W e explore the role of torsion in hybrid deep learning models that incorporate topological data analysis, focusing on autoencoders. While most TDA tools use field coefficients, this conceals torsional features present in integer homology . W e show that torsion can be lost during encoding, altered in the latent space, and in many cases, not reconstructed by standard decoders. Using both synthetic and high-dimensional data, we evaluate torsion sensitivity to perturbations and assess its recoverability across several autoencoder architectures. Our findings reveal key limitations of field-based approaches and underline the need for architectures or loss terms that preserve torsional information for robust data representation.

Geometric deep learning (GDL) models have demonstrated a great potential for the analysis of non-Euclidian data. They are developed to incorporate the geometric and topological information of non-Euclidian data into the end-to-end deep learning architectures. Motivated by the recent success of discrete Ricci curvature in graph neural network (GNNs), we propose TorGNN, an analytic Torsion enhanced Graph Neural Network model. The essential idea is to characterize graph local structures with an analytic torsion based weight formula. Mathematically, analytic torsion is a topological invariant that can distinguish spaces which are homotopy equivalent but not homeomorphic. In our TorGNN, for each edge, a corresponding local simplicial complex is identified, then the analytic torsion (for this local simplicial complex) is calculated, and further used as a weight (for this edge) in message-passing process. Our TorGNN model is validated on link prediction tasks from sixteen different types of networks and node classification tasks from three types of networks. It has been found that our TorGNN can achieve superior performance on both tasks, and outperform various state-of-the-art models. This demonstrates that analytic torsion is a highly efficient topological invariant in the characterization of graph structures and can significantly boost the performance of GNNs.

Application of soft and compliant joints in grasping mechanisms received an increasing attention during recent years. This article suggests the design and development of a novel bio-inspired compliant finger which is composed of a 3D printed rigid endoskeleton covered by a soft matter. The overall integrated system resembles a biological structure in which a finger presents an anthropomorphic look. The mechanical properties of such structure are enhanced through optimization of the repetitive geometrical structures that constructs a flexure bearing as a joint for the fingers. The endoskeleton is formed by additive manufacturing of such geometries with rigid materials. The geometry of the endoskeleton was studied by finite element analysis (FEA) to obtain the desired properties: high stiffness against lateral deflection and twisting, and low stiffness in the desired bending axis of the fingers. Results are validated by experimental analysis.

We consider representation learning of 3D molecular graphs in which each atom is associated with a spatial position in 3D. This is an under-explored area of research, and a principled message passing framework is currently lacking. In this work, we conduct analyses in the spherical coordinate system (SCS) for the complete identification of 3D graph structures. Based on such observations, we propose the spherical message passing (SMP) as a novel and powerful scheme for 3D molecular learning. SMP dramatically reduces training complexity, enabling it to perform efficiently on large-scale molecules. In addition, SMP is capable of distinguishing almost all molecular structures, and the uncovered cases may not exist in practice. Based on meaningful physically-based representations of 3D information, we further propose the SphereNet for 3D molecular learning. Experimental results demonstrate that the use of meaningful 3D information in SphereNet leads to significant performance improvements in prediction tasks. Our results also demonstrate the advantages of SphereNet in terms of capability, efficiency, and scalability. Our code is publicly available as part of the DIG library (https://github.com/divelab/DIG).

Molecular mechanics (MM) potentials have long been a workhorse of computational chemistry. Leveraging accuracy and speed, these functional forms find use in a wide variety of applications from rapid virtual screening to detailed free energy calculations. Traditionally, MM potentials have relied on human-curated, inflexible, and poorly extensible discrete chemical perception rules (atom types) for applying parameters to molecules or biopolymers, making them difficult to optimize to fit quantum chemical or physical property data. Here, we propose an alternative approach that uses graph nets to perceive chemical environments, producing continuous atom embeddings from which valence and nonbonded parameters can be predicted using a feed-forward neural network. Since all stages are built using smooth functions, the entire process of chemical perception and parameter assignment is differentiable end-to-end with respect to model parameters, allowing new force fields to be easily constructed, extended, and applied to arbitrary molecules. We show that this approach has the capacity to reproduce legacy atom types and can be fit to MM and QM energies and forces, among other targets.

Small molecule discovery, binding affinity prediction and medical prescription are the three fields which artificial intelligence seems to have invaded in the pharmaceutical space. Deep Intelligent Pharma (DIP) focuses mainly on building software for providing medical transcription using AI. This Chinese company deploys natural language processing(NLP) frameworks to sift through the exhaustive regulatory documents and assist the pharma companies in manufacturing content which adheres to the law. These AI-enabled writing tools, including automated transcription, tabulated data analysis, document review, and quality control will be used to create content and documents to be submitted to regulatory bodies such as the Food and Drug Administration. The company has raised $26.1 million in funding from Sequoia Capital China and ZhenFund.

Manifold embedding algorithms map high dimensional data, down to coordinates in a much lower dimensional space. One of the aims of the dimension reduction is to find the {\em intrinsic coordinates} that describe the data manifold. However, the coordinates returned by the embedding algorithm are abstract coordinates. Finding their physical, domain related meaning is not formalized and left to the domain experts. This paper studies the problem of recovering the domain-specific meaning of the new low dimensional representation in a semi-automatic, principled fashion. We propose a method to explain embedding coordinates on a manifold as {\em non-linear} compositions of functions from a user-defined dictionary. We show that this problem can be set up as a sparse {\em linear Group Lasso} recovery problem, find sufficient recovery conditions, and demonstrate its effectiveness on data.