Pooling is one of the main elements in convolutional neural networks. The pooling reduces the size of the feature map, enabling training and testing with a limited amount of computation. This paper proposes a new pooling method named universal pooling. Unlike the existing pooling methods such as average pooling, max pooling, and stride pooling with fixed pooling function, universal pooling generates any pooling function, depending on a given problem and dataset. Universal pooling was inspired by attention methods and can be considered as a channel-wise form of local spatial attention. Universal pooling is trained jointly with the main network and it is shown that it includes the existing pooling methods. Finally, when applied to two benchmark problems, the proposed method outperformed the existing pooling methods and performed with the expected diversity, adapting to the given problem.
Most convolutional neural networks use some method for gradually downscaling the size of the hidden layers. This is commonly referred to as pooling, and is applied to reduce the number of parameters, improve invariance to certain distortions, and increase the receptive field size. Since pooling by nature is a lossy process, it is crucial that each such layer maintains the portion of the activations that is most important for the network's discriminability. Yet, simple maximization or averaging over blocks, max or average pooling, or plain downsampling in the form of strided convolutions are the standard. In this paper, we aim to leverage recent results on image downscaling for the purposes of deep learning. Inspired by the human visual system, which focuses on local spatial changes, we propose detail-preserving pooling (DPP), an adaptive pooling method that magnifies spatial changes and preserves important structural detail. Importantly, its parameters can be learned jointly with the rest of the network. We analyze some of its theoretical properties and show its empirical benefits on several datasets and networks, where DPP consistently outperforms previous pooling approaches. OBJECT Bone allografts used for interbody spinal fusion are often preserved through either freeze drying or lowtemperature freezing, each having disadvantages related to graft preparation time and material properties. In response, a glycerol preservation treatment has been developed to maintain the biomechanical properties of allografts at ambient temperatures, requiring no thawing or rehydration and minimal rinsing prior to implantation. The authors conducted a prospective randomized study to compare the clinical results of glycerol-preserved Cloward dowels and those of freezedried Cloward dowels in anterior cervical discectomy and fusion. The primary outcome measures were evidence of fusion and graft subsidence, and the secondary outcome measures included adverse events, pain, and neck disability scores. METHODS Of 106 patients, 53 (113 levels of surgery) were randomly assigned to the glycerol-preserved graft group and 53 (114 levels of surgery) to the freeze-dried graft group. Subsidence was assessed a...  Feature pooling layers (e.g., max pooling) in convolutional neural networks (CNNs) serve the dual purpose of providing increasingly abstract representations as well as yielding computational savings in subsequent convolutional layers. We view the pooling operation in CNNs as a two step procedure: first, a pooling window (e.g., 2&#xd7; 2) slides over the feature map with stride one which leaves the spatial resolution intact, and second, downsampling is performed by selecting one pixel from each non-overlapping pooling window in an often uniform and deterministic (e.g., top-left) manner. Our starting point in this work is the observation that this regularly spaced downsampling arising from non-overlapping windows, although intuitive from a signal processing perspective (which has the goal of signal reconstruction), is not necessarily optimal for learning (where the goal is to generalize). We study this aspect and propose a novel pooling strategy with stochastic spatial sampling (S3Pool), where the regular downsampling is replaced by a more general stochastic version. We observe that this general stochasticity acts as a strong regularizer, and can also be seen as doing implicit data augmentation by introducing distortions in the feature maps. We further introduce a mechanism to control the amount of distortion to suit different datasets and architectures. To demonstrate the effectiveness of the proposed approach, we perform extensive experiments on several popular image classification benchmarks, observing excellent improvements over baseline models. In this work we compute lower Lipschitz bounds of @math pooling operators for @math as well as @math pooling operators preceded by half-rectification layers. These give sufficient conditions for the design of invertible neural network layers. Numerical experiments on MNIST and image patches confirm that pooling layers can be inverted with phase recovery algorithms. Moreover, the regularity of the inverse pooling, controlled by the lower Lipschitz constant, is empirically verified with a nearest neighbor regression. Discrete Fourier transforms provide a significant speedup in the computation of convolutions in deep learning. In this work, we demonstrate that, beyond its advantages for efficient computation, the spectral domain also provides a powerful representation in which to model and train convolutional neural networks (CNNs). We employ spectral representations to introduce a number of innovations to CNN design. First, we propose spectral pooling, which performs dimensionality reduction by truncating the representation in the frequency domain. This approach preserves considerably more information per parameter than other pooling strategies and enables flexibility in the choice of pooling output dimensionality. This representation also enables a new form of stochastic regularization by randomized modification of resolution. We show that these methods achieve competitive results on classification and approximation tasks, without using any dropout or max-pooling. Finally, we demonstrate the effectiveness of complex-coefficient spectral parameterization of convolutional filters. While this leaves the underlying model unchanged, it results in a representation that greatly facilitates optimization. We observe on a variety of popular CNN configurations that this leads to significantly faster convergence during training. We seek to improve deep neural networks by generalizing the pooling operations that play a central role in current architectures. We pursue a careful exploration of approaches to allow pooling to learn and to adapt to complex and variable patterns. The two primary directions lie in (1) learning a pooling function via (two strategies of) combining of max and average pooling, and (2) learning a pooling function in the form of a tree-structured fusion of pooling filters that are themselves learned. In our experiments every generalized pooling operation we explore improves performance when used in place of average or max pooling. We experimentally demonstrate that the proposed pooling operations provide a boost in invariance properties relative to conventional pooling and set the state of the art on several widely adopted benchmark datasets; they are also easy to implement, and can be applied within various deep neural network architectures. These benefits come with only a light increase in computational overhead during training and a very modest increase in the number of model parameters. This paper presents a novel Inter Catchment Wastewater Transfer (ICWT) method for mitigating sewer overflow. The ICWT aims at balancing the spatial mismatch of sewer flow and treatment capacity of Wastewater Treatment Plant (WWTP), through collaborative operation of sewer system facilities. Using a hydraulic model, the effectiveness of ICWT is investigated in a sewer system in Drammen, Norway. Concerning the whole system performance, we found that the S ren Lemmich pump station plays a vital role in the ICWT framework. To enhance the operation of this pump station, it is imperative to construct a multi-step ahead water level prediction model. Hence, one of the most promising artificial intelligence techniques, Long Short Term Memory (LSTM), is employed to undertake this task. Experiments demonstrated that LSTM is superior to Gated Recurrent Unit (GRU), Recurrent Neural Network (RNN), Feed-forward Neural Network (FFNN) and Support Vector Regression (SVR). Abstract: We introduce a simple and effective method for regularizing large convolutional neural networks. We replace the conventional deterministic pooling operations with a stochastic procedure, randomly picking the activation within each pooling region according to a multinomial distribution, given by the activities within the pooling region. The approach is hyper-parameter free and can be combined with other regularization approaches, such as dropout and data augmentation. We achieve state-of-the-art performance on four image datasets, relative to other approaches that do not utilize data augmentation.