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We investigate how the in-plane Zeeman field and the Hubbard interaction can jointly affect the topological states in the Kane-Mele-Hubbard model. At low Zeeman field, the projector quantum Monte Carlo (PQMC) simulations demonstrate Mott transitions between the higher-order topological insulator induced by the in-plane Zeeman field and the antiferromagnetic insulator induced by the Hubbard interaction. The interacting higher-order topological state on a finite-sized honeycomb lattice is characterized by the local density of states derived from the real-space spectral function. In the higher-order topological phase, the mirror-inversion symmetry protected corner states exist on the diamond-shaped honeycomb lattice. By comparing the spatial distribution of corner states between the Kane-Mele and Kane-Mele-Hubbard models, we show that the effect of the Hubbard interaction is to contribute some extra in-plane Zeeman field. At the mean-field level, we calculate the full phase diagram of the Kane-Mele-Hubbard model under the influence of the in-plane Zeeman field. The mean-field phase diagram shows that a high in-plane Zeeman field drives the system into a spin-polarized (topologically trivial) phase. In particular, the upper limit of the Zeeman field that can induce corner states in the Kane-Mele model is found to be $h_c = 1.0(3)$. In the parameter region of PQMC simulations, the mean-field solutions are in fair agreement with the PQMC results., Comment: 9 pages, 11 figures

Machine learning interatomic potentials (MLIPs) have been widely used to facilitate large scale molecular simulations with ab initio level accuracy. However, MLIP-based molecular simulations frequently encounter the issue of collapse due to decreased prediction accuracy for out-of-distribution (OOD) data. To mitigate this issue, it is crucial to enrich the training set with active learning, where uncertainty estimation serves as an effective method for identifying and collecting OOD data. Therefore, a feasible method for uncertainty estimation in MLIPs is desired. The existing methods either require expensive computations or compromise prediction accuracy. In this work, we introduce evidential deep learning for interatomic potentials (eIP) with a physics-inspired design. Our experiments demonstrate that eIP consistently generates reliable uncertainties without incurring notable additional computational costs, while the prediction accuracy remains unchanged. Furthermore, we present an eIP-based active learning workflow, where eIP is used not only to estimate the uncertainty of molecular data but also to perform uncertainty-driven dynamics simulations. Our findings show that eIP enables efficient sampling for a more diverse dataset, thereby advancing the feasibility of MLIP-based molecular simulations.

Retrieval-augmented generation (RAG) enhances the outputs of language models by integrating relevant information retrieved from external knowledge sources. However, when the retrieval process involves private data, RAG systems may face severe privacy risks, potentially leading to the leakage of sensitive information. To address this issue, we propose using synthetic data as a privacy-preserving alternative for the retrieval data. We propose SAGE, a novel two-stage synthetic data generation paradigm. In the stage-1, we employ an attribute-based extraction and generation approach to preserve key contextual information from the original data. In the stage-2, we further enhance the privacy properties of the synthetic data through an agent-based iterative refinement process. Extensive experiments demonstrate that using our synthetic data as the retrieval context achieves comparable performance to using the original data while substantially reducing privacy risks. Our work takes the first step towards investigating the possibility of generating high-utility and privacy-preserving synthetic data for RAG, opening up new opportunities for the safe application of RAG systems in various domains.

Large language models (LLMs) are susceptible to a type of attack known as jailbreaking, which misleads LLMs to output harmful contents. Although there are diverse jailbreak attack strategies, there is no unified understanding on why some methods succeed and others fail. This paper explores the behavior of harmful and harmless prompts in the LLM's representation space to investigate the intrinsic properties of successful jailbreak attacks. We hypothesize that successful attacks share some similar properties: They are effective in moving the representation of the harmful prompt towards the direction to the harmless prompts. We leverage hidden representations into the objective of existing jailbreak attacks to move the attacks along the acceptance direction, and conduct experiments to validate the above hypothesis using the proposed objective. We hope this study provides new insights into understanding how LLMs understand harmfulness information.

Multifaceted ideology detection (MID) aims to detect the ideological leanings of texts towards multiple facets. Previous studies on ideology detection mainly focus on one generic facet and ignore label semantics and explanatory descriptions of ideologies, which are a kind of instructive information and reveal the specific concepts of ideologies. In this paper, we develop a novel concept semantics-enhanced framework for the MID task. Specifically, we propose a bidirectional iterative concept flow (BICo) method to encode multifaceted ideologies. BICo enables the concepts to flow across levels of the schema tree and enriches concept representations with multi-granularity semantics. Furthermore, we explore concept attentive matching and concept-guided contrastive learning strategies to guide the model to capture ideology features with the learned concept semantics. Extensive experiments on the benchmark dataset show that our approach achieves state-of-the-art performance in MID, including in the cross-topic scenario., Comment: 13pages, 4 figures (Accepted to Findings of ACL 2024)

We explore the self-play training procedure of large language models (LLMs) in a two-player adversarial language game called Adversarial Taboo. In this game, an attacker and a defender communicate around a target word only visible to the attacker. The attacker aims to induce the defender to speak the target word unconsciously, while the defender tries to infer the target word from the attacker's utterances. To win the game, both players should have sufficient knowledge about the target word and high-level reasoning ability to infer and express in this information-reserved conversation. Hence, we are curious about whether LLMs' reasoning ability can be further enhanced by self-play in this adversarial language game (SPAG). With this goal, we select several open-source LLMs and let each act as the attacker and play with a copy of itself as the defender on an extensive range of target words. Through reinforcement learning on the game outcomes, we observe that the LLMs' performances uniformly improve on a broad range of reasoning benchmarks. Furthermore, iteratively adopting this self-play process can continuously promote LLMs' reasoning abilities. The code is at https://github.com/Linear95/SPAG., Comment: Preprint

Image fusion aims to combine information from different source images to create a comprehensively representative image. Existing fusion methods are typically helpless in dealing with degradations in low-quality source images and non-interactive to multiple subjective and objective needs. To solve them, we introduce a novel approach that leverages semantic text guidance image fusion model for degradation-aware and interactive image fusion task, termed as Text-IF. It innovatively extends the classical image fusion to the text guided image fusion along with the ability to harmoniously address the degradation and interaction issues during fusion. Through the text semantic encoder and semantic interaction fusion decoder, Text-IF is accessible to the all-in-one infrared and visible image degradation-aware processing and the interactive flexible fusion outcomes. In this way, Text-IF achieves not only multi-modal image fusion, but also multi-modal information fusion. Extensive experiments prove that our proposed text guided image fusion strategy has obvious advantages over SOTA methods in the image fusion performance and degradation treatment. The code is available at https://github.com/XunpengYi/Text-IF., Comment: Accepted by CVPR 2024

Recent advancements in text-to-image diffusion models have demonstrated their remarkable capability to generate high-quality images from textual prompts. However, increasing research indicates that these models memorize and replicate images from their training data, raising tremendous concerns about potential copyright infringement and privacy risks. In our study, we provide a novel perspective to understand this memorization phenomenon by examining its relationship with cross-attention mechanisms. We reveal that during memorization, the cross-attention tends to focus disproportionately on the embeddings of specific tokens. The diffusion model is overfitted to these token embeddings, memorizing corresponding training images. To elucidate this phenomenon, we further identify and discuss various intrinsic findings of cross-attention that contribute to memorization. Building on these insights, we introduce an innovative approach to detect and mitigate memorization in diffusion models. The advantage of our proposed method is that it will not compromise the speed of either the training or the inference processes in these models while preserving the quality of generated images. Our code is available at https://github.com/renjie3/MemAttn .

Retrieval-augmented generation (RAG) is a powerful technique to facilitate language model with proprietary and private data, where data privacy is a pivotal concern. Whereas extensive research has demonstrated the privacy risks of large language models (LLMs), the RAG technique could potentially reshape the inherent behaviors of LLM generation, posing new privacy issues that are currently under-explored. In this work, we conduct extensive empirical studies with novel attack methods, which demonstrate the vulnerability of RAG systems on leaking the private retrieval database. Despite the new risk brought by RAG on the retrieval data, we further reveal that RAG can mitigate the leakage of the LLMs' training data. Overall, we provide new insights in this paper for privacy protection of retrieval-augmented LLMs, which benefit both LLMs and RAG systems builders. Our code is available at https://github.com/phycholosogy/RAG-privacy.

In [Tame_quivers_and_affine_bases_I], we give a Ringel-Hall algebra approach to the canonical bases in the symmetric affine cases. In this paper, we extend the results to general symmetrizable affine cases by using Ringel-Hall algebras of representations of a valued quiver. We obtain a bar-invariant basis $\mathbf{B}'=\{C(\mathbf{c},t_\lambda)|(\mathbf{c},t_\lambda)\in\mathcal{G}^a\}$ in the generic composition algebra $\mathcal{C}^*$ and prove that $\mathcal{B}'=\mathbf{B}'\sqcup(-\mathbf{B}')$ coincides with Lusztig's signed canonical basis $\mathcal{B}$. Moreover, in type $\tilde{B}_n,\tilde{C}_n$, $\mathbf{B}'$ is the canonical basis $\mathbf{B}$., Comment: 33 pages

Generative AI has witnessed rapid advancement in recent years, expanding their capabilities to create synthesized content such as text, images, audio, and code. The high fidelity and authenticity of contents generated by these Deep Generative Models (DGMs) have sparked significant copyright concerns. There have been various legal debates on how to effectively safeguard copyrights in DGMs. This work delves into this issue by providing a comprehensive overview of copyright protection from a technical perspective. We examine from two distinct viewpoints: the copyrights pertaining to the source data held by the data owners and those of the generative models maintained by the model builders. For data copyright, we delve into methods data owners can protect their content and DGMs can be utilized without infringing upon these rights. For model copyright, our discussion extends to strategies for preventing model theft and identifying outputs generated by specific models. Finally, we highlight the limitations of existing techniques and identify areas that remain unexplored. Furthermore, we discuss prospective directions for the future of copyright protection, underscoring its importance for the sustainable and ethical development of Generative AI., Comment: 26 pages

In the domain of large language models (LLMs), in-context learning (ICL) has been recognized for its innovative ability to adapt to new tasks, relying on examples rather than retraining or fine-tuning. This paper delves into the critical issue of ICL's susceptibility to data poisoning attacks, an area not yet fully explored. We wonder whether ICL is vulnerable, with adversaries capable of manipulating example data to degrade model performance. To address this, we introduce ICLPoison, a specialized attacking framework conceived to exploit the learning mechanisms of ICL. Our approach uniquely employs discrete text perturbations to strategically influence the hidden states of LLMs during the ICL process. We outline three representative strategies to implement attacks under our framework, each rigorously evaluated across a variety of models and tasks. Our comprehensive tests, including trials on the sophisticated GPT-4 model, demonstrate that ICL's performance is significantly compromised under our framework. These revelations indicate an urgent need for enhanced defense mechanisms to safeguard the integrity and reliability of LLMs in applications relying on in-context learning.

This paper addresses the challenges associated with decentralized voltage control in power grids due to an increase in distributed generations (DGs). Traditional model-based voltage control methods struggle with the rapid energy fluctuations and uncertainties of these DGs. While multi-agent reinforcement learning (MARL) has shown potential for decentralized secondary control, scalability issues arise when dealing with a large number of DGs. This problem lies in the dominant centralized training and decentralized execution (CTDE) framework, where the critics take global observations and actions. To overcome these challenges, we propose a scalable network-aware (SNA) framework that leverages network structure to truncate the input to the critic's Q-function, thereby improving scalability and reducing communication costs during training. Further, the SNA framework is theoretically grounded with provable approximation guarantee, and it can seamlessly integrate with multiple multi-agent actor-critic algorithms. The proposed SNA framework is successfully demonstrated in a system with 114 DGs, providing a promising solution for decentralized voltage control in increasingly complex power grid systems.

Large language models (LLMs) have show great ability in various natural language tasks. However, there are concerns that LLMs are possible to be used improperly or even illegally. To prevent the malicious usage of LLMs, detecting LLM-generated text becomes crucial in the deployment of LLM applications. Watermarking is an effective strategy to detect the LLM-generated content by encoding a pre-defined secret watermark to facilitate the detection process. However, the majority of existing watermark methods leverage the simple hashes of precedent tokens to partition vocabulary. Such watermark can be easily eliminated by paraphrase and correspondingly the detection effectiveness will be greatly compromised. Thus, to enhance the robustness against paraphrase, we propose a semantics-based watermark framework SemaMark. It leverages the semantics as an alternative to simple hashes of tokens since the paraphrase will likely preserve the semantic meaning of the sentences. Comprehensive experiments are conducted to demonstrate the effectiveness and robustness of SemaMark under different paraphrases., Comment: Accepted to NAACL findings 2024

The Controller Hardware_in_the_loop (CHIL) simulation is gaining popularity as a cost_effective, efficient, and reliable tool in the design and development process of fast_growing electrified transportation power converters. However, it is challenging to implement the conventional CHIL simulations on the railway power converters with complex topologies and high switching frequencies due to strict real_time constraints. Therefore, this paper proposes an event-based synchronization CHIL (ES_CHIL) framework for high_fidelity simulation of these electrified railway power converters. Different from conventional CHIL simulations synchronized through the time axis, the ES_CHIL framework is synchronized through the event axis. Therefore, it can ease the real_time constraint and broaden the upper bound on the system size and switching frequency. Besides, models and algorithms with higher accuracy, such as the diode model with natural commutation processes, can be used in the ES-CHIL framework. The proposed framework is validated for a 350 kW wireless power transformer system containing 24 fully controlled devices and 36 diodes by comparing it with Simulink and physical experiments. This research improves the fidelity and application range of the power converters CHIL simulation. Thus, it helps to accelerate the prototype design and performance evaluation process for electrified railways and other applications with such complex converters.

Compared with silicon (Si) power devices, Silicon carbide (SiC) devices have the advantages of fast switching speed and low on-resistance. However, the effects of non-ideal characteristics of SiC MOSFETs and stray parameters (especially parasitic inductance) on switching losses need to be further evaluated. In this paper, a transient loss model based on SiC MOSFET and SiC Schottky barrier diode (SBD) switching pairs is proposed. The transient process analysis is simplified by time segmentation of the transient process of power switching devices. The electro-thermal simulation calculates the junction temperature and updates the temperature-related parameters with the proposed loss model and the thermal network model. A multi-rate data exchange strategy is proposed to solve the problem of disparity in timescales between circuit simulation and thermal network simulation. The CREE CMF20120D SiC MOSFET device is used for the experimental verification. The experimental results verify the accuracy of the model which provides guidance for the circuit design of SiC MOSFETs. All the parameters of the loss model can be extracted from the datasheet, which is practical in power electronics design.

Railway Wireless Power Transfer (WPT) is a promising non-contact power supply solution, but constructing prototypes for controller testing can be both costly and unsafe. Real-time hardware-in-the-loop simulation is an effective and secure testing tool, but simulating the dynamic charging process of railway WPT systems is challenging due to the continuous changes in the nonlinear magnetic coupling components. To address this challenge, we propose an FPGA-based half-step implicit-explicit (IMEX) simulation solver. The proposed solver adopts an IMEX algorithm to solve the piecewise linear and nonlinear parts of the system separately, which enables FPGAs to solve nonlinear components while achieving high numerical stability. Additionally, we divide a complete integration step into two half-steps to reduce computational time delays. Our proposed method offers a promising solution for the real-time simulation of railway WPT systems. The novelty of our approach lies in the use of the IMEX algorithm and the half-step integration method, which significantly improves the accuracy and efficiency of the simulation. Our simulations and experiments demonstrate the effectiveness and accuracy of the proposed solver, which provides a new approach for simulating and optimizing railway WPT systems with nonlinear magnetic coupling components.

Simulation is an efficient tool in the design and control of power electronic systems. However, quick and accurate simulation of them is still challenging, especially when the system contains a large number of switches and state variables. Conventional general-purpose integration algorithms assume nonlinearity within systems but face inefficiency in handling the piecewise characteristics of power electronic switches. While some specialized algorithms can adapt to the piecewise characteristics, most of these methods require systems to be piecewise linear. In this article, a numerical derivative-based flexible integration algorithm is proposed. This algorithm can adapt to the piecewise characteristic caused by switches and have no difficulty when nonlinear non-switching components are present in the circuit. This algorithm consists of a recursive numerical scheme that obtains high-order time derivatives of nonlinear components and a decoupling strategy that further increases computational efficiency. The proposed method is applied to solve a motor derive system and a large-scale power conversion system (PCS) to verify its accuracy and efficiency by comparing experimental waveforms and simulated results given by commercial software. Our proposed method demonstrates several-fold acceleration compared to multiple commonly used algorithms in Simulink., Comment: 10 pages, 8 figures

Large language models (LLMs) have shown great capabilities in various tasks but also exhibited memorization of training data, raising tremendous privacy and copyright concerns. While prior works have studied memorization during pre-training, the exploration of memorization during fine-tuning is rather limited. Compared to pre-training, fine-tuning typically involves more sensitive data and diverse objectives, thus may bring distinct privacy risks and unique memorization behaviors. In this work, we conduct the first comprehensive analysis to explore language models' (LMs) memorization during fine-tuning across tasks. Our studies with open-sourced and our own fine-tuned LMs across various tasks indicate that memorization presents a strong disparity among different fine-tuning tasks. We provide an intuitive explanation of this task disparity via sparse coding theory and unveil a strong correlation between memorization and attention score distribution.

Backdoor attacks aim to surreptitiously insert malicious triggers into DNN models, granting unauthorized control during testing scenarios. Existing methods lack robustness against defense strategies and predominantly focus on enhancing trigger stealthiness while randomly selecting poisoned samples. Our research highlights the overlooked drawbacks of random sampling, which make that attack detectable and defensible. The core idea of this paper is to strategically poison samples near the model's decision boundary and increase defense difficulty. We introduce a straightforward yet highly effective sampling methodology that leverages confidence scores. Specifically, it selects samples with lower confidence scores, significantly increasing the challenge for defenders in identifying and countering these attacks. Importantly, our method operates independently of existing trigger designs, providing versatility and compatibility with various backdoor attack techniques. We substantiate the effectiveness of our approach through a comprehensive set of empirical experiments, demonstrating its potential to significantly enhance resilience against backdoor attacks in DNNs.

Text-to-image generative models, especially those based on latent diffusion models (LDMs), have demonstrated outstanding ability in generating high-quality and high-resolution images from textual prompts. With this advancement, various fine-tuning methods have been developed to personalize text-to-image models for specific applications such as artistic style adaptation and human face transfer. However, such advancements have raised copyright concerns, especially when the data are used for personalization without authorization. For example, a malicious user can employ fine-tuning techniques to replicate the style of an artist without consent. In light of this concern, we propose FT-Shield, a watermarking solution tailored for the fine-tuning of text-to-image diffusion models. FT-Shield addresses copyright protection challenges by designing new watermark generation and detection strategies. In particular, it introduces an innovative algorithm for watermark generation. It ensures the seamless transfer of watermarks from training images to generated outputs, facilitating the identification of copyrighted material use. To tackle the variability in fine-tuning methods and their impact on watermark detection, FT-Shield integrates a Mixture of Experts (MoE) approach for watermark detection. Comprehensive experiments validate the effectiveness of our proposed FT-Shield.

ChatGPT is one of the most popular language models which achieve amazing performance on various natural language tasks. Consequently, there is also an urgent need to detect the texts generated ChatGPT from human written. One of the extensively studied methods trains classification models to distinguish both. However, existing studies also demonstrate that the trained models may suffer from distribution shifts (during test), i.e., they are ineffective to predict the generated texts from unseen language tasks or topics. In this work, we aim to have a comprehensive investigation on these methods' generalization behaviors under distribution shift caused by a wide range of factors, including prompts, text lengths, topics, and language tasks. To achieve this goal, we first collect a new dataset with human and ChatGPT texts, and then we conduct extensive studies on the collected dataset. Our studies unveil insightful findings which provide guidance for developing future methodologies or data collection strategies for ChatGPT detection.

Quantum hypothesis testing plays a pivotal role in quantum technologies, making decisions or drawing conclusions about quantum systems based on observed data. Recently, quantum control techniques have been successfully applied to quantum hypothesis testing, enabling the reduction of error probabilities in the task of distinguishing magnetic fields in presence of environmental noise. In real-world physical systems, such control is prone to various channels of inaccuracies. Therefore improving the robustness of quantum control in the context of quantum hypothesis testing is crucial. In this work, we utilize optimal control methods to compare scenarios with and without accounting for the effects of signal frequency inaccuracies. For parallel dephasing and spontaneous emission, the optimal control inherently demonstrates a certain level of robustness, while in the case of transverse dephasing with an imperfect signal, it may result in a higher error probability compared to the uncontrolled scheme. To overcome these limitations, we introduce a robust control approach optimized for a range of signal noise, demonstrating superior robustness beyond the predefined tolerance window. On average, both the optimal control and robust control show improvements over the uncontrolled schemes for various dephasing or decay rates, with the robust control yielding the lowest error probability., Comment: 20 pages, 6 figures

In this paper, we rethink the low-light image enhancement task and propose a physically explainable and generative diffusion model for low-light image enhancement, termed as Diff-Retinex. We aim to integrate the advantages of the physical model and the generative network. Furthermore, we hope to supplement and even deduce the information missing in the low-light image through the generative network. Therefore, Diff-Retinex formulates the low-light image enhancement problem into Retinex decomposition and conditional image generation. In the Retinex decomposition, we integrate the superiority of attention in Transformer and meticulously design a Retinex Transformer decomposition network (TDN) to decompose the image into illumination and reflectance maps. Then, we design multi-path generative diffusion networks to reconstruct the normal-light Retinex probability distribution and solve the various degradations in these components respectively, including dark illumination, noise, color deviation, loss of scene contents, etc. Owing to generative diffusion model, Diff-Retinex puts the restoration of low-light subtle detail into practice. Extensive experiments conducted on real-world low-light datasets qualitatively and quantitatively demonstrate the effectiveness, superiority, and generalization of the proposed method., Comment: Accepted by ICCV 2023

Layered van der Waals ferromagnets, which preserve their magnetic properties down to exfoliated monolayers, are fueling an abundance of fundamental research and nanoscale device demonstration. CrGeTe$_3$ is a prime example for this class of materials. Its temperature-pressure phase diagram features an insulator-to-metal transition and a significant increase of ferromagnetic Curie-Weiss temperatures upon entering the metallic state. We use density functional theory to understand the magnetic exchange interactions in CrGeTe$_3$ at ambient and elevated pressure. We calculate Heisenberg exchange couplings, which provide the correct ferromagnetic ground state and explain the experimentally observed pressure dependence of magnetism in CrGeTe$_3$. Furthermore, we combine density functional theory with dynamical mean field theory to investigate the effects of electronic correlations and the nature of the high pressure metallic state in CrGeTe$_3$., Comment: 15 pages, 12 figures

Recently, Generative Diffusion Models (GDMs) have showcased their remarkable capabilities in learning and generating images. A large community of GDMs has naturally emerged, further promoting the diversified applications of GDMs in various fields. However, this unrestricted proliferation has raised serious concerns about copyright protection. For example, artists including painters and photographers are becoming increasingly concerned that GDMs could effortlessly replicate their unique creative works without authorization. In response to these challenges, we introduce a novel watermarking scheme, DiffusionShield, tailored for GDMs. DiffusionShield protects images from copyright infringement by GDMs through encoding the ownership information into an imperceptible watermark and injecting it into the images. Its watermark can be easily learned by GDMs and will be reproduced in their generated images. By detecting the watermark from generated images, copyright infringement can be exposed with evidence. Benefiting from the uniformity of the watermarks and the joint optimization method, DiffusionShield ensures low distortion of the original image, high watermark detection performance, and the ability to embed lengthy messages. We conduct rigorous and comprehensive experiments to show the effectiveness of DiffusionShield in defending against infringement by GDMs and its superiority over traditional watermarking methods. The code for DiffusionShield is accessible in https://github.com/Yingqiancui/DiffusionShield.

Recent research has highlighted the vulnerability of Deep Neural Networks (DNNs) against data poisoning attacks. These attacks aim to inject poisoning samples into the models' training dataset such that the trained models have inference failures. While previous studies have executed different types of attacks, one major challenge that greatly limits their effectiveness is the uncertainty of the re-training process after the injection of poisoning samples, including the re-training initialization or algorithms. To address this challenge, we propose a novel attack method called ''Sharpness-Aware Data Poisoning Attack (SAPA)''. In particular, it leverages the concept of DNNs' loss landscape sharpness to optimize the poisoning effect on the worst re-trained model. It helps enhance the preservation of the poisoning effect, regardless of the specific retraining procedure employed. Extensive experiments demonstrate that SAPA offers a general and principled strategy that significantly enhances various types of poisoning attacks.

We employ the sign-problem-free projector determinant quantum Monte Carlo method to study a microscopic model of SU($N$) fermions with singlet-bond and triplet-current interactions on the square lattice. We find the gapped singlet $p_x$ and gapless triplet $d_{x^2-y^2}$ density wave states in the half-filled $N=4$ model. Specifically, the triplet $d_{x^2-y^2}$ density wave order is observed in the weak triplet-current interaction regime. As the triplet-current interaction strength is further increased, our simulations demonstrate a transition to the singlet $p_x$ density wave state, accompanied by a gapped mixed-ordered area where the two orders coexist. With increasing singlet-bond interaction strength, the triplet $d_{x^2-y^2}$-wave order persists up to a critical point after which the singlet $p_x$ density wave state is stabilized, while the ground state is disordered in between the two ordered phases. The analytical continuation is then performed to derive the single-particle spectrum. In the spectra of triplet $d_{x^2-y^2}$ and singlet $p_x$ density waves, the anisotropic Dirac cone and the parabolic shape around the Dirac point are observed, respectively. As for the mixed-ordered area, a single-particle gap opens and the velocities remain anisotropic at the Dirac point., Comment: 9 pages, 9 figures