Trajectory prediction facilitates effective planning and decision-making, while constrained trajectory prediction integrates regulation into prediction. Recent advances in constrained trajectory prediction focus on structured constraints by constructing optimization objectives. However, handling unstructured constraints is challenging due to the lack of differentiable formal definitions. To address this, we propose a novel method for constrained trajectory prediction using a conditional generative paradigm, named Controllable Trajectory Diffusion (CTD). The key idea is that any trajectory corresponds to a degree of conformity to a constraint. By quantifying this degree and treating it as a condition, a model can implicitly learn to predict trajectories under unstructured constraints. CTD employs a pre-trained scoring model to predict the degree of conformity (i.e., a score), and uses this score as a condition for a conditional diffusion model to generate trajectories. Experimental results demonstrate that CTD achieves high accuracy on the ETH/UCY and SDD benchmarks. Qualitative analysis confirms that CTD ensures adherence to unstructured constraints and can predict trajectories that satisfy combinatorial constraints.

Building mixture-of-experts (MoE) architecture for Low-rank adaptation (LoRA) is emerging as a potential direction in parameter-efficient fine-tuning (PEFT) for its modular design and remarkable performance. However, simply stacking the number of experts cannot guarantee significant improvement. In this work, we first conduct qualitative analysis to indicate that experts collapse to similar representations in vanilla MoE, limiting the capacity of modular design and computational efficiency. Ulteriorly, Our analysis reveals that the performance of previous MoE variants maybe limited by a lack of diversity among experts. Motivated by these findings, we propose Orthogonal Mixture-of-Experts (OMoE), a resource-efficient MoE variant that trains experts in an orthogonal manner to promote diversity. In OMoE, a Gram-Schmidt process is leveraged to enforce that the experts' representations lie within the Stiefel manifold. By applying orthogonal constraints directly to the architecture, OMoE keeps the learning objective unchanged, without compromising optimality. Our method is simple and alleviates memory bottlenecks, as it incurs minimal experts compared to vanilla MoE models. Experiments on diverse commonsense reasoning benchmarks demonstrate that OMoE can consistently achieve stable and efficient performance improvement when compared with the state-of-the-art methods while significantly reducing the number of required experts.

Re-ranking is a process of rearranging ranking list to more effectively meet user demands by accounting for the interrelationships between items. Existing methods predominantly enhance the precision of search results, often at the expense of diversity, leading to outcomes that may not fulfill the varied needs of users. Conversely, methods designed to promote diversity might compromise the precision of the results, failing to satisfy the users' requirements for accuracy. To alleviate the above problems, this paper proposes a Preference-oriented Diversity Model Based on Mutual-information (PODM-MI), which consider both accuracy and diversity in the re-ranking process. Specifically, PODM-MI adopts Multidimensional Gaussian distributions based on variational inference to capture users' diversity preferences with uncertainty. Then we maximize the mutual information between the diversity preferences of the users and the candidate items using the maximum variational inference lower bound to enhance their correlations. Subsequently, we derive a utility matrix based on the correlations, enabling the adaptive ranking of items in line with user preferences and establishing a balance between the aforementioned objectives. Experimental results on real-world online e-commerce systems demonstrate the significant improvements of PODM-MI, and we have successfully deployed PODM-MI on an e-commerce search platform.