Graph neural networks (GNNs) have been shown to be highly sensitive to the choice of aggregation function. While summing over a node's neighbours can approximate any permutation-invariant function over discrete inputs, Cohen-Karlik et al. [2020] proved there are set-aggregation problems for which summing cannot generalise to unbounded inputs, proposing recurrent neural networks regularised towards permutation-invariance as a more expressive aggregator. We show that these results carry over to the graph domain: GNNs equipped with recurrent aggregators are competitive with state-of-the-art permutation-invariant aggregators, on both synthetic benchmarks and real-world problems. However, despite the benefits of recurrent aggregators, their $O(V)$ depth makes them both difficult to parallelise and harder to train on large graphs. Inspired by the observation that a well-behaved aggregator for a GNN is a commutative monoid over its latent space, we propose a framework for constructing learnable, commutative, associative binary operators. And with this, we construct an aggregator of $O(\log V)$ depth, yielding exponential improvements for both parallelism and dependency length while achieving performance competitive with recurrent aggregators. Based on our empirical observations, our proposed learnable commutative monoid (LCM) aggregator represents a favourable tradeoff between efficient and expressive aggregators.

Current language models are considered to have sub-human capabilities at natural language tasks like question-answering or writing code. However, language models are not trained to perform well at these tasks, they are trained to accurately predict the next token given previous tokes in tokenized text. It is not clear whether language models are better or worse than humans at next token prediction. To try to answer this question, we performed two distinct experiments to directly compare humans and language models on this front: one measuring top-1 accuracy and the other measuring perplexity. In both experiments, we find humans to be consistently \emph{worse} than even relatively small language models like GPT3-Ada at next-token prediction.

This paper introduces the use of evolutionary algorithms for solving differential equations. The solution is obtained by optimizing a deep neural network whose loss function is defined by the residual terms from the differential equations. Recent studies have used stochastic gradient descent (SGD) variants to train these physics-informed neural networks (PINNs), but these methods can struggle to find accurate solutions due to optimization challenges. When solving differential equations, it is important to find the globally optimum parameters of the network, rather than just finding a solution that works well during training. SGD only searches along a single gradient direction, so it may not be the best approach for training PINNs with their accompanying complex optimization landscapes. In contrast, evolutionary algorithms perform a parallel exploration of different solutions in order to avoid getting stuck in local optima and can potentially find more accurate solutions. However, evolutionary algorithms can be slow, which can make them difficult to use in practice. To address this, we provide a set of five benchmark problems with associated performance metrics and baseline results to support the development of evolutionary algorithms for enhanced PINN training. As a baseline, we evaluate the performance and speed of using the widely adopted Covariance Matrix Adaptation Evolution Strategy (CMA-ES) for solving PINNs. We provide the loss and training time for CMA-ES run on TensorFlow, and CMA-ES and SGD run on JAX (with GPU acceleration) for the five benchmark problems. Our results show that JAX-accelerated evolutionary algorithms, particularly CMA-ES, can be a useful approach for solving differential equations. We hope that our work will support the exploration and development of alternative optimization algorithms for the complex task of optimizing PINNs.

Purpose: The aim of this study was to demonstrate the utility of unsupervised domain adaptation (UDA) in automated knee osteoarthritis (OA) phenotype classification using a small dataset (n=50). Materials and Methods: For this retrospective study, we collected 3,166 three-dimensional (3D) double-echo steady-state magnetic resonance (MR) images from the Osteoarthritis Initiative dataset and 50 3D turbo/fast spin-echo MR images from our institute (in 2020 and 2021) as the source and target datasets, respectively. For each patient, the degree of knee OA was initially graded according to the MRI Osteoarthritis Knee Score (MOAKS) before being converted to binary OA phenotype labels. The proposed UDA pipeline included (a) pre-processing, which involved automatic segmentation and region-of-interest cropping; (b) source classifier training, which involved pre-training phenotype classifiers on the source dataset; (c) target encoder adaptation, which involved unsupervised adaption of the source encoder to the target encoder and (d) target classifier validation, which involved statistical analysis of the target classification performance evaluated by the area under the receiver operating characteristic curve (AUROC), sensitivity, specificity and accuracy. Additionally, a classifier was trained without UDA for comparison. Results: The target classifier trained with UDA achieved improved AUROC, sensitivity, specificity and accuracy for both knee OA phenotypes compared with the classifier trained without UDA. Conclusion: The proposed UDA approach improves the performance of automated knee OA phenotype classification for small target datasets by utilising a large, high-quality source dataset for training. The results successfully demonstrated the advantages of the UDA approach in classification on small datasets.

Generalized Labeled Multi-Bernoulli (GLMB) densities arise in a host of multi-object system applications analogous to Gaussians in single-object filtering. However, computing the GLMB filtering density requires solving NP-hard problems. To alleviate this computational bottleneck, we develop a linear complexity Gibbs sampling framework for GLMB density computation. Specifically, we propose a tempered Gibbs sampler that exploits the structure of the GLMB filtering density to achieve an $\mathcal{O}(T(P+M))$ complexity, where $T$ is the number of iterations of the algorithm, $P$ and $M$ are the number hypothesized objects and measurements. This innovation enables an $\mathcal{O}(T(P+M+\log(T))+PM)$ complexity implementation of the GLMB filter. Convergence of the proposed Gibbs sampler is established and numerical studies are presented to validate the proposed GLMB filter implementation.

Principal Component Analysis (PCA) and its exponential family extensions have three components: observations, latents and parameters of a linear transformation. We consider a generalised setting where the canonical parameters of the exponential family are a nonlinear transformation of the latents. We show explicit relationships between particular neural network architectures and the corresponding statistical models. We find that deep equilibrium models -- a recently introduced class of implicit neural networks -- solve maximum a-posteriori (MAP) estimates for the latents and parameters of the transformation. Our analysis provides a systematic way to relate activation functions, dropout, and layer structure, to statistical assumptions about the observations, thus providing foundational principles for unsupervised DEQs. For hierarchical latents, individual neurons can be interpreted as nodes in a deep graphical model. Our DEQ feature maps are end-to-end differentiable, enabling fine-tuning for downstream tasks.

National Health and Nutritional Status Survey (NHANSS) is conducted annually by the Ministry of Health in Negara Brunei Darussalam to assess the population health and nutritional patterns and characteristics. The main aim of this study was to discover meaningful patterns (groups) from the obese sample of NHANSS data by applying data reduction and interpretation techniques. The mixed nature of the variables (qualitative and quantitative) in the data set added novelty to the study. Accordingly, the Categorical Principal Component (CATPCA) technique was chosen to interpret the meaningful results. The relationships between obesity and the lifestyle factors like demography, socioeconomic status, physical activity, dietary behavior, history of blood pressure, diabetes, etc., were determined based on the principal components generated by CATPCA. The results were validated with the help of the split method technique to counter verify the authenticity of the generated groups. Based on the analysis and results, two subgroups were found in the data set, and the salient features of these subgroups have been reported. These results can be proposed for the betterment of the healthcare industry.

联合学习（FL）是以分散的方式共同训练机器学习算法的范式。 FL中的大多数研究都集中在基于神经网络的方法上，但是，由于克服算法的迭代和添加性特征的挑战，在联合学习中基于XGBoost的方法（例如XGBOOST）在联合学习中没有得到反应。基于决策树的模型，尤其是XGBoost，可以处理非IID数据，这对于联合学习框架中使用的算法很重要，因为数据的基本特征是分散的，并且具有本质上非IID的风险。在本文中，我们专注于研究通过对各种基于样本量的数据偏斜方案进行实验以及这些模型在各种非IID方案下的性能，通过非IID分布的影响如何受到非IID分布的影响。我们在多个不同的数据集中进行了一组广泛的实验，并进行了不同的数据偏斜分区。我们的实验结果表明，尽管有各种分区比率，但模型的性能保持一致，并且与以集中式方式训练的模型接近或同样良好。

随着在充满挑战的环境中越来越需要多机器人探索未知区域的需求，需要有效的协作探索策略来实现此类壮举。可以部署基于边界的快速探索随机树（RRT）探索来探索未知的环境。然而，它的贪婪行为导致多个机器人探索收入最高的地区，从而导致勘探过程中大规模重叠。为了解决这个问题，我们提出了基于时间内存的RRT（TM-RRT）探索策略，用于多机器人在未知环境中执行强大的探索。它根据每个机器人的相对位置计算分配的每个边界的自适应持续时间，并计算边界的收入。此外，每个机器人都配备了由分配的边界和舰队共享的内存，以防止重复对同一边界的分配。通过模拟和实际部署，我们通过在25.0m x 540m（1350.0m2）区域完成勘探，展示了TM-RRT勘探策略的鲁棒性，而常规的RRT勘探策略则不足。

陆地植物的多样性在维持稳定，健康和生产的生态系统方面起着关键作用。尽管遥感被认为是估计植物多样性的有前途且具有成本效益的代理，但缺乏关于如何从Spaceborne Hyperfectral数据中推断出植物多样性的定量研究。在这项研究中，我们评估了通过DLR接地传感成像光谱仪（DESIS）捕获的高光谱数据的能力，以估计澳大利亚东南部南部梯田和雪山地区的植物物种丰富度。首先通过主成分分析，规范相关分析和部分最小二乘分析从Desis光谱中提取光谱特征。然后在提取的特征和植物物种丰富度之间进行了回归，并具有普通的最小二乘回归，内核脊回归和高斯工艺回归。根据两倍的交叉验证方案，使用相关系数（$ r $）和根平方错误（RMSE）评估结果。凭借最佳性能的模型，$ r $为0.71，而南部塔林群岛地区的RMSE为5.99，而$ R $为0.62，而雪山地区的RMSE为6.20。这项研究中报道的评估结果为未来的研究提供了支持，了解太空传播高光谱测量与陆地植物生物多样性之间的关系。