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1. Simplex Consensus: A Simple and Fast Consensus Protocol

   Benjamin Y. Chan and Rafael Pass (November 2023, TCC'23)
2. Consensus Subspace Clustering

   https://doi.org/10.1109/ICTAI52525.2021.00064  

   Thom, Nathan; Nguyen, Hung; Hand, Emily M. (November 2021, IEEE International Conference on Tools with Artificial Intelligence)

   One significant challenge in the field of supervised deep learning is the lack of large-scale labeled datasets for many problems. In this paper, we propose Consensus Spectral Clustering (CSC), which leverages the strengths of convolutional autoencoders and spectral clustering to provide pseudo labels for image data. This data can be used as weakly-labeled data for training and evaluating classifiers which require supervision. The primary weaknesses of previous works lies in their inability to isolate the object of interest in an image and cluster similar images together. We address these issues by denoising input images to remove pixels which do not contain data pertinent to the target. Additionally, we introduce a voting method for label selection to improve the clustering results. Our extensive experimentation on several benchmark datasets demonstrates that the proposed CSC method achieves competitive performance with state-of-the-art methods. 

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3. Kemeny Consensus Complexity

   https://doi.org/10.24963/ijcai.2021/28  

   Fitzsimmons, Zack; Hemaspaandra, Edith (August 2021, Thirtieth International Joint Conference on Artificial Intelligence (IJCAI))

   null (Ed.)

   The computational study of election problems generally focuses on questions related to the winner or set of winners of an election. But social preference functions such as Kemeny rule output a full ranking of the candidates (a consensus). We study the complexity of consensus-related questions, with a particular focus on Kemeny and its qualitative version Slater. The simplest of these questions is the problem of determining whether a ranking is a consensus, and we show that this problem is coNP-complete. We also study the natural question of the complexity of manipulative actions that have a specific consensus as a goal. Though determining whether a ranking is a Kemeny consensus is hard, the optimal action for manipulators is to simply vote their desired consensus. We provide evidence that this simplicity is caused by the combination of election system (Kemeny), manipulative action (manipulation), and manipulative goal (consensus). In the process we provide the first completeness results at the second level of the polynomial hierarchy for electoral manipulation and for optimal solution recognition. 

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4. Consensus‐based sampling

   https://doi.org/10.1111/sapm.12470  

   Carrillo, J_A; Hoffmann, F.; Stuart, A_M; Vaes, U. (January 2022, Studies in Applied Mathematics)

   Abstract We propose a novel method for sampling and optimization tasks based on a stochastic interacting particle system. We explain how this method can be used for the following two goals: (i) generating approximate samples from a given target distribution and (ii) optimizing a given objective function. The approach is derivative‐free and affine invariant, and is therefore well‐suited for solving inverse problems defined by complex forward models: (i) allows generation of samples from the Bayesian posterior and (ii) allows determination of the maximum a posteriori estimator. We investigate the properties of the proposed family of methods in terms of various parameter choices, both analytically and by means of numerical simulations. The analysis and numerical simulation establish that the method has potential for general purpose optimization tasks over Euclidean space; contraction properties of the algorithm are established under suitable conditions, and computational experiments demonstrate wide basins of attraction for various specific problems. The analysis and experiments also demonstrate the potential for the sampling methodology in regimes in which the target distribution is unimodal and close to Gaussian; indeed we prove that the method recovers a Laplace approximation to the measure in certain parametric regimes and provide numerical evidence that this Laplace approximation attracts a large set of initial conditions in a number of examples. 

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5. Safe Permissionless Consensus

   Pu, Youer; Alvisi, Lorenzo; Eyal, Ittay (October 2022, Leibniz international proceedings in informatics)

   Scheideler, Christian (Ed.)

   Nakamoto’s consensus protocol works in a permissionless model, where nodes can join and leave without notice. However, it guarantees agreement only probabilistically. Is this weaker guarantee a necessary concession to the severe demands of supporting a permissionless model? This paper shows that, at least in a benign failure model, it is not. It presents Sandglass, the first permissionless con- sensus algorithm that guarantees deterministic agreement and termination with probability 1 under general omission failures. Like Nakamoto, Sandglass adopts a hybrid synchronous communication model, where, at all times, a majority of nodes (though their number is unknown) are correct and synchronously connected, and allows nodes to join and leave at any time. 

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