arXiv subjects

Linda Petzold

Publications and source records attributed to Linda Petzold.

At least 19 recordsLinked to original sources

arXiv2025

Flux-Preserving Adaptive Finite State Projection for Multiscale Stochastic Reaction Networks

The Finite State Projection (FSP) method approximates the Chemical Master Equation (CME) by restricting the dynamics to a finite subset of the (typically infinite) state space, enabling direct numerical solution with computable error bounds. Adaptive variants update this subset in time, but multiscale systems with widely separated reaction rates remain challenging, as low-probability bottleneck states can carry essential probability flux and the dynamics alternate between fast transients and slowly evolving stiff regimes. We propose a flux-based adaptive FSP method that uses probability flux to drive both state-space pruning and time-step selection. The pruning rule protects low-probability states with large outgoing flux, preserving connectivity in bottleneck systems, while the time-step rule adapts to the instantaneous total flux to handle rate constants spanning several orders of magnitude. Numerical experiments on stiff, oscillatory, and bottleneck reaction networks show that the method maintains accuracy while using substantially smaller state spaces.

cs.CE↗

arXiv2025

The Vanishing Gradient Problem for Stiff Neural Differential Equations

Gradient-based optimization of neural differential equations and other parameterized dynamical systems fundamentally relies on the ability to differentiate numerical solutions with respect to model parameters. In stiff systems, it has been observed that sensitivities to parameters controlling fast-decaying modes become vanishingly small during training, leading to optimization difficulties. In this paper, we show that this vanishing gradient phenomenon is not an artifact of any particular method, but a universal feature of all A-stable and L-stable stiff numerical integration schemes. We analyze the rational stability function for general stiff integration schemes and demonstrate that the relevant parameter sensitivities, governed by the derivative of the stability function, decay to zero for large stiffness. Explicit formulas for common stiff integration schemes are provided, which illustrate the mechanism in detail. Finally, we rigorously prove that the slowest possible rate of decay for the derivative of the stability function is $O(|z|^{-1})$, revealing a fundamental limitation: all A-stable time-stepping methods inevitably suppress parameter gradients in stiff regimes, posing a significant barrier for training and parameter identification in stiff neural ODEs.

cs.LG↗

arXiv2025

Adaptive Finite State Projection with Quantile-Based Pruning for Solving the Chemical Master Equation

We present an adaptive Finite State Projection (FSP) method for efficiently solving the Chemical Master Equation (CME) with rigorous error control. Our approach integrates time-stepping with dynamic state-space truncation, balancing accuracy and computational cost. Krylov subspace methods approximate the matrix exponential, while quantile-based pruning controls state-space growth by removing low-probability states. Theoretical error bounds ensure that the truncation error remains bounded by the pruned mass at each step, which is user-controlled, and does not propagate forward in time. Numerical experiments on biochemical systems, including the Lotka-Volterra and Michaelis-Menten and bi-stable toggle switch models.

cs.CE↗

arXiv2024

Training Stiff Neural Ordinary Differential Equations with Explicit Exponential Integration Methods

Stiff ordinary differential equations (ODEs) are common in many science and engineering fields, but standard neural ODE approaches struggle to accurately learn these stiff systems, posing a significant barrier to widespread adoption of neural ODEs. In our earlier work, we addressed this challenge by utilizing single-step implicit methods for solving stiff neural ODEs. While effective, these implicit methods are computationally costly and can be complex to implement. This paper expands on our earlier work by exploring explicit exponential integration methods as a more efficient alternative. We evaluate the potential of these explicit methods to handle stiff dynamics in neural ODEs, aiming to enhance their applicability to a broader range of scientific and engineering problems. We found the integrating factor Euler (IF Euler) method to excel in stability and efficiency. While implicit schemes failed to train the stiff Van der Pol oscillator, the IF Euler method succeeded, even with large step sizes. However, IF Euler's first-order accuracy limits its use, leaving the development of higher-order methods for stiff neural ODEs an open research problem.

math.NA↗

arXiv2024

Performance Evaluation of Single-step Explicit Exponential Integration Methods on Stiff Ordinary Differential Equations

Stiff systems of ordinary differential equations (ODEs) arise in a wide range of scientific and engineering disciplines and are traditionally solved using implicit integration methods due to their stability and efficiency. However, these methods are computationally expensive, particularly for applications requiring repeated integration, such as parameter estimation, Bayesian inference, neural ODEs, physics-informed neural networks, and MeshGraphNets. Explicit exponential integration methods have been proposed as a potential alternative, leveraging the matrix exponential to address stiffness without requiring nonlinear solvers. This study evaluates several state-of-the-art explicit single-step exponential schemes against classical implicit methods on benchmark stiff ODE problems, analyzing their accuracy, stability, and scalability with step size. Despite their initial appeal, our results reveal that explicit exponential methods significantly lag behind implicit schemes in accuracy and scalability for stiff ODEs. The backward Euler method consistently outperformed higher-order exponential methods in accuracy at small step sizes, with none surpassing the accuracy of the first-order integrating factor Euler method. Exponential methods fail to improve upon first-order accuracy, revealing the integrating factor Euler method as the only reliable choice for repeated, inexpensive integration in applications such as neural ODEs and parameter estimation. This study exposes the limitations of explicit exponential methods and calls for the development of improved algorithms.

math.NA↗

arXiv2024

Training Stiff Neural Ordinary Differential Equations with Implicit Single-Step Methods

Stiff systems of ordinary differential equations (ODEs) are pervasive in many science and engineering fields, yet standard neural ODE approaches struggle to learn them. This limitation is the main barrier to the widespread adoption of neural ODEs. In this paper, we propose an approach based on single-step implicit schemes to enable neural ODEs to handle stiffness and demonstrate that our implicit neural ODE method can learn stiff dynamics. This work addresses a key limitation in current neural ODE methods, paving the way for their use in a wider range of scientific problems.

math.NA↗

arXiv2024

VREN: Volleyball Rally Dataset with Expression Notation Language

This research is intended to accomplish two goals: The first goal is to curate a large and information rich dataset that contains crucial and succinct summaries on the players' actions and positions and the back-and-forth travel patterns of the volleyball in professional and NCAA Div-I indoor volleyball games. While several prior studies have aimed to create similar datasets for other sports (e.g. badminton and soccer), creating such a dataset for indoor volleyball is not yet realized. The second goal is to introduce a volleyball descriptive language to fully describe the rally processes in the games and apply the language to our dataset. Based on the curated dataset and our descriptive sports language, we introduce three tasks for automated volleyball action and tactic analysis using our dataset: (1) Volleyball Rally Prediction, aimed at predicting the outcome of a rally and helping players and coaches improve decision-making in practice, (2) Setting Type and Hitting Type Prediction, to help coaches and players prepare more effectively for the game, and (3) Volleyball Tactics and Attacking Zone Statistics, to provide advanced volleyball statistics and help coaches understand the game and opponent's tactics better. We conducted case studies to show how experimental results can provide insights to the volleyball analysis community. Furthermore, experimental evaluation based on real-world data establishes a baseline for future studies and applications of our dataset and language. This study bridges the gap between the indoor volleyball field and computer science. The dataset is available at: https://github.com/haotianxia/VREN.

cs.LG↗

arXiv2024

A Survey on Large Language Models for Critical Societal Domains: Finance, Healthcare, and Law

In the fast-evolving domain of artificial intelligence, large language models (LLMs) such as GPT-3 and GPT-4 are revolutionizing the landscapes of finance, healthcare, and law: domains characterized by their reliance on professional expertise, challenging data acquisition, high-stakes, and stringent regulatory compliance. This survey offers a detailed exploration of the methodologies, applications, challenges, and forward-looking opportunities of LLMs within these high-stakes sectors. We highlight the instrumental role of LLMs in enhancing diagnostic and treatment methodologies in healthcare, innovating financial analytics, and refining legal interpretation and compliance strategies. Moreover, we critically examine the ethics for LLM applications in these fields, pointing out the existing ethical concerns and the need for transparent, fair, and robust AI systems that respect regulatory norms. By presenting a thorough review of current literature and practical applications, we showcase the transformative impact of LLMs, and outline the imperative for interdisciplinary cooperation, methodological advancements, and ethical vigilance. Through this lens, we aim to spark dialogue and inspire future research dedicated to maximizing the benefits of LLMs while mitigating their risks in these precision-dependent sectors. To facilitate future research on LLMs in these critical societal domains, we also initiate a reading list that tracks the latest advancements under this topic, which will be continually updated: \url{https://github.com/czyssrs/LLM_X_papers}.

cs.CL↗

arXiv2024

Quokka: An Open-source Large Language Model ChatBot for Material Science

This paper presents the development of a specialized chatbot for materials science, leveraging the Llama-2 language model, and continuing pre-training on the expansive research articles in the materials science domain from the S2ORC dataset. The methodology involves an initial pretraining phase on over one million domain-specific papers, followed by an instruction-tuning process to refine the chatbot's capabilities. The chatbot is designed to assist researchers, educators, and students by providing instant, context-aware responses to queries in the field of materials science. We make the four trained checkpoints (7B, 13B, with or without chat ability) freely available to the research community at https://github.com/Xianjun-Yang/Quokka.

cs.CL↗

arXiv2023

A Survey on Detection of LLMs-Generated Content

The burgeoning capabilities of advanced large language models (LLMs) such as ChatGPT have led to an increase in synthetic content generation with implications across a variety of sectors, including media, cybersecurity, public discourse, and education. As such, the ability to detect LLMs-generated content has become of paramount importance. We aim to provide a detailed overview of existing detection strategies and benchmarks, scrutinizing their differences and identifying key challenges and prospects in the field, advocating for more adaptable and robust models to enhance detection accuracy. We also posit the necessity for a multi-faceted approach to defend against various attacks to counter the rapidly advancing capabilities of LLMs. To the best of our knowledge, this work is the first comprehensive survey on the detection in the era of LLMs. We hope it will provide a broad understanding of the current landscape of LLMs-generated content detection, offering a guiding reference for researchers and practitioners striving to uphold the integrity of digital information in an era increasingly dominated by synthetic content. The relevant papers are summarized and will be consistently updated at https://github.com/Xianjun-Yang/Awesome_papers_on_LLMs_detection.git.

cs.CL↗

arXiv2023

Zero-Shot Detection of Machine-Generated Codes

This work proposes a training-free approach for the detection of LLMs-generated codes, mitigating the risks associated with their indiscriminate usage. To the best of our knowledge, our research is the first to investigate zero-shot detection techniques applied to code generated by advanced black-box LLMs like ChatGPT. Firstly, we find that existing training-based or zero-shot text detectors are ineffective in detecting code, likely due to the unique statistical properties found in code structures. We then modify the previous zero-shot text detection method, DetectGPT (Mitchell et al., 2023) by utilizing a surrogate white-box model to estimate the probability of the rightmost tokens, allowing us to identify code snippets generated by language models. Through extensive experiments conducted on the python codes of the CodeContest and APPS dataset, our approach demonstrates its effectiveness by achieving state-of-the-art detection results on text-davinci-003, GPT-3.5, and GPT-4 models. Moreover, our method exhibits robustness against revision attacks and generalizes well to Java codes. We also find that the smaller code language model like PolyCoder-160M performs as a universal code detector, outperforming the billion-scale counterpart. The codes will be available at https://github.com/ Xianjun-Yang/Code_detection.git

cs.CL↗

arXiv2023

DNA-GPT: Divergent N-Gram Analysis for Training-Free Detection of GPT-Generated Text

Large language models (LLMs) have notably enhanced the fluency and diversity of machine-generated text. However, this progress also presents a significant challenge in detecting the origin of a given text, and current research on detection methods lags behind the rapid evolution of LLMs. Conventional training-based methods have limitations in flexibility, particularly when adapting to new domains, and they often lack explanatory power. To address this gap, we propose a novel training-free detection strategy called Divergent N-Gram Analysis (DNA-GPT). Given a text, we first truncate it in the middle and then use only the preceding portion as input to the LLMs to regenerate the new remaining parts. By analyzing the differences between the original and new remaining parts through N-gram analysis in black-box or probability divergence in white-box, we unveil significant discrepancies between the distribution of machine-generated text and the distribution of human-written text. We conducted extensive experiments on the most advanced LLMs from OpenAI, including text-davinci-003, GPT-3.5-turbo, and GPT-4, as well as open-source models such as GPT-NeoX-20B and LLaMa-13B. Results show that our zero-shot approach exhibits state-of-the-art performance in distinguishing between human and GPT-generated text on four English and one German dataset, outperforming OpenAI's own classifier, which is trained on millions of text. Additionally, our methods provide reasonable explanations and evidence to support our claim, which is a unique feature of explainable detection. Our method is also robust under the revised text attack and can additionally solve model sourcing. Codes are available at https://github.com/Xianjun-Yang/DNA-GPT.

cs.CL↗

arXiv2023

Shadow Alignment: The Ease of Subverting Safely-Aligned Language Models

Warning: This paper contains examples of harmful language, and reader discretion is recommended. The increasing open release of powerful large language models (LLMs) has facilitated the development of downstream applications by reducing the essential cost of data annotation and computation. To ensure AI safety, extensive safety-alignment measures have been conducted to armor these models against malicious use (primarily hard prompt attack). However, beneath the seemingly resilient facade of the armor, there might lurk a shadow. By simply tuning on 100 malicious examples with 1 GPU hour, these safely aligned LLMs can be easily subverted to generate harmful content. Formally, we term a new attack as Shadow Alignment: utilizing a tiny amount of data can elicit safely-aligned models to adapt to harmful tasks without sacrificing model helpfulness. Remarkably, the subverted models retain their capability to respond appropriately to regular inquiries. Experiments across 8 models released by 5 different organizations (LLaMa-2, Falcon, InternLM, BaiChuan2, Vicuna) demonstrate the effectiveness of shadow alignment attack. Besides, the single-turn English-only attack successfully transfers to multi-turn dialogue and other languages. This study serves as a clarion call for a collective effort to overhaul and fortify the safety of open-source LLMs against malicious attackers.

cs.CL↗

arXiv2023

Bayesian polynomial neural networks and polynomial neural ordinary differential equations

Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods provide point estimates for the model parameters and are currently unable to accommodate noisy data. We address this challenge by developing and validating the following Bayesian inference methods: the Laplace approximation, Markov Chain Monte Carlo (MCMC) sampling methods, and variational inference. We have found the Laplace approximation to be the best method for this class of problems. Our work can be easily extended to the broader class of symbolic neural networks to which the polynomial neural network belongs.

cs.LG↗

arXiv2023

Are Large Language Models Ready for Healthcare? A Comparative Study on Clinical Language Understanding

Large language models (LLMs) have made significant progress in various domains, including healthcare. However, the specialized nature of clinical language understanding tasks presents unique challenges and limitations that warrant further investigation. In this study, we conduct a comprehensive evaluation of state-of-the-art LLMs, namely GPT-3.5, GPT-4, and Bard, within the realm of clinical language understanding tasks. These tasks span a diverse range, including named entity recognition, relation extraction, natural language inference, semantic textual similarity, document classification, and question-answering. We also introduce a novel prompting strategy, self-questioning prompting (SQP), tailored to enhance LLMs' performance by eliciting informative questions and answers pertinent to the clinical scenarios at hand. Our evaluation underscores the significance of task-specific learning strategies and prompting techniques for improving LLMs' effectiveness in healthcare-related tasks. Additionally, our in-depth error analysis on the challenging relation extraction task offers valuable insights into error distribution and potential avenues for improvement using SQP. Our study sheds light on the practical implications of employing LLMs in the specialized domain of healthcare, serving as a foundation for future research and the development of potential applications in healthcare settings.

cs.CL↗

arXiv2023

Improving Medical Predictions by Irregular Multimodal Electronic Health Records Modeling

Health conditions among patients in intensive care units (ICUs) are monitored via electronic health records (EHRs), composed of numerical time series and lengthy clinical note sequences, both taken at irregular time intervals. Dealing with such irregularity in every modality, and integrating irregularity into multimodal representations to improve medical predictions, is a challenging problem. Our method first addresses irregularity in each single modality by (1) modeling irregular time series by dynamically incorporating hand-crafted imputation embeddings into learned interpolation embeddings via a gating mechanism, and (2) casting a series of clinical note representations as multivariate irregular time series and tackling irregularity via a time attention mechanism. We further integrate irregularity in multimodal fusion with an interleaved attention mechanism across temporal steps. To the best of our knowledge, this is the first work to thoroughly model irregularity in multimodalities for improving medical predictions. Our proposed methods for two medical prediction tasks consistently outperforms state-of-the-art (SOTA) baselines in each single modality and multimodal fusion scenarios. Specifically, we observe relative improvements of 6.5\%, 3.6\%, and 4.3\% in F1 for time series, clinical notes, and multimodal fusion, respectively. These results demonstrate the effectiveness of our methods and the importance of considering irregularity in multimodal EHRs.

cs.LG↗

arXiv2023

Dynamic Prompting: A Unified Framework for Prompt Tuning

It has been demonstrated that the art of prompt tuning is highly effective in efficiently extracting knowledge from pretrained foundation models, encompassing pretrained language models (PLMs), vision pretrained models, and vision-language (V-L) models. However, the efficacy of employing fixed soft prompts with a predetermined position for concatenation with inputs for all instances, irrespective of their inherent disparities, remains uncertain. Variables such as the position, length, and representations of prompts across diverse instances and tasks can substantially influence the performance of prompt tuning. In this context, we provide a theoretical analysis, which reveals that optimizing the position of the prompt to encompass the input can capture additional semantic information that traditional prefix or postfix prompt tuning methods fail to capture. Building upon our analysis, we present a unified dynamic prompt (DP) tuning strategy that dynamically determines different factors of prompts based on specific tasks and instances. To accomplish this, we employ a lightweight learning network with Gumble-Softmax, allowing us to learn instance-dependent guidance. Experimental results underscore the significant performance improvement achieved by dynamic prompt tuning across a wide range of tasks, including NLP tasks, vision recognition tasks, and vision-language tasks. Furthermore, we establish the universal applicability of our approach under full-data, few-shot, and multitask scenarios. Codes are available at https://github.com/Xianjun-Yang/DPT.

cs.CL↗

arXiv2023

Few-Shot Document-Level Event Argument Extraction

Event argument extraction (EAE) has been well studied at the sentence level but under-explored at the document level. In this paper, we study to capture event arguments that actually spread across sentences in documents. Prior works usually assume full access to rich document supervision, ignoring the fact that the available argument annotation is usually limited. To fill this gap, we present FewDocAE, a Few-Shot Document-Level Event Argument Extraction benchmark, based on the existing document-level event extraction dataset. We first define the new problem and reconstruct the corpus by a novel N -Way-D-Doc sampling instead of the traditional N -Way-K-Shot strategy. Then we adjust the current document-level neural models into the few-shot setting to provide baseline results under in- and cross-domain settings. Since the argument extraction depends on the context from multiple sentences and the learning process is limited to very few examples, we find this novel task to be very challenging with substantively low performance. Considering FewDocAE is closely related to practical use under low-resource regimes, we hope this benchmark encourages more research in this direction. Our data and codes will be available online.

cs.CL↗