This article investigates the effect of explicitly adding auxiliary algebraic trajectory information to neural networks for dynamical systems. We draw inspiration from the field of differential-algebraic equations and differential equations on manifolds and implement related methods in residual neural networks, despite some fundamental scenario differences. Constraint or auxiliary information effects are incorporated through stabilization as well as projection methods, and we show when to use which method based on experiments involving simulations of multi-body pendulums and molecular dynamics scenarios. Several of our methods are easy to implement in existing code and have limited impact on training performance while giving significant boosts in terms of inference.
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神經網絡（Neural Networks）是世界上三個最古老的神經建模學會的檔案期刊:國際神經網絡學會(INNS)、歐洲神經網絡學會(ENNS)和日本神經網絡學會(JNNS)。神經網絡提供了一個論壇，以發展和培育一個國際社會的學者和實踐者感興趣的所有方面的神經網絡和相關方法的計算智能。神經網絡歡迎高質量論文的提交，有助于全面的神經網絡研究，從行為和大腦建模，學習算法，通過數學和計算分析，系統的工程和技術應用，大量使用神經網絡的概念和技術。這一獨特而廣泛的范圍促進了生物和技術研究之間的思想交流，并有助于促進對生物啟發的計算智能感興趣的跨學科社區的發展。因此，神經網絡編委會代表的專家領域包括心理學，神經生物學，計算機科學，工程，數學，物理。該雜志發表文章、信件和評論以及給編輯的信件、社論、時事、軟件調查和專利信息。文章發表在五個部分之一:認知科學，神經科學，學習系統，數學和計算分析、工程和應用。
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Recent advances unveiled physical neural networks as promising machine learning platforms, offering faster and more energy-efficient information processing. Compared with extensively-studied optical neural networks, the development of mechanical neural networks (MNNs) remains nascent and faces significant challenges, including heavy computational demands and learning with approximate gradients. Here, we introduce the mechanical analogue of in situ backpropagation to enable highly efficient training of MNNs. We demonstrate that the exact gradient can be obtained locally in MNNs, enabling learning through their immediate vicinity. With the gradient information, we showcase the successful training of MNNs for behavior learning and machine learning tasks, achieving high accuracy in regression and classification. Furthermore, we present the retrainability of MNNs involving task-switching and damage, demonstrating the resilience. Our findings, which integrate the theory for training MNNs and experimental and numerical validations, pave the way for mechanical machine learning hardware and autonomous self-learning material systems.
Capsule networks are a type of neural network that identify image parts and form the instantiation parameters of a whole hierarchically. The goal behind the network is to perform an inverse computer graphics task, and the network parameters are the mapping weights that transform parts into a whole. The trainability of capsule networks in complex data with high intra-class or intra-part variation is challenging. This paper presents a multi-prototype architecture for guiding capsule networks to represent the variations in the image parts. To this end, instead of considering a single capsule for each class and part, the proposed method employs several capsules (co-group capsules), capturing multiple prototypes of an object. In the final layer, co-group capsules compete, and their soft output is considered the target for a competitive cross-entropy loss. Moreover, in the middle layers, the most active capsules map to the next layer with a shared weight among the co-groups. Consequently, due to the reduction in parameters, implicit weight-sharing makes it possible to have more deep capsule network layers. The experimental results on MNIST, SVHN, C-Cube, CEDAR, MCYT, and UTSig datasets reveal that the proposed model outperforms others regarding image classification accuracy.
In response to the critical need for effective reconnaissance in disaster scenarios, this research article presents the design and implementation of a complete autonomous robot system using the Turtlebot3 with Robotic Operating System (ROS) Noetic. Upon deployment in closed, initially unknown environments, the system aims to generate a comprehensive map and identify any present 'victims' using AprilTags as stand-ins. We discuss our solution for search and rescue missions, while additionally exploring more advanced algorithms to improve search and rescue functionalities. We introduce a Cubature Kalman Filter to help reduce the mean squared error [m] for AprilTag localization and an information-theoretic exploration algorithm to expedite exploration in unknown environments. Just like turtles, our system takes it slow and steady, but when it's time to save the day, it moves at ninja-like speed! Despite Donatello's shell, he's no slowpoke - he zips through obstacles with the agility of a teenage mutant ninja turtle. So, hang on tight to your shells and get ready for a whirlwind of reconnaissance! Full pipeline code //github.com/rzhao5659/MRProject/tree/main Exploration code //github.com/rzhao5659/MRProject/tree/main
The escalating prevalence of diabetes globally underscores the need for diabetes management. Recent research highlights the growing focus on digital biomarkers in diabetes management, with innovations in computational frameworks and noninvasive monitoring techniques using personalized glucose metrics. However, they predominantly focus on insulin dosing and specific glucose values, or with limited attention given to overall glycemic control. This leaves a gap in expanding the scope of digital biomarkers for overall glycemic control in diabetes management. To address such a research gap, we propose GluMarker -- an end-to-end framework for modeling digital biomarkers using broader factors sources to predict glycemic control. Through the assessment and refinement of various machine learning baselines, GluMarker achieves state-of-the-art on Anderson's dataset in predicting next-day glycemic control. Moreover, our research identifies key digital biomarkers for the next day's glycemic control prediction. These identified biomarkers are instrumental in illuminating the daily factors that influence glycemic management, offering vital insights for diabetes care.
This paper introduces an adaptive convolutional neural network (CNN) architecture capable of automating various topology optimization (TO) problems with diverse underlying physics. The proposed architecture has an encoder-decoder-type structure with dense layers added at the bottleneck region to capture complex geometrical features. The network is trained using datasets obtained by the problem-specific open-source TO codes. Tensorflow and Keras are the main libraries employed to develop and to train the model. Effectiveness and robustness of the proposed adaptive CNN model are demonstrated through its performance in compliance minimization problems involving constant and design-dependent loads and in addressing bulk modulus optimization. Once trained, the model takes user's input of the volume fraction as an image and instantly generates an output image of optimized design. The proposed CNN produces high-quality results resembling those obtained via open-source TO codes with negligible performance and volume fraction errors. The paper includes complete associated Python code (Appendix A) for the proposed CNN architecture and explains each part of the code to facilitate reproducibility and ease of learning.
Gradient-based learning in multi-layer neural networks displays a number of striking features. In particular, the decrease rate of empirical risk is non-monotone even after averaging over large batches. Long plateaus in which one observes barely any progress alternate with intervals of rapid decrease. These successive phases of learning often take place on very different time scales. Finally, models learnt in an early phase are typically `simpler' or `easier to learn' although in a way that is difficult to formalize. Although theoretical explanations of these phenomena have been put forward, each of them captures at best certain specific regimes. In this paper, we study the gradient flow dynamics of a wide two-layer neural network in high-dimension, when data are distributed according to a single-index model (i.e., the target function depends on a one-dimensional projection of the covariates). Based on a mixture of new rigorous results, non-rigorous mathematical derivations, and numerical simulations, we propose a scenario for the learning dynamics in this setting. In particular, the proposed evolution exhibits separation of timescales and intermittency. These behaviors arise naturally because the population gradient flow can be recast as a singularly perturbed dynamical system.
Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.
Deep neural network based recommendation systems have achieved great success as information filtering techniques in recent years. However, since model training from scratch requires sufficient data, deep learning-based recommendation methods still face the bottlenecks of insufficient data and computational inefficiency. Meta-learning, as an emerging paradigm that learns to improve the learning efficiency and generalization ability of algorithms, has shown its strength in tackling the data sparsity issue. Recently, a growing number of studies on deep meta-learning based recommenddation systems have emerged for improving the performance under recommendation scenarios where available data is limited, e.g. user cold-start and item cold-start. Therefore, this survey provides a timely and comprehensive overview of current deep meta-learning based recommendation methods. Specifically, we propose a taxonomy to discuss existing methods according to recommendation scenarios, meta-learning techniques, and meta-knowledge representations, which could provide the design space for meta-learning based recommendation methods. For each recommendation scenario, we further discuss technical details about how existing methods apply meta-learning to improve the generalization ability of recommendation models. Finally, we also point out several limitations in current research and highlight some promising directions for future research in this area.
Graph neural networks generalize conventional neural networks to graph-structured data and have received widespread attention due to their impressive representation ability. In spite of the remarkable achievements, the performance of Euclidean models in graph-related learning is still bounded and limited by the representation ability of Euclidean geometry, especially for datasets with highly non-Euclidean latent anatomy. Recently, hyperbolic space has gained increasing popularity in processing graph data with tree-like structure and power-law distribution, owing to its exponential growth property. In this survey, we comprehensively revisit the technical details of the current hyperbolic graph neural networks, unifying them into a general framework and summarizing the variants of each component. More importantly, we present various HGNN-related applications. Last, we also identify several challenges, which potentially serve as guidelines for further flourishing the achievements of graph learning in hyperbolic spaces.
Unsupervised domain adaptation has recently emerged as an effective paradigm for generalizing deep neural networks to new target domains. However, there is still enormous potential to be tapped to reach the fully supervised performance. In this paper, we present a novel active learning strategy to assist knowledge transfer in the target domain, dubbed active domain adaptation. We start from an observation that energy-based models exhibit free energy biases when training (source) and test (target) data come from different distributions. Inspired by this inherent mechanism, we empirically reveal that a simple yet efficient energy-based sampling strategy sheds light on selecting the most valuable target samples than existing approaches requiring particular architectures or computation of the distances. Our algorithm, Energy-based Active Domain Adaptation (EADA), queries groups of targe data that incorporate both domain characteristic and instance uncertainty into every selection round. Meanwhile, by aligning the free energy of target data compact around the source domain via a regularization term, domain gap can be implicitly diminished. Through extensive experiments, we show that EADA surpasses state-of-the-art methods on well-known challenging benchmarks with substantial improvements, making it a useful option in the open world. Code is available at //github.com/BIT-DA/EADA.
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