Stochastic compositional minimax problems are prevalent in machine learning, yet there are only limited established on the convergence of this class of problems. In this paper, we propose a formal definition of the stochastic compositional minimax problem, which involves optimizing a minimax loss with a compositional structure either in primal , dual, or both primal and dual variables. We introduce a simple yet effective algorithm, stochastically Corrected stOchastic gradient Descent Ascent (CODA), which is a descent ascent type algorithm with compositional correction steps, and establish its convergence rate in aforementioned three settings. In the presence of the compositional structure in primal, the objective function typically becomes nonconvex in primal due to function composition. Thus, we consider the nonconvex-strongly-concave and nonconvex-concave settings and show that CODA can efficiently converge to a stationary point. In the case of composition on the dual, the objective function becomes nonconcave in the dual variable, and we demonstrate convergence in the strongly-convex-nonconcave and convex-nonconcave setting. In the case of composition on both variables, the primal and dual variables may lose convexity and concavity, respectively. Therefore, we anaylze the convergence in weakly-convex-weakly-concave setting. We also give a variance reduction version algorithm, CODA+, which achieves the best known rate on nonconvex-strongly-concave and nonconvex-concave compositional minimax problem. This work initiates the theoretical study of the stochastic compositional minimax problem on various settings and may inform modern machine learning scenarios such as domain adaptation or robust model-agnostic meta-learning.

Molecular Property Prediction (MPP) plays a pivotal role across diverse domains, spanning drug discovery, material science, and environmental chemistry. Fueled by the exponential growth of chemical data and the evolution of artificial intelligence, recent years have witnessed remarkable strides in MPP. However, the multifaceted nature of molecular data, such as molecular structures, SMILES notation, and molecular images, continues to pose a fundamental challenge in its effective representation. To address this, representation learning techniques are instrumental as they acquire informative and interpretable representations of molecular data. This article explores recent AI/-based approaches in MPP, focusing on both single and multiple modality representation techniques. It provides an overview of various molecule representations and encoding schemes, categorizes MPP methods by their use of modalities, and outlines datasets and tools available for feature generation. The article also analyzes the performance of recent methods and suggests future research directions to advance the field of MPP.

Despite the considerable advancements achieved by deep neural networks, their performance tends to degenerate when the test environment diverges from the training ones. Domain generalization (DG) solves this issue by learning representations independent of domain-related information, thus facilitating extrapolation to unseen environments. Existing approaches typically focus on formulating tailored training objectives to extract shared features from the source data. However, the disjointed training and testing procedures may compromise robustness, particularly in the face of unforeseen variations during deployment. In this paper, we propose a novel and holistic framework based on causality, named InPer, designed to enhance model generalization by incorporating causal intervention during training and causal perturbation during testing. Specifically, during the training phase, we employ entropy-based causal intervention (EnIn) to refine the selection of causal variables. To identify samples with anti-interference causal variables from the target domain, we propose a novel metric, homeostatic score, through causal perturbation (HoPer) to construct a prototype classifier in test time. Experimental results across multiple cross-domain tasks confirm the efficacy of InPer.

Despite the growing prevalence of artificial neural networks in real-world applications, their vulnerability to adversarial attacks remains a significant concern, which motivates us to investigate the robustness of machine learning models. While various heuristics aim to optimize the distributionally robust risk using the $\infty$-Wasserstein metric, such a notion of robustness frequently encounters computation intractability. To tackle the computational challenge, we develop a novel approach to adversarial training that integrates $\phi$-divergence regularization into the distributionally robust risk function. This regularization brings a notable improvement in computation compared with the original formulation. We develop stochastic gradient methods with biased oracles to solve this problem efficiently, achieving the near-optimal sample complexity. Moreover, we establish its regularization effects and demonstrate it is asymptotic equivalence to a regularized empirical risk minimization framework, by considering various scaling regimes of the regularization parameter and robustness level. These regimes yield gradient norm regularization, variance regularization, or a smoothed gradient norm regularization that interpolates between these extremes. We numerically validate our proposed method in supervised learning, reinforcement learning, and contextual learning and showcase its state-of-the-art performance against various adversarial attacks.

Predictive coding (PC) is an energy-based learning algorithm that performs iterative inference over network activities before weight updates. Recent work suggests that PC can converge in fewer learning steps than backpropagation thanks to its inference procedure. However, these advantages are not always observed, and the impact of PC inference on learning is theoretically not well understood. Here, we study the geometry of the PC energy landscape at the (inference) equilibrium of the network activities. For deep linear networks, we first show that the equilibrated energy is simply a rescaled mean squared error loss with a weight-dependent rescaling. We then prove that many highly degenerate (non-strict) saddles of the loss including the origin become much easier to escape (strict) in the equilibrated energy. Our theory is validated by experiments on both linear and non-linear networks. Based on these results, we conjecture that all the saddles of the equilibrated energy are strict. Overall, this work suggests that PC inference makes the loss landscape more benign and robust to vanishing gradients, while also highlighting the challenge of speeding up PC inference on large-scale models.

Accurately measuring protein-RNA binding affinity is crucial in many biological processes and drug design. Previous computational methods for protein-RNA binding affinity prediction rely on either sequence or structure features, unable to capture the binding mechanisms comprehensively. The recent emerging pre-trained language models trained on massive unsupervised sequences of protein and RNA have shown strong representation ability for various in-domain downstream tasks, including binding site prediction. However, applying different-domain language models collaboratively for complex-level tasks remains unexplored. In this paper, we propose CoPRA to bridge pre-trained language models from different biological domains via Complex structure for Protein-RNA binding Affinity prediction. We demonstrate for the first time that cross-biological modal language models can collaborate to improve binding affinity prediction. We propose a Co-Former to combine the cross-modal sequence and structure information and a bi-scope pre-training strategy for improving Co-Former's interaction understanding. Meanwhile, we build the largest protein-RNA binding affinity dataset PRA310 for performance evaluation. We also test our model on a public dataset for mutation effect prediction. CoPRA reaches state-of-the-art performance on all the datasets. We provide extensive analyses and verify that CoPRA can (1) accurately predict the protein-RNA binding affinity; (2) understand the binding affinity change caused by mutations; and (3) benefit from scaling data and model size.

In scattered data approximation, the span of a finite number of translates of a chosen radial basis function is used as approximation space and the basis of translates is used for representing the approximate. However, this natural choice is by no means mandatory and different choices, like, for example, the Lagrange basis, are possible and might offer additional features. In this article, we discuss different alternatives together with their canonical duals. We study a localized version of the Lagrange basis, localized orthogonal bases, such as the Newton basis, and multiresolution versions thereof, constructed by means of samplets. We argue that the choice of orthogonal bases is particularly useful as they lead to symmetric preconditioners. All bases under consideration are compared numerically to illustrate their feasibility for scattered data approximation. We provide benchmark experiments in two spatial dimensions and consider the reconstruction of an implicit surface as a relevant application from computer graphics.

Recent advances in unsupervised deep graph clustering have been significantly promoted by contrastive learning. Despite the strides, most graph contrastive learning models face challenges: 1) graph augmentation is used to improve learning diversity, but commonly used random augmentation methods may destroy inherent semantics and cause noise; 2) the fixed positive and negative sample selection strategy is limited to deal with complex real data, thereby impeding the model's capability to capture fine-grained patterns and relationships. To reduce these problems, we propose the Clustering-guided Curriculum Graph contrastive Learning (CCGL) framework. CCGL uses clustering entropy as the guidance of the following graph augmentation and contrastive learning. Specifically, according to the clustering entropy, the intra-class edges and important features are emphasized in augmentation. Then, a multi-task curriculum learning scheme is proposed, which employs the clustering guidance to shift the focus from the discrimination task to the clustering task. In this way, the sample selection strategy of contrastive learning can be adjusted adaptively from early to late stage, which enhances the model's flexibility for complex data structure. Experimental results demonstrate that CCGL has achieved excellent performance compared to state-of-the-art competitors.

Rule-based neural networks stand out for enabling interpretable classification by learning logical rules for both prediction and interpretation. However, existing models often lack flexibility due to the fixed model structure. Addressing this, we introduce the Normal Form Rule Learner (NFRL) algorithm, leveraging a selective discrete neural network, that treat weight parameters as hard selectors, to learn rules in both Conjunctive Normal Form (CNF) and Disjunctive Normal Form (DNF) for enhanced accuracy and interpretability. Instead of adopting a deep, complex structure, the NFRL incorporates two specialized Normal Form Layers (NFLs) with adaptable AND/OR neurons, a Negation Layer for input negations, and a Normal Form Constraint (NFC) to streamline neuron connections. We also show the novel network architecture can be optimized using adaptive gradient update together with Straight-Through Estimator to overcome the gradient vanishing challenge. Through extensive experiments on 11 datasets, NFRL demonstrates superior classification performance, quality of learned rules, efficiency and interpretability compared to 12 state-of-the-art alternatives. Code and data are available at \url{https://anonymous.4open.science/r/NFRL-27B4/}.

The availability of temporal geospatial data in multiple modalities has been extensively leveraged to enhance the performance of machine learning models. While efforts on the design of adequate model architectures are approaching a level of saturation, focusing on a data-centric perspective can complement these efforts to achieve further enhancements in data usage efficiency and model generalization capacities. This work contributes to this direction. We leverage model explanation methods to identify the features crucial for the model to reach optimal performance and the smallest set of features sufficient to achieve this performance. We evaluate our approach on three temporal multimodal geospatial datasets and compare multiple model explanation techniques. Our results reveal that some datasets can reach their optimal accuracy with less than 20% of the temporal instances, while in other datasets, the time series of a single band from a single modality is sufficient.