The weak form is a ubiquitous, well-studied, and widely-utilized mathematical tool in modern computational and applied mathematics. In this work we provide a survey of both the history and recent developments for several fields in which the weak form can play a critical role. In particular, we highlight several recent advances in weak form versions of equation learning, parameter estimation, and coarse graining, which offer surprising noise robustness, accuracy, and computational efficiency. We note that this manuscript is a companion piece to our October 2024 SIAM News article of the same name. Here we provide more detailed explanations of mathematical developments as well as a more complete list of references. Lastly, we note that the software with which to reproduce the results in this manuscript is also available on our group's GitHub website https://github.com/MathBioCU .

Recently, Retrieval-Augmented Generation (RAG) has achieved remarkable success in addressing the challenges of Large Language Models (LLMs) without necessitating retraining. By referencing an external knowledge base, RAG refines LLM outputs, effectively mitigating issues such as ``hallucination'', lack of domain-specific knowledge, and outdated information. However, the complex structure of relationships among different entities in databases presents challenges for RAG systems. In response, GraphRAG leverages structural information across entities to enable more precise and comprehensive retrieval, capturing relational knowledge and facilitating more accurate, context-aware responses. Given the novelty and potential of GraphRAG, a systematic review of current technologies is imperative. This paper provides the first comprehensive overview of GraphRAG methodologies. We formalize the GraphRAG workflow, encompassing Graph-Based Indexing, Graph-Guided Retrieval, and Graph-Enhanced Generation. We then outline the core technologies and training methods at each stage. Additionally, we examine downstream tasks, application domains, evaluation methodologies, and industrial use cases of GraphRAG. Finally, we explore future research directions to inspire further inquiries and advance progress in the field. In order to track recent progress in this field, we set up a repository at \url{https://github.com/pengboci/GraphRAG-Survey}.

Large language models (LLMs) have shown great potential for automatic code generation and form the basis for various tools such as GitHub Copilot. However, recent studies highlight that many LLM-generated code contains serious security vulnerabilities. While previous work tries to address this by training models that generate secure code, these attempts remain constrained by limited access to training data and labor-intensive data preparation. In this paper, we introduce HexaCoder, a novel approach to enhance the ability of LLMs to generate secure codes by automatically synthesizing secure codes, which reduces the effort of finding suitable training data. HexaCoder comprises two key components: an oracle-guided data synthesis pipeline and a two-step process for secure code generation. The data synthesis pipeline generates pairs of vulnerable and fixed codes for specific Common Weakness Enumeration (CWE) types by utilizing a state-of-the-art LLM for repairing vulnerable code. A security oracle identifies vulnerabilities, and a state-of-the-art LLM repairs them by extending and/or editing the codes, creating data pairs for fine-tuning using the Low-Rank Adaptation (LoRA) method. Each example of our fine-tuning dataset includes the necessary security-related libraries and code that form the basis of our novel two-step generation approach. This allows the model to integrate security-relevant libraries before generating the main code, significantly reducing the number of generated vulnerable codes by up to 85% compared to the baseline methods. We perform extensive evaluations on three different benchmarks for four LLMs, demonstrating that HexaCoder not only improves the security of the generated code but also maintains a high level of functional correctness.

This literature review studies the field of automated process extraction, i.e., transforming textual descriptions into structured processes using Natural Language Processing (NLP). We found that Machine Learning (ML) / Deep Learning (DL) methods are being increasingly used for the NLP component. In some cases, they were chosen for their suitability towards process extraction, and results show that they can outperform classic rule-based methods. We also found a paucity of gold-standard, scalable annotated datasets, which currently hinders objective evaluations as well as the training or fine-tuning of ML / DL methods. Finally, we discuss preliminary work on the application of LLMs for automated process extraction, as well as promising developments in this field.

A key challenge in artificial intelligence is the creation of systems capable of autonomously advancing scientific understanding by exploring novel domains, identifying complex patterns, and uncovering previously unseen connections in vast scientific data. In this work, we present SciAgents, an approach that leverages three core concepts: (1) the use of large-scale ontological knowledge graphs to organize and interconnect diverse scientific concepts, (2) a suite of large language models (LLMs) and data retrieval tools, and (3) multi-agent systems with in-situ learning capabilities. Applied to biologically inspired materials, SciAgents reveals hidden interdisciplinary relationships that were previously considered unrelated, achieving a scale, precision, and exploratory power that surpasses traditional human-driven research methods. The framework autonomously generates and refines research hypotheses, elucidating underlying mechanisms, design principles, and unexpected material properties. By integrating these capabilities in a modular fashion, the intelligent system yields material discoveries, critique and improve existing hypotheses, retrieve up-to-date data about existing research, and highlights their strengths and limitations. Our case studies demonstrate scalable capabilities to combine generative AI, ontological representations, and multi-agent modeling, harnessing a `swarm of intelligence' similar to biological systems. This provides new avenues for materials discovery and accelerates the development of advanced materials by unlocking Nature's design principles.

Deep neural networks (DNNs) have long been recognized as vulnerable to backdoor attacks. By providing poisoned training data in the fine-tuning process, the attacker can implant a backdoor into the victim model. This enables input samples meeting specific textual trigger patterns to be classified as target labels of the attacker's choice. While such black-box attacks have been well explored in both computer vision and natural language processing (NLP), backdoor attacks relying on white-box attack philosophy have hardly been thoroughly investigated. In this paper, we take the first step to introduce a new type of backdoor attack that conceals itself within the underlying model architecture. Specifically, we propose to design separate backdoor modules consisting of two functions: trigger detection and noise injection. The add-on modules of model architecture layers can detect the presence of input trigger tokens and modify layer weights using Gaussian noise to disturb the feature distribution of the baseline model. We conduct extensive experiments to evaluate our attack methods using two model architecture settings on five different large language datasets. We demonstrate that the training-free architectural backdoor on a large language model poses a genuine threat. Unlike the-state-of-art work, it can survive the rigorous fine-tuning and retraining process, as well as evade output probability-based defense methods (i.e. BDDR). All the code and data is available https://github.com/SiSL-URI/Arch_Backdoor_LLM.

The Complex Emotion Recognition System (CERS) deciphers complex emotional states by examining combinations of basic emotions expressed, their interconnections, and the dynamic variations. Through the utilization of advanced algorithms, CERS provides profound insights into emotional dynamics, facilitating a nuanced understanding and customized responses. The attainment of such a level of emotional recognition in machines necessitates the knowledge distillation and the comprehension of novel concepts akin to human cognition. The development of AI systems for discerning complex emotions poses a substantial challenge with significant implications for affective computing. Furthermore, obtaining a sizable dataset for CERS proves to be a daunting task due to the intricacies involved in capturing subtle emotions, necessitating specialized methods for data collection and processing. Incorporating physiological signals such as Electrocardiogram (ECG) and Electroencephalogram (EEG) can notably enhance CERS by furnishing valuable insights into the user's emotional state, enhancing the quality of datasets, and fortifying system dependability. A comprehensive literature review was conducted in this study to assess the efficacy of machine learning, deep learning, and meta-learning approaches in both basic and complex emotion recognition utilizing EEG, ECG signals, and facial expression datasets. The chosen research papers offer perspectives on potential applications, clinical implications, and results of CERSs, with the objective of promoting their acceptance and integration into clinical decision-making processes. This study highlights research gaps and challenges in understanding CERSs, encouraging further investigation by relevant studies and organizations. Lastly, the significance of meta-learning approaches in improving CERS performance and guiding future research endeavors is underscored.

Recent breakthroughs of large language models (LLMs) have exhibited superior capability across major industries and stimulated multi-hundred-billion-dollar investment in AI-centric data centers in the next 3-5 years. This, in turn, bring the increasing concerns on sustainability and AI-related energy usage. However, there is a largely overlooked issue as challenging and critical as AI model and infrastructure efficiency: the disruptive dynamic power consumption behaviour. With fast, transient dynamics, AI infrastructure features ultra-low inertia, sharp power surge and dip, and a significant peak-idle power ratio. The power scale covers from several hundred watts to megawatts, even to gigawatts. These never-seen-before characteristics make AI a very unique load and pose threats to the power grid reliability and resilience. To reveal this hidden problem, this paper examines the scale of AI power consumption, analyzes AI transient behaviour in various scenarios, develops high-level mathematical models to depict AI workload behaviour and discusses the multifaceted challenges and opportunities they potentially bring to existing power grids. Observing the rapidly evolving machine learning (ML) and AI technologies, this work emphasizes the critical need for interdisciplinary approaches to ensure reliable and sustainable AI infrastructure development, and provides a starting point for researchers and practitioners to tackle such challenges.

The Orienteering Problem (OP) is a well-studied routing problem that has been extended to incorporate uncertainties, reflecting stochastic or dynamic travel costs, prize-collection costs, and prizes. Existing approaches may, however, be inefficient in real-world applications due to insufficient modeling knowledge and initially unknowable parameters in online scenarios. Thus, we propose the Uncertain and Dynamic Orienteering Problem (UDOP), modeling travel costs as distributions with unknown and time-variant parameters. UDOP also associates uncertain travel costs with dynamic prizes and prize-collection costs for its objective and budget constraints. To address UDOP, we develop an ADaptive Approach for Probabilistic paThs - ADAPT, that iteratively performs 'execution' and 'online planning' based on an initial 'offline' solution. The execution phase updates system status and records online cost observations. The online planner employs a Bayesian approach to adaptively estimate power consumption and optimize path sequence based on safety beliefs. We evaluate ADAPT in a practical Unmanned Aerial Vehicle (UAV) charging scheduling problem for Wireless Rechargeable Sensor Networks. The UAV must optimize its path to recharge sensor nodes efficiently while managing its energy under uncertain conditions. ADAPT maintains comparable solution quality and computation time while offering superior robustness. Extensive simulations show that ADAPT achieves a 100% Mission Success Rate (MSR) across all tested scenarios, outperforming comparable heuristic-based and frequentist approaches that fail up to 70% (under challenging conditions) and averaging 67% MSR, respectively. This work advances the field of OP with uncertainties, offering a reliable and efficient approach for real-world applications in uncertain and dynamic environments.

For audio-driven visual dubbing, it remains a considerable challenge to uphold and highlight speaker's persona while synthesizing accurate lip synchronization. Existing methods fall short of capturing speaker's unique speaking style or preserving facial details. In this paper, we present PersonaTalk, an attention-based two-stage framework, including geometry construction and face rendering, for high-fidelity and personalized visual dubbing. In the first stage, we propose a style-aware audio encoding module that injects speaking style into audio features through a cross-attention layer. The stylized audio features are then used to drive speaker's template geometry to obtain lip-synced geometries. In the second stage, a dual-attention face renderer is introduced to render textures for the target geometries. It consists of two parallel cross-attention layers, namely Lip-Attention and Face-Attention, which respectively sample textures from different reference frames to render the entire face. With our innovative design, intricate facial details can be well preserved. Comprehensive experiments and user studies demonstrate our advantages over other state-of-the-art methods in terms of visual quality, lip-sync accuracy and persona preservation. Furthermore, as a person-generic framework, PersonaTalk can achieve competitive performance as state-of-the-art person-specific methods. Project Page: https://grisoon.github.io/PersonaTalk/.