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Reservoir computing is a machine learning framework that has been shown to be able to replicate the chaotic attractor, including the fractal dimension and the entire Lyapunov spectrum, of the dynamical system on which it is trained. We quantitatively relate the generalized synchronization dynamics of a driven reservoir during the training stage to the performance of the trained reservoir computer at the attractor reconstruction task. We show that, in order to obtain successful attractor reconstruction and Lyapunov spectrum estimation, the largest conditional Lyapunov exponent of the driven reservoir must be significantly more negative than the most negative Lyapunov exponent of the target system. We also find that the maximal conditional Lyapunov exponent of the reservoir depends strongly on the spectral radius of the reservoir adjacency matrix, and therefore, for attractor reconstruction and Lyapunov spectrum estimation, small spectral radius reservoir computers perform better in general. Our arguments are supported by numerical examples on well-known chaotic systems.

We explore the Ziv-Lempel and Crochemore factorizations of some classical automatic sequences making an extensive use of the theorem prover Walnut.

We present a novel framework for the development of fourth-order lattice Boltzmann schemes to tackle multidimensional nonlinear systems of conservation laws. Our numerical schemes preserve two fundamental characteristics inherent in classical lattice Boltzmann methods: a local relaxation phase and a transport phase composed of elementary shifts on a Cartesian grid. Achieving fourth-order accuracy is accomplished through the composition of second-order time-symmetric basic schemes utilizing rational weights. This enables the representation of the transport phase in terms of elementary shifts. Introducing local variations in the relaxation parameter during each stage of relaxation ensures the entropic nature of the schemes. This not only enhances stability in the long-time limit but also maintains fourth-order accuracy. To validate our approach, we conduct comprehensive testing on scalar equations and systems in both one and two spatial dimensions.

We propose a material design method via gradient-based optimization on compositions, overcoming the limitations of traditional methods: exhaustive database searches and conditional generation models. It optimizes inputs via backpropagation, aligning the model's output closely with the target property and facilitating the discovery of unlisted materials and precise property determination. Our method is also capable of adaptive optimization under new conditions without retraining. Applying to exploring high-Tc superconductors, we identified potential compositions beyond existing databases and discovered new hydrogen superconductors via conditional optimization. This method is versatile and significantly advances material design by enabling efficient, extensive searches and adaptability to new constraints.

Large language model (LLM) has marked a pivotal moment in the field of machine learning and deep learning. Recently its capability for query planning has been investigated, including both single-modal and multi-modal queries. However, there is no work on the query optimization capability of LLM. As a critical (or could even be the most important) step that significantly impacts the execution performance of the query plan, such analysis and attempts should not be missed. From another aspect, existing query optimizers are usually rule-based or rule-based + cost-based, i.e., they are dependent on manually created rules to complete the query plan rewrite/transformation. Given the fact that modern optimizers include hundreds to thousands of rules, designing a multi-modal query optimizer following a similar way is significantly time-consuming since we will have to enumerate as many multi-modal optimization rules as possible, which has not been well addressed today. In this paper, we investigate the query optimization ability of LLM and use LLM to design LaPuda, a novel LLM and Policy based multi-modal query optimizer. Instead of enumerating specific and detailed rules, LaPuda only needs a few abstract policies to guide LLM in the optimization, by which much time and human effort are saved. Furthermore, to prevent LLM from making mistakes or negative optimization, we borrow the idea of gradient descent and propose a guided cost descent (GCD) algorithm to perform the optimization, such that the optimization can be kept in the correct direction. In our evaluation, our methods consistently outperform the baselines in most cases. For example, the optimized plans generated by our methods result in 1~3x higher execution speed than those by the baselines.

Regression models for compositional data are common in several areas of knowledge. As in other classes of regression models, it is desirable to perform diagnostic analysis in these models using residuals that are approximately standard normally distributed. However, for regression models for compositional data, there has not been any multivariate residual that meets this requirement. In this work, we introduce a class of asymptotically standard normally distributed residuals for compositional data based on bootstrap. Monte Carlo simulation studies indicate that the distributions of the residuals of this class are well approximated by the standard normal distribution in small samples. An application to simulated data also suggests that one of the residuals of the proposed class is better to identify model misspecification than its competitors. Finally, the usefulness of the best residual of the proposed class is illustrated through an application on sleep stages. The class of residuals proposed here can also be used in other classes of multivariate regression models.

Loop-closure detection, also known as place recognition, aiming to identify previously visited locations, is an essential component of a SLAM system. Existing research on lidar-based loop closure heavily relies on dense point cloud and 360 FOV lidars. This paper proposes an out-of-the-box NDT (Normal Distribution Transform) based global descriptor, NDT-Map-Code, designed for both on-road driving and underground valet parking scenarios. NDT-Map-Code can be directly extracted from the NDT map without the need for a dense point cloud, resulting in excellent scalability and low maintenance cost. The NDT representation is leveraged to identify representative patterns, which are further encoded according to their spatial location (bearing, range, and height). Experimental results on the NIO underground parking lot dataset and the KITTI dataset demonstrate that our method achieves significantly better performance compared to the state-of-the-art.

This research's primary motivation of this study is to address the high hardware and computational demands typically associated with LLMs.Therefore,our goal is to find a balance between model lightness and performance,striving to maximize performance while using a comparatively lightweight model. Hyacinth6B was developed with this objective in mind,aiming to fully leverage the core capabilities of LLMs without incurring substantial resource costs, effectively pushing the boundaries of smaller model's performance. The training approach involves parameter efficient finetuning using the LoRA method.

Regent is an implicitly parallel programming language that allows the development of a single codebase for heterogeneous platforms targeting CPUs and GPUs. This paper presents the development of a parallel meshfree solver in Regent for two-dimensional inviscid compressible flows. The meshfree solver is based on the least squares kinetic upwind method. Example codes are presented to show the difference between the Regent and CUDA-C implementations of the meshfree solver on a GPU node. For CPU parallel computations, details are presented on how the data communication and synchronisation are handled by Regent and Fortran+MPI codes. The Regent solver is verified by applying it to the standard test cases for inviscid flows. Benchmark simulations are performed on coarse to very fine point distributions to assess the solver's performance. The computational efficiency of the Regent solver on an A100 GPU is compared with an equivalent meshfree solver written in CUDA-C. The codes are then profiled to investigate the differences in their performance. The performance of the Regent solver on CPU cores is compared with an equivalent explicitly parallel Fortran meshfree solver based on MPI. Scalability results are shown to offer insights into performance.

We present ResMLP, an architecture built entirely upon multi-layer perceptrons for image classification. It is a simple residual network that alternates (i) a linear layer in which image patches interact, independently and identically across channels, and (ii) a two-layer feed-forward network in which channels interact independently per patch. When trained with a modern training strategy using heavy data-augmentation and optionally distillation, it attains surprisingly good accuracy/complexity trade-offs on ImageNet. We will share our code based on the Timm library and pre-trained models.