Evaluating Generalization Ability of Convolutional Neural Networks and Capsule Networks for Image Classification via Top-2 Classification

Image classification is a challenging problem which aims to identify the category of object in the image. In recent years, deep Convolutional Neural Networks (CNNs) have been applied to handle this task, and impressive improvement has been achieved. However, some research showed the output of CNNs can be easily altered by adding relatively small perturbations to the input image, such as modifying few pixels. Recently, Capsule Networks (CapsNets) are proposed, which can help eliminating this limitation. Experiments on MNIST dataset revealed that capsules can better characterize the features of object than CNNs. But it's hard to find a suitable quantitative method to compare the generalization ability of CNNs and CapsNets. In this paper, we propose a new image classification task called Top-2 classification to evaluate the generalization ability of CNNs and CapsNets. The models are trained on single label image samples same as the traditional image classification task. But in the test stage, we randomly concatenate two test image samples which contain different labels, and then use the trained models to predict the top-2 labels on the unseen newly-created two label image samples. This task can provide us precise quantitative results to compare the generalization ability of CNNs and CapsNets. Back to the CapsNet, because it uses Full Connectivity (FC) mechanism among all capsules, it requires many parameters. To reduce the number of parameters, we introduce the Parameter-Sharing (PS) mechanism between capsules. Experiments on five widely used benchmark image datasets demonstrate the method significantly reduces the number of parameters, without losing the effectiveness of extracting features. Further, on the Top-2 classification task, the proposed PS CapsNets obtain impressive higher accuracy compared to the traditional CNNs and FC CapsNets by a large margin.Comment: This paper is under consideration at Computer Vision and Image Understandin

Distributed Data Summarization in Well-Connected Networks

We study distributed algorithms for some fundamental problems in data summarization. Given a communication graph G of n nodes each of which may hold a value initially, we focus on computing sum_{i=1}^N g(f_i), where f_i is the number of occurrences of value i and g is some fixed function. This includes important statistics such as the number of distinct elements, frequency moments, and the empirical entropy of the data. In the CONGEST~ model, a simple adaptation from streaming lower bounds shows that it requires Omega~(D+ n) rounds, where D is the diameter of the graph, to compute some of these statistics exactly. However, these lower bounds do not hold for graphs that are well-connected. We give an algorithm that computes sum_{i=1}^{N} g(f_i) exactly in {tau_{G}} * 2^{O(sqrt{log n})} rounds where {tau_{G}} is the mixing time of G. This also has applications in computing the top k most frequent elements. We demonstrate that there is a high similarity between the GOSSIP~ model and the CONGEST~ model in well-connected graphs. In particular, we show that each round of the GOSSIP~ model can be simulated almost perfectly in O~({tau_{G}}) rounds of the CONGEST~ model. To this end, we develop a new algorithm for the GOSSIP~ model that 1 +/- epsilon approximates the p-th frequency moment F_p = sum_{i=1}^N f_i^p in O~(epsilon^{-2} n^{1-k/p}) roundsfor p >= 2, when the number of distinct elements F_0 is at most O(n^{1/(k-1)}). This result can be translated back to the CONGEST~ model with a factor O~({tau_{G}}) blow-up in the number of rounds

Ant-Inspired Density Estimation via Random Walks

Many ant species employ distributed population density estimation in applications ranging from quorum sensing [Pra05], to task allocation [Gor99], to appraisal of enemy colony strength [Ada90]. It has been shown that ants estimate density by tracking encounter rates -- the higher the population density, the more often the ants bump into each other [Pra05,GPT93]. We study distributed density estimation from a theoretical perspective. We prove that a group of anonymous agents randomly walking on a grid are able to estimate their density within a small multiplicative error in few steps by measuring their rates of encounter with other agents. Despite dependencies inherent in the fact that nearby agents may collide repeatedly (and, worse, cannot recognize when this happens), our bound nearly matches what would be required to estimate density by independently sampling grid locations. From a biological perspective, our work helps shed light on how ants and other social insects can obtain relatively accurate density estimates via encounter rates. From a technical perspective, our analysis provides new tools for understanding complex dependencies in the collision probabilities of multiple random walks. We bound the strength of these dependencies using $local\ mixing\ properties$ of the underlying graph. Our results extend beyond the grid to more general graphs and we discuss applications to size estimation for social networks and density estimation for robot swarms

Optimal Gossip Algorithms for Exact and Approximate Quantile Computations

This paper gives drastically faster gossip algorithms to compute exact and approximate quantiles. Gossip algorithms, which allow each node to contact a uniformly random other node in each round, have been intensely studied and been adopted in many applications due to their fast convergence and their robustness to failures. Kempe et al. [FOCS'03] gave gossip algorithms to compute important aggregate statistics if every node is given a value. In particular, they gave a beautiful $O(\log n + \log \frac{1}{\epsilon})$ round algorithm to $\epsilon$-approximate the sum of all values and an $O(\log^2 n)$ round algorithm to compute the exact $\phi$-quantile, i.e., the the $\lceil \phi n \rceil$ smallest value. We give an quadratically faster and in fact optimal gossip algorithm for the exact $\phi$-quantile problem which runs in $O(\log n)$ rounds. We furthermore show that one can achieve an exponential speedup if one allows for an $\epsilon$-approximation. We give an $O(\log \log n + \log \frac{1}{\epsilon})$ round gossip algorithm which computes a value of rank between $\phi n$ and $(\phi+\epsilon)n$ at every node.% for any $0 \leq \phi \leq 1$ and $0 < \epsilon < 1$. Our algorithms are extremely simple and very robust - they can be operated with the same running times even if every transmission fails with a, potentially different, constant probability. We also give a matching $\Omega(\log \log n + \log \frac{1}{\epsilon})$ lower bound which shows that our algorithm is optimal for all values of $\epsilon$