arXiv subjects
Publications and source records attributed to Chen Wan.
In this paper, we provide a complete list of anomaly-free hyperspherical Hamiltonian spaces for simple reductive groups, as well as their conjectural dual spaces in the sense of BZSV duality.
Vision-language pre-training (VLP) models are vulnerable to adversarial examples, particularly in black-box scenarios. Existing multimodal attacks often suffer from limited perturbation diversity and unstable multi-stage pipelines. To address these challenges, we propose 2S-GDA, a two-stage globally-diverse attack framework. The proposed method first introduces textual perturbations through a globally-diverse strategy by combining candidate text expansion with globally-aware replacement. To enhance visual diversity, image-level perturbations are generated using multi-scale resizing and block-shuffle rotation. Extensive experiments on VLP models demonstrate that 2S-GDA consistently improves attack success rates over state-of-the-art methods, with gains of up to 11.17\% in black-box settings. Our framework is modular and can be easily combined with existing methods to further enhance adversarial transferability.
In this paper, motivated by some previous works in residue method and the recent theory of the relative Langlands duality, we prove a relative trace formula identity that compares the period integral of non-tempered spherical varieties with the period integral of a tempered spherical varieties associated to a Levi subgroup. This allows us to incorporate numerous relative trace formula comparisons studied during the last four decades under the relative Langlands duality framework. We will also propose a conjectural comparison for general non-tempered Hamiltonian spaces.
The transferability of adversarial examples poses a significant security challenge for deep neural networks, which can be attacked without knowing anything about them. In this paper, we propose a new Segmented Gaussian Pyramid (SGP) attack method to enhance the transferability, particularly against defense models. Unlike existing methods that generally focus on single-scale images, our approach employs Gaussian filtering and three types of downsampling to construct a series of multi-scale examples. Then, the gradients of the loss function with respect to each scale are computed, and their average is used to determine the adversarial perturbations. The proposed SGP can be considered an input transformation with high extensibility that is easily integrated into most existing adversarial attacks. Extensive experiments demonstrate that in contrast to the state-of-the-art methods, SGP significantly enhances attack success rates against black-box defense models, with average attack success rates increasing by 2.3% to 32.6%, based only on transferability.
Adversarial attacks have become a significant challenge in the security of machine learning models, particularly in the context of black-box defense strategies. Existing methods for enhancing adversarial transferability primarily focus on the spatial domain. This paper presents Frequency-Space Attack (FSA), a new adversarial attack framework that effectively integrates frequency-domain and spatial-domain transformations. FSA combines two key techniques: (1) High-Frequency Augmentation, which applies Fourier transform with frequency-selective amplification to diversify inputs and emphasize the critical role of high-frequency components in adversarial attacks, and (2) Hierarchical-Gradient Fusion, which merges multi-scale gradient decomposition and fusion to capture both global structures and fine-grained details, resulting in smoother perturbations. Our experiment demonstrates that FSA consistently outperforms state-of-the-art methods across various black-box models. Notably, our proposed FSA achieves an average attack success rate increase of 23.6% compared with BSR (CVPR 2024) on eight black-box defense models.
In this paper, we give a complete list of strongly tempered hyperspherical Hamiltonian spaces. We show that the period integrals attached to the list contains many previously studied Rankin-Selberg integrals and period integrals, thus give a new conceptual understanding of these integrals. The list also proposes many new interesting period integrals to study.
In this paper, we prove the geometric expansion of a local twisted trace formula for the Whittaker induction of any symmetric pairs that are coregular. This generalizes the local (twisted) trace formula for reductive groups proved by Arthur \cite{A91} and Waldspurger \cite{WalFTLtordue}. We also prove a formula for the regular germs of quasi-characters associated to strongly cuspidal functions in terms of certain weighted orbital integrals. As a consequence of our trace formula and the formula for regular germs of quasi-characters, we prove a simple local trace formula of those models for strongly cuspidal test functions which implies a multiplicity formula for these models. We also present various applications of our trace formula and multiplicity formula, including a necessary condition for a discrete L-packet to contain a representation with a unitary Shalika model (resp. a Galois model for classical groups) in terms of the associated Langlands parameter, and we also compute the summation of the corresponding multiplicities for certain discrete L-packets.
We propose two families of relative trace formula comparisons in the study of relative Langlands duality conjectured by Ben-Zvi--Sakellaridis--Venkatesh. This allows us to incorporate numerous relative trace formula comparisons studied during the last four decades under the BZSV duality framework. For the proposed relative trace formula comparisons associated to some strongly tempered spherical varieties, we will prove the fundamental lemma and smooth transfer in the $p$-adic case. Moreover, inspired by the BZSV duality conjecture, we propose a conjecture regarding the degenerate Whittaker period, which generalizes Lapid-Mao's conjecture of the Whittaker period
In this paper, we form a conjecture about the multiplicities of all the strongly tempered spherical varieties without Type N root for tempered representations. This generalizes the epsilon dichotomy conjectures of Gan-Gross-Prasad and Wan-Zhang.
Deep neural networks (DNNs) are vulnerable to adversarial examples obtained by adding small perturbations to original examples. The added perturbations in existing attacks are mainly determined by the gradient of the loss function with respect to the inputs. In this paper, the close relationship between gradient-based attacks and the numerical methods for solving ordinary differential equation (ODE) is studied for the first time. Inspired by the numerical solution of ODE, a new prediction-correction (PC) based adversarial attack is proposed. In our proposed PC-based attack, some existing attack can be selected to produce a predicted example first, and then the predicted example and the current example are combined together to determine the added perturbations. The proposed method possesses good extensibility and can be applied to all available gradient-based attacks easily. Extensive experiments demonstrate that compared with the state-of-the-art gradient-based adversarial attacks, our proposed PC-based attacks have higher attack success rates, and exhibit better transferability.
In this paper, we study the local multiplicity of 10 strongly tempered spherical varieties. We will formulate a uniform epsilon dichotomy conjecture for all these models regarding the unique distinguished element in tempered $L$-packets. Then we will prove this conjecture in many cases, including all the Archimedean cases.
In this paper, by proving a simple local trace formula for real reductive groups, we prove a multiplicity formula of K-types for all irreducible representations of real reductive groups. This multiplicity formula expresses the K-characters in terms of the Harish-Chandra characters.
In this paper, we compute the local relative character for 10 strongly tempered spherical varieties in the unramified case. We also study the local multiplicity for these models. By proving a multiplicity formula, we show that the summation of the multiplicities is always equal to 1 over each local tempered Vogan $L$-packet defined on the pure inner forms of the spherical varieties. Finally, we formulate the Ichino-Ikeda type conjecture on a relation between the period integrals and the central values of certain automorphic $L$-functions for those strongly tempered spherical varieties.
In this paper, we propose a conjectural multiplicity formula for general spherical varieties. For all the cases where a multiplicity formula has been proved, including Whittaker model, Gan-Gross-Prasad model, Ginzburg-Rallis model, Galois model and Shalika model, we show that the multiplicity formula in our conjecture matches the multiplicity formula that has been proved. We also give a proof of this multiplicity formula in two new cases.
By applying the residue method for period integrals and Langlands-Shahidi's theory for residues of Eisenstein series, we study the period integrals for six spherical varieties. For each spherical variety, we prove a relation between the period integrals and certain automorphic L-functions. In some cases, we also study the local multiplicity of the spherical varieties.
We consider the local multiplicity problems of the analogy of the Ginzburg-Rallis model for the unitary group and the unitary similitude group cases. For the unitary similitude group case, by proving a local trace formula for the model, we are able to prove a multiplicity formula for all tempered representations, which implies that the summation of the multiplicities is equal to $1$ over every tempered local Vogan $L$-packet. For the unitary group case, we also prove a multiplicity formula for all tempered representations which implies that the summation of the multiplicities is equal to $2$ over every tempered local Vogan $L$-packet.
We calculate a $\mathrm{G}_2$-period of a Fourier coefficient of a cuspidal Eisenstein series on the split simply-connected group $\mathrm{E}_6$, and relate this period to the Ginzburg-Rallis period of cusp forms on $\mathrm{GL}_6$. This gives us a relation between the Ginzburg-Rallis period and the central value of the exterior cube L-function of $\mathrm{GL}_6$
We study local multiplicities associated to the so-called generalized Shalika models. By establishing a local trace formula for these kind of models, we are able to prove a multiplicity formula for discrete series. As a result, we can show that these multiplicities are constant over every discrete Vogan $L$-packet and that they are related to local exterior square $L$-functions.