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Deep generative models have recently emerged as a promising de novo drug design method. In this respect, deep generative conditional variational autoencoder (CVAE) models are a powerful approach for generating novel molecules with desired drug-like properties. However, molecular graph-based models with disentanglement and multivariate explicit latent conditioning have not been fully elucidated. To address this, we proposed a molecular-graph $\beta$-CVAE model for de novo drug design. Here, we empirically tuned the value of disentanglement and assessed its ability to generate molecules with optimised univariate- or-multivariate properties. In particular, we optimised the octanol-water partition coefficient (ClogP), molar refractivity (CMR), quantitative estimate of drug-likeness (QED), and synthetic accessibility score (SAS). Results suggest that a lower $\beta$ value increases the uniqueness of generated molecules (exploration). Univariate optimisation results showed our model generated molecular property averages of ClogP = 41.07% $\pm$ 0.01% and CMR 66.76% $\pm$ 0.01% by the Ghose filter. Multivariate property optimisation results showed that our model generated an average of 30.07% $\pm$ 0.01% molecules for both desired properties. Furthermore, our model improved the QED and SAS (exploitation) of molecules generated. Together, these results suggest that the $\beta$-CVAE could balance exploration and exploitation through disentanglement and is a promising model for de novo drug design, thus providing a basis for future studies.

This paper focuses on investigating the density convergence of a fully discrete finite difference method when applied to numerically solve the stochastic Cahn--Hilliard equation driven by multiplicative space-time white noises. The main difficulty lies in the control of the drift coefficient that is neither globally Lipschitz nor one-sided Lipschitz. To handle this difficulty, we propose a novel localization argument and derive the strong convergence rate of the numerical solution to estimate the total variation distance between the exact and numerical solutions. This along with the existence of the density of the numerical solution finally yields the convergence of density in $L^1(\mathbb{R})$ of the numerical solution. Our results partially answer positively to the open problem emerged in [J. Cui and J. Hong, J. Differential Equations (2020)] on computing the density of the exact solution numerically.

The languages of mathematical physics and modelling are endowed with a rich "grammar of dimensions" that common abstractions of programming languages fail to represent. We propose a dependently typed domain-specific language (embedded in Idris) that captures this grammar. We apply it to explain basic notions of dimensional analysis and Buckingham's Pi theorem. We argue that the language makes mathematical physics more accessible to computer scientists and functional programming more palatable to modelers and physicists.

In this paper, we establish anti-concentration inequalities for additive noise mechanisms which achieve $f$-differential privacy ($f$-DP), a notion of privacy phrased in terms of a tradeoff function (a.k.a. ROC curve) $f$ which limits the ability of an adversary to determine which individuals were in the database. We show that canonical noise distributions (CNDs), proposed by Awan and Vadhan (2023), match the anti-concentration bounds at half-integer values, indicating that their tail behavior is near-optimal. We also show that all CNDs are sub-exponential, regardless of the $f$-DP guarantee. In the case of log-concave CNDs, we show that they are the stochastically smallest noise compared to any other noise distributions with the same privacy guarantee. In terms of integer-valued noise, we propose a new notion of discrete CND and prove that a discrete CND always exists, can be constructed by rounding a continuous CND, and that the discrete CND is unique when designed for a statistic with sensitivity 1. We further show that the discrete CND at sensitivity 1 is stochastically smallest compared to other integer-valued noises. Our theoretical results shed light on the different types of privacy guarantees possible in the $f$-DP framework and can be incorporated in more complex mechanisms to optimize performance.

In the technical report, we provide our solution for OGB-LSC 2022 Graph Regression Task. The target of this task is to predict the quantum chemical property, HOMO-LUMO gap for a given molecule on PCQM4Mv2 dataset. In the competition, we designed two kinds of models: Transformer-M-ViSNet which is an geometry-enhanced graph neural network for fully connected molecular graphs and Pretrained-3D-ViSNet which is a pretrained ViSNet by distilling geomeotric information from optimized structures. With an ensemble of 22 models, ViSNet Team achieved the MAE of 0.0723 eV on the test-challenge set, dramatically reducing the error by 39.75% compared with the best method in the last year competition.

Nowadays, deep learning based methods have demonstrated impressive performance on ideal super-resolution (SR) datasets, but most of these methods incur dramatically performance drops when directly applied in real-world SR reconstruction tasks with unpredictable blur kernels. To tackle this issue, blind SR methods are proposed to improve the visual results on random blur kernels, which causes unsatisfactory reconstruction effects on ideal low-resolution images similarly. In this paper, we propose a double-win framework for ideal and blind SR task, named S2R, including a light-weight transformer-based SR model (S2R transformer) and a novel coarse-to-fine training strategy, which can achieve excellent visual results on both ideal and random fuzzy conditions. On algorithm level, S2R transformer smartly combines some efficient and light-weight blocks to enhance the representation ability of extracted features with relatively low number of parameters. For training strategy, a coarse-level learning process is firstly performed to improve the generalization of the network with the help of a large-scale external dataset, and then, a fast fine-tune process is developed to transfer the pre-trained model to real-world SR tasks by mining the internal features of the image. Experimental results show that the proposed S2R outperforms other single-image SR models in ideal SR condition with only 578K parameters. Meanwhile, it can achieve better visual results than regular blind SR models in blind fuzzy conditions with only 10 gradient updates, which improve convergence speed by 300 times, significantly accelerating the transfer-learning process in real-world situations.

Algebraic Multigrid (AMG) is one of the most used iterative algorithms for solving large sparse linear equations $Ax=b$. In AMG, the coarse grid is a key component that affects the efficiency of the algorithm, the construction of which relies on the strong threshold parameter $\theta$. This parameter is generally chosen empirically, with a default value in many current AMG solvers of 0.25 for 2D problems and 0.5 for 3D problems. However, for many practical problems, the quality of the coarse grid and the efficiency of the AMG algorithm are sensitive to $\theta$; the default value is rarely optimal, and sometimes is far from it. Therefore, how to choose a better $\theta$ is an important question. In this paper, we propose a deep learning based auto-tuning method, AutoAMG($\theta$) for multiscale sparse linear equations, which are widely used in practical problems. The method uses Graph Neural Networks (GNNs) to extract matrix features, and a Multilayer Perceptron (MLP) to build the mapping between matrix features and the optimal $\theta$, which can adaptively output $\theta$ values for different matrices. Numerical experiments show that AutoAMG($\theta$) can achieve significant speedup compared to the default $\theta$ value.

We study the task of zero-shot vision-and-language navigation (ZS-VLN), a practical yet challenging problem in which an agent learns to navigate following a path described by language instructions without requiring any path-instruction annotation data. Normally, the instructions have complex grammatical structures and often contain various action descriptions (e.g., "proceed beyond", "depart from"). How to correctly understand and execute these action demands is a critical problem, and the absence of annotated data makes it even more challenging. Note that a well-educated human being can easily understand path instructions without the need for any special training. In this paper, we propose an action-aware zero-shot VLN method ($A^2$Nav) by exploiting the vision-and-language ability of foundation models. Specifically, the proposed method consists of an instruction parser and an action-aware navigation policy. The instruction parser utilizes the advanced reasoning ability of large language models (e.g., GPT-3) to decompose complex navigation instructions into a sequence of action-specific object navigation sub-tasks. Each sub-task requires the agent to localize the object and navigate to a specific goal position according to the associated action demand. To accomplish these sub-tasks, an action-aware navigation policy is learned from freely collected action-specific datasets that reveal distinct characteristics of each action demand. We use the learned navigation policy for executing sub-tasks sequentially to follow the navigation instruction. Extensive experiments show $A^2$Nav achieves promising ZS-VLN performance and even surpasses the supervised learning methods on R2R-Habitat and RxR-Habitat datasets.

Click-through rate (CTR) prediction plays a critical role in recommender systems and online advertising. The data used in these applications are multi-field categorical data, where each feature belongs to one field. Field information is proved to be important and there are several works considering fields in their models. In this paper, we proposed a novel approach to model the field information effectively and efficiently. The proposed approach is a direct improvement of FwFM, and is named as Field-matrixed Factorization Machines (FmFM, or $FM^2$). We also proposed a new explanation of FM and FwFM within the FmFM framework, and compared it with the FFM. Besides pruning the cross terms, our model supports field-specific variable dimensions of embedding vectors, which acts as soft pruning. We also proposed an efficient way to minimize the dimension while keeping the model performance. The FmFM model can also be optimized further by caching the intermediate vectors, and it only takes thousands of floating-point operations (FLOPs) to make a prediction. Our experiment results show that it can out-perform the FFM, which is more complex. The FmFM model's performance is also comparable to DNN models which require much more FLOPs in runtime.

Most existing works in visual question answering (VQA) are dedicated to improving the accuracy of predicted answers, while disregarding the explanations. We argue that the explanation for an answer is of the same or even more importance compared with the answer itself, since it makes the question and answering process more understandable and traceable. To this end, we propose a new task of VQA-E (VQA with Explanation), where the computational models are required to generate an explanation with the predicted answer. We first construct a new dataset, and then frame the VQA-E problem in a multi-task learning architecture. Our VQA-E dataset is automatically derived from the VQA v2 dataset by intelligently exploiting the available captions. We have conducted a user study to validate the quality of explanations synthesized by our method. We quantitatively show that the additional supervision from explanations can not only produce insightful textual sentences to justify the answers, but also improve the performance of answer prediction. Our model outperforms the state-of-the-art methods by a clear margin on the VQA v2 dataset.