Natural laws are often described through differential equations yet finding a differential equation that describes the governing law underlying observed data is a challenging and still mostly manual task. In this paper we make a step towards the automation of this process: we propose a transformer-based sequence-to-sequence model that recovers scalar autonomous ordinary differential equations (ODEs) in symbolic form from time-series data of a single observed solution of the ODE. Our method is efficiently scalable: after one-time pretraining on a large set of ODEs, we can infer the governing laws of a new observed solution in a few forward passes of the model. Then we show that our model performs better or on par with existing methods in various test cases in terms of accurate symbolic recovery of the ODE, especially for more complex expressions.
As bird's-eye-view (BEV) semantic segmentation is simple-to-visualize and easy-to-handle, it has been applied in autonomous driving to provide the surrounding information to downstream tasks. Inferring BEV semantic segmentation conditioned on multi-camera-view images is a popular scheme in the community as cheap devices and real-time processing. The recent work implemented this task by learning the content and position relationship via the vision Transformer (ViT). However, the quadratic complexity of ViT confines the relationship learning only in the latent layer, leaving the scale gap to impede the representation of fine-grained objects. And their plain fusion method of multi-view features does not conform to the information absorption intention in representing BEV features. To tackle these issues, we propose a novel cross-scale hierarchical Transformer with correspondence-augmented attention for semantic segmentation inferring. Specifically, we devise a hierarchical framework to refine the BEV feature representation, where the last size is only half of the final segmentation. To save the computation increase caused by this hierarchical framework, we exploit the cross-scale Transformer to learn feature relationships in a reversed-aligning way, and leverage the residual connection of BEV features to facilitate information transmission between scales. We propose correspondence-augmented attention to distinguish conducive and inconducive correspondences. It is implemented in a simple yet effective way, amplifying attention scores before the Softmax operation, so that the position-view-related and the position-view-disrelated attention scores are highlighted and suppressed. Extensive experiments demonstrate that our method has state-of-the-art performance in inferring BEV semantic segmentation conditioned on multi-camera-view images.
Previous works on video object segmentation (VOS) are trained on densely annotated videos. Nevertheless, acquiring annotations in pixel level is expensive and time-consuming. In this work, we demonstrate the feasibility of training a satisfactory VOS model on sparsely annotated videos-we merely require two labeled frames per training video while the performance is sustained. We term this novel training paradigm as two-shot video object segmentation, or two-shot VOS for short. The underlying idea is to generate pseudo labels for unlabeled frames during training and to optimize the model on the combination of labeled and pseudo-labeled data. Our approach is extremely simple and can be applied to a majority of existing frameworks. We first pre-train a VOS model on sparsely annotated videos in a semi-supervised manner, with the first frame always being a labeled one. Then, we adopt the pre-trained VOS model to generate pseudo labels for all unlabeled frames, which are subsequently stored in a pseudo-label bank. Finally, we retrain a VOS model on both labeled and pseudo-labeled data without any restrictions on the first frame. For the first time, we present a general way to train VOS models on two-shot VOS datasets. By using 7.3% and 2.9% labeled data of YouTube-VOS and DAVIS benchmarks, our approach achieves comparable results in contrast to the counterparts trained on fully labeled set. Code and models are available at https://github.com/yk-pku/Two-shot-Video-Object-Segmentation.
Inflation is a major determinant for allocation decisions and its forecast is a fundamental aim of governments and central banks. However, forecasting inflation is not a trivial task, as its prediction relies on low frequency, highly fluctuating data with unclear explanatory variables. While classical models show some possibility of predicting inflation, reliably beating the random walk benchmark remains difficult. Recently, (deep) neural networks have shown impressive results in a multitude of applications, increasingly setting the new state-of-the-art. This paper investigates the potential of the transformer deep neural network architecture to forecast different inflation rates. The results are compared to a study on classical time series and machine learning models. We show that our adapted transformer, on average, outperforms the baseline in 6 out of 16 experiments, showing best scores in two out of four investigated inflation rates. Our results demonstrate that a transformer based neural network can outperform classical regression and machine learning models in certain inflation rates and forecasting horizons.
In this work, we give sufficient conditions for the almost global asymptotic stability of a cascade in which the inner loop and the unforced outer loop are each almost globally asymptotically stable. Our qualitative approach relies on the absence of chain recurrence for non-equilibrium points of the unforced outer loop, the hyperbolicity of equilibria, and the precompactness of forward trajectories. We show that the required structure of the chain recurrent set can be readily verified, and describe two important classes of systems with this property. We also show that the precompactness requirement can be verified by growth rate conditions on the interconnection term coupling the subsystems. Our results stand in contrast to prior works that require either global asymptotic stability of the subsystems (impossible for smooth systems evolving on general manifolds), time scale separation between the subsystems, or strong disturbance robustness properties of the outer loop. The approach has clear applications in stability certification of cascaded controllers for systems evolving on manifolds.
This study presents a novel deep learning method, called GATv2-GCN, for predicting player performance in sports. To construct a dynamic player interaction graph, we leverage player statistics and their interactions during gameplay. We use a graph attention network to capture the attention that each player pays to each other, allowing for more accurate modeling of the dynamic player interactions. To handle the multivariate player statistics time series, we incorporate a temporal convolution layer, which provides the model with temporal predictive power. We evaluate the performance of our model using real-world sports data, demonstrating its effectiveness in predicting player performance. Furthermore, we explore the potential use of our model in a sports betting context, providing insights into profitable strategies that leverage our predictive power. The proposed method has the potential to advance the state-of-the-art in player performance prediction and to provide valuable insights for sports analytics and betting industries.
Combined with demonstrations, deep reinforcement learning can efficiently develop policies for manipulators. However, it takes time to collect sufficient high-quality demonstrations in practice. And human demonstrations may be unsuitable for robots. The non-Markovian process and over-reliance on demonstrations are further challenges. For example, we found that RL agents are sensitive to demonstration quality in manipulation tasks and struggle to adapt to demonstrations directly from humans. Thus it is challenging to leverage low-quality and insufficient demonstrations to assist reinforcement learning in training better policies, and sometimes, limited demonstrations even lead to worse performance. We propose a new algorithm named TD3fG (TD3 learning from a generator) to solve these problems. It forms a smooth transition from learning from experts to learning from experience. This innovation can help agents extract prior knowledge while reducing the detrimental effects of the demonstrations. Our algorithm performs well in Adroit manipulator and MuJoCo tasks with limited demonstrations.
We study the parameterized complexity of training two-layer neural networks with respect to the dimension of the input data and the number of hidden neurons, considering ReLU and linear threshold activation functions. Albeit the computational complexity of these problems has been studied numerous times in recent years, several questions are still open. We answer questions by Arora et al. [ICLR '18] and Khalife and Basu [IPCO '22] showing that both problems are NP-hard for two dimensions, which excludes any polynomial-time algorithm for constant dimension. We also answer a question by Froese et al. [JAIR '22] proving W[1]-hardness for four ReLUs (or two linear threshold neurons) with zero training error. Finally, in the ReLU case, we show fixed-parameter tractability for the combined parameter number of dimensions and number of ReLUs if the network is assumed to compute a convex map. Our results settle the complexity status regarding these parameters almost completely.
We consider perception-based control using state estimates that are obtained from high-dimensional sensor measurements via learning-enabled perception maps. However, these perception maps are not perfect and result in state estimation errors that can lead to unsafe system behavior. Stochastic sensor noise can make matters worse and result in estimation errors that follow unknown distributions. We propose a perception-based control framework that i) quantifies estimation uncertainty of perception maps, and ii) integrates these uncertainty representations into the control design. To do so, we use conformal prediction to compute valid state estimation regions, which are sets that contain the unknown state with high probability. We then devise a sampled-data controller for continuous-time systems based on the notion of measurement robust control barrier functions. Our controller uses idea from self-triggered control and enables us to avoid using stochastic calculus. Our framework is agnostic to the choice of the perception map, independent of the noise distribution, and to the best of our knowledge the first to provide probabilistic safety guarantees in such a setting. We demonstrate the effectiveness of our proposed perception-based controller for a LiDAR-enabled F1/10th car.
Traffic congestion has been a major challenge in many urban road networks. Extensive research studies have been conducted to highlight traffic-related congestion and address the issue using data-driven approaches. Currently, most traffic congestion analyses are done using simulation software that offers limited insight due to the limitations in the tools and utilities being used to render various traffic congestion scenarios. All that impacts the formulation of custom business problems which vary from place to place and country to country. By exploiting the power of the knowledge graph, we model a traffic congestion problem into the Neo4j graph and then use the load balancing, optimization algorithm to identify congestion-free road networks. We also show how traffic propagates backward in case of congestion or accident scenarios and its overall impact on other segments of the roads. We also train a sequential RNN-LSTM (Long Short-Term Memory) deep learning model on the real-time traffic data to assess the accuracy of simulation results based on a road-specific congestion. Our results show that graph-based traffic simulation, supplemented by AI ML-based traffic prediction can be more effective in estimating the congestion level in a road network.