This paper proposes a new 3D molecule generation framework, called GOAT, for fast and effective 3D molecule generation based on the flow-matching optimal transport objective. Specifically, we formulate a geometric transport formula for measuring the cost of mapping multi-modal features (e.g., continuous atom coordinates and categorical atom types) between a base distribution and a target data distribution. Our formula is solved within a joint, equivariant, and smooth representation space. This is achieved by transforming the multi-modal features into a continuous latent space with equivariant networks. In addition, we find that identifying optimal distributional coupling is necessary for fast and effective transport between any two distributions. We further propose a mechanism for estimating and purifying optimal coupling to train the flow model with optimal transport. By doing so, GOAT can turn arbitrary distribution couplings into new deterministic couplings, leading to an estimated optimal transport plan for fast 3D molecule generation. The purification filters out the subpar molecules to ensure the ultimate generation quality. We theoretically and empirically prove that the proposed optimal coupling estimation and purification yield transport plan with non-increasing cost. Finally, extensive experiments show that GOAT enjoys the efficiency of solving geometric optimal transport, leading to a double speedup compared to the sub-optimal method while achieving the best generation quality regarding validity, uniqueness, and novelty.

Algorithm selection aims to identify the optimal performing algorithm before execution. Existing techniques typically focus on the observed correlations between algorithm performance and meta-features. However, little research has explored the underlying mechanisms of algorithm selection, specifically what characteristics an algorithm must possess to effectively tackle problems with certain feature values. This gap not only limits the explainability but also makes existing models vulnerable to data bias and distribution shift. This paper introduces directed acyclic graph (DAG) to describe this mechanism, proposing a novel modeling paradigm that aligns more closely with the fundamental logic of algorithm selection. By leveraging DAG to characterize the algorithm feature distribution conditioned on problem features, our approach enhances robustness against marginal distribution changes and allows for finer-grained predictions through the reconstruction of optimal algorithm features, with the final decision relying on differences between reconstructed and rejected algorithm features. Furthermore, we demonstrate that, the learned DAG and the proposed counterfactual calculations offer our approach with both model-level and instance-level explainability.

The reasoning capabilities of large language models (LLMs) have advanced rapidly, particularly following the release of DeepSeek-R1, which has inspired a surge of research into data quality and reinforcement learning (RL) algorithms. Despite the pivotal role diversity plays in RL, its influence on LLM reasoning remains largely underexplored. To bridge this gap, this work presents a systematic investigation into the impact of diversity in RL-based training for LLM reasoning, and proposes a novel diversity-aware policy optimization method. Across evaluations on 12 LLMs, we observe a strong positive correlation between the solution diversity and potential@k (a novel metric quantifying an LLM’s reasoning potential) in high-performing models. This finding motivates our method to explicitly promote diversity during RL training. Specifically, we design a token-level diversity and reformulate it into a practical objective, then we selectively apply it to positive samples. Integrated into the R1-zero training framework, our method achieves a 3.5\% average improvement across four mathematical reasoning benchmarks, while generating more diverse and robust solutions.

Model merging is a technique that combines multiple large pretrained models into a single model, enhancing performance and broadening task adaptability without original data or additional training. However, most existing model merging methods focus primarily on exploring the parameter space, merging models with identical architectures. Despite its potential, merging in the architecture space remains in its early stages due to the vast search space and challenges related to layer compatibility. This paper designs a hierarchical model merging framework named HM3, formulating a bilevel multi-objective model merging problem across both parameter and architecture spaces. At the parameter level, HM3 integrates existing merging methods to quickly identify optimal parameters. Based on these, an actor-critic strategy with efficient policy discretization is employed at the architecture level to explore inference paths with Markov property in the layer-granularity search space for reconstructing these optimal models. By training reusable policy and value networks, HM3 learns Pareto optimal models to provide customized solutions for various tasks. Experimental results on language and vision tasks demonstrate that HM3 outperforms methods focusing solely on the parameter or architecture space.