of the divide-and-conquer method for electronic structure calculations. The analysis is conducted for a prototypical subdomain problem in the method. We prove that the pointwise difference between electron densities of the global system and the subsystem decays exponentially as a function of the distance away from the boundary of the subsystem, under the gap assumption of both the global system and the subsystem. We show that gap assumption is crucial for the accuracy of the divide-and-conquer method by numerical examples. In particular, we show examples with the loss of accuracy when the gap assumption of the subsystem is invalid

Facial Motion Prior Networks for Facial Expression Recognition

Deep learning based facial expression recognition (FER) has received a lot of attention in the past few years. Most of the existing deep learning based FER methods do not consider domain knowledge well, which thereby fail to extract representative features. In this work, we propose a novel FER framework, named Facial Motion Prior Networks (FMPN). Particularly, we introduce an addition branch to generate a facial mask so as to focus on facial muscle moving regions. To guide the facial mask learning, we propose to incorporate prior domain knowledge by using the average differences between neutral faces and the corresponding expressive faces as the training guidance. Extensive experiments on three facial expression benchmark datasets demonstrate the effectiveness of the proposed method, compared with the state-of-the-art approaches.Comment: VCIP 2019, Oral. Code is available at https://github.com/donydchen/FMPN-FE

Language-Based Image Editing with Recurrent Attentive Models

We investigate the problem of Language-Based Image Editing (LBIE). Given a source image and a natural language description, we want to generate a target image by editing the source image based on the description. We propose a generic modeling framework for two sub-tasks of LBIE: language-based image segmentation and image colorization. The framework uses recurrent attentive models to fuse image and language features. Instead of using a fixed step size, we introduce for each region of the image a termination gate to dynamically determine after each inference step whether to continue extrapolating additional information from the textual description. The effectiveness of the framework is validated on three datasets. First, we introduce a synthetic dataset, called CoSaL, to evaluate the end-to-end performance of our LBIE system. Second, we show that the framework leads to state-of-the-art performance on image segmentation on the ReferIt dataset. Third, we present the first language-based colorization result on the Oxford-102 Flowers dataset.Comment: Accepted to CVPR 2018 as a Spotligh

Maximum likelihood decoding of neuronal inputs from an interspike interval distribution

An expression for the probability distribution of the interspike interval of a leaky integrate-and-fire (LIF) model neuron is rigorously derived, based on recent theoretical developments in the theory of stochastic processes. This enables us to find for the first time a way of developing maximum likelihood estimates (MLE) of the input information (e.g., afferent rate and variance) for an LIF neuron from a set of recorded spike trains. Dynamic inputs to pools of LIF neurons both with and without interactions are efficiently and reliably decoded by applying the MLE, even within time windows as short as 25 msec