Preventing Model Collapse in Gaussian Process Latent Variable Models

Gaussian process latent variable models (GPLVMs) are a versatile family of unsupervised learning models, commonly used for dimensionality reduction. However, common challenges in modeling data with GPLVMs include inadequate kernel flexibility and improper selection of the projection noise, which leads to a type of model collapse characterized primarily by vague latent representations that do not reflect the underlying structure of the data. This paper addresses these issues by, first, theoretically examining the impact of the projection variance on model collapse through the lens of a linear GPLVM. Second, we address the problem of model collapse due to inadequate kernel flexibility by integrating the spectral mixture (SM) kernel and a differentiable random Fourier feature (RFF) kernel approximation, which ensures computational scalability and efficiency through off-the-shelf automatic differentiation tools for learning the kernel hyperparameters, projection variance, and latent representations within the variational inference framework. The proposed GPLVM, named advisedRFLVM, is evaluated across diverse datasets and consistently outperforms various salient competing models, including state-of-the-art variational autoencoders (VAEs) and GPLVM variants, in terms of informative latent representations and missing data imputation.

Regularization-Based Efficient Continual Learning in Deep State-Space Models

Deep state-space models (DSSMs) have gained popularity in recent years due to their potent modeling capacity for dynamic systems. However, existing DSSM works are limited to single-task modeling, which requires retraining with historical task data upon revisiting a forepassed task. To address this limitation, we propose continual learning DSSMs (CLDSSMs), which are capable of adapting to evolving tasks without catastrophic forgetting. Our proposed CLDSSMs integrate mainstream regularization-based continual learning (CL) methods, ensuring efficient updates with constant computational and memory costs for modeling multiple dynamic systems. We also conduct a comprehensive cost analysis of each CL method applied to the respective CLDSSMs, and demonstrate the efficacy of CLDSSMs through experiments on real-world datasets. The results corroborate that while various competing CL methods exhibit different merits, the proposed CLDSSMs consistently outperform traditional DSSMs in terms of effectively addressing catastrophic forgetting, enabling swift and accurate parameter transfer to new tasks.

Inverse Design of Photonic Crystal Surface Emitting Lasers is a Sequence Modeling Problem

Photonic Crystal Surface Emitting Lasers (PCSEL)'s inverse design demands expert knowledge in physics, materials science, and quantum mechanics which is prohibitively labor-intensive. Advanced AI technologies, especially reinforcement learning (RL), have emerged as a powerful tool to augment and accelerate this inverse design process. By modeling the inverse design of PCSEL as a sequential decision-making problem, RL approaches can construct a satisfactory PCSEL structure from scratch. However, the data inefficiency resulting from online interactions with precise and expensive simulation environments impedes the broader applicability of RL approaches. Recently, sequential models, especially the Transformer architecture, have exhibited compelling performance in sequential decision-making problems due to their simplicity and scalability to large language models. In this paper, we introduce a novel framework named PCSEL Inverse Design Transformer (PiT) that abstracts the inverse design of PCSEL as a sequence modeling problem. The central part of our PiT is a Transformer-based structure that leverages the past trajectories and current states to predict the current actions. Compared with the traditional RL approaches, PiT can output the optimal actions and achieve target PCSEL designs by leveraging offline data and conditioning on the desired return. Results demonstrate that PiT achieves superior performance and data efficiency compared to baselines.

Exploring Large Language Model based Intelligent Agents: Definitions, Methods, and Prospects

Intelligent agents stand out as a potential path toward artificial general intelligence (AGI). Thus, researchers have dedicated significant effort to diverse implementations for them. Benefiting from recent progress in large language models (LLMs), LLM-based agents that use universal natural language as an interface exhibit robust generalization capabilities across various applications -- from serving as autonomous general-purpose task assistants to applications in coding, social, and economic domains, LLM-based agents offer extensive exploration opportunities. This paper surveys current research to provide an in-depth overview of LLM-based intelligent agents within single-agent and multi-agent systems. It covers their definitions, research frameworks, and foundational components such as their composition, cognitive and planning methods, tool utilization, and responses to environmental feedback. We also delve into the mechanisms of deploying LLM-based agents in multi-agent systems, including multi-role collaboration, message passing, and strategies to alleviate communication issues between agents. The discussions also shed light on popular datasets and application scenarios. We conclude by envisioning prospects for LLM-based agents, considering the evolving landscape of AI and natural language processing.

Ensemble Kalman Filtering-Aided Variational Inference for Gaussian Process State-Space Models

Gaussian process state-space models (GPSSMs) are a flexible and principled approach for modeling dynamical systems. However, existing variational learning and inference methods for GPSSMs often necessitate optimizing a substantial number of variational distribution parameters, leading to inadequate performance and efficiency. To overcome this issue, we propose incorporating the ensemble Kalman filter (EnKF), a well-established model-based filtering technique, into the variational inference framework to approximate the posterior distribution of latent states. This utilization of EnKF can effectively exploit the dependencies between latent states and GP dynamics, while eliminating the need for parameterizing the variational distribution, thereby significantly reducing the number of variational parameters. Moreover, we show that our proposed algorithm allows straightforward evaluation of an approximated evidence lower bound (ELBO) in variational inference via simply summating multiple terms with readily available closed-form solutions. Leveraging automatic differentiation tools, we hence can maximize the ELBO and train the GPSSM efficiently. We also extend the proposed algorithm to an online setting and provide detailed algorithmic analyses and insights. Extensive evaluation on diverse real and synthetic datasets demonstrates the superiority of our EnKF-aided variational inference algorithms in terms of learning and inference performance compared to existing methods.

Joint DOA estimation and distorted sensor detection under entangled low-rank and row-sparse constraints

The problem of joint direction-of-arrival estimation and distorted sensor detection has received a lot of attention in recent decades. Most state-of-the-art work formulated such a problem via low-rank and row-sparse decomposition, where the low-rank and row-sparse components were treated in an isolated manner. Such a formulation results in a performance loss. Differently, in this paper, we entangle the low-rank and row-sparse components by exploring their inherent connection. Furthermore, we take into account the maximal distortion level of the sensors. An alternating optimization scheme is proposed to solve the low-rank component and the sparse component, where a closed-form solution is derived for the low-rank component and a quadratic programming is developed for the sparse component. Numerical results exhibit the effectiveness and superiority of the proposed method.

Attentional Graph Neural Networks for Robust Massive Network Localization

Graph neural networks (GNNs) have gained significant popularity for classification tasks in machine learning, yet their applications to regression problems remain limited. Concurrently, attention mechanisms have emerged as powerful tools in sequential learning tasks. In this paper, we employ GNNs and attention mechanisms to address a classical but challenging nonlinear regression problem: network localization. We propose a novel GNN-based network localization method that achieves exceptional stability and accuracy in the presence of severe non-line-of-sight (NLOS) propagations, while eliminating the need for laborious offline calibration or NLOS identification. Extensive experimental results validate the effectiveness and high accuracy of our GNN-based localization model, particularly in challenging NLOS scenarios. However, the proposed GNN-based model exhibits limited flexibility, and its accuracy is highly sensitive to a specific hyperparameter that determines the graph structure. To address the limitations and extend the applicability of the GNN-based model to real scenarios, we introduce two attentional graph neural networks (AGNNs) that offer enhanced flexibility and the ability to automatically learn the optimal hyperparameter for each node. Experimental results confirm that the AGNN models are able to enhance localization accuracy, providing a promising solution for real-world applications. We also provide some analyses of the improved performance achieved by the AGNN models from the perspectives of dynamic attention and signal denoising characteristics.

Gaussian Processes with Linear Multiple Kernel: Spectrum Design and Distributed Learning for Multi-Dimensional Data

Gaussian processes (GPs) have emerged as a prominent technique for machine learning and signal processing. A key component in GP modeling is the choice of kernel, and linear multiple kernels (LMKs) have become an attractive kernel class due to their powerful modeling capacity and interpretability. This paper focuses on the grid spectral mixture (GSM) kernel, an LMK that can approximate arbitrary stationary kernels. Specifically, we propose a novel GSM kernel formulation for multi-dimensional data that reduces the number of hyper-parameters compared to existing formulations, while also retaining a favorable optimization structure and approximation capability. In addition, to make the large-scale hyper-parameter optimization in the GSM kernel tractable, we first introduce the distributed SCA (DSCA) algorithm. Building on this, we propose the doubly distributed SCA (D$^2$SCA) algorithm based on the alternating direction method of multipliers (ADMM) framework, which allows us to cooperatively learn the GSM kernel in the context of big data while maintaining data privacy. Furthermore, we tackle the inherent communication bandwidth restriction in distributed frameworks, by quantizing the hyper-parameters in D$^2$SCA, resulting in the quantized doubly distributed SCA (QD$^2$SCA) algorithm. Theoretical analysis establishes convergence guarantees for the proposed algorithms, while experiments on diverse datasets demonstrate the superior prediction performance and efficiency of our methods.

Towards Efficient Modeling and Inference in Multi-Dimensional Gaussian Process State-Space Models

The Gaussian process state-space model (GPSSM) has attracted extensive attention for modeling complex nonlinear dynamical systems. However, the existing GPSSM employs separate Gaussian processes (GPs) for each latent state dimension, leading to escalating computational complexity and parameter proliferation, thus posing challenges for modeling dynamical systems with high-dimensional latent states. To surmount this obstacle, we propose to integrate the efficient transformed Gaussian process (ETGP) into the GPSSM, which involves pushing a shared GP through multiple normalizing flows to efficiently model the transition function in high-dimensional latent state space. Additionally, we develop a corresponding variational inference algorithm that surpasses existing methods in terms of parameter count and computational complexity. Experimental results on diverse synthetic and real-world datasets corroborate the efficiency of the proposed method, while also demonstrating its ability to achieve similar inference performance compared to existing methods. Code is available at \url{https://github.com/zhidilin/gpssmProj}.

Bayesian-Boosted MetaLoc: Efficient Training and Guaranteed Generalization for Indoor Localization

Existing localization approaches utilizing environment-specific channel state information (CSI) excel under specific environment but struggle to generalize across varied environments. This challenge becomes even more pronounced when confronted with limited training data. To address these issues, we present the Bayes-Optimal Meta-Learning for Localization (BOML-Loc) framework, inspired by the PAC-Optimal Hyper-Posterior (PACOH) algorithm. Improving on our earlier MetaLoc~\cite{MetaLoc}, BOML-Loc employs a Bayesian approach, reducing the need for extensive training, lowering overfitting risk, and offering per-test-point uncertainty estimation. Even with very limited training tasks, BOML-Loc guarantees robust localization and impressive generalization. In both LOS and NLOS environments with site-surveyed data, BOML-Loc surpasses existing models, demonstrating enhanced localization accuracy, generalization abilities, and reduced overfitting in new and previously unseen environments.