Acceleration of stochastic gradient descent with momentum by averaging: finite-sample rates and asymptotic normality

Stochastic gradient descent with momentum (SGDM) has been widely used in many machine learning and statistical applications. Despite the observed empirical benefits of SGDM over traditional SGD, the theoretical understanding of the role of momentum for different learning rates in the optimization process remains widely open. We analyze the finite-sample convergence rate of SGDM under the strongly convex settings and show that, with a large batch size, the mini-batch SGDM converges faster than mini-batch SGD to a neighborhood of the optimal value. Furthermore, we analyze the Polyak-averaging version of the SGDM estimator, establish its asymptotic normality, and justify its asymptotic equivalence to the averaged SGD

Distributed optimization with inexact oracle

summary:In this paper, we study the distributed optimization problem using approximate first-order information. We suppose the agent can repeatedly call an inexact first-order oracle of each individual objective function and exchange information with its time-varying neighbors. We revisit the distributed subgradient method in this circumstance and show its suboptimality under square summable but not summable step sizes. We also present several conditions on the inexactness of the local oracles to ensure an exact convergence of the iterative sequences towards the global optimal solution. A numerical example is given to verify the efficiency of our algorithm

Observer-based Leader-following Consensus for Positive Multi-agent Systems Over Time-varying Graphs

This paper addresses the leader-following consensus problem for discrete-time positive multi-agent systems over time-varying graphs. We assume that the followers may have mutually different positive dynamics which can also be different from the leader. Compared with most existing positive consensus works for homogeneous multi-agent systems, the formulated problem is more general and challenging due to the interplay between the positivity requirement and high-order heterogeneous dynamics. To solve the problem, we present an extended version of existing observer-based design for positive multi-agent systems. By virtue of the common quadratic Lyapunov function technique, we show the followers will maintain their state variables in the positive orthant and finally achieve an output consensus specified by the leader. A numerical example is used to verify the efficacy of our algorithms

ONeRF: Unsupervised 3D Object Segmentation from Multiple Views

We present ONeRF, a method that automatically segments and reconstructs object instances in 3D from multi-view RGB images without any additional manual annotations. The segmented 3D objects are represented using separate Neural Radiance Fields (NeRFs) which allow for various 3D scene editing and novel view rendering. At the core of our method is an unsupervised approach using the iterative Expectation-Maximization algorithm, which effectively aggregates 2D visual features and the corresponding 3D cues from multi-views for joint 3D object segmentation and reconstruction. Unlike existing approaches that can only handle simple objects, our method produces segmented full 3D NeRFs of individual objects with complex shapes, topologies and appearance. The segmented ONeRfs enable a range of 3D scene editing, such as object transformation, insertion and deletion

Instance Neural Radiance Field

This paper presents one of the first learning-based NeRF 3D instance segmentation pipelines, dubbed as Instance Neural Radiance Field, or Instance NeRF. Taking a NeRF pretrained from multi-view RGB images as input, Instance NeRF can learn 3D instance segmentation of a given scene, represented as an instance field component of the NeRF model. To this end, we adopt a 3D proposal-based mask prediction network on the sampled volumetric features from NeRF, which generates discrete 3D instance masks. The coarse 3D mask prediction is then projected to image space to match 2D segmentation masks from different views generated by existing panoptic segmentation models, which are used to supervise the training of the instance field. Notably, beyond generating consistent 2D segmentation maps from novel views, Instance NeRF can query instance information at any 3D point, which greatly enhances NeRF object segmentation and manipulation. Our method is also one of the first to achieve such results without ground-truth instance information during inference. Experimented on synthetic and real-world NeRF datasets with complex indoor scenes, Instance NeRF surpasses previous NeRF segmentation works and competitive 2D segmentation methods in segmentation performance on unseen views. See the demo video at https://youtu.be/wW9Bme73coI

NeRF-RPN: A general framework for object detection in NeRFs

This paper presents the first significant object detection framework, NeRF-RPN, which directly operates on NeRF. Given a pre-trained NeRF model, NeRF-RPN aims to detect all bounding boxes of objects in a scene. By exploiting a novel voxel representation that incorporates multi-scale 3D neural volumetric features, we demonstrate it is possible to regress the 3D bounding boxes of objects in NeRF directly without rendering the NeRF at any viewpoint. NeRF-RPN is a general framework and can be applied to detect objects without class labels. We experimented the NeRF-RPN with various backbone architectures, RPN head designs and loss functions. All of them can be trained in an end-to-end manner to estimate high quality 3D bounding boxes. To facilitate future research in object detection for NeRF, we built a new benchmark dataset which consists of both synthetic and real-world data with careful labeling and clean up. Please click https://youtu.be/M8_4Ih1CJjE for visualizing the 3D region proposals by our NeRF-RPN. Code and dataset will be made available

NMDA receptor activation stimulates transcription-independent rapid wnt5a protein synthesis via the MAPK signaling pathway

Wnt proteins are emerging key regulators of the plasticity and functions of adult brains. However, the mechanisms by which the expression of Wnt proteins is regulated in neurons are unclear. Using cortical primary cultures, we show here that activation of NMDA receptors (NMDARs) induces rapid Wnt5a protein synthesis and secretion. This NMDAR-regulated Wnt5a synthesis does not require transcription and is a result of activity-dependent translation. We also show that NMDAR-regulated Wnt5a translation depends on MAPK signaling but not mTOR signaling. Our findings suggest that the synaptic activity of CNS neurons activates NMDARs, which in turn stimulate translation from stored Wnt5a mRNA via the MAPK signaling pathway