In this work, we present an abstract theory for the approximation of operator-valued Riccati equations posed on Hilbert spaces. It is demonstrated here, under the assumption of compactness in the coefficient operators, that the error of the approximate solution to the operator-valued Riccati equation is bounded above by the approximation error of the governing semigroup. One significant outcome of this result is the correct prediction of optimal convergence for finite element approximations of the operator-valued Riccati equations for when the governing semigroup involves parabolic, as well as hyperbolic processes. We derive the abstract theory for the time-dependent and time-independent operator-valued Riccati equations in the first part of this work. In the second part, we prove optimal convergence rates for the finite element approximation of the functional gain associated with model one-dimensional weakly damped wave and thermal LQR control systems. These theoretical claims are then corroborated with computational evidence.
In this paper, we introduce a new class of parameterized controllers, drawing inspiration from Model Predictive Control (MPC). The controller resembles a Quadratic Programming (QP) solver of a linear MPC problem, with the parameters of the controller being trained via Deep Reinforcement Learning (DRL) rather than derived from system models. This approach addresses the limitations of common controllers with Multi-Layer Perceptron (MLP) or other general neural network architecture used in DRL, in terms of verifiability and performance guarantees, and the learned controllers possess verifiable properties like persistent feasibility and asymptotic stability akin to MPC. On the other hand, numerical examples illustrate that the proposed controller empirically matches MPC and MLP controllers in terms of control performance and has superior robustness against modeling uncertainty and noises. Furthermore, the proposed controller is significantly more computationally efficient compared to MPC and requires fewer parameters to learn than MLP controllers. Real-world experiments on vehicle drift maneuvering task demonstrate the potential of these controllers for robotics and other demanding control tasks.
There is an emerging line of research on multimodal instruction tuning, and a line of benchmarks has been proposed for evaluating these models recently. Instead of evaluating the models directly, in this paper, we try to evaluate the Vision-Language Instruction-Tuning (VLIT) datasets. Also, we seek the way of building a dataset for developing an all-powerful VLIT model, which we believe could also be of utility for establishing a grounded protocol for benchmarking VLIT models. For effective evaluation of VLIT datasets that remains an open question, we propose a tune-cross-evaluation paradigm: tuning on one dataset and evaluating on the others in turn. For each single tune-evaluation experiment set, we define the Meta Quality (MQ) as the mean score obtained by a set of caption metrics including BLEU, METEOR, and ROUGE-L to quantify the quality of a certain dataset or a sample. On this basis, to evaluate the comprehensiveness of a dataset, we develop the Dataset Quality (DQ) covering all tune-evaluation sets. To lay the foundation for building a comprehensive dataset and developing an all-powerful model for practical applications, we define the Sample Quality (SQ) to quantify the all-sided quality of each sample. Extensive experiments validate the rationality of the proposed evaluation paradigm. Based on the holistic evaluation, we build a new dataset, REVO-LION (REfining VisiOn-Language InstructiOn tuNing), by collecting samples with higher SQ from each dataset. Remarkably, even with only half of the complete data, the model trained on REVO-LION can achieve the performance comparable to simply adding all VLIT datasets up. Furthermore, REVO-LION not only facilitates the development of a powerful model but also incorporates an evaluation set, which is designed to serve as a convenient benchmark for future research in the field.
We consider the optimization problem associated with fitting two-layer ReLU networks with respect to the squared loss, where labels are assumed to be generated by a target network. Focusing first on standard Gaussian inputs, we show that the structure of spurious local minima detected by stochastic gradient descent (SGD) is, in a well-defined sense, the \emph{least loss of symmetry} with respect to the target weights. A closer look at the analysis indicates that this principle of least symmetry breaking may apply to a broader range of settings. Motivated by this, we conduct a series of experiments which corroborate this hypothesis for different classes of non-isotropic non-product distributions, smooth activation functions and networks with a few layers.
In this work, we consider a fundamental task in quantum many-body physics - finding and learning ground states of quantum Hamiltonians and their properties. Recent works have studied the task of predicting the ground state expectation value of sums of geometrically local observables by learning from data. For short-range gapped Hamiltonians, a sample complexity that is logarithmic in the number of qubits and quasipolynomial in the error was obtained. Here we extend these results beyond the local requirements on both Hamiltonians and observables, motivated by the relevance of long-range interactions in molecular and atomic systems. For interactions decaying as a power law with exponent greater than twice the dimension of the system, we recover the same efficient logarithmic scaling with respect to the number of qubits, but the dependence on the error worsens to exponential. Further, we show that learning algorithms equivariant under the automorphism group of the interaction hypergraph achieve a sample complexity reduction, leading in particular to a constant number of samples for learning sums of local observables in systems with periodic boundary conditions. We demonstrate the efficient scaling in practice by learning from DMRG simulations of $1$D long-range and disordered systems with up to $128$ qubits. Finally, we provide an analysis of the concentration of expectation values of global observables stemming from central limit theorem, resulting in increased prediction accuracy.
Recent research has extended beyond assessing the performance of Large Language Models (LLMs) to examining their characteristics from a psychological standpoint, acknowledging the necessity of understanding their behavioral characteristics. The administration of personality tests to LLMs has emerged as a noteworthy area in this context. However, the suitability of employing psychological scales, initially devised for humans, on LLMs is a matter of ongoing debate. Our study aims to determine the reliability of applying personality assessments to LLMs, explicitly investigating whether LLMs demonstrate consistent personality traits. Analyzing responses under 2,500 settings reveals that gpt-3.5-turbo shows consistency in responses to the Big Five Inventory, indicating a high degree of reliability. Furthermore, our research explores the potential of gpt-3.5-turbo to emulate diverse personalities and represent various groups, which is a capability increasingly sought after in social sciences for substituting human participants with LLMs to reduce costs. Our findings reveal that LLMs have the potential to represent different personalities with specific prompt instructions. By shedding light on the personalization of LLMs, our study endeavors to pave the way for future explorations in this field. We have made our experimental results and the corresponding code openly accessible via //github.com/CUHK-ARISE/LLMPersonality.
We apply the U-Net model for compressive light field synthesis. Compared to methods based on stacked CNN and iterative algorithms, this method offers better image quality, uniformity and less computation.
Voronoi tessellation, also known as Voronoi diagram, is an important computational geometry technique that has applications in various scientific disciplines. It involves dividing a given space into regions based on the proximity to a set of points. Autodifferentiation is a powerful tool for solving optimization tasks. Autodifferentiation assumes constructing a computational graph that allows to compute gradients using backpropagation algorithm. However, often the Voronoi tessellation remains the only non-differentiable part of a pipeline, prohibiting end-to-end differentiation. We present the method for autodifferentiation of the 2D Voronoi tessellation. The method allows one to construct the Voronoi tessellation and pass gradients, making the construction end-to-end differentiable. We provide the implementation details and present several important applications. To the best of our knowledge this is the first autodifferentiable realization of the Voronoi tessellation providing full set of Voronoi geometrical parameters in a differentiable way.
Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.
In pace with developments in the research field of artificial intelligence, knowledge graphs (KGs) have attracted a surge of interest from both academia and industry. As a representation of semantic relations between entities, KGs have proven to be particularly relevant for natural language processing (NLP), experiencing a rapid spread and wide adoption within recent years. Given the increasing amount of research work in this area, several KG-related approaches have been surveyed in the NLP research community. However, a comprehensive study that categorizes established topics and reviews the maturity of individual research streams remains absent to this day. Contributing to closing this gap, we systematically analyzed 507 papers from the literature on KGs in NLP. Our survey encompasses a multifaceted review of tasks, research types, and contributions. As a result, we present a structured overview of the research landscape, provide a taxonomy of tasks, summarize our findings, and highlight directions for future work.
Machine learning techniques have deeply rooted in our everyday life. However, since it is knowledge- and labor-intensive to pursue good learning performance, human experts are heavily involved in every aspect of machine learning. In order to make machine learning techniques easier to apply and reduce the demand for experienced human experts, automated machine learning (AutoML) has emerged as a hot topic with both industrial and academic interest. In this paper, we provide an up to date survey on AutoML. First, we introduce and define the AutoML problem, with inspiration from both realms of automation and machine learning. Then, we propose a general AutoML framework that not only covers most existing approaches to date but also can guide the design for new methods. Subsequently, we categorize and review the existing works from two aspects, i.e., the problem setup and the employed techniques. Finally, we provide a detailed analysis of AutoML approaches and explain the reasons underneath their successful applications. We hope this survey can serve as not only an insightful guideline for AutoML beginners but also an inspiration for future research.