(1) Purpose: This work aims at developing a generalizable MRI reconstruction model in the meta-learning framework. The standard benchmarks in meta-learning are challenged by learning on diverse task distributions. The proposed network learns the regularization function in a variational model and reconstructs MR images with various under-sampling ratios or patterns that may or may not be seen in the training data by leveraging a heterogeneous dataset. (2) Methods: We propose an unrolling network induced by learnable optimization algorithms (LOA) for solving our nonconvex nonsmooth variational model for MRI reconstruction. In this model, the learnable regularization function contains a task-invariant common feature encoder and task-specific learner represented by a shallow network. To train the network we split the training data into two parts: training and validation, and introduce a bilevel optimization algorithm. The lower-level optimization trains task-invariant parameters for the feature encoder with fixed parameters of the task-specific learner on the training dataset, and the upper-level optimizes the parameters of the task-specific learner on the validation dataset. (3) Results: The PSNR increases 1.5 dB on average compared to the network trained through conventional supervised learning on the seen CS ratios. We test the result of quick adaption on the unseen tasks after meta-training, the average PSNR arises 1.22 dB compared to the conventional learning procedure that is directly trained on the unseen CS ratios in the meanwhile saving half of the training time. The average PSNR arises 1.87 dB for unseen sampling patterns comparing to conventional learning; (4) Conclusion: We proposed a meta-learning framework consisting of the base network architecture, design of regularization, and bi-level optimization-based training. The network inherits the convergence property of the LOA and interpretation of the variational model. The generalization ability is improved by the designated regularization and bilevel optimization-based training algorithm.

Deep learning machines are computational models composed of multiple processing layers of adaptive weights to learn representations of data with multiple levels of abstraction. Their structure is mainly reflecting the intuitive plausibility of decomposing a problem into multiple levels of computation and representation since it is believed that higher layers of representation allow a system to learn complex functions. Surprisingly, after decades of research, from learning and design perspectives these models are still deployed in a heuristic manner. In this paper, deep learning feed-forward machines are modeled from a statistical mechanics point of view as disordered physical systems where its macroscopic behavior is determined in terms of the interactions defined between the basic constituent of these models, namely, the artificial neuron. They are viewed as the equilibrium states of a theoretical body that is subject to the law of increase of the entropy. The study of the changes in energy of the body when passing from one equilibrium state to another is used to understand the structure and role of the phase space of the system, the stability of the equilibrium states, and the resulting degree of disorder. It is shown that the topology of these models is strongly linked to their stability and resulting level of disorder. Furthermore, the proposed theoretical characterization permit to assess the thermodynamic efficiency with which information can be processed by these models, and to provide a practical methodology to quantitatively estimate and compare their expected learning and generalization capabilities. These theoretical results provides new insights to the theory of deep learning and their implications are shown to be consistent through a set of benchmarks designed to experimentally assess their validity.

Lower Back Pain (LBP) is a disease that needs immediate attention. Person with back pain shall go immediately to doctor for treatment. Injury, excessive works and some medical conditions are result of back pain. Back pain is common to any age of human for different reasons. Due to factors such as previous occupation and degenerative disk disease the chance of developing lower back pain increases for older people. It hampers the working condition of people common reason for seeking medical treatment. The result is absence from work and is unable to normal due to pain. It creates uncomfortable and debilitating situations. Hence, detecting this disease at an early stage will assist the medical field experts to suggest counter measures to the patients. Detection of lower back pain is implemented in this paper by applying ensemble machine learning technique. This paper proposes Stacking ensemble classifier as an automated tool that will predict lower back pain tendency of a patient. Experimental result implies that the proposed method reaches an accuracy of 76.34%, f1-score of 0.76 and MSE of 0.34.

In theory and applications, it is often inevitable to work with projectors onto convex sets, where a linear transform is involved. In this article, a novel projector is presented, which generalizes previous results in that it admits a broader family of linear transforms, but on the other hand it is limited to box-type convex sets in the transformed domain. The new projector has an explicit formula and it can be interpreted within the framework of proximal optimization. The benefit of the new projector is demonstrated on an example from signal processing, where it was possible to speed up the convergence of a signal declipping algorithm by a factor of more than two.

A common challenge in real-world classification scenarios with sequentially appending target domain data is insufficient training datasets during the training phase. Therefore, conventional deep learning and transfer learning classifiers are not applicable especially when individual classes are not represented or are severely underrepresented at the outset. Domain Generalization approaches reach their limits when domain shifts become too large, making them occasionally unsuitable as well. In many (technical) domains, however, it is only the defect/ worn/ reject classes that are insufficiently represented, while the non-defect class is often available from the beginning. The proposed classification approach addresses such conditions and is based on a CNN encoder. Following a contrastive learning approach, it is trained with a modified triplet loss function using two datasets: Besides the non-defective target domain class (= 1st dataset), a state-of-the-art labeled source domain dataset that contains highly related classes (e.g., a related manufacturing error or wear defect) but originates from a (highly) different domain (e.g., different product, material, or appearance) (= 2nd dataset) is utilized. The approach learns the classification features from the source domain dataset while at the same time learning the differences between the source and the target domain in a single training step, aiming to transfer the relevant features to the target domain. The classifier becomes sensitive to the classification features and – by architecture – robust against the highly domain-specific context. The approach is benchmarked in a technical and a non-technical domain and shows convincing classification results. In particular, it is shown that the domain generalization capabilities and classification results are improved by the proposed architecture, allowing for larger domain shifts between source and target domains.

The objective of this study was to develop guidelines for rainwater harvesting system sizing of shopping centres in South Africa. Three generalized dimensionless relationships relating rainwater supply and demand to tank size, yield and reliability were developed based on 101 years long daily time step simulations of rainwater harvesting of 19 shopping centres located in four regions. Daily rainfalls were obtained from nearby rainfall stations and daily non-potable demands were based on the size of the retail area. The simulations revealed within-year storage behaviour with considerable variation of the yield specified as the number of days for which demand was met each year. The Weibull plotting position formula was applied on the time series of yields to obtain yield-reliability relationships. Simulation results of the hydrologically optimum systems were used to develop two of the generalized relationships and an additional one based on the dependence of the slope of the reliability – yield plots on the optimum yield was formulated to enable analysis of hydrologically non-optimal systems. Most of the relationships fitted best to the non-linear power law form with high correlation coefficients averaging 0.92 and ranging from 0.82 to 1.00. The application of the models for tank sizing and assessing system performance is demonstrated.

Bayesian formulations of learning imply that whenever the evidence for a correlation between events in an animal’s habitat is sufficient, the correlation is learned. This implies that regularities can be learnt rapidly, from small numbers of learning examples. This speed of learning gives maximum possible fitness, and no faster learning is possible. There is evidence in many domains that animals and people can learn at nearly Bayesian optimal speeds. These domains include associative conditioning, and the more complex domains of navigation and language. There are computational models of learning which learn at near-Bayesian speeds in complex domains, and which can scale well – to learn thousands of pieces of knowledge (i.e., relations and associations). These are not neural net models. They can be defined in computational terms, as algorithms and data structures at David Marr’s [1] Level Two. Their key data structures are composite feature structures, which are graphs of multiple linked nodes. This leads to the hypothesis that animal learning results not from deep neural nets (which typically require thousands of training exam-ples), but from neural implementations of the Level Two models of fast learning; and that neu-rons provide the facilities needed to implement those models at Marr’s Level Three. The required facilities include feature structures, dynamic binding, one-shot memory for many feature struc-tures, pattern-based associative retrieval, unification and generalization of feature structures. These may be supported by multiplexing of data and metadata in the same neural fibres.

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2},\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2}% ,\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

One of the most rapidly advancing areas of deep learning research aims at creating models that learn to disentangle the latent factors of variation from a data distribution. However, modeling joint probability mass functions is usually prohibitive, which motivates the use of conditional models assuming that some information is given as input. In the domain of numerical cognition, deep learning architectures have successfully demonstrated that approximate numerosity representations can emerge in multi-layer networks that build latent representations of a set of images with a varying number of items. However, existing models have focused on tasks requiring to conditionally estimate numerosity information from a given image. Here we focus on a set of much more challenging tasks, which require to conditionally generate synthetic images containing a given number of items. We show that attention-based architectures operating at the pixel level can learn to produce well-formed images approximately containing a specific number of items, even when the target numerosity was not present in the training distribution.

In the paper, the authors present unified generalizations for the Bell numbers and polynomials, establish explicit formulas and inversion formulas for these generalizations in terms of the Stirling numbers of the first and second kinds with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem connected with the Stirling numbers of the first and second kinds, construct determinantal and product inequalities for these generalizations with aid of properties of the completely monotonic functions, and derive the logarithmic convexity for the sequence of these generalizations.