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Yuanqing Cai

Publications and source records attributed to Yuanqing Cai.

12 recordsLinked to original sources

MixRea: Benchmarking Explicit-Implicit Reasoning in Large Language Models

Large language models (LLMs) are increasingly integrated into high-stakes decision-making. Inspired by the theory of \emph{inattentional blindness} in human cognition, we investigate whether LLMs, trained on human-preferred corpora that embed attentional biases, exhibit a similar limitation: \emph{failing to attend to subtle yet important contextual cues under explicit task instructions}. To evaluate this, we introduce the task of \textbf{explicit-implicit reasoning} and present \textbf{MixRea}, a benchmark of 2,246 multiple-choice questions across 9 reasoning types with varying distributions of explicit and implicit information. Evaluation of 21 advanced LLMs shows that even the best-performing reasoning model (Gemini 2.5 Pro) achieves only 42.8\% consistency, revealing widespread inattentional blindness. To mitigate this, we propose \textbf{Potential Relation Completion Prompting (PRCP)}, a prompting method that improves reasoning by recovering overlooked causal relations. Further analysis shows that this limitation persists across diverse multi-source reasoning tasks, highlighting the need for more cognitively aligned models.

cs.CL

Doubling constructions: Global functoriality for non-generic cuspidal representations

We study the generalized doubling method for pairs of representations of $G\times GL_k$ where $G$ is a symplectic group, split special orthogonal group or split general spin group. We analyze the poles of the local integrals, and prove that the global completed $L$-function with a cuspidal representation of $GL_k$ twisted by a highly ramified Hecke character is entire. We obtain a new proof of the weak functorial transfer of cuspidal automorphic representations of $G$ to the natural general linear group, which is independent of the trace formula and its prerequisites, by combining our results with the Converse Theorem.

math.NT

Quaternionic Speh representations

For a central division algebra $D$, we study a family of representations of $\mathrm{GL}_{k,D}$ (both locally and globally), which can be viewed as analogues of the Speh representations. Locally, we study unique models for these representations. Globally, we show that these representations support certain non-vanishing Fourier coefficients.

math.RT

The generalized doubling method: $(k,c)$ models

One of the key ingredients in the recent construction of the generalized doubling method is a new class of models, called $(k,c)$ models, for local components of generalized Speh representations. We construct a family of $(k,c)$ representations, in a purely local setting, and discuss their realizations using inductive formulas. Our main result is a uniqueness theorem which is essential for the proof that the generalized doubling integral is Eulerian.

math.NT

Twisted doubling integrals for classical groups

We describe the twisted doubling integrals of Cai-Friedberg-Ginzburg-Kaplan in a conceptual way. This also extends the construction to the quaternionic unitary groups. We carry out the unfolding argument uniformly in this article. To do so, we define a family of degenerate Whittaker coefficients that are suitable in this setup and study some of their properties. We also prove certain related global and local results that use the same tools.

math.NT

On the crystal graph description of the stable Weyl group multiple Dirichlet series

For a semisimple Lie algebra admitting a good enumeration, we prove a parametrization for the elements in its Weyl group. As an application, we give a coordinate-free comparison between the crystal graph description (when it is known) and the Lie-theoretic description of the Weyl group multiple Dirichlet series in the stable range.

math.RT

Doubling Constructions and Tensor Product ${L}$-Functions: the linear case

We present an integral representation for the tensor product $L$-function of a pair of automorphic cuspidal representations, one of a classical group, the other of a general linear group. Our construction is uniform over all classical groups, and is applicable to all cuspidal representations; it does not require genericity. The main new ideas of the construction are the use of generalized Speh representations as inducing data for the Eisenstein series and the introduction of a new (global and local) model, which generalizes the Whittaker model. This is the first in a series of papers, treating symplectic and even orthogonal groups. Subsequent papers (in preparation) will treat odd orthogonal and general spin groups, the metaplectic covering version of these integrals, and applications to functoriality coming from combining this work with the converse theorem (and independent of the trace formula).

math.NT

Fourier Coefficients for Theta Representations on Covers of General Linear Groups

We show that the theta representations on certain covers of general linear groups support certain types of unique functionals. The proof involves two types of Fourier coefficients. The first are semi-Whittaker coefficients, which generalize coefficients introduced by Bump and Ginzburg for the double cover. The covers for which these coefficients vanish identically (resp. do not vanish for some choice of data) are determined in full. The second are the Fourier coefficients associated with general unipotent orbits. In particular, we determine the unipotent orbit attached, in the sense of Ginzburg, to the theta representations.

math.RT

Fourier Coefficients for Degenerate Eisenstein Series and the Descending Decomposition

We determine the unipotent orbits attached to degenerate Eisenstein series on general linear groups. This confirms a conjecture of David Ginzburg. This also shows that any unipotent orbit of general linear groups does occur as the unipotent orbit attached to a specific automorphic representation. The key ingredient is a root-theoretic result. To prove it, we introduce the notion of the descending decomposition, which expresses every Weyl group element as a product of simple reflections in a certain way. It is suitable for induction and allows us to translate the question into a combinatorial statement.

math.RT

Doubling Constructions for Covering Groups and Tensor Product L-Functions

This is a research announcement concerning a series of constructions obtained by applying the "doubling method" from the theory of automorphic forms to covering groups. Using these constructions, we obtain partial tensor product L-functions attached to generalized Shimura lifts, which may be defined in a natural way since at almost all places the representations are unramified principal series.

math.NT