Despite the impressive numerical performance of the quasi-Newton and Anderson/nonlinear acceleration methods, their global convergence rates have remained elusive for over 50 years. This study addresses this long-standing issue by introducing a framework that derives novel, adaptive quasi-Newton and nonlinear/Anderson acceleration schemes. Under mild assumptions, the proposed iterative methods exhibit explicit, non-asymptotic convergence rates that blend those of the gradient descent and Cubic Regularized Newton's methods. The proposed approach also includes an accelerated version for convex functions. Notably, these rates are achieved adaptively without prior knowledge of the function's parameters. The framework presented in this study is generic, and its special cases includes algorithms such as Newton's method with random subspaces, finite-differences, or lazy Hessian. Numerical experiments demonstrated the efficiency of the proposed framework, even compared to the l-BFGS algorithm with Wolfe line-search.
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Physics-Informed Neural Networks for High-Frequency and Multi-Scale Problems using Transfer Learning
Physics-informed neural network (PINN) is a data-driven solver for partial and ordinary differential equations(ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the objective function often leads to training failures. This issue is particularly prominent when solving high-frequency and multi-scale problems. We proposed using transfer learning to boost the robustness and convergence of training PINN, starting training from low-frequency problems and gradually approaching high-frequency problems. Through two case studies, we discovered that transfer learning can effectively train PINN to approximate solutions from low-frequency problems to high-frequency problems without increasing network parameters. Furthermore, it requires fewer data points and less training time. We elaborately described our training strategy, including optimizer selection, and suggested guidelines for using transfer learning to train neural networks for solving more complex problems.
Semantic communication is a promising communication paradigm that utilizes Deep Neural Networks (DNNs) to extract the information relevant to downstream tasks, hence significantly reducing the amount of transmitted data. In current practice, the semantic communication transmitter for a specific task is typically pre-trained and shared by all users. However, due to user heterogeneity, it is desirable to use different transmitters according to the available computational and communication resources of users. In this paper, we first show that it is possible to dynamically adjust the computational and communication overhead of DNN-based transmitters, thereby achieving adaptive semantic communication. After that, we investigate the user association and resource allocation problem in a multi-cell network where users are equipped with adaptive semantic communication transmitters. To solve this problem, we decompose it into three subproblems involving the scheduling of each user, the resource allocation of each base station (BS), and the user association between users and BSs. Then we solve each problem progressively based on the solution of the previous subproblem. The final algorithm can obtain near-optimal solutions in polynomial time. Numerical results show that our algorithm outperforms benchmarks under various situations.
CoCoT: Contrastive Chain-of-Thought Prompting for Large Multimodal Models with Multiple Image Inputs
When exploring the development of Artificial General Intelligence (AGI), a critical task for these models involves interpreting and processing information from multiple image inputs. However, Large Multimodal Models (LMMs) encounter two issues in such scenarios: (1) a lack of fine-grained perception, and (2) a tendency to blend information across multiple images. We first extensively investigate the capability of LMMs to perceive fine-grained visual details when dealing with multiple input images. The research focuses on two aspects: first, image-to-image matching (to evaluate whether LMMs can effectively reason and pair relevant images), and second, multi-image-to-text matching (to assess whether LMMs can accurately capture and summarize detailed image information). We conduct evaluations on a range of both open-source and closed-source large models, including GPT-4V, Gemini, OpenFlamingo, and MMICL. To enhance model performance, we further develop a Contrastive Chain-of-Thought (CoCoT) prompting approach based on multi-input multimodal models. This method requires LMMs to compare the similarities and differences among multiple image inputs, and then guide the models to answer detailed questions about multi-image inputs based on the identified similarities and differences. Our experimental results showcase CoCoT's proficiency in enhancing the multi-image comprehension capabilities of large multimodal models.
We present Neural Quantile Estimation (NQE), a novel Simulation-Based Inference (SBI) method based on conditional quantile regression. NQE autoregressively learns individual one dimensional quantiles for each posterior dimension, conditioned on the data and previous posterior dimensions. Posterior samples are obtained by interpolating the predicted quantiles using monotonic cubic Hermite spline, with specific treatment for the tail behavior and multi-modal distributions. We introduce an alternative definition for the Bayesian credible region using the local Cumulative Density Function (CDF), offering substantially faster evaluation than the traditional Highest Posterior Density Region (HPDR). In case of limited simulation budget and/or known model misspecification, a post-processing broadening step can be integrated into NQE to ensure the unbiasedness of the posterior estimation with negligible additional computational cost. We demonstrate that the proposed NQE method achieves state-of-the-art performance on a variety of benchmark problems.
In the realm of artificial intelligence, the emergence of foundation models, backed by high computing capabilities and extensive data, has been revolutionary. Segment Anything Model (SAM), built on the Vision Transformer (ViT) model with millions of parameters and vast training dataset SA-1B, excels in various segmentation scenarios relying on its significance of semantic information and generalization ability. Such achievement of visual foundation model stimulates continuous researches on specific downstream tasks in computer vision. The ClassWise-SAM-Adapter (CWSAM) is designed to adapt the high-performing SAM for landcover classification on space-borne Synthetic Aperture Radar (SAR) images. The proposed CWSAM freezes most of SAM's parameters and incorporates lightweight adapters for parameter efficient fine-tuning, and a classwise mask decoder is designed to achieve semantic segmentation task. This adapt-tuning method allows for efficient landcover classification of SAR images, balancing the accuracy with computational demand. In addition, the task specific input module injects low frequency information of SAR images by MLP-based layers to improve the model performance. Compared to conventional state-of-the-art semantic segmentation algorithms by extensive experiments, CWSAM showcases enhanced performance with fewer computing resources, highlighting the potential of leveraging foundational models like SAM for specific downstream tasks in the SAR domain. The source code is available at: //github.com/xypu98/CWSAM.
This work focuses on the synergy of rate-splitting multiple access (RSMA) and beyond diagonal reconfigurable intelligent surface (BD-RIS) to enlarge the coverage, improve the performance, and save on antennas. Specifically, we employ a multi-sector BD-RIS modeled as a prism, which can achieve highly directional full-space coverage, in a multiuser multiple input single output communication system. With the multi-sector BD-RIS aided RSMA model, we jointly design the transmit precoder and BD-RIS matrix under the imperfect channel state information (CSI) conditions. The robust design is performed by solving a stochastic average sum-rate maximization problem. With sample average approximation and weighted minimum mean square error-rate relationship, the stochastic problem is transformed into a deterministic one with multiple blocks, each of which is iteratively designed. Simulation results show that multi-sector BD-RIS aided RSMA outperforms space division multiple access schemes. More importantly, synergizing multi-sector BD-RIS with RSMA is an efficient strategy to reduce the number of active antennas at the transmitter and the number of passive antennas in BD-RIS.
Background: Identifying and characterising the longitudinal patterns of multimorbidity associated with stroke is needed to better understand patients' needs and inform new models of care. Methods: We used an unsupervised patient-oriented clustering approach to analyse primary care electronic health records (EHR) of 30 common long-term conditions (LTC), in patients with stroke aged over 18, registered in 41 general practices in south London between 2005 and 2021. Results: Of 849,968 registered patients, 9,847 (1.16%) had a record of stroke, 46.5% were female and median age at record was 65.0 year (IQR: 51.5 to 77.0). The median number of LTCs in addition to stroke was 3 (IQR: from 2 to 5). Patients were stratified in eight clusters. These clusters revealed contrasted patterns of multimorbidity, socio-demographic characteristics (age, gender and ethnicity) and risk factors. Beside a core of 3 clusters associated with conventional stroke risk-factors, minor clusters exhibited less common but recurrent combinations of LTCs including mental health conditions, asthma, osteoarthritis and sickle cell anaemia. Importantly, complex profiles combining mental health conditions, infectious diseases and substance dependency emerged. Conclusion: This patient-oriented approach to EHRs uncovers the heterogeneity of profiles of multimorbidity and socio-demographic characteristics associated with stroke. It highlights the importance of conventional stroke risk factors as well as the association of mental health conditions in complex profiles of multimorbidity displayed in a significant proportion of patients. These results address the need for a better understanding of stroke-associated multimorbidity and complexity to inform more efficient and patient-oriented healthcare models.
Benefitting from the vast spatial degrees of freedom, the amalgamation of integrated sensing and communication (ISAC) and massive multiple-input multiple-output (MIMO) is expected to simultaneously improve spectral and energy efficiencies as well as the sensing capability. However, a large number of antennas deployed in massive MIMO-ISAC raises critical challenges in acquiring both accurate channel state information and target parameter information. To overcome these two challenges with a unified framework, we first analyze their underlying system models and then propose a novel tensor-based approach that addresses both the channel estimation and target sensing problems. Specifically, by parameterizing the high-dimensional communication channel exploiting a small number of physical parameters, we associate the channel state information with the sensing parameters of targets in terms of angular, delay, and Doppler dimensions. Then, we propose a shared training pattern adopting the same time-frequency resources such that both the channel estimation and target parameter estimation can be formulated as a canonical polyadic decomposition problem with a similar mathematical expression. On this basis, we first investigate the uniqueness condition of the tensor factorization and the maximum number of resolvable targets by utilizing the specific Vandermonde
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.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.
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