Fast Gradient Computation for Gromov-Wasserstein Distance

The Gromov-Wasserstein distance is a notable extension of optimal transport. In contrast to the classic Wasserstein distance, it solves a quadratic assignment problem that minimizes the pair-wise distance distortion under the transportation of distributions and thus could apply to distributions in different spaces. These properties make Gromov-Wasserstein widely applicable to many fields, such as computer graphics and machine learning. However, the computation of the Gromov-Wasserstein distance and transport plan is expensive. The well-known Entropic Gromov-Wasserstein approach has a cubic complexity since the matrix multiplication operations need to be repeated in computing the gradient of Gromov-Wasserstein loss. This becomes a key bottleneck of the method. Currently, existing methods accelerate the computation focus on sampling and approximation, which leads to low accuracy or incomplete transport plan. In this work, we propose a novel method to accelerate accurate gradient computation by dynamic programming techniques, reducing the complexity from cubic to quadratic. In this way, the original computational bottleneck is broken and the new entropic solution can be obtained with total quadratic time, which is almost optimal complexity. Furthermore, it can be extended to some variants easily. Extensive experiments validate the efficiency and effectiveness of our method.

BDG-Net: Boundary Distribution Guided Network for Accurate Polyp Segmentation

Colorectal cancer (CRC) is one of the most common fatal cancer in the world. Polypectomy can effectively interrupt the progression of adenoma to adenocarcinoma, thus reducing the risk of CRC development. Colonoscopy is the primary method to find colonic polyps. However, due to the different sizes of polyps and the unclear boundary between polyps and their surrounding mucosa, it is challenging to segment polyps accurately. To address this problem, we design a Boundary Distribution Guided Network (BDG-Net) for accurate polyp segmentation. Specifically, under the supervision of the ideal Boundary Distribution Map (BDM), we use Boundary Distribution Generate Module (BDGM) to aggregate high-level features and generate BDM. Then, BDM is sent to the Boundary Distribution Guided Decoder (BDGD) as complementary spatial information to guide the polyp segmentation. Moreover, a multi-scale feature interaction strategy is adopted in BDGD to improve the segmentation accuracy of polyps with different sizes. Extensive quantitative and qualitative evaluations demonstrate the effectiveness of our model, which outperforms state-of-the-art models remarkably on five public polyp datasets while maintaining low computational complexity.

ChemiRise: a data-driven retrosynthesis engine

We have developed an end-to-end, retrosynthesis system, named ChemiRise, that can propose complete retrosynthesis routes for organic compounds rapidly and reliably. The system was trained on a processed patent database of over 3 million organic reactions. Experimental reactions were atom-mapped, clustered, and extracted into reaction templates. We then trained a graph convolutional neural network-based one-step reaction proposer using template embeddings and developed a guiding algorithm on the directed acyclic graph (DAG) of chemical compounds to find the best candidate to explore. The atom-mapping algorithm and the one-step reaction proposer were benchmarked against previous studies and showed better results. The final product was demonstrated by retrosynthesis routes reviewed and rated by human experts, showing satisfying functionality and a potential productivity boost in real-life use cases.

Molecular modeling with machine-learned universal potential functions

Molecular modeling is an important topic in drug discovery. Decades of research have led to the development of high quality scalable molecular force fields. In this paper, we show that neural networks can be used to train an universal approximator for energy potential functions. By incorporating a fully automated training process we have been able to train smooth, differentiable, and predictive potential functions on large scale crystal structures. A variety of tests have also performed to show the superiority and versatility of the machine-learned model.

Notes on neighborhood semantics for logics of unknown truths and false beliefs

In this article, we study logics of unknown truths and false beliefs under neighborhood semantics. We compare the relative expressivity of the two logics. It turns out that they are incomparable over various classes of neighborhood models, and the combination of the two logics are equally expressive as standard modal logic over any class of neighborhood models. We propose morphisms for each logic, which can help us explore the frame definability problem, show a general soundness and completeness result, and generalize some results in the literature. We axiomatize the two logics over various classes of neighborhood frames. Last but not least, we extend the results to the case of public announcements, which has good applications to Moore sentences and some others.

A family of neighborhood contingency logics

This article proposes the axiomatizations of contingency logics of various natural classes of neighborhood frames. In particular, by defining a suitable canonical neighborhood function, we give sound and complete axiomatizations of monotone contingency logic and regular contingency logic, thereby answering two open questions raised by Bakhtiari, van Ditmarsch, and Hansen. The canonical function is inspired by a function proposed by Kuhn in~1995. We show that Kuhn's function is actually equal to a related function originally given by Humberstone.

Chemi-net: a graph convolutional network for accurate drug property prediction

Absorption, distribution, metabolism, and excretion (ADME) studies are critical for drug discovery. Conventionally, these tasks, together with other chemical property predictions, rely on domain-specific feature descriptors, or fingerprints. Following the recent success of neural networks, we developed Chemi-Net, a completely data-driven, domain knowledge-free, deep learning method for ADME property prediction. To compare the relative performance of Chemi-Net with Cubist, one of the popular machine learning programs used by Amgen, a large-scale ADME property prediction study was performed on-site at Amgen. The results showed that our deep neural network method improved current methods by a large margin. We foresee that the significantly increased accuracy of ADME prediction seen with Chemi-Net over Cubist will greatly accelerate drug discovery.

Prediction of amino acid side chain conformation using a deep neural network

A deep neural network based architecture was constructed to predict amino acid side chain conformation with unprecedented accuracy. Amino acid side chain conformation prediction is essential for protein homology modeling and protein design. Current widely-adopted methods use physics-based energy functions to evaluate side chain conformation. Here, using a deep neural network architecture without physics-based assumptions, we have demonstrated that side chain conformation prediction accuracy can be improved by more than 25%, especially for aromatic residues compared with current standard methods. More strikingly, the prediction method presented here is robust enough to identify individual conformational outliers from high resolution structures in a protein data bank without providing its structural factors. We envisage that our amino acid side chain predictor could be used as a quality check step for future protein structure model validation and many other potential applications such as side chain assignment in Cryo-electron microscopy, crystallography model auto-building, protein folding and small molecule ligand docking.

Knowing Whether

Knowing whether a proposition is true means knowing that it is true or knowing that it is false. In this paper, we study logics with a modal operator Kw for knowing whether but without a modal operator K for knowing that. This logic is not a normal modal logic, because we do not have Kw (phi -> psi) -> (Kw phi -> Kw psi). Knowing whether logic cannot define many common frame properties, and its expressive power less than that of basic modal logic over classes of models without reflexivity. These features make axiomatizing knowing whether logics non-trivial. We axiomatize knowing whether logic over various frame classes. We also present an extension of knowing whether logic with public announcement operators and we give corresponding reduction axioms for that. We compare our work in detail to two recent similar proposals.