Learning State-Space Models for Mapping Spatial Motion Patterns

Mapping the surrounding environment is essential for the successful operation of autonomous robots. While extensive research has focused on mapping geometric structures and static objects, the environment is also influenced by the movement of dynamic objects. Incorporating information about spatial motion patterns can allow mobile robots to navigate and operate successfully in populated areas. In this paper, we propose a deep state-space model that learns the map representations of spatial motion patterns and how they change over time at a certain place. To evaluate our methods, we use two different datasets: one generated dataset with specific motion patterns and another with real-world pedestrian data. We test the performance of our model by evaluating its learning ability, mapping quality, and application to downstream tasks. The results demonstrate that our model can effectively learn the corresponding motion pattern, and has the potential to be applied to robotic application tasks.Comment: 6 pages, 5 figures, to be published in ECMR 2023 conference proceeding

Provable Guarantees for Neural Networks via Gradient Feature Learning

Neural networks have achieved remarkable empirical performance, while the current theoretical analysis is not adequate for understanding their success, e.g., the Neural Tangent Kernel approach fails to capture their key feature learning ability, while recent analyses on feature learning are typically problem-specific. This work proposes a unified analysis framework for two-layer networks trained by gradient descent. The framework is centered around the principle of feature learning from gradients, and its effectiveness is demonstrated by applications in several prototypical problems, such as mixtures of Gaussians and parity functions. The framework also sheds light on interesting network learning phenomena such as feature learning beyond kernels and the lottery ticket hypothesis.Comment: NeurIPS 2023, 71 page

The Minimization of Piecewise Functions: Pseudo Stationarity

There are many significant applied contexts that require the solution of discontinuous optimization problems in finite dimensions. Yet these problems are very difficult, both computationally and analytically. With the functions being discontinuous and a minimizer (local or global) of the problems, even if it exists, being impossible to verifiably compute, a foremost question is what kind of ''stationary solutions'' one can expect to obtain; these solutions provide promising candidates for minimizers; i.e., their defining conditions are necessary for optimality. Motivated by recent results on sparse optimization, we introduce in this paper such a kind of solution, termed ''pseudo B- (for Bouligand) stationary solution'', for a broad class of discontinuous piecewise continuous optimization problems with objective and constraint defined by indicator functions of the positive real axis composite with functions that are possibly nonsmooth. We present two approaches for computing such a solution. One approach is based on lifting the problem to a higher dimension via the epigraphical formulation of the indicator functions; this requires the addition of some auxiliary variables. The other approach is based on certain continuous (albeit not necessarily differentiable) piecewise approximations of the indicator functions and the convergence to a pseudo B-stationary solution of the original problem is established. The conditions for convergence are discussed and illustrated by an example

Towards Few-Shot Adaptation of Foundation Models via Multitask Finetuning

Foundation models have emerged as a powerful tool for many AI problems. Despite the tremendous success of foundation models, effective adaptation to new tasks, particularly those with limited labels, remains an open question and lacks theoretical understanding. An emerging solution with recent success in vision and NLP involves finetuning a foundation model on a selection of relevant tasks, before its adaptation to a target task with limited labeled samples. In this paper, we study the theoretical justification of this multitask finetuning approach. Our theoretical analysis reveals that with a diverse set of related tasks, this multitask finetuning leads to reduced error in the target task, in comparison to directly adapting the same pretrained model. We quantify the relationship between finetuning tasks and target tasks by diversity and consistency metrics, and further propose a practical task selection algorithm. We substantiate our theoretical claims with extensive empirical evidence. Further, we present results affirming our task selection algorithm adeptly chooses related finetuning tasks, providing advantages to the model performance on target tasks. We believe our study shed new light on the effective adaptation of foundation models to new tasks that lack abundant labels. Our code is available at https://github.com/OliverXUZY/Foudation-Model_Multitask.Comment: Published at ICLR 2024. 54 page

Fabrication of densified wood via synergy of chemical pretreatment, hot-pressing and post mechanical fixation

Article describes examination of the appearance, color, chemical composition, and physiology and mechanical properties of densified Abies wood before and after densification treatment using a colorimeter, FTIR and mechanical testing machine

Nonlinear Gossip Algorithms for Wireless Sensor Networks

We study some nonlinear gossip algorithms for wireless sensor networks. Firstly, two types of nonlinear single gossip algorithms are proposed. By using Lyapunov theory, Lagrange mean value theorem, and stochastic Lasalle’s invariance principle, we prove that the nonlinear single gossip algorithms can converge to the average of initial states with probability one. Secondly, two types of nonlinear multigossip algorithms are also presented and the convergence is proved by the same methods. Finally, computer simulation is also given to show the validity of the theoretical results

In Situ TEM Study of the Degradation of PbSe Nanocrystals in Air

PbSe nanocrystals have attracted widespread attention due to a variety of potential applications. However, the practical utility of these nanocrystals has been hindered by their poor air stability, which induces undesired changes in the optical and electronic properties. An understanding of the degradation of PbSe nanocrystals when they are exposed to air is critical for improving the stability and enhancing their applications. Here, we use in situ transmission electron microscopy (TEM) with an environmental cell connected to air to study PbSe nanocrystal degradation triggered by air exposure. We have also conducted a series of complementary studies, including in situ environmental TEM study of PbSe nanocrystals exposed to pure oxygen and PbSe nanocrystals in H2O using a liquid cell, and ex situ experiments, such as O2 plasma treatment and thermal heating of PbSe nanocrystals under different air exposure. Our in situ observations reveal that when PbSe nanocrystals are exposed to air (or oxygen) under electron beam irradiation, they experience a series of changes, including shape evolution of individual nanocrystals with the cuboid intermediates, coalescence between nanocrystals, and formation of PbSe thin films through drastic solid-state fusion. Further studies show that the PbSe thin films transform into an amorphous Pb rich phase or eventually pure Pb, which suggest that Se reacts with oxygen and can be evaporated under electron beam illumination. These various in situ and ex situ experimental results indicate that PbSe nanocrystal degradation in air is initiated by the dissociation and removal of ligands from the PbSe nanocrystal surface