Qiqi Wang

Paul G. Constantine, Qiqi Wang

We present a method for approximating the solution of a parameterized, nonlinear dynamical system using an affine combination of solutions computed at other points in the input parameter space. The coefficients of the affine combination are computed with a nonlinear least squares procedure that minimizes the residual of the governing equations. The approximation properties of this residual minimizing scheme are comparable to existing reduced basis and POD-Galerkin model reduction methods, but its implementation requires only independent evaluations of the nonlinear forcing function. It is particularly appropriate when one wishes to approximate the states at a few points in time without time marching from the initial conditions. We prove some interesting characteristics of the scheme including an interpolatory property, and we present heuristics for mitigating the effects of the ill-conditioning and reducing the overall cost of the method. We apply the method to representative numerical examples from kinetics - a three state system with one parameter controlling the stiffness - and conductive heat transfer - a nonlinear parabolic PDE with a random field model for the thermal conductivity.

Qiqi Wang, Steven Gomez, Patrick Blonigan et al.

We present a reformulation of unsteady turbulent flow simulations. The initial condition is relaxed and information is allowed to propagate both forward and backward in time. Simulations of chaotic dynamical systems with this reformulation can be proven to be well-conditioned time domain boundary value problems. The reformulation can enable scalable parallel-in-time simulation of turbulent flows.

Maitham Makki Alhubail, Qiqi Wang, John Williams

This article describes a method to accelerate parallel, explicit time integration of two-dimensional unsteady PDEs. The method is motivated by our observation that latency, not bandwidth, often limits how fast PDEs can be solved in parallel. The method is called the swept rule of space-time domain decomposition. Compared to conventional, space-only domain decomposition, it communicates similar amount of data, but in fewer messages. The swept rule achieves this by decomposing space and time among computing nodes in ways that exploit the domains of influence and the domain of dependency, making it possible to communicate once per many time steps with no redundant computation. By communicating less often, the swept rule effectively breaks the latency barrier, advancing on average more than one time step per ping-pong latency of the network. The article presents simple theoretical analysis to the performance of the swept rule in two spatial dimensions, and supports the analysis with numerical experiments.

Paul G. Constantine, Qiqi Wang

This manuscript is superseded by Constantine, Dow, and Wang's "Active Subspaces in Theory and Practice: Applications to Kriging Surfaces" [SIAM J. of Sci. Comput., 36 (2014), pp. A1500-A1524]. Many multivariate functions encountered in practice vary primarily along a few directions in the space of input parameters. When these directions correspond with coordinate directions, one may apply global sensitivity measures to determine the parameters with the greatest contribution to the function's variability. However, these methods perform poorly when the directions of variability are not aligned with the natural coordinates of the input space. We present a method for detecting the directions of variability of a function using evaluations of its derivative with respect to the input parameters. We demonstrate how to exploit these directions to construct a surrogate function that depends on fewer variables than the original function, thus reducing the dimension of the original problem. We apply this procedure to an exercise in uncertainty quantification using an elliptic PDE with a model for the coefficients that depends on 250 independent parameters. The dimension reduction procedure identifies a 5-dimensional subspace suitable for constructing surrogates.

Qiqi Wang

In parallel solution of partial differential equations, a complex stencil update formula that accesses multiple layers of neighboring grid points sometimes must be decomposed into atomic stages, ones that access only immediately neighboring grid points. This paper shows that this requirement can be formulated as constraints of an optimization problem, which is equivalent to the dual of a minimum-cost network flow problem. An optimized decomposition of a single stencil on one set of grid points can thereby be computed efficiently.

Xiaoran Liu, Ruixiao Li, Mianqiu Huang et al.

Long context is an important topic in Natural Language Processing (NLP), running through the development of NLP architectures, and offers immense opportunities for Large Language Models (LLMs), giving LLMs the lifelong learning potential akin to humans. Unfortunately, the pursuit of a long context is accompanied by numerous obstacles. Nevertheless, long context remains a core competitive advantage for LLMs. In the past two years, the context length of LLMs has achieved a breakthrough extension to millions of tokens. Moreover, research on long-context LLMs has expanded beyond length extrapolation to a comprehensive focus on architecture, infrastructure, training, and evaluation technologies. Inspired by the symphonic poem, Thus Spake Zarathustra, we draw an analogy between the journey of extending the context of LLM and the attempts of humans to transcend their mortality. In this survey, we will illustrate how LLM struggles between the tremendous need for a longer context and its equal need to accept the fact that it is ultimately finite. To achieve this, we give a global picture of the lifecycle of long-context LLMs from four perspectives: architecture, infrastructure, training, and evaluation, showcasing the full spectrum of long-context technologies. At the end of this survey, we will present 10 unanswered questions currently faced by long-context LLMs. We hope this survey can serve as a systematic introduction to research on long-context LLMs. Video: https://www.bilibili.com/video/BV11h9AYoEYj. Github: https://github.com/OpenMOSS/Thus-Spake-Long-Context-LLM.

Siyang He, Qiqi Wang, Xiaoran Liu et al.

Despite the non-autoregressive potential of diffusion language models (dLLMs), existing decoding strategies demonstrate positional bias, failing to fully unlock the potential of arbitrary generation. In this work, we delve into the inherent spectral characteristics of dLLMs and present the first frequency-domain analysis showing that low-frequency components in hidden states primarily encode global structural information and long-range dependencies, while high-frequency components are responsible for characterizing local details. Based on this observation, we propose FourierSampler, which leverages a frequency-domain sliding window mechanism to dynamically guide the model to achieve a "structure-to-detail" generation. FourierSampler outperforms other inference enhancement strategies on LLADA and SDAR, achieving relative improvements of 20.4% on LLaDA1.5-8B and 16.0% on LLaDA-8B-Instruct. It notably surpasses similarly sized autoregressive models like Llama3.1-8B-Instruct.

Yuchen Su, Shaoxin Zhong, Yonghua Zhu et al.

Puns represent a typical linguistic phenomenon that exploits polysemy and phonetic ambiguity to generate humour, posing unique challenges for natural language understanding. Within pun research, audio plays a central role in human communication except text and images, while datasets and systematic resources for spoken puns remain scarce, leaving this crucial modality largely underexplored. In this paper, we present APUN-Bench, the first benchmark dedicated to evaluating large audio language models (LALMs) on audio pun understanding. Our benchmark contains 4,434 audio samples annotated across three stages: pun recognition, pun word location and pun meaning inference. We conduct a deep analysis of APUN-Bench by systematically evaluating 10 state-of-the-art LALMs, uncovering substantial performance gaps in recognizing, localizing, and interpreting audio puns. This analysis reveals key challenges, such as positional biases in audio pun location and error cases in meaning inference, offering actionable insights for advancing humour-aware audio intelligence.

Weizhe Shi, Qiqi Wang, Yihong Pan et al.

A criminal judicial opinion represents the judge's disposition of a case, including the decision rationale and sentencing. Automatically generating such opinions can assist in analyzing sentencing consistency and provide judges with references to similar past cases. However, current research typically approaches this task by dividing it into two isolated subtasks: legal reasoning and sentencing prediction. This separation often leads to inconsistency between the reasoning and predictions, failing to meet real-world judicial requirements. Furthermore, prior studies rely on manually curated knowledge to enhance applicability, yet such methods remain limited in practical deployment. To address these limitations and better align with legal practice, we propose a new LegalAI task: Judicial Opinion Generation, which simultaneously produces both legal reasoning and sentencing decisions. To achieve this, we introduce LegalChainReasoner, a framework that applies structured legal chains to guide the model through comprehensive case assessments. By integrating factual premises, composite legal conditions, and sentencing conclusions, our approach ensures flexible knowledge injection and end-to-end opinion generation. Experiments on two real-world and open-source Chinese legal case datasets demonstrate that our method outperforms baseline models.

Xiaoran Liu, Siyang He, Qiqi Wang et al.

Large Language Models struggle with memory demands from the growing Key-Value (KV) cache as context lengths increase. Existing compression methods homogenize head dimensions or rely on attention-guided token pruning, often sacrificing accuracy or introducing computational overhead. We propose FourierAttention, a training-free framework that exploits the heterogeneous roles of transformer head dimensions: lower dimensions prioritize local context, while upper ones capture long-range dependencies. By projecting the long-context-insensitive dimensions onto orthogonal Fourier bases, FourierAttention approximates their temporal evolution with fixed-length spectral coefficients. Evaluations on LLaMA models show that FourierAttention achieves the best long-context accuracy on LongBench and Needle-In-A-Haystack (NIAH). Besides, a custom Triton kernel, FlashFourierAttention, is designed to optimize memory via streamlined read-write operations, enabling efficient deployment without performance compromise.

Qiqi Wang, Xulong Zhang, Jianzong Wang et al.

Any-to-any voice conversion problem aims to convert voices for source and target speakers, which are out of the training data. Previous works wildly utilize the disentangle-based models. The disentangle-based model assumes the speech consists of content and speaker style information and aims to untangle them to change the style information for conversion. Previous works focus on reducing the dimension of speech to get the content information. But the size is hard to determine to lead to the untangle overlapping problem. We propose the Disentangled Representation Voice Conversion (DRVC) model to address the issue. DRVC model is an end-to-end self-supervised model consisting of the content encoder, timbre encoder, and generator. Instead of the previous work for reducing speech size to get content, we propose a cycle for restricting the disentanglement by the Cycle Reconstruct Loss and Same Loss. The experiments show there is an improvement for converted speech on quality and voice similarity.

Paul G. Constantine, Eric Dow, Qiqi Wang

Many multivariate functions in engineering models vary primarily along a few directions in the space of input parameters. When these directions correspond to coordinate directions, one may apply global sensitivity measures to determine the most influential parameters. However, these methods perform poorly when the directions of variability are not aligned with the natural coordinates of the input space. We present a method to first detect the directions of the strongest variability using evaluations of the gradient and subsequently exploit these directions to construct a response surface on a low-dimensional subspace---i.e., the active subspace---of the inputs. We develop a theoretical framework with error bounds, and we link the theoretical quantities to the parameters of a kriging response surface on the active subspace. We apply the method to an elliptic PDE model with coefficients parameterized by 100 Gaussian random variables and compare it with a local sensitivity analysis method for dimension reduction.