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The Impact of Neural Network Overparameterization on Gradient Confusion and Stochastic Gradient Descent

arXiv.org Machine Learning

The goal of this paper is to study why stochastic gradient descent (SGD) is efficient for neural networks, and how neural net design affects SGD. In particular, we investigate how overparameterization -- an increase in the number of parameters beyond the number of training data -- affects the dynamics of SGD. We introduce a simple concept called gradient confusion. When confusion is high, stochastic gradients produced by different data samples may be negatively correlated, slowing down convergence. But when gradient confusion is low, we show that SGD has better convergence properties than predicted by classical theory. Using theoretical and experimental results, we study how overparameterization affects gradient confusion, and thus the convergence of SGD, on linear models and neural networks. We show that increasing the number of parameters of linear models or increasing the width of neural networks leads to lower gradient confusion, and thus faster and easier model training. We also show how overparameterization by increasing the depth of neural networks results in higher gradient confusion, making deeper models harder to train. Finally, we observe empirically that techniques like batch normalization and skip connections reduce gradient confusion, which helps reduce the training burden of deep networks.


Low-Power Computer Vision: Status, Challenges, Opportunities

arXiv.org Artificial Intelligence

Computer vision has achieved impressive progress in recent years. Meanwhile, mobile phones have become the primary computing platforms for millions of people. In addition to mobile phones, many autonomous systems rely on visual data for making decisions and some of these systems have limited energy (such as unmanned aerial vehicles also called drones and mobile robots). These systems rely on batteries and energy efficiency is critical. This article serves two main purposes: (1) Examine the state-of-the-art for low-power solutions to detect objects in images. Since 2015, the IEEE Annual International Low-Power Image Recognition Challenge (LPIRC) has been held to identify the most energy-efficient computer vision solutions. This article summarizes 2018 winners' solutions. (2) Suggest directions for research as well as opportunities for low-power computer vision.


How Widely Can Prediction Models be Generalized? An Analysis of Performance Prediction in Blended Courses

arXiv.org Machine Learning

Blended courses that mix in-person instruction with online platforms are increasingly popular in secondary education. These tools record a rich amount of data on students' study habits and social interactions. Prior research has shown that these metrics are correlated with students' performance in face to face classes. However, predictive models for blended courses are still limited and have not yet succeeded at early prediction or cross-class predictions even for repeated offerings of the same course. In this work, we use data from two offerings of two different undergraduate courses to train and evaluate predictive models on student performance based upon persistent student characteristics including study habits and social interactions. We analyze the performance of these models on the same offering, on different offerings of the same course, and across courses to see how well they generalize. We also evaluate the models on different segments of the courses to determine how early reliable predictions can be made. This work tells us in part how much data is required to make robust predictions and how cross-class data may be used, or not, to boost model performance. The results of this study will help us better understand how similar the study habits, social activities, and the teamwork styles are across semesters for students in each performance category. These trained models also provide an avenue to improve our existing support platforms to better support struggling students early in the semester with the goal of providing timely intervention.


Modified online Newton step based on element wise multiplication

arXiv.org Machine Learning

The second order method as Newton Step is a suitable technique in Online Learning to guarantee regret bound. The large data is a challenge in Newton method to store second order matrices as hessian. In this paper, we have proposed an modified online Newton step that store first and second order matrices of dimension m (classes) by d (features). we have used element wise arithmetic operation to retain matrices size same. The modified second order matrix size results in faster computations. Also, the mistake rate is at par with respect to popular methods in literature. The experiments outcome indicate that proposed method could be helpful to handle large multi class datasets in common desktop machines using second order method as Newton step.


Deep CNNs Meet Global Covariance Pooling: Better Representation and Generalization

arXiv.org Artificial Intelligence

Compared with global average pooling in existing deep convolutional neural networks (CNNs), global covariance pooling can capture richer statistics of deep features, having potential for improving representation and generalization abilities of deep CNNs. However, integration of global covariance pooling into deep CNNs brings two challenges: (1) robust covariance estimation given deep features of high dimension and small sample; (2) appropriate use of geometry of covariances. To address these challenges, we propose a global Matrix Power Normalized COVariance (MPN-COV) Pooling. Our MPN-COV conforms to a robust covariance estimator, very suitable for scenario of high dimension and small sample. It can also be regarded as power-Euclidean metric between covariances, effectively exploiting their geometry. Furthermore, a global Gaussian embedding method is proposed to incorporate first-order statistics into MPN-COV. For fast training of MPN-COV networks, we propose an iterative matrix square root normalization, avoiding GPU unfriendly eigen-decomposition inherent in MPN-COV. Additionally, progressive 1x1 and group convolutions are introduced to compact covariance representations. The MPN-COV and its variants are highly modular, readily plugged into existing deep CNNs. Extensive experiments are conducted on large-scale object classification, scene categorization, fine-grained visual recognition and texture classification, showing our methods are superior to the counterparts and achieve state-of-the-art performance.


6 Digitization Trends Coming From AI and Blockchain - InformationWeek

#artificialintelligence

Blockchain and artificial intelligence are two emerging technologies that are quickly bringing about further digitization in the business world. Here are six ways they are changing how businesses operate and will continue to do so for the foreseeable future. One of the advantages of blockchain technology for businesses is that it offers more transparency about shipments and how products move through the supply chain. People cannot edit information once it gets entered into the digital ledger. Then, businesses don't have to worry about potential records tampering.


How artificial intelligence is influencing Unilever's marketing - Digiday

#artificialintelligence

Unilever is using artificial intelligence to influence more of its marketing, from processing insights to finding influencers. The advertiser has 26 data centers across the globe where scientists are using AI to synthesize insights from a range of sources including social listening, CRM and traditional marketing research. Like other advertisers, Unilever hopes the investments fuel a move away from mass reach channels toward more personalized communications that are also cheaper to produce and localize at scale. Unilever has been using AI and machine learning to sort through structured data within a database for years, but it hasn't been able to do the same for unstructured data until recently. Unstructured data is qualitative, which makes gleaning insights from content such as text, audio, social media and mobile activity harder.


Analysis of the Gradient Descent Algorithm for a Deep Neural Network Model with Skip-connections

arXiv.org Machine Learning

The behavior of the gradient descent (GD) algorithm is analyzed for a deep neural network model with skip-connections. It is proved that in the over-parametrized regime, for a suitable initialization, with high probability GD can find a global minimum exponentially fast. Generalization error estimates along the GD path are also established. As a consequence, it is shown that when the target function is in the reproducing kernel Hilbert space (RKHS) with a kernel defined by the initialization, there exist generalizable early-stopping solutions along the GD path. In addition, it is also shown that the GD path is uniformly close to the functions given by the related random feature model. Consequently, in this "implicit regularization" setting, the deep neural network model deteriorates to a random feature model. Our results hold for neural networks of any width larger than the input dimension.


Pre-training of Context-aware Item Representation for Next Basket Recommendation

arXiv.org Machine Learning

Next basket recommendation, which aims to predict the next a few items that a user most probably purchases given his historical transactions, plays a vital role in market basket analysis. From the viewpoint of item, an item could be purchased by different users together with different items, for different reasons. Therefore, an ideal recommender system should represent an item considering its transaction contexts. Existing state-of-the-art deep learning methods usually adopt the static item representations, which are invariant among all of the transactions and thus cannot achieve the full potentials of deep learning. Inspired by the pre-trained representations of BERT in natural language processing, we propose to conduct context-aware item representation for next basket recommendation, called Item Encoder Representations from Transformers (IERT). In the offline phase, IERT pre-trains deep item representations conditioning on their transaction contexts. In the online recommendation phase, the pre-trained model is further fine-tuned with an additional output layer. The output contextualized item embeddings are used to capture users' sequential behaviors and general tastes to conduct recommendation. Experimental results on the Ta-Feng data set show that IERT outperforms the state-of-the-art baseline methods, which demonstrated the effectiveness of IERT in next basket representation.


Random Projection in Neural Episodic Control

arXiv.org Artificial Intelligence

End-to-end deep reinforcement learning has enabled agents to learn with little preprocessing by humans. However, it is still difficult to learn stably and efficiently because the learning method usually uses a nonlinear function approximation. Neural Episodic Control (NEC), which has been proposed in order to improve sample efficiency, is able to learn stably by estimating action values using a non-parametric method. In this paper, we propose an architecture that incorporates random projection into NEC to train with more stability. In addition, we verify the effectiveness of our architecture by Atari's five games. The main idea is to reduce the number of parameters that have to learn by replacing neural networks with random projection in order to reduce dimensions while keeping the learning end-to-end.