arXiv subjects

Hongwei Yuan

Publications and source records attributed to Hongwei Yuan.

9 recordsLinked to original sources

arXiv2026

An Adjoint-Sensitivity Framework for Lost-in-the-Middle Phenomena in Causal Residual Transformers

We develop an adjoint-sensitivity framework for positional influence in causal residual Transformers and separate unconditional analytic results from conditional boundary-shape conclusions. The principal unconditional theorem is the residual-to-depth-flow estimate for layer controls converging in $L^1$, complemented by a finite-token-to-Volterra attention estimate that explicitly controls the first cells near the causal endpoint. We define a normalized adjoint-energy influence density and derive its exact evolution along full-batch gradient flow. The adjoint admits an exact generator-term decomposition into residual transmission, nonlocal Volterra, and local channels, including all covariance cross terms. Causal masking can amplify early-position sensitivity and residual identity paths can transmit a right-localized terminal bias, but neither mechanism alone forces a U-shaped profile. We therefore state boundary advantages under independently checkable energy, correlation, and local-channel bounds; these conditions are sufficient rather than necessary. Finite-token influence balancing, positional reweighting, and task-aligned observability are presented as diagnostics or regularizers with explicit differentiation requirements, computational costs, and limitations. Controlled simulations illustrate that each intervention controls its designated surrogate, while observability balance or outer-loop reweighting need not monotonically reduce the influence-based Lost-in-the-Middle diagnostic.

stat.ML↗

arXiv2026

A First-Order Mean Field Control Analysis of Transformer Layers under Cross-Entropy Training

We study Transformer-type residual layers under cross-entropy training through a continuous-depth mean field control viewpoint. Depth is treated as time, layer parameters as controls, and the residual Transformer recursion as an explicit Euler scheme for a controlled hidden-state flow. For fixed controls, we prove an $O(\varepsilon)$ pathwise approximation of finite-depth trajectories by the continuous flow and combine this with high-probability sampling bounds for the empirical cross-entropy risk. We formulate the limiting population problem as a first-order transport control problem for the law of hidden states and derive a Pontryagin condition whose terminal adjoint contains the softmax residual. We also give finite-class and metric-entropy uniform estimates, compare optimal values, and discuss existence, stability, continuous-to-discrete recovery, initialization, and range estimates for continuous minimizers.

math.OC↗

arXiv2026

A Liouville theorem for bounded empirical-harmonic functions on $\mathcal{P}_2(M)$

The classical Liouville theorem states that every bounded harmonic function on Euclidean space is constant. On complete Riemannian manifolds, analogous conclusions hold under geometric assumptions such as nonnegative Ricci curvature. The quadratic Wasserstein space $\mathcal{P}_2(M)$ has no canonical infinite-dimensional Riemannian volume and hence no canonical Laplace--Beltrami operator. We introduce a natural finite-particle notion of harmonicity: a continuous function $u:\mathcal{P}_2(M)\to\mathbb{R}$ is called empirically harmonic if, for every $N\geq1$, its pullback under the empirical map $$ \iota_N(x_1,\ldots,x_N)=\frac1N\sum_{i=1}^N\delta_{x_i} $$ is weakly harmonic on $M^N$. We prove that if $M$ has the finite-product Liouville property, then every bounded empirically harmonic function on $\mathcal{P}_2(M)$ is constant. In particular, the result applies to $M=\mathbb{R}^d$ and to every complete connected Riemannian manifold with nonnegative Ricci curvature. We also derive a finite-particle chain rule for sufficiently regular functionals on $\mathcal{P}_2(\mathbb{R}^d)$ and show that the empirical Laplacian is exactly the Hessian trace of a discrete $N$-particle lift. Finally, if $M$ admits a nonconstant bounded harmonic function, then $\mathcal{P}_2(M)$ admits a nonconstant bounded empirically harmonic linear statistic.

math.AP↗

arXiv2025

Agentar-Scale-SQL: Advancing Text-to-SQL through Orchestrated Test-Time Scaling

State-of-the-art (SOTA) Text-to-SQL methods still lag significantly behind human experts on challenging benchmarks like BIRD. Current approaches that explore test-time scaling lack an orchestrated strategy and neglect the model's internal reasoning process. To bridge this gap, we introduce Agentar-Scale-SQL, a novel framework leveraging scalable computation to improve performance. Agentar-Scale-SQL implements an Orchestrated Test-Time Scaling strategy that synergistically combines three distinct perspectives: i) Internal Scaling via RL-enhanced Intrinsic Reasoning, ii) Sequential Scaling through Iterative Refinement, and iii) Parallel Scaling using Diverse Synthesis and Tournament Selection. Agentar-Scale-SQL is a general-purpose framework designed for easy adaptation to new databases and more powerful language models. Extensive experiments show that Agentar-Scale-SQL achieves SOTA performance on the BIRD benchmark, reaching 81.67% execution accuracy on the test set and ranking first on the official leaderboard, demonstrating an effective path toward human-level performance.

cs.CL↗

arXiv2025

The steady inviscid compressible self-similar flows and the stability analysis

We investigate the steady inviscid compressible self-similar flows which depends only on the polar angle in spherical coordinates. It is shown that besides the purely supersonic and subsonic self-similar flows, there exists purely sonic flows, Beltrami flows with a nonconstant proportionnality factor and smooth transonic self-similar flows with large vorticity. For a constant supersonic incoming flow past an infinitely long circular cone, a conic shock attached to the tip of the cone will form, provided the opening angle of the cone is less than a critical value. We introduce the shock polar for the radial and polar components of the velocity and show that there exists a monotonicity relation between the shock angle and the radial velocity, which seems to be new and not been observed before. If a supersonic incoming flow is self-similar with nonzero azimuthal velocity, a conic shock also form attached to the tip of the cone. The state at the downstream may change smoothly from supersonic to subsonic, thus the shock can be supersonic-supersonic, supersonic-subsonic and even supersonic-sonic where the shock front and the sonic front coincide. We further investigate the structural stability of smooth self-similar irrotational transonic flows and analyze the corresponding linear mixed type second order equation of Tricomi type. By exploring some key properties of the self-similar solutions, we find a multiplier and identify a class of admissible boundary conditions for the linearized mixed type second-order equation. We also prove the existence and uniqueness of a class of smooth transonic flows with nonzero vorticity which depends only on the polar and azimuthal angles in spherical coordinates.

math.AP↗

arXiv2023

Global Well-Posedness of First-Order Mean Field Games and Master Equations with Nonlinear Dynamics

This article presents the variant of the approach introduced in the recent work of Bensoussan, Wong, Yam and Yuan [13] to the generic first-order mean field game problem. A major contribution here is the provision of new crucial a priori estimates, whose establishment is fundamentally different from the mentioned work since the associated forward-backward ordinary differential equation (FBODE) system is notably different. In addition, we require monotonicity conditions intimately on the coefficient functions but not on the Hamiltonians to handle their non-separable nature and nonlinear dynamics; as tackling Hamiltonians directly, it potentially dissolves much useful information. Compared with the assumptions used in [13], we introduce an additional requirement that the first-order derivative of the drift function in the measure variable cannot be too large relative to the convexity of the running cost function; this requirement only arises when the Hamiltonian is non-separable, and this phenomenon can also be seen in the existing literature. On the other hand, we require less here for the second-order differentiability of the coefficient functions in comparison to that in [13]. Our approach involves first demonstrating the local existence of a solution over small time interval, followed by the provision of new crucial a priori estimates for the sensitivity of the backward equation with respect to the initial condition of forward dynamics; and finally, smoothly gluing the local solutions together to form a global solution. In addition, we establish the local and global existence and uniqueness of classical solutions for the mean field game and its master equation.

math.OC↗

arXiv2023

A Theory of First Order Mean Field Type Control Problems and their Equations

In this article, by using several new crucial {\it a priori} estimates which are still absent in the literature, we provide a comprehensive resolution of the first order generic mean field type control problems and also establish the global-in-time classical solutions of their Bellman and master equations. Rather than developing the analytical approach via tackling the Bellman and master equation directly, we apply the maximum principle approach by considering the induced forward-backward ordinary differential equation (FBODE) system; indeed, we first show the local-in-time unique existence of the solution of the FBODE system for a variety of terminal data by Banach fixed point argument, and then provide crucial a priori estimates of bounding the sensitivity of the terminal data for the backward equation by utilizing a monotonicity condition that can be deduced from the positive definiteness of the Schur complement of the Hessian matrix of the Lagrangian in the lifted version and manipulating first order condition appropriately; this uniform bound over the whole planning horizon $[0,T]$ allows us to partition $[0,T]$ into a number of sub-intervals with a common small length and then glue the consecutive local-in-time solutions together to form the unique global-in-time solution of the FBODE system. The regularity of the global-in-time solution follows from that of the local ones due to the regularity assumptions on the coefficient functions. Moreover, the regularity of the value function will also be shown with the aid of the regularity of the solution couple of the FBODE system and the regularity assumptions on the coefficient functions, with which we can further deduce that this value function and its linear functional derivative satisfy the Bellman and master equations, respectively.

math.OC↗

arXiv2021

On Some Smooth Symmetric Transonic Flows with Nonzero Angular Velocity and Vorticity

This paper concerns the structural stability of smooth cylindrically symmetric transonic flows in a concentric cylinder. Both cylindrical and axi-symmetric perturbations are considered. The governing system here is of mixed elliptic-hyperbolic and changes type and the suitable formulation of boundary conditions at the boundaries is of great importance. First, we establish the existence and uniqueness of smooth cylindrical transonic spiral solutions with nonzero angular velocity and vorticity which are close to the background transonic flow with small perturbations of the Bernoulli's function and the entropy at the outer cylinder and the flow angles at both the inner and outer cylinders independent of the symmetric axis, and it is shown that in this case, the sonic points of the flow are nonexceptional and noncharacteristically degenerate, and form a cylindrical surface. Second, we also prove the existence and uniqueness of axi-symmetric smooth transonic rotational flows which are adjacent to the background transonic flow, whose sonic points form an axi-symmetric surface. The key elements in our analysis are to utilize the deformation-curl decomposition for the steady Euler system introduced in \cite{WengXin19} to deal with the hyperbolicity in subsonic regions and to find an appropriate multiplier for the linearized second order mixed type equations which are crucial to identify the suitable boundary conditions and to yield the important basic energy estimates.

math.AP↗

arXiv2021

Steady Compressible Radially Symmetric Flows with Nonzero Angular Velocity in an Annulus

In this paper, we investigate steady inviscid compressible flows with radial symmetry in an annulus. The major concerns are transonic flows with or without shocks. One of the main motivations is to elucidate the role played by the angular velocity in the structure of steady inviscid compressible flows. We give a complete classification of flow patterns in terms of boundary conditions at the inner and outer circle. Due to the nonzero angular velocity, many new flow patterns will appear. There exists accelerating or decelerating smooth transonic flows in an annulus satisfying one side boundary conditions at the inner or outer circle with all sonic points being nonexceptional and noncharacteristically degenerate. More importantly, it is found that besides the well-known supersonic-subsonic shock in a divergent nozzle as in the case without angular velocity, there exists a supersonic-supersonic shock solution, where the downstream state may change smoothly from supersonic to subsonic. Furthermore, there exists a supersonic-sonic shock solution where the shock circle and the sonic circle coincide, which is new and interesting.

math.AP↗