A common pipeline in functional data analysis is to first convert the discretely observed data to smooth functions, and then represent the functions by a finite-dimensional vector of coefficients summarizing the information. Existing methods for data smoothing and dimensional reduction mainly focus on learning the linear mappings from the data space to the representation space, however, learning only the linear representations may not be sufficient. In this study, we propose to learn the nonlinear representations of functional data using neural network autoencoders designed to process data in the form it is usually collected without the need of preprocessing. We design the encoder to employ a projection layer computing the weighted inner product of the functional data and functional weights over the observed timestamp, and the decoder to apply a recovery layer that maps the finite-dimensional vector extracted from the functional data back to functional space using a set of predetermined basis functions. The developed architecture can accommodate both regularly and irregularly spaced data. Our experiments demonstrate that the proposed method outperforms functional principal component analysis in terms of prediction and classification, and maintains superior smoothing ability and better computational efficiency in comparison to the conventional autoencoders under both linear and nonlinear settings.

Uncertainty quantification for estimation through stochastic optimization solutions in an online setting has gained popularity recently. This paper introduces a novel inference method focused on constructing confidence intervals with efficient computation and fast convergence to the nominal level. Specifically, we propose to use a small number of independent multi-runs to acquire distribution information and construct a t-based confidence interval. Our method requires minimal additional computation and memory beyond the standard updating of estimates, making the inference process almost cost-free. We provide a rigorous theoretical guarantee for the confidence interval, demonstrating that the coverage is approximately exact with an explicit convergence rate and allowing for high confidence level inference. In particular, a new Gaussian approximation result is developed for the online estimators to characterize the coverage properties of our confidence intervals in terms of relative errors. Additionally, our method also allows for leveraging parallel computing to further accelerate calculations using multiple cores. It is easy to implement and can be integrated with existing stochastic algorithms without the need for complicated modifications.

Two-timescale stochastic approximation (TTSA) is among the most general frameworks for iterative stochastic algorithms. This includes well-known stochastic optimization methods such as SGD variants and those designed for bilevel or minimax problems, as well as reinforcement learning like the family of gradient-based temporal difference (GTD) algorithms. In this paper, we conduct an in-depth asymptotic analysis of TTSA under controlled Markovian noise via central limit theorem (CLT), uncovering the coupled dynamics of TTSA influenced by the underlying Markov chain, which has not been addressed by previous CLT results of TTSA only with Martingale difference noise. Building upon our CLT, we expand its application horizon of efficient sampling strategies from vanilla SGD to a wider TTSA context in distributed learning, thus broadening the scope of Hu et al. (2022). In addition, we leverage our CLT result to deduce the statistical properties of GTD algorithms with nonlinear function approximation using Markovian samples and show their identical asymptotic performance, a perspective not evident from current finite-time bounds.

Elliptic partial differential equations (PDEs) are a major class of time-independent PDEs that play a key role in many scientific and engineering domains such as fluid dynamics, plasma physics, and solid mechanics. Recently, neural operators have emerged as a promising technique to solve elliptic PDEs more efficiently by directly mapping the input to solutions. However, existing networks typically cannot handle complex geometries and inhomogeneous boundary values present in the real world. Here we introduce Boundary-Embedded Neural Operators (BENO), a novel neural operator architecture that embeds the complex geometries and inhomogeneous boundary values into the solving of elliptic PDEs. Inspired by classical Green's function, BENO consists of two branches of Graph Neural Networks (GNNs) for interior source term and boundary values, respectively. Furthermore, a Transformer encoder maps the global boundary geometry into a latent vector which influences each message passing layer of the GNNs. We test our model extensively in elliptic PDEs with various boundary conditions. We show that all existing baseline methods fail to learn the solution operator. In contrast, our model, endowed with boundary-embedded architecture, outperforms state-of-the-art neural operators and strong baselines by an average of 60.96\%. Our source code can be found https://github.com/AI4Science-WestlakeU/beno.git.

The growing prevalence and rapid evolution of offensive language in social media amplify the complexities of detection, particularly highlighting the challenges in identifying such content across diverse languages. This survey presents a systematic and comprehensive exploration of Cross-Lingual Transfer Learning (CLTL) techniques in offensive language detection in social media. Our study stands as the first holistic overview to focus exclusively on the cross-lingual scenario in this domain. We analyse 67 relevant papers and categorise these studies across various dimensions, including the characteristics of multilingual datasets used, the cross-lingual resources employed, and the specific CLTL strategies implemented. According to "what to transfer", we also summarise three main CLTL transfer approaches: instance, feature, and parameter transfer. Additionally, we shed light on the current challenges and future research opportunities in this field. Furthermore, we have made our survey resources available online, including two comprehensive tables that provide accessible references to the multilingual datasets and CLTL methods used in the reviewed literature.

Robot learning tasks are extremely compute-intensive and hardware-specific. Thus the avenues of tackling these challenges, using a diverse dataset of offline demonstrations that can be used to train robot manipulation agents, is very appealing. The Train-Offline-Test-Online (TOTO) Benchmark provides a well-curated open-source dataset for offline training comprised mostly of expert data and also benchmark scores of the common offline-RL and behaviour cloning agents. In this paper, we introduce DiffClone, an offline algorithm of enhanced behaviour cloning agent with diffusion-based policy learning, and measured the efficacy of our method on real online physical robots at test time. This is also our official submission to the Train-Offline-Test-Online (TOTO) Benchmark Challenge organized at NeurIPS 2023. We experimented with both pre-trained visual representation and agent policies. In our experiments, we find that MOCO finetuned ResNet50 performs the best in comparison to other finetuned representations. Goal state conditioning and mapping to transitions resulted in a minute increase in the success rate and mean-reward. As for the agent policy, we developed DiffClone, a behaviour cloning agent improved using conditional diffusion.

Antibody-drug conjugate (ADC) has revolutionized the field of cancer treatment in the era of precision medicine due to their ability to precisely target cancer cells and release highly effective drug. Nevertheless, the realization of rational design of ADC is very difficult because the relationship between their structures and activities is difficult to understand. In the present study, we introduce a unified deep learning framework called ADCNet to help design potential ADCs. The ADCNet highly integrates the protein representation learning language model ESM-2 and small-molecule representation learning language model FG-BERT models to achieve activity prediction through learning meaningful features from antigen and antibody protein sequences of ADC, SMILES strings of linker and payload, and drug-antibody ratio (DAR) value. Based on a carefully designed and manually tailored ADC data set, extensive evaluation results reveal that ADCNet performs best on the test set compared to baseline machine learning models across all evaluation metrics. For example, it achieves an average prediction accuracy of 87.12%, a balanced accuracy of 0.8689, and an area under receiver operating characteristic curve of 0.9293 on the test set. In addition, cross-validation, ablation experiments, and external independent testing results further prove the stability, advancement, and robustness of the ADCNet architecture. For the convenience of the community, we develop the first online platform (https://ADCNet.idruglab.cn) for the prediction of ADCs activity based on the optimal ADCNet model, and the source code is publicly available at https://github.com/idrugLab/ADCNet.

Local stochastic gradient descent (Local-SGD), also referred to as federated averaging, is an approach to distributed optimization where each device performs more than one SGD update per communication. This work presents an empirical study of {\it asynchronous} Local-SGD for training language models; that is, each worker updates the global parameters as soon as it has finished its SGD steps. We conduct a comprehensive investigation by examining how worker hardware heterogeneity, model size, number of workers, and optimizer could impact the learning performance. We find that with naive implementations, asynchronous Local-SGD takes more iterations to converge than its synchronous counterpart despite updating the (global) model parameters more frequently. We identify momentum acceleration on the global parameters when worker gradients are stale as a key challenge. We propose a novel method that utilizes a delayed Nesterov momentum update and adjusts the workers' local training steps based on their computation speed. This approach, evaluated with models up to 150M parameters on the C4 dataset, matches the performance of synchronous Local-SGD in terms of perplexity per update step, and significantly surpasses it in terms of wall clock time.

Accurate and robust localization and mapping are essential components for most autonomous robots. In this paper, we propose a SLAM system for building globally consistent maps, called PIN-SLAM, that is based on an elastic and compact point-based implicit neural map representation. Taking range measurements as input, our approach alternates between incremental learning of the local implicit signed distance field and the pose estimation given the current local map using a correspondence-free, point-to-implicit model registration. Our implicit map is based on sparse optimizable neural points, which are inherently elastic and deformable with the global pose adjustment when closing a loop. Loops are also detected using the neural point features. Extensive experiments validate that PIN-SLAM is robust to various environments and versatile to different range sensors such as LiDAR and RGB-D cameras. PIN-SLAM achieves pose estimation accuracy better or on par with the state-of-the-art LiDAR odometry or SLAM systems and outperforms the recent neural implicit SLAM approaches while maintaining a more consistent, and highly compact implicit map that can be reconstructed as accurate and complete meshes. Finally, thanks to the voxel hashing for efficient neural points indexing and the fast implicit map-based registration without closest point association, PIN-SLAM can run at the sensor frame rate on a moderate GPU. Codes will be available at: https://github.com/PRBonn/PIN_SLAM.

Knowledge graph (KG) based reasoning has been regarded as an effective means for the analysis of semantic networks and is of great usefulness in areas of information retrieval, recommendation, decision-making, and man-machine interaction. It is widely used in recommendation, decision-making, question-answering, search, and other fields. However, previous studies mainly used low-level knowledge in the KG for reasoning, which may result in insufficient generalization and poor robustness of reasoning. To this end, this paper proposes a new inference approach using a novel knowledge augmentation strategy to improve the generalization capability of KG. This framework extracts high-level pyramidal knowledge from low-level knowledge and applies it to reasoning in a multi-level hierarchical KG, called knowledge pyramid in this paper. We tested some medical data sets using the proposed approach, and the experimental results show that the proposed knowledge pyramid has improved the knowledge inference performance with better generalization. Especially, when there are fewer training samples, the inference accuracy can be significantly improved.