Algebraic Structures Based on a Classifying Space of a Compact Lie Group

We analyze the algebraic structures based on a classifying space of a compact Lie group. We construct the connected graded free Lie algebra structure by considering the rationally nontrivial indecomposable and decomposable generators of homotopy groups and the cohomology cup products, and we show that the homomorphic image of homology generators can be expressed in terms of the Lie brackets in rational homology. By using the Milnor-Moore theorem, we also investigate the concrete primitive elements in the Pontrjagin algebra

Grouping-matrix based Graph Pooling with Adaptive Number of Clusters

Graph pooling is a crucial operation for encoding hierarchical structures within graphs. Most existing graph pooling approaches formulate the problem as a node clustering task which effectively captures the graph topology. Conventional methods ask users to specify an appropriate number of clusters as a hyperparameter, then assume that all input graphs share the same number of clusters. In inductive settings where the number of clusters can vary, however, the model should be able to represent this variation in its pooling layers in order to learn suitable clusters. Thus we propose GMPool, a novel differentiable graph pooling architecture that automatically determines the appropriate number of clusters based on the input data. The main intuition involves a grouping matrix defined as a quadratic form of the pooling operator, which induces use of binary classification probabilities of pairwise combinations of nodes. GMPool obtains the pooling operator by first computing the grouping matrix, then decomposing it. Extensive evaluations on molecular property prediction tasks demonstrate that our method outperforms conventional methods.Comment: 10 pages, 3 figure

Geometrically Aligned Transfer Encoder for Inductive Transfer in Regression Tasks

Transfer learning is a crucial technique for handling a small amount of data that is potentially related to other abundant data. However, most of the existing methods are focused on classification tasks using images and language datasets. Therefore, in order to expand the transfer learning scheme to regression tasks, we propose a novel transfer technique based on differential geometry, namely the Geometrically Aligned Transfer Encoder (GATE). In this method, we interpret the latent vectors from the model to exist on a Riemannian curved manifold. We find a proper diffeomorphism between pairs of tasks to ensure that every arbitrary point maps to a locally flat coordinate in the overlapping region, allowing the transfer of knowledge from the source to the target data. This also serves as an effective regularizer for the model to behave in extrapolation regions. In this article, we demonstrate that GATE outperforms conventional methods and exhibits stable behavior in both the latent space and extrapolation regions for various molecular graph datasets.Comment: 12+11 pages, 6+1 figures, 0+7 table

Novel twin-roll-cast Ti/Al clad sheets with excellent tensile properties

Pure Ti or Ti alloys are recently spot-lighted in construction industries because they have excellent resistance to corrosions, chemicals, and climates as well as various coloring characteristics, but their wide applications are postponed by their expensiveness and poor formability. We present a new fabrication process of Ti/Al clad sheets by bonding a thin Ti sheet on to a 5052 Al alloy melt during vertical-twin-roll casting. This process has merits of reduced production costs as well as improved tensile properties. In the as-twin-roll-cast clad sheet, the homogeneously cast microstructure existed in the Al alloy substrate side, while the Ti/Al interface did not contain any reaction products, pores, cracks, or lateral delamination, which indicated the successful twin-roll casting. When this sheet was annealed at 350 degrees C-600 degrees C, the metallurgical bonding was expanded by interfacial diffusion, thereby leading to improvement in tensile properties over those calculated by a rule of mixtures. The ductility was also improved over that of 5052-O Al alloy (25%) or pure Ti (25%) by synergic effect of homogeneous deformation due to excellent Ti/Al bonding. This work provides new applications of Ti/Al clad sheets to lightweight-alloy clad sheets requiring excellent formability and corrosion resistance as well as alloy cost saving.112Ysciescopu

3D Denoisers are Good 2D Teachers: Molecular Pretraining via Denoising and Cross-Modal Distillation

Pretraining molecular representations from large unlabeled data is essential for molecular property prediction due to the high cost of obtaining ground-truth labels. While there exist various 2D graph-based molecular pretraining approaches, these methods struggle to show statistically significant gains in predictive performance. Recent work have thus instead proposed 3D conformer-based pretraining under the task of denoising, which led to promising results. During downstream finetuning, however, models trained with 3D conformers require accurate atom-coordinates of previously unseen molecules, which are computationally expensive to acquire at scale. In light of this limitation, we propose D&D, a self-supervised molecular representation learning framework that pretrains a 2D graph encoder by distilling representations from a 3D denoiser. With denoising followed by cross-modal knowledge distillation, our approach enjoys use of knowledge obtained from denoising as well as painless application to downstream tasks with no access to accurate conformers. Experiments on real-world molecular property prediction datasets show that the graph encoder trained via D&D can infer 3D information based on the 2D graph and shows superior performance and label-efficiency against other baselines.Comment: 16 pages, 5 figure