The Riemannian Geometry of Deep Generative Models

Deep generative models learn a mapping from a low dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate the Riemannian geometry of these generated manifolds. First, we develop efficient algorithms for computing geodesic curves, which provide an intrinsic notion of distance between points on the manifold. Second, we develop an algorithm for parallel translation of a tangent vector along a path on the manifold. We show how parallel translation can be used to generate analogies, i.e., to transport a change in one data point into a semantically similar change of another data point. Our experiments on real image data show that the manifolds learned by deep generative models, while nonlinear, are surprisingly close to zero curvature. The practical implication is that linear paths in the latent space closely approximate geodesics on the generated manifold. However, further investigation into this phenomenon is warranted, to identify if there are other architectures or datasets where curvature plays a more prominent role. We believe that exploring the Riemannian geometry of deep generative models, using the tools developed in this paper, will be an important step in understanding the high-dimensional, nonlinear spaces these models learn.Comment: 9 page

Lift-Based Bidding in Ad Selection

Real-time bidding (RTB) has become one of the largest online advertising markets in the world. Today the bid price per ad impression is typically decided by the expected value of how it can lead to a desired action event (e.g., registering an account or placing a purchase order) to the advertiser. However, this industry standard approach to decide the bid price does not consider the actual effect of the ad shown to the user, which should be measured based on the performance lift among users who have been or have not been exposed to a certain treatment of ads. In this paper, we propose a new bidding strategy and prove that if the bid price is decided based on the performance lift rather than absolute performance value, advertisers can actually gain more action events. We describe the modeling methodology to predict the performance lift and demonstrate the actual performance gain through blind A/B test with real ad campaigns in an industry-leading Demand-Side Platform (DSP). We also discuss the relationship between attribution models and bidding strategies. We prove that, to move the DSPs to bid based on performance lift, they should be rewarded according to the relative performance lift they contribute.Comment: AAAI 201

A Novel Convolutional Neural Network Architecture with a Continuous Symmetry

This paper introduces a new Convolutional Neural Network (ConvNet) architecture inspired by a class of partial differential equations (PDEs) called quasi-linear hyperbolic systems. With comparable performance on the image classification task, it allows for the modification of the weights via a continuous group of symmetry. This is a significant shift from traditional models where the architecture and weights are essentially fixed. We wish to promote the (internal) symmetry as a new desirable property for a neural network, and to draw attention to the PDE perspective in analyzing and interpreting ConvNets in the broader Deep Learning community.Comment: Accepted by the 3rd CAAI International Conference on Artificial Intelligence (CICAI), 2023; with Addendum + minor edit

M3DSSD: Monocular 3D Single Stage Object Detector

In this paper, we propose a Monocular 3D Single Stage object Detector (M3DSSD) with feature alignment and asymmetric non-local attention. Current anchor-based monocular 3D object detection methods suffer from feature mismatching. To overcome this, we propose a two-step feature alignment approach. In the first step, the shape alignment is performed to enable the receptive field of the feature map to focus on the pre-defined anchors with high confidence scores. In the second step, the center alignment is used to align the features at 2D/3D centers. Further, it is often difficult to learn global information and capture long-range relationships, which are important for the depth prediction of objects. Therefore, we propose a novel asymmetric non-local attention block with multi-scale sampling to extract depth-wise features. The proposed M3DSSD achieves significantly better performance than the monocular 3D object detection methods on the KITTI dataset, in both 3D object detection and bird's eye view tasks.Comment: Accepted to CVPR 202

Building quantum neural networks based on swap test

Artificial neural network, consisting of many neurons in different layers, is an important method to simulate humain brain. Usually, one neuron has two operations: one is linear, the other is nonlinear. The linear operation is inner product and the nonlinear operation is represented by an activation function. In this work, we introduce a kind of quantum neuron whose inputs and outputs are quantum states. The inner product and activation operator of the quantum neurons can be realized by quantum circuits. Based on the quantum neuron, we propose a model of quantum neural network in which the weights between neurons are all quantum states. We also construct a quantum circuit to realize this quantum neural network model. A learning algorithm is proposed meanwhile. We show the validity of learning algorithm theoretically and demonstrate the potential of the quantum neural network numerically.Comment: 10 pages, 13 figure