DBSN: Measuring Uncertainty through Bayesian Learning of Deep Neural Network Structures. (arXiv:1911.09804v1 [cs.LG])

Bayesian neural networks (BNNs) introduce uncertainty estimation to deep networks by performing Bayesian inference on network weights. However, such models bring the challenges of inference, and further BNNs with weight uncertainty rarely achieve superior performance to standard models. In this paper, we investigate a new line of Bayesian deep learning by performing Bayesian reasoning on…

Machine learning for protein folding and dynamics. (arXiv:1911.09811v1 [physics.bio-ph])

Many aspects of the study of protein folding and dynamics have been affected by the recent advances in machine learning. Methods for the prediction of protein structures from their sequences are now heavily based on machine learning tools. The way simulations are performed to explore the energy landscape of protein systems is also changing as…

2SDR: Applying Kronecker Envelope PCA to denoise Cryo-EM Images. (arXiv:1911.09816v1 [eess.IV])

Principal component analysis (PCA) is arguably the most widely used dimension reduction method for vector type data. When applied to image data, PCA demands the images to be portrayed as vectors. The resulting computation is heavy because it will solve an eigenvalue problem of a huge covariance matrix due to the vectorization step. To mitigate…

Order Matters at Fanatics Recommending Sequentially Ordered Products by LSTM Embedded with Word2Vec. (arXiv:1911.09818v1 [cs.LG])

A unique challenge for e-commerce recommendation is that customers are often interested in products that are more advanced than their already purchased products, but not reversed. The few existing recommender systems modeling unidirectional sequence output a limited number of categories or continuous variables. To model the ordered sequence, we design the first recommendation system that…

Factorized Multimodal Transformer for Multimodal Sequential Learning. (arXiv:1911.09826v1 [cs.LG])

The complex world around us is inherently multimodal and sequential (continuous). Information is scattered across different modalities and requires multiple continuous sensors to be captured. As machine learning leaps towards better generalization to real world, multimodal sequential learning becomes a fundamental research area. Arguably, modeling arbitrarily distributed spatio-temporal dynamics within and across modalities is the…

Lecture Notes on Chern-Simons Perturbation Theory. (arXiv:1911.09744v1 [math-ph])

The goal of these lectures is to exhibit the framing anomaly in the Batalin-Vilkovisky formulation of perturbative Chern-Simons theory. Concretely, we show that the partition function fails to satisfy the Quantum Master Equation, and show that this can be remedied at the cost of introducing a framing. Along the way, we discuss principal bundles and…

An Efficient Parametric Linear Programming Solver and Application to Polyhedral Projection. (arXiv:1911.09755v1 [math.OC])

Polyhedral projection is a main operation of the polyhedron abstract domain.It can be computed via parametric linear programming (PLP), which is more efficient than the classic Fourier-Motzkin elimination method.In prior work, PLP was done in arbitrary precision rational arithmetic.In this paper, we present an approach where most of the computation is performed in floating-point arithmetic,…

A multi-material topology optimization algorithm based on the topological derivative. (arXiv:1911.09757v1 [math.OC])

We present a level-set based topology optimization algorithm for design optimization problems involving an arbitrary number of different materials, where the evolution of a design is solely guided by topological derivatives. Our method can be seen as an extension of the algorithm that was introduced in (Amstutz, Andrae 2006) for two materials to the case…

Geometric stochastic analysis on path spaces. (arXiv:1911.09764v1 [math.PR])

An approach to analysis on path spaces of Riemannian manifolds is described. The spaces are furnished with `Brownian motion’ measure which lies on continuous paths, though differentiation is restricted to directions given by tangent paths of finite energy. An introduction describes the background for paths on ${\mathbb R}^m$ and Malliavin calculus. For manifold valued paths…