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Linear time-invariant systems are very popular models in system theory and applications. A fundamental problem in system identification that remains rather unaddressed in extant literature is to leverage commonalities amongst related linear systems to estimate their transition matrices more accurately. To address this problem, the current paper investigates methods for jointly estimating the transition matrices of multiple systems. It is assumed that the transition matrices are unknown linear functions of some unknown shared basis matrices. We establish finite-time estimation error rates that fully reflect the roles of trajectory lengths, dimension, and number of systems under consideration. The presented results are fairly general and show the significant gains that can be achieved by pooling data across systems in comparison to learning each system individually. Further, they are shown to be robust against model misspecifications. To obtain the results, we develop novel techniques that are of interest for addressing similar joint-learning problems. They include tightly bounding estimation errors in terms of the eigen-structures of transition matrices, establishing sharp high probability bounds for singular values of dependent random matrices, and capturing effects of misspecified transition matrices as the systems evolve over time.

We describe a new general method for segmentation in MRI scans using Topological Data Analysis (TDA), offering several advantages over traditional machine learning approaches. It works in three steps, first identifying the whole object to segment via automatic thresholding, then detecting a distinctive subset whose topology is known in advance, and finally deducing the various components of the segmentation. Although convoking classical ideas of TDA, such an algorithm has never been proposed separately from deep learning methods. To achieve this, our approach takes into account, in addition to the homology of the image, the localization of representative cycles, a piece of information that seems never to have been exploited in this context. In particular, it offers the ability to perform segmentation without the need for large annotated data sets. TDA also provides a more interpretable and stable framework for segmentation by explicitly mapping topological features to segmentation components. By adapting the geometric object to be detected, the algorithm can be adjusted to a wide range of data segmentation challenges. We carefully study the examples of glioblastoma segmentation in brain MRI, where a sphere is to be detected, as well as myocardium in cardiac MRI, involving a cylinder, and cortical plate detection in fetal brain MRI, whose 2D slices are circles. We compare our method to state-of-the-art algorithms.

We introduce a new approach for identifying and characterizing voids within two-dimensional (2D) point distributions through the integration of Delaunay triangulation and Voronoi diagrams, combined with a Minimal Distance Scoring algorithm. Our methodology initiates with the computational determination of the Convex Hull vertices within the point cloud, followed by a systematic selection of optimal line segments, strategically chosen for their likelihood of intersecting internal void regions. We then utilize Delaunay triangulation in conjunction with Voronoi diagrams to ascertain the initial points for the construction of the maximal internal curve envelope by adopting a pseudo-recursive approach for higher-order void identification. In each iteration, the existing collection of maximal internal curve envelope points serves as a basis for identifying additional candidate points. This iterative process is inherently self-converging, ensuring progressive refinement of the void's shape with each successive computation cycle. The mathematical robustness of this method allows for an efficient convergence to a stable solution, reflecting both the geometric intricacies and the topological characteristics of the voids within the point cloud. Our findings introduce a method that aims to balance geometric accuracy with computational practicality. The approach is designed to improve the understanding of void shapes within point clouds and suggests a potential framework for exploring more complex, multi-dimensional data analysis.

Comprehensive and accurate evaluation of general-purpose AI systems such as large language models allows for effective mitigation of their risks and deepened understanding of their capabilities. Current evaluation methodology, mostly based on benchmarks of specific tasks, falls short of adequately assessing these versatile AI systems, as present techniques lack a scientific foundation for predicting their performance on unforeseen tasks and explaining their varying performance on specific task items or user inputs. Moreover, existing benchmarks of specific tasks raise growing concerns about their reliability and validity. To tackle these challenges, we suggest transitioning from task-oriented evaluation to construct-oriented evaluation. Psychometrics, the science of psychological measurement, provides a rigorous methodology for identifying and measuring the latent constructs that underlie performance across multiple tasks. We discuss its merits, warn against potential pitfalls, and propose a framework to put it into practice. Finally, we explore future opportunities of integrating psychometrics with the evaluation of general-purpose AI systems.

Current prompting approach for language model inference mainly rely on Language Model's (LLM) autonomous exploration of reasoning paths, confronts an inevitable retracing operation when erroneous routes are encountered. This is followed by the pursuit of alternative reasoning paths. However, humans are adept at abstracting optimal solutions from problems, thereby facilitating swift and precise reasoning for similar problems resolution. In light of this, we delves into the potential of harnessing expert knowledge to enhance problem-solving within LLMs. We introduce a novel paradigm, the State Machine of Thought (SMoT), which employs predefined state machines to furnish LLMs with efficient reasoning paths, thereby eliminating fruitless exploration. Furthermore, we propose a multi-agent mechanism that assigns different objectives to agents, aiming to enhance the accuracy of SMoT reasoning. The experimental results, derived from an array reasoning task, reveal that SMoT realizes an extraordinary accuracy of 95\%, surpassing the performance of the state-of-the-art baselines.

Residual networks (ResNets) have displayed impressive results in pattern recognition and, recently, have garnered considerable theoretical interest due to a perceived link with neural ordinary differential equations (neural ODEs). This link relies on the convergence of network weights to a smooth function as the number of layers increases. We investigate the properties of weights trained by stochastic gradient descent and their scaling with network depth through detailed numerical experiments. We observe the existence of scaling regimes markedly different from those assumed in neural ODE literature. Depending on certain features of the network architecture, such as the smoothness of the activation function, one may obtain an alternative ODE limit, a stochastic differential equation or neither of these. These findings cast doubts on the validity of the neural ODE model as an adequate asymptotic description of deep ResNets and point to an alternative class of differential equations as a better description of the deep network limit.

The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional relations among them. In this paper, we present evolutionary state graph, a dynamic graph structure designed to systematically represent the evolving relations (edges) among states (nodes) along time. We conduct analysis on the dynamic graphs constructed from the time-series data and show that changes on the graph structures (e.g., edges connecting certain state nodes) can inform the occurrences of events (i.e., time-series fluctuation). Inspired by this, we propose a novel graph neural network model, Evolutionary State Graph Network (EvoNet), to encode the evolutionary state graph for accurate and interpretable time-series event prediction. Specifically, Evolutionary State Graph Network models both the node-level (state-to-state) and graph-level (segment-to-segment) propagation, and captures the node-graph (state-to-segment) interactions over time. Experimental results based on five real-world datasets show that our approach not only achieves clear improvements compared with 11 baselines, but also provides more insights towards explaining the results of event predictions.

Retrieving object instances among cluttered scenes efficiently requires compact yet comprehensive regional image representations. Intuitively, object semantics can help build the index that focuses on the most relevant regions. However, due to the lack of bounding-box datasets for objects of interest among retrieval benchmarks, most recent work on regional representations has focused on either uniform or class-agnostic region selection. In this paper, we first fill the void by providing a new dataset of landmark bounding boxes, based on the Google Landmarks dataset, that includes $94k$ images with manually curated boxes from $15k$ unique landmarks. Then, we demonstrate how a trained landmark detector, using our new dataset, can be leveraged to index image regions and improve retrieval accuracy while being much more efficient than existing regional methods. In addition, we further introduce a novel regional aggregated selective match kernel (R-ASMK) to effectively combine information from detected regions into an improved holistic image representation. R-ASMK boosts image retrieval accuracy substantially at no additional memory cost, while even outperforming systems that index image regions independently. Our complete image retrieval system improves upon the previous state-of-the-art by significant margins on the Revisited Oxford and Paris datasets. Code and data will be released.

We introduce a multi-task setup of identifying and classifying entities, relations, and coreference clusters in scientific articles. We create SciERC, a dataset that includes annotations for all three tasks and develop a unified framework called Scientific Information Extractor (SciIE) for with shared span representations. The multi-task setup reduces cascading errors between tasks and leverages cross-sentence relations through coreference links. Experiments show that our multi-task model outperforms previous models in scientific information extraction without using any domain-specific features. We further show that the framework supports construction of a scientific knowledge graph, which we use to analyze information in scientific literature.

High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.