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Open-domain long-form text generation requires generating coherent, comprehensive responses that address complex queries with both breadth and depth. This task is challenging due to the need to accurately capture diverse facets of input queries. Existing iterative retrieval-augmented generation (RAG) approaches often struggle to delve deeply into each facet of complex queries and integrate knowledge from various sources effectively. This paper introduces ConTReGen, a novel framework that employs a context-driven, tree-structured retrieval approach to enhance the depth and relevance of retrieved content. ConTReGen integrates a hierarchical, top-down in-depth exploration of query facets with a systematic bottom-up synthesis, ensuring comprehensive coverage and coherent integration of multifaceted information. Extensive experiments on multiple datasets, including LFQA and ODSUM, alongside a newly introduced dataset, ODSUM-WikiHow, demonstrate that ConTReGen outperforms existing state-of-the-art RAG models., Comment: Accepted at EMNLP'24 Findings

Topic modeling is a powerful technique for uncovering hidden themes within a collection of documents. However, the effectiveness of traditional topic models often relies on sufficient word co-occurrence, which is lacking in short texts. Therefore, existing approaches, whether probabilistic or neural, frequently struggle to extract meaningful patterns from such data, resulting in incoherent topics. To address this challenge, we propose a novel approach that leverages large language models (LLMs) to extend short texts into more detailed sequences before applying topic modeling. To further improve the efficiency and solve the problem of semantic inconsistency from LLM-generated texts, we propose to use prefix tuning to train a smaller language model coupled with a variational autoencoder for short-text topic modeling. Our method significantly improves short-text topic modeling performance, as demonstrated by extensive experiments on real-world datasets with extreme data sparsity, outperforming current state-of-the-art topic models., Comment: EMNLP Findings 2024. arXiv admin note: substantial text overlap with arXiv:2310.15420

Black-box context-free grammar inference presents a significant challenge in many practical settings due to limited access to example programs. The state-of-the-art methods, Arvada and Treevada, employ heuristic approaches to generalize grammar rules, initiating from flat parse trees and exploring diverse generalization sequences. We have observed that these approaches suffer from low quality and readability, primarily because they process entire example strings, adding to the complexity and substantially slowing down computations. To overcome these limitations, we propose a novel method that segments example strings into smaller units and incrementally infers the grammar. Our approach, named Kedavra, has demonstrated superior grammar quality (enhanced precision and recall), faster runtime, and improved readability through empirical comparison., Comment: Accepted by ASE'24

The electric resistivity is examined in the constrained Hilbert space of a doped Mott insulator, which is dictated by a non-Ioffe-Larkin composition rule due to the underlying mutual Chern-Simons topological gauge structure. In the low-temperature pseudogap phase, where holons remain condensed while spinons proliferate, the charge transport is governed by a chiral spinon excitation, comprising a bosonic spin-$1/2$ at the core of a supercurrent vortex. It leads to a vanishing resistivity with the "confinement" of the spinons in the superconducting phase but a low-$T$ divergence of the resistivity once the spinon confinement is disrupted by external magnetic fields. In the latter, the chiral spinons will generate a Hall number $n_H =$ doping concentration $\delta$ and a Nernst effect to signal an underlying long-range entanglement between the charge and spin degrees of freedom. Their presence is further reflected in thermodynamic quantities such as specific heat and spin susceptibility. Finally, in the high-temperature spin-disordered phase, it is shown that the holons exhibit a linear-$T$ resistivity by scattering with the spinons acting as free local moments, which generate randomized gauge fluxes as perceived by the charge degree of freedom., Comment: 6+6 pages, 6 figures

Public participation is indispensable for an insightful understanding of the ethics issues raised by AI technologies. Twitter is selected in this paper to serve as an online public sphere for exploring discourse on AI ethics, facilitating broad and equitable public engagement in the development of AI technology. A research framework is proposed to demonstrate how to transform AI ethics-related discourse on Twitter into coherent and readable narratives. It consists of two parts: 1) combining neural networks with large language models to construct a topic hierarchy that contains popular topics of public concern without ignoring small but important voices, thus allowing a fine-grained exploration of meaningful information. 2) transforming fragmented and difficult-to-understand social media information into coherent and easy-to-read stories through narrative visualization, providing a new perspective for understanding the information in Twitter data. This paper aims to advocate for policy makers to enhance public oversight of AI technologies so as to promote their fair and sustainable development., Comment: 22 pages, 6 figures

Gradient Inversion Attacks invert the transmitted gradients in Federated Learning (FL) systems to reconstruct the sensitive data of local clients and have raised considerable privacy concerns. A majority of gradient inversion methods rely heavily on explicit prior knowledge (e.g., a well pre-trained generative model), which is often unavailable in realistic scenarios. To alleviate this issue, researchers have proposed to leverage the implicit prior knowledge of an over-parameterized network. However, they only utilize a fixed neural architecture for all the attack settings. This would hinder the adaptive use of implicit architectural priors and consequently limit the generalizability. In this paper, we further exploit such implicit prior knowledge by proposing Gradient Inversion via Neural Architecture Search (GI-NAS), which adaptively searches the network and captures the implicit priors behind neural architectures. Extensive experiments verify that our proposed GI-NAS can achieve superior attack performance compared to state-of-the-art gradient inversion methods, even under more practical settings with high-resolution images, large-sized batches, and advanced defense strategies.

Dark sector may exist and interact with Standard Model (SM) through the $U(1)$ kinetic mixing. Through this portal-type interaction, dark photon from dark sector couples to SM fermions, and may explain the discrepancy between experimental data and SM calculations on muon anomalous magnetic moment, muon $g-2$. However, current searches for dark photon impose stringent constraints on the mixing parameter $\varepsilon$ for various dark photon masses, excluding the favorite parameter space for muon $g-2$. In this paper, we study the case where a global $U(1)$ in dark sector is spontaneously broken, resulting a light pseudo-Goldstone, axion-like particle (ALP) $a$, which couples to dark photon and SM photon, $g_{a\gamma\gamma'}$. Through this interaction, dark photon may decay into photon and ALP when this channel is kinematically allowed. As a result, the experimental constraints on dark photon change significantly, and dark photon is able to explain the muon $g-2$ anomaly when its mass is heavier than $10$ GeV., Comment: 9 pages, 3 figures

Multi-squeezed states, also known as generalized squeezed states, are valuable quantum non-Gaussian resources, because they can feature non-classical properties such as large phase-space Wigner negativities. In this work, we introduce a novel shortcuts to adiabaticity (STA) method for the fast preparation of multi-squeezed states. In contrast to previous STA methods, which rely on the use of counterdiabatic control to suppress unwanted non-adiabatic effects, our method simplifies the process and accelerates state preparation by selecting an appropriate sampling along a quantum evolution path. We demonstrate the high-fidelity and fast preparation of multi-squeezed states, as well as hybrid entangled states between a bosonic mode and a qubit.

In the field of heterogeneous federated learning (FL), the key challenge is to efficiently and collaboratively train models across multiple clients with different data distributions, model structures, task objectives, computational capabilities, and communication resources. This diversity leads to significant heterogeneity, which increases the complexity of model training. In this paper, we first outline the basic concepts of heterogeneous federated learning and summarize the research challenges in federated learning in terms of five aspects: data, model, task, device, and communication. In addition, we explore how existing state-of-the-art approaches cope with the heterogeneity of federated learning, and categorize and review these approaches at three different levels: data-level, model-level, and architecture-level. Subsequently, the paper extensively discusses privacy-preserving strategies in heterogeneous federated learning environments. Finally, the paper discusses current open issues and directions for future research, aiming to promote the further development of heterogeneous federated learning.

A scotogenic model can radiatively generate the observed neutrino mass, provide a dark matter candidate, and lead to rare lepton flavor-violating processes. We aim to extend the model to establish a potential connection to the quark flavor-related processes within the framework of scotogenesis, enhancing the unexpectedly large branching ratio (BR) of $B^+\to K^+ \nu \bar\nu$, observed by Belle II Collaboration. Meanwhile, the model can address tensions between some experimental measurements and standard model (SM) predictions in flavor physics, such as the muon $g-2$ excess and the higher BR of $B_s \to \mu^- \mu^+$. We introduce in the model the following dark particles: a neutral singlet Dirac-type lepton ($N$); two inert Higgs doublets ($\eta_{1,2}$), with one of which carrying a lepton number; a charged singlet dark scalar $(\chi^+)$, and a singlet vector-like up-type dark quark ($T$). The first two entities are responsible for the radiative neutrino mass, and $\chi^+$ couples to right-handed quarks and leptons and can resolve the tensions existing in muon $g-2$ and $B_s\to \mu^- \mu^+$. Furthermore, the BR of $B^+ \to K^+ \nu \bar\nu$ can be enhanced up to a factor of 2 compared to the SM prediction through the mediations of the dark $T$ and the charged scalars. In addition, we also study the impacts on the $K\to \pi \nu \bar\nu$ decays., Comment: 34 pages, 6 figures, references added, text revised

Recently, the success of large models has demonstrated the importance of scaling up model size. This has spurred interest in exploring collaborative training of large-scale models from federated learning perspective. Due to computational constraints, many institutions struggle to train a large-scale model locally. Thus, training a larger global model using only smaller local models has become an important scenario (i.e., the \textbf{small-to-large scenario}). Although recent device-heterogeneity federated learning approaches have started to explore this area, they face limitations in fully covering the parameter space of the global model. In this paper, we propose a method called \textbf{FedBRB} (\underline{B}lock-wise \underline{R}olling and weighted \underline{B}roadcast) based on the block concept. FedBRB can uses small local models to train all blocks of the large global model, and broadcasts the trained parameters to the entire space for faster information interaction. Experiments demonstrate FedBRB yields substantial performance gains, achieving state-of-the-art results in this scenario. Moreover, FedBRB using only minimal local models can even surpass baselines using larger local models.

Estimating the average treatment effect in social networks is challenging due to individuals influencing each other. One approach to address interference is ego cluster experiments, where each cluster consists of a central individual (ego) and its peers (alters). Clusters are randomized, and only the effects on egos are measured. In this work, we propose an improved framework for ego cluster experiments called ego group partition (EGP), which directly generates two groups and an ego sub-population instead of ego clusters. Under specific model assumptions, we propose two ego group partition algorithms. Compared to the original ego clustering algorithm, our algorithms produce more egos, yield smaller biases, and support parallel computation. The performance of our algorithms is validated through simulation and real-world case studies.

In social media platforms, user behavior is often influenced by interactions with other users, complicating the accurate estimation of causal effects in traditional A/B experiments. This study investigates situations where an individual's outcome can be broken down into the sum of multiple pairwise outcomes, a reflection of user interactions. These outcomes, referred to as dyadic data, are prevalent in many social network contexts. Utilizing a Bernoulli randomized design, we introduce a novel unbiased estimator for the total treatment effect (TTE), which quantifies the difference in population mean when all individuals are assigned to treatment versus control groups. We further explore the bias of our estimator in scenarios where it is impractical to include all individuals in the experiment, a common constraint in online control experiments. Our numerical results reveal that our proposed estimator consistently outperforms some commonly used estimators, underscoring its potential for more precise causal effect estimation in social media environments.

To defend against privacy leakage of user data, differential privacy is widely used in federated learning, but it is not free. The addition of noise randomly disrupts the semantic integrity of the model and this disturbance accumulates with increased communication rounds. In this paper, we introduce a novel federated learning framework with rigorous privacy guarantees, named FedCEO, designed to strike a trade-off between model utility and user privacy by letting clients ''Collaborate with Each Other''. Specifically, we perform efficient tensor low-rank proximal optimization on stacked local model parameters at the server, demonstrating its capability to flexibly truncate high-frequency components in spectral space. This implies that our FedCEO can effectively recover the disrupted semantic information by smoothing the global semantic space for different privacy settings and continuous training processes. Moreover, we improve the SOTA utility-privacy trade-off bound by an order of $\sqrt{d}$, where $d$ is the input dimension. We illustrate our theoretical results with experiments on representative image datasets. It observes significant performance improvements and strict privacy guarantees under different privacy settings., Comment: 22 pages, 8 figures

Introduced to enhance the efficiency of large language model (LLM) inference, speculative decoding operates by having a smaller model generate a draft. A larger target model then reviews this draft to align with its output, and any acceptance by the target model results in a reduction of the number of the target model runs, ultimately improving efficiency. However, the drafting process in speculative decoding includes slow autoregressive generation and allocates equal time to generating tokens, irrespective of their importance. These inefficiencies collectively contribute to the suboptimal performance of speculative decoding. To further improve LLM inference, we introduce Cascade Speculative Drafting (CS Drafting), a speculative execution algorithm that incorporates two types of cascades. The Vertical Cascade eliminates autoregressive generation from neural models, while the Horizontal Cascade optimizes time allocation in drafting for improved efficiency. Combining both cascades, CS Drafting achieves up to an 81 percent additional speedup over speculative decoding in our experiments, while maintaining the same output distribution as the target model. Our code is publicly available at https://github.com/lfsszd/CS-Drafting., Comment: Preprint in progress

Anomalous high energy photons, known as GRB221009A, with 18 TeV and 251 TeV were observed by LHAASO and Carpet-2 recently. Such observation of high energy gamma-ray bursts from distant source causes a mystery since high energy photons suffer severe attenuation before reaching the earth. One possibility is the existence of axion-like particles (ALP), and high energy photons at the source can convert to these ALPs which travel intergalactically. In this paper, we study the effects of extra dimensions on the conversion probability between photon and ALPs. The conversion probability saturates and may reach almost $100\%$ for high energy photons. We show that the size of extra dimension affects the energy at which saturation occurs. The observations of high-energy photons may support the possibility of smaller extra dimension.

With the development of practical deep learning models like generative AI, their excellent performance has brought huge economic value. For instance, ChatGPT has attracted more than 100 million users in three months. Since the model training requires a lot of data and computing power, a well-performing deep learning model is behind a huge effort and cost. Facing various model attacks, unauthorized use and abuse from the network that threaten the interests of model owners, in addition to considering legal and other administrative measures, it is equally important to protect the model's copyright from the technical means. By using the model watermarking technology, we point out the possibility of building a unified platform for model ownership verification. Given the application history of blockchain in copyright verification and the drawbacks of a centralized third-party, this paper considers combining model watermarking technology and blockchain to build a unified model copyright protection platform. By a new solution we called Tokenized Model, it protects the model's copyright by reliable ownership record and verification mechanism. It also promotes the financial value of model by constructing the model's transaction process and contribution shares of a model. In the typical case study, we also study the various performance under usual scenario to verify the effectiveness of this platform.

In recent years, graph contrastive learning (GCL) has emerged as one of the optimal solutions for various supervised tasks at the node level. However, for unsupervised and structure-related tasks such as community detection, current GCL algorithms face difficulties in acquiring the necessary community-level information, resulting in poor performance. In addition, general contrastive learning algorithms improve the performance of downstream tasks by increasing the number of negative samples, which leads to severe class collision and unfairness of community detection. To address above issues, we propose a novel Community-aware Efficient Graph Contrastive Learning Framework (CEGCL) to jointly learn community partition and node representations in an end-to-end manner. Specifically, we first design a personalized self-training (PeST) strategy for unsupervised scenarios, which enables our model to capture precise community-level personalized information in a graph. With the benefit of the PeST, we alleviate class collision and unfairness without sacrificing the overall model performance. Furthermore, the aligned graph clustering (AlGC) is employed to obtain the community partition. In this module, we align the clustering space of our downstream task with that in PeST to achieve more consistent node embeddings. Finally, we demonstrate the effectiveness of our model for community detection both theoretically and experimentally. Extensive experimental results also show that our CEGCL exhibits state-of-the-art performance on three benchmark datasets with different scales., Comment: 12 pages, 7 figures

Long-form question answering (LFQA) poses a challenge as it involves generating detailed answers in the form of paragraphs, which go beyond simple yes/no responses or short factual answers. While existing QA models excel in questions with concise answers, LFQA requires handling multiple topics and their intricate relationships, demanding comprehensive explanations. Previous attempts at LFQA focused on generating long-form answers by utilizing relevant contexts from a corpus, relying solely on the question itself. However, they overlooked the possibility that the question alone might not provide sufficient information to identify the relevant contexts. Additionally, generating detailed long-form answers often entails aggregating knowledge from diverse sources. To address these limitations, we propose an LFQA model with iterative Planning, Retrieval, and Generation. This iterative process continues until a complete answer is generated for the given question. From an extensive experiment on both an open domain and a technical domain QA dataset, we find that our model outperforms the state-of-the-art models on various textual and factual metrics for the LFQA task.

Recently, nonnegative matrix factorization (NMF) has been widely adopted for community detection, because of its better interpretability. However, the existing NMF-based methods have the following three problems: 1) they directly transform the original network into community membership space, so it is difficult for them to capture the hierarchical information; 2) they often only pay attention to the topology of the network and ignore its node attributes; 3) it is hard for them to learn the global structure information necessary for community detection. Therefore, we propose a new community detection algorithm, named Contrastive Deep Nonnegative Matrix Factorization (CDNMF). Firstly, we deepen NMF to strengthen its capacity for information extraction. Subsequently, inspired by contrastive learning, our algorithm creatively constructs network topology and node attributes as two contrasting views. Furthermore, we utilize a debiased negative sampling layer and learn node similarity at the community level, thereby enhancing the suitability of our model for community detection. We conduct experiments on three public real graph datasets and the proposed model has achieved better results than state-of-the-art methods. Code available at https://github.com/6lyc/CDNMF.git., Comment: In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) 2024. Source Code available at: https://github.com/6lyc/CDNMF.git

Topic models are one of the compelling methods for discovering latent semantics in a document collection. However, it assumes that a document has sufficient co-occurrence information to be effective. However, in short texts, co-occurrence information is minimal, which results in feature sparsity in document representation. Therefore, existing topic models (probabilistic or neural) mostly fail to mine patterns from them to generate coherent topics. In this paper, we take a new approach to short-text topic modeling to address the data-sparsity issue by extending short text into longer sequences using existing pre-trained language models (PLMs). Besides, we provide a simple solution extending a neural topic model to reduce the effect of noisy out-of-topics text generation from PLMs. We observe that our model can substantially improve the performance of short-text topic modeling. Extensive experiments on multiple real-world datasets under extreme data sparsity scenarios show that our models can generate high-quality topics outperforming state-of-the-art models.

Text style transfer is a prominent task that aims to control the style of text without inherently changing its factual content. To cover more text modification applications, such as adapting past news for current events and repurposing educational materials, we propose the task of text fact transfer, which seeks to transfer the factual content of a source text between topics without modifying its style. We find that existing language models struggle with text fact transfer, due to their inability to preserve the specificity and phrasing of the source text, and tendency to hallucinate errors. To address these issues, we design ModQGA, a framework that minimally modifies a source text with a novel combination of end-to-end question generation and specificity-aware question answering. Through experiments on four existing datasets adapted for text fact transfer, we show that ModQGA can accurately transfer factual content without sacrificing the style of the source text., Comment: Accepted to EMNLP 2023 Main Conference

We introduce a new task called *entity-centric question generation* (ECQG), motivated by real-world applications such as topic-specific learning, assisted reading, and fact-checking. The task aims to generate questions from an entity perspective. To solve ECQG, we propose a coherent PLM-based framework GenCONE with two novel modules: content focusing and question verification. The content focusing module first identifies a focus as "what to ask" to form draft questions, and the question verification module refines the questions afterwards by verifying the answerability. We also construct a large-scale open-domain dataset from SQuAD to support this task. Our extensive experiments demonstrate that GenCONE significantly and consistently outperforms various baselines, and two modules are effective and complementary in generating high-quality questions., Comment: Accepted to the Findings of EMNLP 2023. Camera-ready version

We present a novel system that automatically extracts and generates informative and descriptive sentences from the biomedical corpus and facilitates the efficient search for relational knowledge. Unlike previous search engines or exploration systems that retrieve unconnected passages, our system organizes descriptive sentences as a relational graph, enabling researchers to explore closely related biomedical entities (e.g., diseases treated by a chemical) or indirectly connected entities (e.g., potential drugs for treating a disease). Our system also uses ChatGPT and a fine-tuned relation synthesis model to generate concise and reliable descriptive sentences from retrieved information, reducing the need for extensive human reading effort. With our system, researchers can easily obtain both high-level knowledge and detailed references and interactively steer to the information of interest. We spotlight the application of our system in COVID-19 research, illustrating its utility in areas such as drug repurposing and literature curation., Comment: EMNLP 2023 Demo

Topic models are popular statistical tools for detecting latent semantic topics in a text corpus. They have been utilized in various applications across different fields. However, traditional topic models have some limitations, including insensitivity to user guidance, sensitivity to the amount and quality of data, and the inability to adapt learned topics from one corpus to another. To address these challenges, this paper proposes a neural topic model, TopicAdapt, that can adapt relevant topics from a related source corpus and also discover new topics in a target corpus that are absent in the source corpus. The proposed model offers a promising approach to improve topic modeling performance in practical scenarios. Experiments over multiple datasets from diverse domains show the superiority of the proposed model against the state-of-the-art topic models.

With the rapid advancement of large language models (LLMs), there is a pressing need for a comprehensive evaluation suite to assess their capabilities and limitations. Existing LLM leaderboards often reference scores reported in other papers without consistent settings and prompts, which may inadvertently encourage cherry-picking favored settings and prompts for better results. In this work, we introduce GPT-Fathom, an open-source and reproducible LLM evaluation suite built on top of OpenAI Evals. We systematically evaluate 10+ leading LLMs as well as OpenAI's legacy models on 20+ curated benchmarks across 7 capability categories, all under aligned settings. Our retrospective study on OpenAI's earlier models offers valuable insights into the evolutionary path from GPT-3 to GPT-4. Currently, the community is eager to know how GPT-3 progressively improves to GPT-4, including technical details like whether adding code data improves LLM's reasoning capability, which aspects of LLM capability can be improved by SFT and RLHF, how much is the alignment tax, etc. Our analysis sheds light on many of these questions, aiming to improve the transparency of advanced LLMs., Comment: Accepted by NAACL 2024

Leptoquarks (LQs) have been extensively studied in the context of $B$ anomalies. When $U(1)_{L_\mu-L_\tau}$ is introduced to a scalar LQ model with the LQ $S_1$ charged under the new symmetry, $S_1$ primarily couples to the third-generation leptons while its couplings to first and second-generation leptons are naturally suppressed. Furthermore, only $S_1$ in the scalar LQ models has the feature that down-type quarks merely couple to neutrinos but not the charged leptons, avoiding strict restrictions from $b\to s \mu^+ \mu^-$. With this distinctive characteristic of $S_1$, we investigate its impact on rare processes involving the $d_i \to d_j \nu \bar\nu$ transitions. Under the dominant constraints from $\Delta F=2$ processes, we find that the $S_1$ contributions to the branching ratios (BRs) of $B\to K(K^*) \nu \bar\nu$ and $K_L \to \pi^0 \nu \bar\nu$ can be factorized into the same multiplicative factor multiplying the standard model predictions. Enhancement in the BRs can possibly exceed a factor of 2. In particular, ${\cal B}(K^+\to \pi^+ \nu \bar\nu)$ can reach the upper $1\sigma$ error of the experimental value, i.e., $\simeq 15.4 \times 10^{-11}$. We also show that the model can fit the new world averages of $R(D)$ and $R(D^*)$., Comment: 14 pages, 3 figures, figures updated, typos corrected, references added

In this paper, we investigate the in-context learning ability of retrieval-augmented encoder-decoder language models. We first conduct a comprehensive analysis of existing models and identify their limitations in in-context learning, primarily due to a mismatch between pretraining and inference, as well as a restricted context length. To address these issues, we propose RAVEN, a model that combines retrieval-augmented masked language modeling and prefix language modeling. We further introduce Fusion-in-Context Learning to enhance the few-shot performance by enabling the model to leverage more in-context examples without requiring additional training. Through extensive experiments, we demonstrate that our simple yet effective design significantly improves performance, achieving results comparable to the most advanced language models in certain scenarios, despite having substantially fewer parameters. Our work underscores the potential of retrieval-augmented encoder-decoder language models for in-context learning and encourages further research in this direction., Comment: COLM 2024

We examine the dynamical magnetic response in a two-component resonating-valence-bond (RVB) description of the doped Mott insulator. The half-filled antiferromagnetic phase described by the Schwinger-boson mean-field theory will evolve into a bosonic-RVB state in the superconducting phase upon doping, where the doped holes introduce another fermionic itinerant spinon which forms a BCS-like RVB order. The spin excitations are thus composed of a resonance-like mode from the former and a weak dispersive mode from the itinerant component at the mean-field level. These two-component spinons are shown to give rise to an hourglass-like spin excitation at the RPA level via an antiferromagnetic coupling between the two modes, which provides an unconventional explanation of the experimental observations in the cuprate. In particular, we also discuss an instability towards an incommensurate magnetic order in this theoretical framework., Comment: 14 pages, 9 figures