Deep learning models exhibit a preference for statistical fitting over logical reasoning. Spurious correlations might be memorized when there exists statistical bias in training data, which severely limits the model performance especially in small da
ta scenarios. In this work, we introduce Counterfactual Adversarial Training framework (CAT) to tackle the problem from a causality perspective. Particularly, for a specific sample, CAT first generates a counterfactual representation through latent space interpolation in an adversarial manner, and then performs Counterfactual Risk Minimization (CRM) on each original-counterfactual pair to adjust sample-wise loss weight dynamically, which encourages the model to explore the true causal effect. Extensive experiments demonstrate that CAT achieves substantial performance improvement over SOTA across different downstream tasks, including sentence classification, natural language inference and question answering.
This paper aims to reduce the power losses and to enhance the
voltage profile of the power system while maintaining the loading of the
transmission lines within the allowable limits, through the optimal
placement of the Unified Power Flow Controller (UPFC).
In this paper, we present two new methods for finding
the numerical solutions of systems of the nonlinear equations.
The basic idea depend on
founding relationship between minimum of a function and the
solution of systems of the nonlinear equatio
ns. The first method
seeks the numerical solution with a sequence of search
directions, which is depended on gradient and Hessian matrix of
function, while the second method is based on a sequence of
conjugate search directions. The study shows that our two
methods are convergent, and they can find exact solutions for
quadratic functions, so they can find high accurate solutions for
over quadratic functions. The purposed two algorithms are
programmed by Mathematica Version9. The approximate
solutions of some test problems are given. Comparisons of our
results with other methods illustrate the efficiency and highly
accurate of our suggested methods.
