Despite the success of large language models (LLMs), the task of theorem proving still remains one of the hardest reasoning tasks that is far from being fully solved. Prior methods using language models have demonstrated promising results, but they still struggle to prove even middle school level theorems. One common limitation of these methods is that they assume a fixed theorem library during the whole theorem proving process. However, as we all know, creating new useful theorems or even new theories is not only helpful but crucial and necessary for advancing mathematics and proving harder and deeper results. In this work, we present LEGO-Prover, which employs a growing skill library containing verified lemmas as skills to augment the capability of LLMs used in theorem proving. By constructing the proof modularly, LEGO-Prover enables LLMs to utilize existing skills retrieved from the library and to create new skills during the proving process. These skills are further evolved (by prompting an LLM) to enrich the library on another scale. Modular and reusable skills are constantly added to the library to enable tackling increasingly intricate mathematical problems. Moreover, the learned library further bridges the gap between human proofs and formal proofs by making it easier to impute missing steps. LEGO-Prover advances the state-of-the-art pass rate on miniF2F-valid (48.0% to 57.0%) and miniF2F-test (45.5% to 47.1%). During the proving process, LEGO-Prover also manages to generate over 20,000 skills (theorems/lemmas) and adds them to the growing library. Our ablation study indicates that these newly added skills are indeed helpful for proving theorems, resulting in an improvement from a success rate of 47.1% to 50.4%. We also release our code and all the generated skills.

Automated theorem proving (ATP) has become an appealing domain for exploring the reasoning ability of the recent successful generative language models. However, current ATP benchmarks mainly focus on symbolic inference, but rarely involve the understanding of complex number combination reasoning. In this work, we propose TRIGO, an ATP benchmark that not only requires a model to reduce a trigonometric expression with step-by-step proofs but also evaluates a generative LM's reasoning ability on formulas and its capability to manipulate, group, and factor number terms. We gather trigonometric expressions and their reduced forms from the web, annotate the simplification process manually, and translate it into the Lean formal language system. We then automatically generate additional examples from the annotated samples to expand the dataset. Furthermore, we develop an automatic generator based on Lean-Gym to create dataset splits of varying difficulties and distributions in order to thoroughly analyze the model's generalization ability. Our extensive experiments show our proposed TRIGO poses a new challenge for advanced generative LM's including GPT-4 which is pre-trained on a considerable amount of open-source formal theorem-proving language data, and provide a new tool to study the generative LM's ability on both formal and mathematical reasoning.

Existing works have made great progress in improving adversarial robustness, but typically test their method only on data from the same distribution as the training data, i.e. in-distribution (ID) testing. As a result, it is unclear how such robustness generalizes under input distribution shifts, i.e. out-of-distribution (OOD) testing. This is a concerning omission as such distribution shifts are unavoidable when methods are deployed in the wild. To address this issue we propose a benchmark named OODRobustBench to comprehensively assess OOD adversarial robustness using 23 dataset-wise shifts (i.e. naturalistic shifts in input distribution) and 6 threat-wise shifts (i.e., unforeseen adversarial threat models). OODRobustBench is used to assess 706 robust models using 60.7K adversarial evaluations. This large-scale analysis shows that: 1) adversarial robustness suffers from a severe OOD generalization issue; 2) ID robustness correlates strongly with OOD robustness, in a positive linear way, under many distribution shifts. The latter enables the prediction of OOD robustness from ID robustness. Based on this, we are able to predict the upper limit of OOD robustness for existing robust training schemes. The results suggest that achieving OOD robustness requires designing novel methods beyond the conventional ones. Last, we discover that extra data, data augmentation, advanced model architectures and particular regularization approaches can improve OOD robustness. Noticeably, the discovered training schemes, compared to the baseline, exhibit dramatically higher robustness under threat shift while keeping high ID robustness, demonstrating new promising solutions for robustness against both multi-attack and unforeseen attacks.

Federated Learning (FL) is currently one of the most popular technologies in the field of Artificial Intelligence (AI) due to its collaborative learning and ability to preserve client privacy. However, it faces challenges such as non-identically and non-independently distributed (non-IID) and data with imbalanced labels among local clients. To address these limitations, the research community has explored various approaches such as using local model parameters, federated generative adversarial learning, and federated representation learning. In our study, we propose a novel Clustered FedStack framework based on the previously published Stacked Federated Learning (FedStack) framework. The local clients send their model predictions and output layer weights to a server, which then builds a robust global model. This global model clusters the local clients based on their output layer weights using a clustering mechanism. We adopt three clustering mechanisms, namely K-Means, Agglomerative, and Gaussian Mixture Models, into the framework and evaluate their performance. We use Bayesian Information Criterion (BIC) with the maximum likelihood function to determine the number of clusters. The Clustered FedStack models outperform baseline models with clustering mechanisms. To estimate the convergence of our proposed framework, we use Cyclical learning rates.

Large AI models, or foundation models, are models recently emerging with massive scales both parameter-wise and data-wise, the magnitudes of which can reach beyond billions. Once pretrained, large AI models demonstrate impressive performance in various downstream tasks. A prime example is ChatGPT, whose capability has compelled people's imagination about the far-reaching influence that large AI models can have and their potential to transform different domains of our lives. In health informatics, the advent of large AI models has brought new paradigms for the design of methodologies. The scale of multi-modal data in the biomedical and health domain has been ever-expanding especially since the community embraced the era of deep learning, which provides the ground to develop, validate, and advance large AI models for breakthroughs in health-related areas. This article presents a comprehensive review of large AI models, from background to their applications. We identify seven key sectors in which large AI models are applicable and might have substantial influence, including 1) bioinformatics; 2) medical diagnosis; 3) medical imaging; 4) medical informatics; 5) medical education; 6) public health; and 7) medical robotics. We examine their challenges, followed by a critical discussion about potential future directions and pitfalls of large AI models in transforming the field of health informatics.

Reinforcement learning has been increasingly applied in monitoring applications because of its ability to learn from previous experiences and can make adaptive decisions. However, existing machine learning-based health monitoring applications are mostly supervised learning algorithms, trained on labels and they cannot make adaptive decisions in an uncertain complex environment. This study proposes a novel and generic system, predictive deep reinforcement learning (PDRL) with multiple RL agents in a time series forecasting environment. The proposed generic framework accommodates virtual Deep Q Network (DQN) agents to monitor predicted future states of a complex environment with a well-defined reward policy so that the agent learns existing knowledge while maximizing their rewards. In the evaluation process of the proposed framework, three DRL agents were deployed to monitor a subject's future heart rate, respiration, and temperature predicted using a BiLSTM model. With each iteration, the three agents were able to learn the associated patterns and their cumulative rewards gradually increased. It outperformed the baseline models for all three monitoring agents. The proposed PDRL framework is able to achieve state-of-the-art performance in the time series forecasting process. The proposed DRL agents and deep learning model in the PDRL framework are customized to implement the transfer learning in other forecasting applications like traffic and weather and monitor their states. The PDRL framework is able to learn the future states of the traffic and weather forecasting and the cumulative rewards are gradually increasing over each episode.

Deep neural networks are vulnerable to adversarial examples. Adversarial training (AT) is an effective defense against adversarial examples. However, AT is prone to overfitting which degrades robustness substantially. Recently, data augmentation (DA) was shown to be effective in mitigating robust overfitting if appropriately designed and optimized for AT. This work proposes a new method to automatically learn online, instance-wise, DA policies to improve robust generalization for AT. A novel policy learning objective, consisting of Vulnerability, Affinity and Diversity, is proposed and shown to be sufficiently effective and efficient to be practical for automatic DA generation during AT. This allows our method to efficiently explore a large search space for a more effective DA policy and evolve the policy as training progresses. Empirically, our method is shown to outperform or match all competitive DA methods across various model architectures (CNNs and ViTs) and datasets (CIFAR10, SVHN and Imagenette). Our DA policy reinforced vanilla AT to surpass several state-of-the-art AT methods (with baseline DA) in terms of both accuracy and robustness. It can also be combined with those advanced AT methods to produce a further boost in robustness.

Federated Learning (FL), a privacy-oriented distributed ML paradigm, is being gaining great interest in Internet of Things because of its capability to protect participants data privacy. Studies have been conducted to address challenges existing in standard FL, including communication efficiency and privacy-preserving. But they cannot achieve the goal of making a tradeoff between communication efficiency and model accuracy while guaranteeing privacy. This paper proposes a Conditional Random Sampling (CRS) method and implements it into the standard FL settings (CRS-FL) to tackle the above-mentioned challenges. CRS explores a stochastic coefficient based on Poisson sampling to achieve a higher probability of obtaining zero-gradient unbiasedly, and then decreases the communication overhead effectively without model accuracy degradation. Moreover, we dig out the relaxation Local Differential Privacy (LDP) guarantee conditions of CRS theoretically. Extensive experiment results indicate that (1) in communication efficiency, CRS-FL performs better than the existing methods in metric accuracy per transmission byte without model accuracy reduction in more than 7% sampling ratio (# sampling size / # model size); (2) in privacy-preserving, CRS-FL achieves no accuracy reduction compared with LDP baselines while holding the efficiency, even exceeding them in model accuracy under more sampling ratio conditions.

Deep neural networks can be easily fooled into making incorrect predictions through corruption of the input by adversarial perturbations: human-imperceptible artificial noise. So far adversarial training has been the most successful defense against such adversarial attacks. This work focuses on improving adversarial training to boost adversarial robustness. We first analyze, from an instance-wise perspective, how adversarial vulnerability evolves during adversarial training. We find that during training an overall reduction of adversarial loss is achieved by sacrificing a considerable proportion of training samples to be more vulnerable to adversarial attack, which results in an uneven distribution of adversarial vulnerability among data. Such "uneven vulnerability", is prevalent across several popular robust training methods and, more importantly, relates to overfitting in adversarial training. Motivated by this observation, we propose a new adversarial training method: Instance-adaptive Smoothness Enhanced Adversarial Training (ISEAT). It jointly smooths both input and weight loss landscapes in an adaptive, instance-specific, way to enhance robustness more for those samples with higher adversarial vulnerability. Extensive experiments demonstrate the superiority of our method over existing defense methods. Noticeably, our method, when combined with the latest data augmentation and semi-supervised learning techniques, achieves state-of-the-art robustness against $\ell_{\infty}$-norm constrained attacks on CIFAR10 of 59.32% for Wide ResNet34-10 without extra data, and 61.55% for Wide ResNet28-10 with extra data. Code is available at https://github.com/TreeLLi/Instance-adaptive-Smoothness-Enhanced-AT.

Place recognition is a challenging yet crucial task in robotics. Existing 3D LiDAR place recognition methods suffer from limited feature representation capability and long search times. To address these challenges, we propose a novel coarse-to-fine framework for 3D LiDAR place recognition that combines Birds' Eye View (BEV) feature extraction, coarse-grained matching, and fine-grained verification. In the coarse stage, our framework leverages the rich contextual information contained in BEV features to produce global descriptors. Then the top-\textit{K} most similar candidates are identified via descriptor matching, which is fast but coarse-grained. In the fine stage, our overlap estimation network reuses the corresponding BEV features to predict the overlap region, enabling meticulous and precise matching. Experimental results on the KITTI odometry benchmark demonstrate that our framework achieves leading performance compared to state-of-the-art methods. Our code is available at: \url{https://github.com/fcchit/OverlapNetVLAD}.