We consider the problem of synthesizing optimized circuits for reversible functions using NOT, CNOT and Toffoli gates (NCT), which has important applications in circuit design and quantum cryptography. By defining the state space and state transitions from NCT gates, we transform the synthesis problem into a reachability problem of finding the shortest path connecting the identity function and the targeted function that is to be synthesized. Using Bounded Model Checking (BMC), we propose an algorithm for synthesizing the optimized circuit for reversible functions. For the synthesis of linear reversible functions, we design another method by directly parametrizing the linear invertible matrix. Our methods can produce optimal synthesis of reversible circuits when the number of bits is small, and also can be used as a subroutine of heuristic methods for large bits. Experimental results show the effectiveness of our methods.
Partial multi-label learning (PML) tackles the problem that each example is assigned a candidate label set, of which only a subset is the ground-truth labels. By decomposing the problem using the first-order strategy, we found that PML is similar to the problem of learning with label noise. Motivated by this observation, we proposed a novel method, PML-CV, which tackles the PML problem with a cross-validation approach. To be specific, PML-CV enhances potentially correct labels by using cross-validation. And then use an example refining scheme to weaken the impact of noisy labels further. We also provide some theoretical analysis to explain the effectiveness of our proposed method. Finally, we conduct extensive experiments on different datasets to verify the effectiveness of our method. The experimental results verify that our method is comparable to current state-of-the-art methods.
Recent deep learning models developed to address classification problems related to medical imaging for diagnosis focus on supervised models. However, supervised models are highly dependent on a large amount of accurately labeled training data to train the models. Obtaining such accurately labeled training data is expensive, time-consuming, and requires human expertise, which challenges the generalizing ability of deep learning models in many medical fields. To address this problem, we propose MeanMatch, a semi-supervised method that use a limited amount of labeled data and many unlabeled data to train deep models. We also employ the voting technical to assemble the deep models to improve the generalization performance. Finally, we conduct experiments on the breast-ultrasound image dataset to verify the effectiveness of our approach and compare it to the current state-of-the-art semi-supervised methods. Experimental results show that our method achieves the highest classification accuracy of 83.0\% on the test set, which outperforms or is comparable to the comparison methods and the supervised models.
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