10,341 research outputs found
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
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
round algorithm to -approximate
the sum of all values and an round algorithm to compute the exact
-quantile, i.e., the the smallest value.
We give an quadratically faster and in fact optimal gossip algorithm for the
exact -quantile problem which runs in rounds. We furthermore
show that one can achieve an exponential speedup if one allows for an
-approximation. We give an
round gossip algorithm which computes a value of rank between and
at every node.% for any and . 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
lower bound which shows that
our algorithm is optimal for all values of
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