Yeyu Zhang

Yan Fang, Jialin Chen, Chun Gan et al.

LLM-native advertising embeds sponsored content directly into model-generated responses, shifting the unit of sale from a fixed slot to a moment within an evolving conversation. Existing LLM ad-auction mechanisms primarily operate within a single response, settling the winner but not the timing. The extension is nontrivial: with one native insertion opportunity per session, the stopping time depends on bids, coupling timing with allocation, so static truthfulness arguments no longer apply. We propose the LLM-based Optimal Stopping Dynamic Auction (LLM-OSDA), a dynamic cost-per-click auction that integrates Bellman optimal stopping, winner allocation, and envelope pricing. A bid-independent LLM layer estimates contextual click quality and seamlessly renders the winning ad, while bids enter only the committed auction mechanism. Under an exact Bellman oracle, the expected discounted-click allocation is monotone in each advertiser's bid, and the corresponding envelope payment makes truthful bidding weakly dominant in expectation. For practical deployment, a learned StopNet approximates the Bellman action values. We show that its decisions differ from the optimal policy only near the stopping boundary and bound the resulting incentive loss in terms of its approximation error. Experiments on a simulated conversational advertising corpus show that LLM-OSDA improves net revenue by 11 percent over the strongest fixed-timing baseline while maintaining comparable user retention. Code is at https://github.com/2025Fang2025/llm-osda.

Jiaxiao Xu, Changhong Mou, Yeyu Zhang et al.

Neural operators approximate PDE solution maps, but they need not respect the symmetries of the governing equation. In out-of-distribution (OOD) regimes, a standard neural operator must often learn coordinate alignment and physical evolution within a single map, which can hurt generalization. We use known continuous symmetries of evolution equations on periodic domains to separate these two roles. We propose the Physics-Aligned Canonical Equivariant Fourier Neural Operator (PACE-FNO), which estimates the input frame with a Lie-algebra coordinate estimator, maps the field to a reference frame, applies a standard Fourier Neural Operator (FNO), and restores the prediction to the target frame. We train alignment and operator prediction jointly using bounded symmetry perturbations, with an optional low-dimensional refinement step that updates the estimated frame at inference. Equivariance is enforced by the input and output transformations, while the FNO architecture remains unchanged. Across 1-D and 2-D Burgers, shallow-water, and Navier-Stokes equations on periodic domains, PACE-FNO matches the in-distribution (ID) accuracy of standard neural operators and reduces out-of-distribution (OOD) relative error by up to 12x over FNO with symmetry augmentation (FNO+Aug) under translations and Galilean shifts, with smaller gains for coupled rotation-translation shifts. Ablations show that aligning the input and restoring the output frame account for most OOD gains; inference-time refinement provides a smaller correction.