scholarly journals Critical Point-Finding Methods Reveal Gradient-Flat Regions of Deep Network Losses

2021 ◽  
pp. 1-29
Author(s):  
Charles G. Frye ◽  
James Simon ◽  
Neha S. Wadia ◽  
Andrew Ligeralde ◽  
Michael R. DeWeese ◽  
...  

Abstract Despite the fact that the loss functions of deep neural networks are highly nonconvex, gradient-based optimization algorithms converge to approximately the same performance from many random initial points. One thread of work has focused on explaining this phenomenon by numerically characterizing the local curvature near critical points of the loss function, where the gradients are near zero. Such studies have reported that neural network losses enjoy a no-bad-local-minima property, in disagreement with more recent theoretical results. We report here that the methods used to find these putative critical points suffer from a bad local minima problem of their own: they often converge to or pass through regions where the gradient norm has a stationary point. We call these gradient-flat regions, since they arise when the gradient is approximately in the kernel of the Hessian, such that the loss is locally approximately linear, or flat, in the direction of the gradient. We describe how the presence of these regions necessitates care in both interpreting past results that claimed to find critical points of neural network losses and in designing second-order methods for optimizing neural networks.

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Florian Stelzer ◽  
André Röhm ◽  
Raul Vicente ◽  
Ingo Fischer ◽  
Serhiy Yanchuk

AbstractDeep neural networks are among the most widely applied machine learning tools showing outstanding performance in a broad range of tasks. We present a method for folding a deep neural network of arbitrary size into a single neuron with multiple time-delayed feedback loops. This single-neuron deep neural network comprises only a single nonlinearity and appropriately adjusted modulations of the feedback signals. The network states emerge in time as a temporal unfolding of the neuron’s dynamics. By adjusting the feedback-modulation within the loops, we adapt the network’s connection weights. These connection weights are determined via a back-propagation algorithm, where both the delay-induced and local network connections must be taken into account. Our approach can fully represent standard Deep Neural Networks (DNN), encompasses sparse DNNs, and extends the DNN concept toward dynamical systems implementations. The new method, which we call Folded-in-time DNN (Fit-DNN), exhibits promising performance in a set of benchmark tasks.


2021 ◽  
Vol 2 (1) ◽  
pp. 1-25
Author(s):  
Yongsen Ma ◽  
Sheheryar Arshad ◽  
Swetha Muniraju ◽  
Eric Torkildson ◽  
Enrico Rantala ◽  
...  

In recent years, Channel State Information (CSI) measured by WiFi is widely used for human activity recognition. In this article, we propose a deep learning design for location- and person-independent activity recognition with WiFi. The proposed design consists of three Deep Neural Networks (DNNs): a 2D Convolutional Neural Network (CNN) as the recognition algorithm, a 1D CNN as the state machine, and a reinforcement learning agent for neural architecture search. The recognition algorithm learns location- and person-independent features from different perspectives of CSI data. The state machine learns temporal dependency information from history classification results. The reinforcement learning agent optimizes the neural architecture of the recognition algorithm using a Recurrent Neural Network (RNN) with Long Short-Term Memory (LSTM). The proposed design is evaluated in a lab environment with different WiFi device locations, antenna orientations, sitting/standing/walking locations/orientations, and multiple persons. The proposed design has 97% average accuracy when testing devices and persons are not seen during training. The proposed design is also evaluated by two public datasets with accuracy of 80% and 83%. The proposed design needs very little human efforts for ground truth labeling, feature engineering, signal processing, and tuning of learning parameters and hyperparameters.


Author(s):  
Chen Qi ◽  
Shibo Shen ◽  
Rongpeng Li ◽  
Zhifeng Zhao ◽  
Qing Liu ◽  
...  

AbstractNowadays, deep neural networks (DNNs) have been rapidly deployed to realize a number of functionalities like sensing, imaging, classification, recognition, etc. However, the computational-intensive requirement of DNNs makes it difficult to be applicable for resource-limited Internet of Things (IoT) devices. In this paper, we propose a novel pruning-based paradigm that aims to reduce the computational cost of DNNs, by uncovering a more compact structure and learning the effective weights therein, on the basis of not compromising the expressive capability of DNNs. In particular, our algorithm can achieve efficient end-to-end training that transfers a redundant neural network to a compact one with a specifically targeted compression rate directly. We comprehensively evaluate our approach on various representative benchmark datasets and compared with typical advanced convolutional neural network (CNN) architectures. The experimental results verify the superior performance and robust effectiveness of our scheme. For example, when pruning VGG on CIFAR-10, our proposed scheme is able to significantly reduce its FLOPs (floating-point operations) and number of parameters with a proportion of 76.2% and 94.1%, respectively, while still maintaining a satisfactory accuracy. To sum up, our scheme could facilitate the integration of DNNs into the common machine-learning-based IoT framework and establish distributed training of neural networks in both cloud and edge.


2016 ◽  
Vol 807 ◽  
pp. 155-166 ◽  
Author(s):  
Julia Ling ◽  
Andrew Kurzawski ◽  
Jeremy Templeton

There exists significant demand for improved Reynolds-averaged Navier–Stokes (RANS) turbulence models that are informed by and can represent a richer set of turbulence physics. This paper presents a method of using deep neural networks to learn a model for the Reynolds stress anisotropy tensor from high-fidelity simulation data. A novel neural network architecture is proposed which uses a multiplicative layer with an invariant tensor basis to embed Galilean invariance into the predicted anisotropy tensor. It is demonstrated that this neural network architecture provides improved prediction accuracy compared with a generic neural network architecture that does not embed this invariance property. The Reynolds stress anisotropy predictions of this invariant neural network are propagated through to the velocity field for two test cases. For both test cases, significant improvement versus baseline RANS linear eddy viscosity and nonlinear eddy viscosity models is demonstrated.


2021 ◽  
Author(s):  
Luke Gundry ◽  
Gareth Kennedy ◽  
Alan Bond ◽  
Jie Zhang

The use of Deep Neural Networks (DNNs) for the classification of electrochemical mechanisms based on training with simulations of the initial cycle of potential have been reported. In this paper,...


Author(s):  
E. Yu. Shchetinin

The recognition of human emotions is one of the most relevant and dynamically developing areas of modern speech technologies, and the recognition of emotions in speech (RER) is the most demanded part of them. In this paper, we propose a computer model of emotion recognition based on an ensemble of bidirectional recurrent neural network with LSTM memory cell and deep convolutional neural network ResNet18. In this paper, computer studies of the RAVDESS database containing emotional speech of a person are carried out. RAVDESS-a data set containing 7356 files. Entries contain the following emotions: 0 – neutral, 1 – calm, 2 – happiness, 3 – sadness, 4 – anger, 5 – fear, 6 – disgust, 7 – surprise. In total, the database contains 16 classes (8 emotions divided into male and female) for a total of 1440 samples (speech only). To train machine learning algorithms and deep neural networks to recognize emotions, existing audio recordings must be pre-processed in such a way as to extract the main characteristic features of certain emotions. This was done using Mel-frequency cepstral coefficients, chroma coefficients, as well as the characteristics of the frequency spectrum of audio recordings. In this paper, computer studies of various models of neural networks for emotion recognition are carried out on the example of the data described above. In addition, machine learning algorithms were used for comparative analysis. Thus, the following models were trained during the experiments: logistic regression (LR), classifier based on the support vector machine (SVM), decision tree (DT), random forest (RF), gradient boosting over trees – XGBoost, convolutional neural network CNN, recurrent neural network RNN (ResNet18), as well as an ensemble of convolutional and recurrent networks Stacked CNN-RNN. The results show that neural networks showed much higher accuracy in recognizing and classifying emotions than the machine learning algorithms used. Of the three neural network models presented, the CNN + BLSTM ensemble showed higher accuracy.


2021 ◽  
pp. 1-15
Author(s):  
Wenjun Tan ◽  
Luyu Zhou ◽  
Xiaoshuo Li ◽  
Xiaoyu Yang ◽  
Yufei Chen ◽  
...  

BACKGROUND: The distribution of pulmonary vessels in computed tomography (CT) and computed tomography angiography (CTA) images of lung is important for diagnosing disease, formulating surgical plans and pulmonary research. PURPOSE: Based on the pulmonary vascular segmentation task of International Symposium on Image Computing and Digital Medicine 2020 challenge, this paper reviews 12 different pulmonary vascular segmentation algorithms of lung CT and CTA images and then objectively evaluates and compares their performances. METHODS: First, we present the annotated reference dataset of lung CT and CTA images. A subset of the dataset consisting 7,307 slices for training and 3,888 slices for testing was made available for participants. Second, by analyzing the performance comparison of different convolutional neural networks from 12 different institutions for pulmonary vascular segmentation, the reasons for some defects and improvements are summarized. The models are mainly based on U-Net, Attention, GAN, and multi-scale fusion network. The performance is measured in terms of Dice coefficient, over segmentation ratio and under segmentation rate. Finally, we discuss several proposed methods to improve the pulmonary vessel segmentation results using deep neural networks. RESULTS: By comparing with the annotated ground truth from both lung CT and CTA images, most of 12 deep neural network algorithms do an admirable job in pulmonary vascular extraction and segmentation with the dice coefficients ranging from 0.70 to 0.85. The dice coefficients for the top three algorithms are about 0.80. CONCLUSIONS: Study results show that integrating methods that consider spatial information, fuse multi-scale feature map, or have an excellent post-processing to deep neural network training and optimization process are significant for further improving the accuracy of pulmonary vascular segmentation.


2020 ◽  
Vol 10 (6) ◽  
pp. 2104
Author(s):  
Michał Tomaszewski ◽  
Paweł Michalski ◽  
Jakub Osuchowski

This article presents an analysis of the effectiveness of object detection in digital images with the application of a limited quantity of input. The possibility of using a limited set of learning data was achieved by developing a detailed scenario of the task, which strictly defined the conditions of detector operation in the considered case of a convolutional neural network. The described solution utilizes known architectures of deep neural networks in the process of learning and object detection. The article presents comparisons of results from detecting the most popular deep neural networks while maintaining a limited training set composed of a specific number of selected images from diagnostic video. The analyzed input material was recorded during an inspection flight conducted along high-voltage lines. The object detector was built for a power insulator. The main contribution of the presented papier is the evidence that a limited training set (in our case, just 60 training frames) could be used for object detection, assuming an outdoor scenario with low variability of environmental conditions. The decision of which network will generate the best result for such a limited training set is not a trivial task. Conducted research suggests that the deep neural networks will achieve different levels of effectiveness depending on the amount of training data. The most beneficial results were obtained for two convolutional neural networks: the faster region-convolutional neural network (faster R-CNN) and the region-based fully convolutional network (R-FCN). Faster R-CNN reached the highest AP (average precision) at a level of 0.8 for 60 frames. The R-FCN model gained a worse AP result; however, it can be noted that the relationship between the number of input samples and the obtained results has a significantly lower influence than in the case of other CNN models, which, in the authors’ assessment, is a desired feature in the case of a limited training set.


Entropy ◽  
2020 ◽  
Vol 22 (12) ◽  
pp. 1365
Author(s):  
Bogdan Muşat ◽  
Răzvan Andonie

Convolutional neural networks utilize a hierarchy of neural network layers. The statistical aspects of information concentration in successive layers can bring an insight into the feature abstraction process. We analyze the saliency maps of these layers from the perspective of semiotics, also known as the study of signs and sign-using behavior. In computational semiotics, this aggregation operation (known as superization) is accompanied by a decrease of spatial entropy: signs are aggregated into supersign. Using spatial entropy, we compute the information content of the saliency maps and study the superization processes which take place between successive layers of the network. In our experiments, we visualize the superization process and show how the obtained knowledge can be used to explain the neural decision model. In addition, we attempt to optimize the architecture of the neural model employing a semiotic greedy technique. To the extent of our knowledge, this is the first application of computational semiotics in the analysis and interpretation of deep neural networks.


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