Lei Ma | Searcharxiv

arXiv2026

SAM-D2Q: Aligning Multimodal Doc2Query with Search Demand and Conversion for E-commerce

E-commerce search often suffers from vocabulary mismatch between user queries and merchant-authored product titles, since short titles cannot fully cover diverse user expressions or visual product attributes. Although Doc2Query alleviates this issue by generating pseudo-queries for document expansion, traditional methods are text-only and not optimized for e-commerce business objectives. As a result, they may produce semantically plausible but commercially ineffective expansions and miss key attributes present in product images. To this end, we propose E-commerce Search-Aligned Multimodal Doc2Query (SAM-D2Q), a business-aligned multimodal document expansion framework for e-commerce search under Boolean retrieval constraints. SAM-D2Q consists of three stages: (1) task-adapted multimodal supervised fine-tuning to enhance vision-language understanding of product titles, images, and user queries; (2) multimodal data augmentation to improve perception of key visual attributes and expansion coverage; and (3) reinforcement-learning-based preference alignment toward search business objectives, encouraging the model to generate pseudo-queries that better match user intent and commercial value. Offline experiments show that SAM-D2Q substantially improves retrieval performance over traditional Doc2Query methods. Deployed in the AliExpress production search system, SAM-D2Q improves online business metrics, increasing GMV by +3.38% and Pay Count by +2.27%.

cs.IR↗

arXiv2026

Schrödinger Bridges on Lie Group Manifolds for Probabilistic Intrinsic Generation

Generative modeling directly on geometric manifolds can avoid errors introduced by flattening non-Euclidean data, repeated ambient projection, and coordinate inconsistency in Euclidean representations. Schrodinger bridges provide a probabilistic generative framework for entropy-regularized transport between prescribed endpoint distributions. We study Schrodinger bridges for kinetic dynamics on Lie group manifolds with state X_t = (g_t, xi_t) in G x g, allowing endpoint observations to constrain only the variables that are actually measured. In particular, the entropy projection determines the conditional law of the unobserved endpoint velocities. For the same observed endpoint bridge, we develop two computational realizations: Wrapped-Kernel Bridge Calibration (WKBC) uses an explicit periodized kinetic kernel on compact Abelian groups, whereas Reciprocal Conditional-Control Bridge Matching (RCCBM) handles compact non-Abelian groups through two-sided endpoint calibration and mollified conditional-control matching. The canonical teacher-mixture path law is itself a Markov reciprocal law, so forward generation uses a calibrated initial law and one learned Doob controller. Moreover, we establish a modular error bound in the bounded-Lipschitz path metric that provides a clean separation of errors due to endpoints, control regression, initialization, discretization, and related approximations. Experiments on multiple Lie group manifold datasets validate the feasibility and consistency of our proposed method, covering protein and RNA torsions, SO(3), U(n), and the Protein Conformational Transition Pathway Generation task using mdCATH trajectories in a compact reduced representation. The source code is publicly available at https://github.com/cafferyzhang12/Schr-dinger_Bridge_on_LieGroup.

stat.ML↗