Most of the conventional models for opinion dynamics mainly account for a fully local influence, where myopic agents decide their actions after they interact with other agents that are adjacent to them. For example, in the case of social interactions, this includes family, friends, and other immediate strong social ties. The model proposed in this paper embodies a global influence as well where by global we mean that each node also observes a sample of the average behavior of the entire population; e.g., in the social example, people observe other people on the streets, subway, and other social venues. We consider the case where nodes have dichotomous states; examples of applications include elections with two major parties, whether or not to adopt a new technology or product, and any yes no opinion such as in voting on a referendum. The dynamics of states on a network with arbitrary degree distribution are studied. For a given initial condition, we find the probability to reach consensus on each state and the expected time reach to consensus. To model mass media, the effect of an exogenous bias on the average orientation of the system is investigated. To do so, we add an external field to the model that favors one of the states over the other. This field interferes with the regular decision process of each node and creates a constant probability to lean towards one of the states. We solve for the average state of the system as a function of time for given initial conditions. Then anti-conformists (stubborn nodes who never revise their states) are added to the network, in an effort to circumvent the external bias. We find necessary conditions on the number of these defiant nodes required to cancel the effect of the external bias. Our analysis is based on a mean field approximation of the agent opinions.
Learning and trust have been incorporated in the models, where each node has an estimate of how reliable its observations might be @cite_56 @cite_22 @cite_14 @cite_45 @cite_25 @cite_52 . In some models, nodes only interact with neighbors whose opinions are close to their own @cite_17 @cite_33 @cite_21 @cite_46 . @cite_43 , agents have inertia in the sense that the longer they have had a particular state, the less probable it is for them to deviate from it. The reader is also referred to @cite_15 for a broad review.
@cite_14 @cite_22 @cite_33 @cite_15 @cite_21 @cite_52 @cite_56 @cite_43 @cite_45 @cite_46 @cite_25 @cite_17
2887603965 1949110650 2101396617 2068322213
The prediction accuracy has been the long-lasting and sole standard for comparing the performance of different image classification models, including the ImageNet competition. However, recent studies have highlighted the lack of robustness in well-trained deep neural networks to adversarial examples. Visually imperceptible perturbations to natural images can easily be crafted and mislead the image classifiers towards misclassification. To demystify the trade-offs between robustness and accuracy, in this paper we thoroughly benchmark 18 ImageNet models using multiple robustness metrics, including the distortion, success rate and transferability of adversarial examples between 306 pairs of models. Our extensive experimental results reveal several new insights: (1) linear scaling law - the empirical ( _2 ) and ( _ ) distortion metrics scale linearly with the logarithm of classification error; (2) model architecture is a more critical factor to robustness than model size, and the disclosed accuracy-robustness Pareto frontier can be used as an evaluation criterion for ImageNet model designers; (3) for a similar network architecture, increasing network depth slightly improves robustness in ( _ ) distortion; (4) there exist models (in VGG family) that exhibit high adversarial transferability, while most adversarial examples crafted from one model can only be transferred within the same family. Experiment code is publicly available at https: github.com huanzhang12 Adversarial_Survey. We consider the following distributed consensus problem: Each node in a complete communication network of size n initially holds an opinion, which is chosen arbitrarily from a finite set Σ. The system must converge toward a consensus state in which all, or almost all nodes, hold the same opinion. Moreover, this opinion should be valid, i.e., it should be one among those initially present in the system. This condition should be met even in the presence of a malicious adversary who can modify the opinions of a bounded subset of nodes, adaptively chosen in every round. We consider the 3-majority dynamics: At every round, every node pulls the opinion from three random neighbors and sets his new opinion to the majority one (ties are broken arbitrarily). Let k be the number of valid opinions. We show that, if k ≤ nα, where α is a suitable positive constant, the 3-majority dynamics converges in time polynomial in k and log n with high probability even in the presence of an adversary who can affect up to o([EQUATION]) nodes at each round. Previously, the convergence of the 3-majority protocol was known for |Σ| = 2 only, with an argument that is robust to adversarial errors. On the other hand, no anonymous, uniform-gossip protocol that is robust to adversarial errors was known for |Σ| > 2. Many real-life graphs such as social networks and peer-to-peer networks capture the relationships among the nodes by using trust scores to label the edges. Important usage of such networks includes trust prediction, finding the most reliable or trusted node in a local subgraph, etc. For many of these applications, it is crucial to assess the prestige and bias of a node. The bias of a node denotes its propensity to trust mistrust its neighbours and is closely related to truthfulness. If a node trusts all its neighbours, its recommendation of another node as trustworthy is less reliable. It is based on the idea that the recommendation of a highly biased node should weigh less. In this paper, we propose an algorithm to compute the bias and prestige of nodes in networks where the edge weight denotes the trust score. Unlike most other graph-based algorithms, our method works even when the edge weights are not necessarily positive. The algorithm is iterative and runs in O(km) time where k is the number of iterations and m is the total number of edges in the network. The algorithm exhibits several other desirable properties. It converges to a unique value very quickly. Also, the error in bias and prestige values at any particular iteration is bounded. Further, experiments show that our model conforms well to social theories such as the balance theory (enemy of a friend is an enemy, etc.). In this paper, we study the question of how efficiently a collection of interconnected nodes can perform a global computation in the GOSSIP model of communication. In this model, nodes do not know the global topology of the network, and they may only initiate contact with a single neighbor in each round. This model contrasts with the much less restrictive LOCAL model, where a node may simultaneously communicate with all of its neighbors in a single round. A basic question in this setting is how many rounds of communication are required for the information dissemination problem, in which each node has some piece of information and is required to collect all others. In the LOCAL model, this is quite simple: each node broadcasts all of its information in each round, and the number of rounds required will be equal to the diameter of the underlying communication graph. In the GOSSIP model, each node must independently choose a single neighbor to contact, and the lack of global information makes it difficult to make any sort of principled choice. As such, researchers have focused on the uniform gossip algorithm, in which each node independently selects a neighbor uniformly at random. When the graph is well-connected, this works quite well. In a string of beautiful papers, researchers proved a sequence of successively stronger bounds on the number of rounds required in terms of the conductance φ and graph size n, culminating in a bound of O(φ-1 log n). In this paper, we show that a fairly simple modification of the protocol gives an algorithm that solves the information dissemination problem in at most O(D + polylog (n)) rounds in a network of diameter D, with no dependence on the conductance. This is at most an additive polylogarithmic factor from the trivial lower bound of D, which applies even in the LOCAL model. In fact, we prove that something stronger is true: any algorithm that requires T rounds in the LOCAL model can be simulated in O(T + polylog(n)) rounds in the GOSSIP model. We thus prove that these two models of distributed computation are essentially equivalent.