Differentiable Genetic Programming for High-dimensional Symbolic Regression

Symbolic regression (SR) is the process of discovering hidden relationships from data with mathematical expressions, which is considered an effective way to reach interpretable machine learning (ML). Genetic programming (GP) has been the dominator in solving SR problems. However, as the scale of SR problems increases, GP often poorly demonstrates and cannot effectively address the real-world high-dimensional problems. This limitation is mainly caused by the stochastic evolutionary nature of traditional GP in constructing the trees. In this paper, we propose a differentiable approach named DGP to construct GP trees towards high-dimensional SR for the first time. Specifically, a new data structure called differentiable symbolic tree is proposed to relax the discrete structure to be continuous, thus a gradient-based optimizer can be presented for the efficient optimization. In addition, a sampling method is proposed to eliminate the discrepancy caused by the above relaxation for valid symbolic expressions. Furthermore, a diversification mechanism is introduced to promote the optimizer escaping from local optima for globally better solutions. With these designs, the proposed DGP method can efficiently search for the GP trees with higher performance, thus being capable of dealing with high-dimensional SR. To demonstrate the effectiveness of DGP, we conducted various experiments against the state of the arts based on both GP and deep neural networks. The experiment results reveal that DGP can outperform these chosen peer competitors on high-dimensional regression benchmarks with dimensions varying from tens to thousands. In addition, on the synthetic SR problems, the proposed DGP method can also achieve the best recovery rate even with different noisy levels. It is believed this work can facilitate SR being a powerful alternative to interpretable ML for a broader range of real-world problems.

Communication-efficient Federated Learning with Single-Step Synthetic Features Compressor for Faster Convergence

Reducing communication overhead in federated learning (FL) is challenging but crucial for large-scale distributed privacy-preserving machine learning. While methods utilizing sparsification or others can largely lower the communication overhead, the convergence rate is also greatly compromised. In this paper, we propose a novel method, named single-step synthetic features compressor (3SFC), to achieve communication-efficient FL by directly constructing a tiny synthetic dataset based on raw gradients. Thus, 3SFC can achieve an extremely low compression rate when the constructed dataset contains only one data sample. Moreover, 3SFC's compressing phase utilizes a similarity-based objective function so that it can be optimized with just one step, thereby considerably improving its performance and robustness. In addition, to minimize the compressing error, error feedback (EF) is also incorporated into 3SFC. Experiments on multiple datasets and models suggest that 3SFC owns significantly better convergence rates compared to competing methods with lower compression rates (up to 0.02%). Furthermore, ablation studies and visualizations show that 3SFC can carry more information than competing methods for every communication round, further validating its effectiveness.

Differentiable Search of Accurate and Robust Architectures

Deep neural networks (DNNs) are found to be vulnerable to adversarial attacks, and various methods have been proposed for the defense. Among these methods, adversarial training has been drawing increasing attention because of its simplicity and effectiveness. However, the performance of the adversarial training is greatly limited by the architectures of target DNNs, which often makes the resulting DNNs with poor accuracy and unsatisfactory robustness. To address this problem, we propose DSARA to automatically search for the neural architectures that are accurate and robust after adversarial training. In particular, we design a novel cell-based search space specially for adversarial training, which improves the accuracy and the robustness upper bound of the searched architectures by carefully designing the placement of the cells and the proportional relationship of the filter numbers. Then we propose a two-stage search strategy to search for both accurate and robust neural architectures. At the first stage, the architecture parameters are optimized to minimize the adversarial loss, which makes full use of the effectiveness of the adversarial training in enhancing the robustness. At the second stage, the architecture parameters are optimized to minimize both the natural loss and the adversarial loss utilizing the proposed multi-objective adversarial training method, so that the searched neural architectures are both accurate and robust. We evaluate the proposed algorithm under natural data and various adversarial attacks, which reveals the superiority of the proposed method in terms of both accurate and robust architectures. We also conclude that accurate and robust neural architectures tend to deploy very different structures near the input and the output, which has great practical significance on both hand-crafting and automatically designing of accurate and robust neural architectures.

Personalized Federated Learning with Hidden Information on Personalized Prior

Federated learning (FL for simplification) is a distributed machine learning technique that utilizes global servers and collaborative clients to achieve privacy-preserving global model training without direct data sharing. However, heterogeneous data problem, as one of FL's main problems, makes it difficult for the global model to perform effectively on each client's local data. Thus, personalized federated learning (PFL for simplification) aims to improve the performance of the model on local data as much as possible. Bayesian learning, where the parameters of the model are seen as random variables with a prior assumption, is a feasible solution to the heterogeneous data problem due to the tendency that the more local data the model use, the more it focuses on the local data, otherwise focuses on the prior. When Bayesian learning is applied to PFL, the global model provides global knowledge as a prior to the local training process. In this paper, we employ Bayesian learning to model PFL by assuming a prior in the scaled exponential family, and therefore propose pFedBreD, a framework to solve the problem we model using Bregman divergence regularization. Empirically, our experiments show that, under the prior assumption of the spherical Gaussian and the first order strategy of mean selection, our proposal significantly outcompetes other PFL algorithms on multiple public benchmarks.

Partial Differential Equations Meet Deep Neural Networks: A Survey

Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics such as computational fluid dynamics, multiphysics simulation, molecular dynamics, or even dynamical systems. It is a vibrant multi-disciplinary field of increasing importance and with extraordinary potential. At the same time, solving PDEs efficiently has been a long-standing challenge. Generally, except for a few differential equations for which analytical solutions are directly available, many more equations must rely on numerical approaches such as the finite difference method, finite element method, finite volume method, and boundary element method to be solved approximately. These numerical methods usually divide a continuous problem domain into discrete points and then concentrate on solving the system at each of those points. Though the effectiveness of these traditional numerical methods, the vast number of iterative operations accompanying each step forward significantly reduces the efficiency. Recently, another equally important paradigm, data-based computation represented by deep learning, has emerged as an effective means of solving PDEs. Surprisingly, a comprehensive review for this interesting subfield is still lacking. This survey aims to categorize and review the current progress on Deep Neural Networks (DNNs) for PDEs. We discuss the literature published in this subfield over the past decades and present them in a common taxonomy, followed by an overview and classification of applications of these related methods in scientific research and engineering scenarios. The origin, developing history, character, sort, as well as the future trends in each potential direction of this subfield are also introduced.

Reconciliation of Pre-trained Models and Prototypical Neural Networks in Few-shot Named Entity Recognition

Incorporating large-scale pre-trained models with the prototypical neural networks is a de-facto paradigm in few-shot named entity recognition. Existing methods, unfortunately, are not aware of the fact that embeddings from pre-trained models contain a prominently large amount of information regarding word frequencies, biasing prototypical neural networks against learning word entities. This discrepancy constrains the two models' synergy. Thus, we propose a one-line-code normalization method to reconcile such a mismatch with empirical and theoretical grounds. Our experiments based on nine benchmark datasets show the superiority of our method over the counterpart models and are comparable to the state-of-the-art methods. In addition to the model enhancement, our work also provides an analytical viewpoint for addressing the general problems in few-shot name entity recognition or other tasks that rely on pre-trained models or prototypical neural networks.

Deep Fair Clustering via Maximizing and Minimizing Mutual Information

Fair clustering aims to divide data into distinct clusters, while preventing sensitive attributes (e.g., gender, race, RNA sequencing technique) from dominating the clustering. Although a number of works have been conducted and achieved huge success in recent, most of them are heuristical, and there lacks a unified theory for algorithm design. In this work, we fill this blank by developing a mutual information theory for deep fair clustering and accordingly designing a novel algorithm, dubbed FCMI. In brief, through maximizing and minimizing mutual information, FCMI is designed to achieve four characteristics highly expected by deep fair clustering, i.e., compact, balanced, and fair clusters, as well as informative features. Besides the contributions to theory and algorithm, another contribution of this work is proposing a novel fair clustering metric built upon information theory as well. Unlike existing evaluation metrics, our metric measures the clustering quality and fairness in a whole instead of separate manner. To verify the effectiveness of the proposed FCMI, we carry out experiments on six benchmarks including a single-cell RNA-seq atlas compared with 11 state-of-the-art methods in terms of five metrics. Code will be released after the acceptance.

Draft, Command, and Edit: Controllable Text Editing in E-Commerce

Product description generation is a challenging and under-explored task. Most such work takes a set of product attributes as inputs then generates a description from scratch in a single pass. However, this widespread paradigm might be limited when facing the dynamic wishes of users on constraining the description, such as deleting or adding the content of a user-specified attribute based on the previous version. To address this challenge, we explore a new draft-command-edit manner in description generation, leading to the proposed new task-controllable text editing in E-commerce. More specifically, we allow systems to receive a command (deleting or adding) from the user and then generate a description by flexibly modifying the content based on the previous version. It is easier and more practical to meet the new needs by modifying previous versions than generating from scratch. Furthermore, we design a data augmentation method to remedy the low resource challenge in this task, which contains a model-based and a rule-based strategy to imitate the edit by humans. To accompany this new task, we present a human-written draft-command-edit dataset called E-cEdits and a new metric "Attribute Edit". Our experimental results show that using the new data augmentation method outperforms baselines to a greater extent in both automatic and human evaluations.