Anh Tuan Nguyen

An Vuong, Minh Nhat Vu, Toan Tien Nguyen et al.

Scene synthesis is a challenging problem with several industrial applications. Recently, substantial efforts have been directed to synthesize the scene using human motions, room layouts, or spatial graphs as the input. However, few studies have addressed this problem from multiple modalities, especially combining text prompts. In this paper, we propose a language-driven scene synthesis task, which is a new task that integrates text prompts, human motion, and existing objects for scene synthesis. Unlike other single-condition synthesis tasks, our problem involves multiple conditions and requires a strategy for processing and encoding them into a unified space. To address the challenge, we present a multi-conditional diffusion model, which differs from the implicit unification approach of other diffusion literature by explicitly predicting the guiding points for the original data distribution. We demonstrate that our approach is theoretically supportive. The intensive experiment results illustrate that our method outperforms state-of-the-art benchmarks and enables natural scene editing applications. The source code and dataset can be accessed at https://lang-scene-synth.github.io/.

Anh Tuan Nguyen, Viet Anh Nguyen

Projection methods aim to reduce the dimensionality of the optimization instance, thereby improving the scalability of high-dimensional problems. Recently, Sakaue and Oki proposed a data-driven approach for linear programs (LPs), where the projection matrix is learned from observed problem instances drawn from an application-specific distribution of problems. We analyze the generalization guarantee for the data-driven projection matrix learning for convex quadratic programs (QPs). Unlike in LPs, the optimal solutions of convex QPs are not confined to the vertices of the feasible polyhedron, and this complicates the analysis of the optimal value function. To overcome this challenge, we demonstrate that the solutions of convex QPs can be localized within a feasible region corresponding to a special active set, utilizing Caratheodory's theorem. Building on such observation, we propose the unrolled active set method, which models the computation of the optimal value as a Goldberg-Jerrum (GJ) algorithm with bounded complexities, thereby establishing learning guarantees. We then further extend our analysis to other settings, including learning to match the optimal solution and input-aware setting, where we learn a mapping from QP problem instances to projection matrices.