Many datasets in scientific and engineering applications are comprised of objects which have specific geometric structure. A common example is data which inhabits a representation of the group SO$(3)$ of 3D rotations: scalars, vectors, tensors, \textit{etc}. One way for a neural network to exploit prior knowledge of this structure is to enforce SO$(3)$-equivariance throughout its layers, and several such architectures have been proposed. While general methods for handling arbitrary SO$(3)$ representations exist, they computationally intensive and complicated to implement. We show that by judicious symmetry breaking, we can efficiently increase the expressiveness of a network operating only on vector and order-2 tensor representations of SO$(2)$. We demonstrate the method on an important problem from High Energy Physics known as \textit{b-tagging}, where particle jets originating from b-meson decays must be discriminated from an overwhelming QCD background. In this task, we find that augmenting a standard architecture with our method results in a \ensuremath{2.3\times} improvement in rejection score.
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Networking：IFIP International Conferences on Networking。
Explanation：國際網絡會(hui)議。
Publisher：IFIP。
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Stability is an important characteristic of network models that has implications for other desirable aspects such as controllability. The stability of a Boolean network depends on various factors, such as the topology of its wiring diagram and the type of the functions describing its dynamics. In this paper, we study the stability of linear Boolean networks by computing Derrida curves and quantifying the number of attractors and cycle lengths imposed by their network topologies. Derrida curves are commonly used to measure the stability of Boolean networks and several parameters such as the average in-degree K and the output bias p can indicate if a network is stable, critical, or unstable. For random unbiased Boolean networks there is a critical connectivity value Kc=2 such that if K<Kc networks operate in the ordered regime, and if K>Kc networks operate in the chaotic regime. Here, we show that for linear networks, which are the least canalizing and most unstable, the phase transition from order to chaos already happens at an average in-degree of Kc=1. Consistently, we also show that unstable networks exhibit a large number of attractors with very long limit cycles while stable and critical networks exhibit fewer attractors with shorter limit cycles. Additionally, we present theoretical results to quantify important dynamical properties of linear networks. First, we present a formula for the proportion of attractor states in linear systems. Second, we show that the expected number of fixed points in linear systems is 2, while general Boolean networks possess on average one fixed point. Third, we present a formula to quantify the number of bijective linear Boolean networks and provide a lower bound for the percentage of this type of network.
While the 5th generation (5G) of mobile networks has landed in the commercial area, the research community is exploring new functionalities for 6th generation (6G) networks, for example non-terrestrial networks (NTNs) via space/air nodes such as Unmanned Aerial Vehicles (UAVs), High Altitute Platforms (HAPs) or satellites. Specifically, satellite-based communication offers new opportunities for future wireless applications, such as providing connectivity to remote or otherwise unconnected areas, complementing terrestrial networks to reduce connection downtime, as well as increasing traffic efficiency in hot spot areas. In this context, an accurate characterization of the NTN channel is the first step towards proper protocol design. Along these lines, this paper provides an ns-3 implementation of the 3rd Generation Partnership Project (3GPP) channel and antenna models for NTN described in Technical Report 38.811. In particular, we extend the ns-3 code base with new modules to implement the attenuation of the signal in air/space due to atmospheric gases and scintillation, and new mobility and fading models to account for the Geocentric Cartesian coordinate system of satellites. Finally, we validate the accuracy of our ns-3 module via simulations against 3GPP calibration results
In recent years neural networks have achieved impressive results on many technological and scientific tasks. Yet, the mechanism through which these models automatically select features, or patterns in data, for prediction remains unclear. Identifying such a mechanism is key to advancing performance and interpretability of neural networks and promoting reliable adoption of these models in scientific applications. In this paper, we identify and characterize the mechanism through which deep fully connected neural networks learn features. We posit the Deep Neural Feature Ansatz, which states that neural feature learning occurs by implementing the average gradient outer product to up-weight features strongly related to model output. Our ansatz sheds light on various deep learning phenomena including emergence of spurious features and simplicity biases and how pruning networks can increase performance, the "lottery ticket hypothesis." Moreover, the mechanism identified in our work leads to a backpropagation-free method for feature learning with any machine learning model. To demonstrate the effectiveness of this feature learning mechanism, we use it to enable feature learning in classical, non-feature learning models known as kernel machines and show that the resulting models, which we refer to as Recursive Feature Machines, achieve state-of-the-art performance on tabular data.
Purpose: We propose a novel method for continual learning based on the increasing depth of neural networks. This work explores whether extending neural network depth may be beneficial in a life-long learning setting. Methods: We propose a novel approach based on adding new layers on top of existing ones to enable the forward transfer of knowledge and adapting previously learned representations. We employ a method of determining the most similar tasks for selecting the best location in our network to add new nodes with trainable parameters. This approach allows for creating a tree-like model, where each node is a set of neural network parameters dedicated to a specific task. The Progressive Neural Network concept inspires the proposed method. Therefore, it benefits from dynamic changes in network structure. However, Progressive Neural Network allocates a lot of memory for the whole network structure during the learning process. The proposed method alleviates this by adding only part of a network for a new task and utilizing a subset of previously trained weights. At the same time, we may retain the benefit of PNN, such as no forgetting guaranteed by design, without needing a memory buffer. Results: Experiments on Split CIFAR and Split Tiny ImageNet show that the proposed algorithm is on par with other continual learning methods. In a more challenging setup with a single computer vision dataset as a separate task, our method outperforms Experience Replay. Conclusion: It is compatible with commonly used computer vision architectures and does not require a custom network structure. As an adaptation to changing data distribution is made by expanding the architecture, there is no need to utilize a rehearsal buffer. For this reason, our method could be used for sensitive applications where data privacy must be considered.
The application of the deep learning model in classification plays an important role in the accurate detection of the target objects. However, the accuracy is affected by the activation function in the hidden and output layer. In this paper, an activation function called TaLU, which is a combination of Tanh and Rectified Linear Units (ReLU), is used to improve the prediction. ReLU activation function is used by many deep learning researchers for its computational efficiency, ease of implementation, intuitive nature, etc. However, it suffers from a dying gradient problem. For instance, when the input is negative, its output is always zero because its gradient is zero. A number of researchers used different approaches to solve this issue. Some of the most notable are LeakyReLU, Softplus, Softsign, Elu, ThresholdedReLU, etc. This research developed TaLU, a modified activation function combining Tanh and ReLU, which mitigates the dying gradient problem of ReLU. The deep learning model with the proposed activation function was tested on MNIST and CIFAR-10, and it outperforms ReLU and some other studied activation functions in terms of accuracy(from 0\% upto 6\% in most cases, when used with Batch Normalization and a reasonable learning rate).
Most existing studies on linear bandits focus on the one-dimensional characterization of the overall system. While being representative, this formulation may fail to model applications with high-dimensional but favorable structures, such as the low-rank tensor representation for recommender systems. To address this limitation, this work studies a general tensor bandits model, where actions and system parameters are represented by tensors as opposed to vectors, and we particularly focus on the case that the unknown system tensor is low-rank. A novel bandit algorithm, coined TOFU (Tensor Optimism in the Face of Uncertainty), is developed. TOFU first leverages flexible tensor regression techniques to estimate low-dimensional subspaces associated with the system tensor. These estimates are then utilized to convert the original problem to a new one with norm constraints on its system parameters. Lastly, a norm-constrained bandit subroutine is adopted by TOFU, which utilizes these constraints to avoid exploring the entire high-dimensional parameter space. Theoretical analyses show that TOFU improves the best-known regret upper bound by a multiplicative factor that grows exponentially in the system order. A novel performance lower bound is also established, which further corroborates the efficiency of TOFU.
Neural networks have shown tremendous growth in recent years to solve numerous problems. Various types of neural networks have been introduced to deal with different types of problems. However, the main goal of any neural network is to transform the non-linearly separable input data into more linearly separable abstract features using a hierarchy of layers. These layers are combinations of linear and nonlinear functions. The most popular and common non-linearity layers are activation functions (AFs), such as Logistic Sigmoid, Tanh, ReLU, ELU, Swish and Mish. In this paper, a comprehensive overview and survey is presented for AFs in neural networks for deep learning. Different classes of AFs such as Logistic Sigmoid and Tanh based, ReLU based, ELU based, and Learning based are covered. Several characteristics of AFs such as output range, monotonicity, and smoothness are also pointed out. A performance comparison is also performed among 18 state-of-the-art AFs with different networks on different types of data. The insights of AFs are presented to benefit the researchers for doing further research and practitioners to select among different choices. The code used for experimental comparison is released at: \url{//github.com/shivram1987/ActivationFunctions}.
Graph Neural Networks (GNNs) have proven to be useful for many different practical applications. However, many existing GNN models have implicitly assumed homophily among the nodes connected in the graph, and therefore have largely overlooked the important setting of heterophily, where most connected nodes are from different classes. In this work, we propose a novel framework called CPGNN that generalizes GNNs for graphs with either homophily or heterophily. The proposed framework incorporates an interpretable compatibility matrix for modeling the heterophily or homophily level in the graph, which can be learned in an end-to-end fashion, enabling it to go beyond the assumption of strong homophily. Theoretically, we show that replacing the compatibility matrix in our framework with the identity (which represents pure homophily) reduces to GCN. Our extensive experiments demonstrate the effectiveness of our approach in more realistic and challenging experimental settings with significantly less training data compared to previous works: CPGNN variants achieve state-of-the-art results in heterophily settings with or without contextual node features, while maintaining comparable performance in homophily settings.
Graph Neural Networks (GNNs) have been shown to be effective models for different predictive tasks on graph-structured data. Recent work on their expressive power has focused on isomorphism tasks and countable feature spaces. We extend this theoretical framework to include continuous features - which occur regularly in real-world input domains and within the hidden layers of GNNs - and we demonstrate the requirement for multiple aggregation functions in this context. Accordingly, we propose Principal Neighbourhood Aggregation (PNA), a novel architecture combining multiple aggregators with degree-scalers (which generalize the sum aggregator). Finally, we compare the capacity of different models to capture and exploit the graph structure via a novel benchmark containing multiple tasks taken from classical graph theory, alongside existing benchmarks from real-world domains, all of which demonstrate the strength of our model. With this work, we hope to steer some of the GNN research towards new aggregation methods which we believe are essential in the search for powerful and robust models.
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.
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