Yikun Zhang

Yuanqi Du, Botao Yu, Tianyu Liu et al.

There has been unprecedented interest in developing agents that expand the boundary of scientific discovery, primarily by optimizing quantitative objective functions specified by scientists. However, for grand challenges in science , these objectives are only imperfect proxies. We argue that automating objective function design is a central, yet unmet requirement for scientific discovery agents. In this work, we introduce the Scientific Autonomous Goal-evolving Agent (SAGA) to amend this challenge. SAGA employs a bi-level architecture in which an outer loop of LLM agents analyzes optimization outcomes, proposes new objectives, and converts them into computable scoring functions, while an inner loop performs solution optimization under the current objectives. This bi-level design enables systematic exploration of the space of objectives and their trade-offs, rather than treating them as fixed inputs. We demonstrate the framework through a broad spectrum of applications, including antibiotic design, inorganic materials design, functional DNA sequence design, and chemical process design, showing that automating objective formulation can substantially improve the effectiveness of scientific discovery agents.

Yikun Zhang, Geyan Ye, Chaohao Yuan et al.

Molecule-and-text cross-modal representation learning has emerged as a promising direction for enhancing the quality of molecular representation, thereby improving performance in various scientific fields. However, most approaches employ a global alignment approach to learn the knowledge from different modalities that may fail to capture fine-grained information, such as molecule-and-text fragments and stereoisomeric nuances, which is crucial for downstream tasks. Furthermore, it is incapable of modeling such information using a similar global alignment strategy due to the lack of annotations about the fine-grained fragments in the existing dataset. In this paper, we propose Atomas, a hierarchical molecular representation learning framework that jointly learns representations from SMILES strings and text. We design a Hierarchical Adaptive Alignment model to automatically learn the fine-grained fragment correspondence between two modalities and align these representations at three semantic levels. Atomas's end-to-end training framework supports understanding and generating molecules, enabling a wider range of downstream tasks. Atomas achieves superior performance across 12 tasks on 11 datasets, outperforming 11 baseline models thus highlighting the effectiveness and versatility of our method. Scaling experiments further demonstrate Atomas's robustness and scalability. Moreover, visualization and qualitative analysis, validated by human experts, confirm the chemical relevance of our approach. Codes are released on https://github.com/yikunpku/Atomas.

Yikun Zhang, Yen-Chi Chen

The set of local modes and density ridge lines are important summary characteristics of the data-generating distribution. In this work, we focus on estimating local modes and density ridges from point cloud data in a product space combining two or more Euclidean and/or directional metric spaces. Specifically, our approach extends the (subspace constrained) mean shift algorithm to such product spaces, addressing potential challenges in the generalization process. We establish the algorithmic convergence of the proposed methods, along with practical implementation guidelines. Experiments on simulated and real-world datasets demonstrate the effectiveness of our proposed methods.

Yikun Zhang, Yen-Chi Chen

This paper studies the linear convergence of the subspace constrained mean shift (SCMS) algorithm, a well-known algorithm for identifying a density ridge defined by a kernel density estimator. By arguing that the SCMS algorithm is a special variant of a subspace constrained gradient ascent (SCGA) algorithm with an adaptive step size, we derive the linear convergence of such SCGA algorithm. While the existing research focuses mainly on density ridges in the Euclidean space, we generalize density ridges and the SCMS algorithm to directional data. In particular, we establish the stability theorem of density ridges with directional data and prove the linear convergence of our proposed directional SCMS algorithm.

Yikun Zhang, Yen-Chi Chen

The directional mean shift (DMS) algorithm is a nonparametric method for pursuing local modes of densities defined by kernel density estimators on the unit hypersphere. In this paper, we show that any DMS iteration can be viewed as a generalized Expectation-Maximization (EM) algorithm; in particular, when the von Mises kernel is applied, it becomes an exact EM algorithm. Under the (generalized) EM framework, we provide a new proof for the ascending property of density estimates and demonstrate the global convergence of directional mean shift sequences. Finally, we give a new insight into the linear convergence of the DMS algorithm.

Yikun Zhang, Yen-Chi Chen

Directional data consist of observations distributed on a (hyper)sphere, and appear in many applied fields, such as astronomy, ecology, and environmental science. This paper studies both statistical and computational problems of kernel smoothing for directional data. We generalize the classical mean shift algorithm to directional data, which allows us to identify local modes of the directional kernel density estimator (KDE). The statistical convergence rates of the directional KDE and its derivatives are derived, and the problem of mode estimation is examined. We also prove the ascending property of the directional mean shift algorithm and investigate a general problem of gradient ascent on the unit hypersphere. To demonstrate the applicability of the algorithm, we evaluate it as a mode clustering method on both simulated and real-world data sets.