The expressive power of message passing neural networks (MPNNs) is known to match the expressive power of the 1-dimensional Weisfeiler-Leman graph (1-WL) isomorphism test. To boost the expressive power of MPNNs, a number of graph neural network architectures have recently been proposed based on higher-dimensional Weisfeiler-Leman tests. In this paper we consider the two-dimensional (2-WL) test and introduce a new type of MPNNs, referred to as $\ell$-walk MPNNs, which aggregate features along walks of length $\ell$ between vertices. We show that $2$-walk MPNNs match 2-WL in expressive power. More generally, $\ell$-walk MPNNs, for any $\ell\geq 2$, are shown to match the expressive power of the recently introduced $\ell$-walk refinement procedure (W[$\ell$]). Based on a correspondence between 2-WL and W[$\ell$], we observe that $\ell$-walk MPNNs and $2$-walk MPNNs have the same expressive power, i.e., they can distinguish the same pairs of graphs, but $\ell$-walk MPNNs can possibly distinguish pairs of graphs faster than $2$-walk MPNNs. When it comes to concrete learnable graph neural network (GNN) formalisms that match 2-WL or W[$\ell$] in expressive power, we consider second-order graph neural networks that allow for non-linear layers. In particular, to match W[$\ell$] in expressive power, we allow $\ell-1$ matrix multiplications in each layer. We propose different versions of second-order GNNs depending on the type of features (i.e., coming from a countable set, or coming from an uncountable set) as this affects the number of dimensions needed to represent the features. Our results indicate that increasing non-linearity in layers by means of allowing multiple matrix multiplications does not increase expressive power. At the very best, it results in a faster distinction of input graphs.

Various existing approaches to formalize machine learning (ML) problem are discussed. The concept of Intelligent Learning (IL) as a context of ML is introduced. IL is described following traditions of Hegel's logic. A general formalization of classification as Optimal Class Separation problem is proposed. The formalization includes two criteria, direct and proximity loss, introduced here. It is demonstrated that $k$-NN, Naive Bayes, decision trees, linear SVM solve Optimal Class Separation problem.

These authors contributed equally to this work. Abstract--Legged robots can pass through complex field environments by selecting gaits and discrete footholds carefully. Traditional methods plan gait and foothold separately and treat them as the single-step optimal process. However, such processing causes its poor passability in a sparse foothold environment. This paper novelly proposes a coordinative planning method for hexapod robots that regards the planning of gait and foothold as a sequence optimization problem with the consideration of dealing with the harshness of the environment as leg fault. The Monte Carlo tree search algorithm(MCTS) is used to optimize the entire sequence. Two methods, FastMCTS, and SlidingMCTS are proposed to solve some defeats of the standard MCTS applicating in the field of legged robot planning. The proposed planning algorithm combines the fault-tolerant gait method to improve the passability of the algorithm. For rule-based method, when walking in complicated terrain, which leads them to execute motor tasks a periodic gait, assuming that all footsteps are valid, legged on fields such as field rescue and planetary exploration in robots move forward in a fixed swing sequence, which is the future. The hexapod robots that have higher stability usually taken as 3+3 tripod gait, 4+2 quadruped gait or 5+1 and superior load capacity than biped robots and quadruped wave gait for hexapod robots[7]. Because these gaits are robots are widely used[1][2][3].

The activity-based workspace (ABW) paradigm is becoming more popular in commercial office spaces. In this strategy, occupants are given a choice of spaces to do their work and personal activities on a day-to-day basis. This paper shows the implementation and testing of the Spacematch platform that was designed to improve the allocation and management of ABW. An experiment was implemented to test the ability to characterize the preferences of occupants to match them with suitable environmentally-comfortable and spatially-efficient flexible workspaces. This approach connects occupants with a catalog of available work desks using a web-based mobile application and enables them to provide real-time environmental feedback. In this work, we tested the ability for this feedback data to be merged with indoor environmental values from Internet-of-Things (IoT) sensors to optimize space and energy use by grouping occupants with similar preferences. This paper outlines a case study implementation of this platform on two office buildings. This deployment collected 1,182 responses from 25 field-based research participants over a 30-day study. From this initial data set, the results show that the ABW occupants can be segmented into specific types of users based on their accumulated preference data, and matching preferences can be derived to build a recommendation platform.

Building machine learning models from decentralized datasets located in different centers with federated learning (FL) is a promising approach to circumvent local data scarcity while preserving privacy. However, the prominent Cox proportional hazards (PH) model, used for survival analysis, does not fit the FL framework, as its loss function is non-separable with respect to the samples. The na\"ive method to bypass this non-separability consists in calculating the losses per center, and minimizing their sum as an approximation of the true loss. We show that the resulting model may suffer from important performance loss in some adverse settings. Instead, we leverage the discrete-time extension of the Cox PH model to formulate survival analysis as a classification problem with a separable loss function. Using this approach, we train survival models using standard FL techniques on synthetic data, as well as real-world datasets from The Cancer Genome Atlas (TCGA), showing similar performance to a Cox PH model trained on aggregated data. Compared to previous works, the proposed method is more communication-efficient, more generic, and more amenable to using privacy-preserving techniques.

The increased use of convolutional neural networks for face recognition in science, governance, and broader society has created an acute need for methods that can show how these 'black box' decisions are made. To be interpretable and useful to humans, such a method should convey a model's learned classification strategy in a way that is robust to random initializations or spurious correlations in input data. To this end, we applied the decompositional pixel-wise attribution method of layer-wise relevance propagation (LRP) to resolve the decisions of several classes of VGG-16 models trained for face recognition. We then quantified how these relevance measures vary with and generalize across key model parameters, such as the pretraining dataset (ImageNet or VGGFace), the finetuning task (gender or identity classification), and random initializations of model weights. Using relevance-based image masking, we find that relevance maps for face classification prove generally stable across random initializations, and can generalize across finetuning tasks. However, there is markedly less generalization across pretraining datasets, indicating that ImageNet- and VGGFace-trained models sample face information differently even as they achieve comparably high classification performance. Fine-grained analyses of relevance maps across models revealed asymmetries in generalization that point to specific benefits of choice parameters, and suggest that it may be possible to find an underlying set of important face image pixels that drive decisions across convolutional neural networks and tasks. Finally, we evaluated model decision weighting against human measures of similarity, providing a novel framework for interpreting face recognition decisions across human and machine.

Stochastic network modeling is often limited by high computational costs to generate a large number of networks enough for meaningful statistical evaluation. In this study, Deep Convolutional Generative Adversarial Networks (DCGANs) were applied to quickly reproduce drainage networks from the already generated network samples without repetitive long modeling of the stochastic network model, Gibb's model. In particular, we developed a novel connectivity-informed method that converts the drainage network images to the directional information of flow on each node of the drainage network, and then transform it into multiple binary layers where the connectivity constraints between nodes in the drainage network are stored. DCGANs trained with three different types of training samples were compared; 1) original drainage network images, 2) their corresponding directional information only, and 3) the connectivity-informed directional information. Comparison of generated images demonstrated that the novel connectivity-informed method outperformed the other two methods by training DCGANs more effectively and better reproducing accurate drainage networks due to its compact representation of the network complexity and connectivity. This work highlights that DCGANs can be applicable for high contrast images common in earth and material sciences where the network, fractures, and other high contrast features are important.

Emotion perception is essential to affective and cognitive development which involves distributed brain circuits. The ability of emotion identification begins in infancy and continues to develop throughout childhood and adolescence. Understanding the development of brain's emotion circuitry may help us explain the emotional changes observed during adolescence. Our previous study delineated the trajectory of brain functional connectivity (FC) from late childhood to early adulthood during emotion identification tasks. In this work, we endeavour to deepen our understanding from association to causation. We proposed a Bayesian incorporated linear non-Gaussian acyclic model (BiLiNGAM), which incorporated our previous association model into the prior estimation pipeline. In particular, it can jointly estimate multiple directed acyclic graphs (DAGs) for multiple age groups at different developmental stages. Simulation results indicated more stable and accurate performance over various settings, especially when the sample size was small (high-dimensional cases). We then applied to the analysis of real data from the Philadelphia Neurodevelopmental Cohort (PNC). This included 855 individuals aged 8-22 years who were divided into five different adolescent stages. Our network analysis revealed the development of emotion-related intra- and inter- modular connectivity and pinpointed several emotion-related hubs. We further categorized the hubs into two types: in-hubs and out-hubs, as the center of receiving and distributing information. Several unique developmental hub structures and group-specific patterns were also discovered. Our findings help provide a causal understanding of emotion development in the human brain.

For the more than 300 million surgeries performed worldwide every year, managing post-surgical pain is critical for successful surgical outcomes. Pain is the most prominent post-surgical concern, with an estimated 86% of surgical patients in the United States experiencing pain after surgery, with 75% of these patients reporting at least moderate to extreme pain [1]. Higher postoperative pain is associated with more postoperative complications [2], indicating the importance of pain management. Furthermore, the use of opioid analgesics is a powerful tool for managing pain but can pose risks of adverse drug events (experienced by 10% of surgical patients), leading to prolonged length of stay, high hospitalization costs, and potentially addiction [3]. Thus, regular and careful pain assessment is important for balancing between pain relief and potential side effects of powerful opioid analgesics [4]. However, one of the challenges of pain management is accurately assessing the pain level of patients. Pain is inherently subjective, and the personal experience of pain is difficult to observe and measure objectively by those not experiencing it [5] (e.g., care providers). The standard practice used in clinical care requires patients to self-report their pain intensity level using a numeric or visual scale, such as the popular Numerical Pain Rating Scale [6].

Transfer learning has emerged as a powerful technique for improving the performance of machine learning models on new domains where labeled training data may be scarce. In this approach a model trained for a source task, where plenty of labeled training data is available, is used as a starting point for training a model on a related target task with only few labeled training data. Despite recent empirical success of transfer learning approaches, the benefits and fundamental limits of transfer learning are poorly understood. In this paper we develop a statistical minimax framework to characterize the fundamental limits of transfer learning in the context of regression with linear and one-hidden layer neural network models. Specifically, we derive a lower-bound for the target generalization error achievable by any algorithm as a function of the number of labeled source and target data as well as appropriate notions of similarity between the source and target tasks. Our lower bound provides new insights into the benefits and limitations of transfer learning. We further corroborate our theoretical finding with various experiments.