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Molecular representation learning has emerged as a promising approach for modeling molecules with deep learning in chemistry and beyond. While 3D geometric models effectively capture molecular structure, they typically process single static conformers, overlooking the inherent flexibility and dynamics of molecules. In reality, many molecular properties depend on distributions of thermodynamically accessible conformations rather than single structures. Recent works show that learning from conformer ensembles can improve molecular representations, but existing approaches either produce unphysical structures through averaging or require restrictive molecular alignment. In this paper, we propose Symmetry-Preserving Conformer Ensemble networks (SPiCE), which introduces two key innovations: (1) geometric mixture-of-experts for selective processing of scalar and vector features, and (2) hierarchical ensemble encoding that combines ensemble level representation with cross-conformer integration. Crucially, SPiCE ensures physically meaningful representations by maintaining joint equivariance to geometric transformations of individual conformers and conformer permutations. Extensive experiments demonstrate that SPiCE consistently outperforms existing conformer ensemble methods and state-of-the-art structural aggregation models across quantum mechanical and biological property prediction tasks. 

Optimizing objectives under constraints, where both the objectives and constraints are black box functions, is a common scenario in real-world applications such as the design of medical therapies, industrial process optimization, and hyperparameter optimization. One popular approach to handle these complex scenarios is Bayesian Optimization (BO). However, when it comes to the theoretical understanding of constrained Bayesian optimization (CBO), the existing framework often relies on heuristics, approximations, or relaxation of objectives and, therefore, lacks the same level of theoretical guarantees as in canonical BO. In this paper, we exclude the boundary candidates that could be compromised by noise perturbation and aim to find the interior optimum of the black-box-constrained objective. We rely on the insight that optimizing the objective and learning the constraints can both help identify the high-confidence regions of interest (ROI) that potentially contain the interior optimum. We propose an efficient CBO framework that intersects the ROIs identified from each aspect on a discretized search space to determine the general ROI. Then, on the ROI, we optimize the acquisition functions, balancing the learning of the constraints and the optimization of the objective. We showcase the efficiency and robustness of our proposed CBO framework through the high probability regret bounds for the algorithm and extensive empirical evidence. 

Bayesian optimization (BO) is a powerful paradigm for optimizing expensive black-box functions. Traditional BO methods typically rely on separate hand-crafted acquisition functions and surrogate models for the underlying function, and often operate in a myopic manner. In this paper, we propose a novel direct regret optimization approach that jointly learns the optimal model and non-myopic acquisition by distilling from a set of candidate models and acquisitions, and explicitly targets minimizing the multi-step regret. Our framework leverages an ensemble of Gaussian Processes (GPs) with varying hyperparameters to generate simulated BO trajectories, each guided by an acquisition function chosen from a pool of conventional choices, until a Bayesian early stop criterion is met. These simulated trajectories, capturing multi-step exploration strategies, are used to train an end-to-end decision transformer that directly learns to select next query points aimed at improving the ultimate objective. We further adopt a dense training–sparse learning paradigm: The decision transformer is trained offline with abundant simulated data sampled from ensemble GPs and acquisitions, while a limited number of real evaluations refine the GPs online. Experimental results on synthetic and real-world benchmarks suggest that our method consistently outperforms BO baselines, achieving lower simple regret and demonstrating more robust exploration in high-dimensional or noisy settings.