We first prove the direction Z T SI(Z;T) = 0, which is equivalent to prove I(Z;T) = 0 SI(Z;T) = 0. We prove the contrapositive, i.e. rather than show LHS = RHS, we show that RHS = LHS. Now assume that supwi,vj ρ(w i Z i,v j T j) > ϵ for some i,j. Then by setting those elements in w,v unrelated to Z i,T j to zero, and those related to Z i,T j exactlythesameaswi,vj,weknowthatsupw,vρ(w Z,v T) > ϵ. All neural networks are trained by Adam with its default settings and a learning rate η = 0.001. Early stopping is an useful technique for avoiding overfitting, however it needs to be carefully considered when applied to adversarial methods.

Since the principal subgraphs are common subgraphs in the molecular graphs, they should be relatively stable with respect to the scale of training set.

In this paper, we present an approach to automated solving of triangle ruler-and-compass construction problems using finite-domain constraint solvers. The constraint model is described in the MiniZinc modeling language, and is based on the automated planning. The main benefit of using general constraint solvers for such purpose, instead of developing dedicated tools, is that we can rely on the efficient search that is already implemented within the solver, enabling us to focus on geometric aspects of the problem. We may also use the solver's built-in optimization capabilities to search for the shortest possible constructions. We evaluate our approach on 74 solvable problems from the Wernick's list, and compare it to the dedicated triangle construction solver ArgoTriCS. The results show that our approach is comparable to dedicated tools, while it requires much less effort to implement. Also, our model often finds shorter constructions, thanks to the optimization capabilities offered by the constraint solvers.

Various works have utilized deep reinforcement learning (DRL) to address the query optimization problem in database system. They either learn to construct plans from scratch in a bottom-up manner or guide the plan generation behavior of traditional optimizer using hints. While these methods have achieved some success, they face challenges in either low training efficiency or limited plan search space. To address these challenges, we introduce FOSS, a novel DRL-based framework for query optimization. FOSS initiates optimization from the original plan generated by a traditional optimizer and incrementally refines suboptimal nodes of the plan through a sequence of actions. Additionally, we devise an asymmetric advantage model to evaluate the advantage between two plans. We integrate it with a traditional optimizer to form a simulated environment. Leveraging this simulated environment, FOSS can bootstrap itself to rapidly generate a large amount of high-quality simulated experiences. FOSS then learns and improves its optimization capability from these simulated experiences. We evaluate the performance of FOSS on Join Order Benchmark, TPC-DS, and Stack Overflow. The experimental results demonstrate that FOSS outperforms the state-of-the-art methods in terms of latency performance and optimization time. Compared to PostgreSQL, FOSS achieves savings ranging from 15% to 83% in total latency across different benchmarks.

Ensemble-based methods are highly popular approaches that increase the accuracy of a decision by aggregating the opinions of individual voters. The common point is to maximize accuracy; however, a natural limitation occurs if incremental costs are also assigned to the individual voters. Consequently, we investigate creating ensembles under an additional constraint on the total cost of the members. This task can be formulated as a knapsack problem, where the energy is the ensemble accuracy formed by some aggregation rules. However, the generally applied aggregation rules lead to a nonseparable energy function, which takes the common solution tools -- such as dynamic programming -- out of action. We introduce a novel stochastic approach that considers the energy as the joint probability function of the member accuracies. This type of knowledge can be efficiently incorporated in a stochastic search process as a stopping rule, since we have the information on the expected accuracy or, alternatively, the probability of finding more accurate ensembles. Experimental analyses of the created ensembles of pattern classifiers and object detectors confirm the efficiency of our approach. Moreover, we propose a novel stochastic search strategy that better fits the energy, compared with general approaches such as simulated annealing.