Sedimentary microfacies identification is fundamental for reservoir characterization, directly influencing hydrocarbon exploration and production strategies. However, traditional methods relying on core analysis, seismic interpretation, and manual well‐log analysis face significant challenges: (1) high costs and limited coverage of coring data, (2) subjectivity in seismic facies interpretation, and (3) poor generalization of conventional machine learning models when trained on small datasets. To overcome these limitations, this study proposes Hopular—a novel deep learning architecture leveraging modern Hopfield networks. We validated the framework using 4000 normalized data points from 10 wells, covering eight logging parameters and five microfacies types. Evaluations across small (≤ 500 samples), medium (≤ 2000), and large (≥ 3000) datasets demonstrated robust performance, with R 2 scores of 0.704 (±0.021), 0.809 (±0.059), and 0.925, respectively. The model excels in capturing data relationships, particularly in small data regimes (11.6% R 2 improvement over ensemble methods). In summary, Hopular provides an accurate, data‐efficient solution for microfacies identification and supports exploration in data‐scarce settings. This work advances reservoir characterization by combining Hopfield networks’ associative memory with deep learning, offering reliable technical support for subsurface interpretation.

An adversarial attack is typically implemented by solving a constrained optimization problem. In top-k adversarial attacks implementation for multi-label learning, the attack failure degree (AFD) and attack cost (AC) of a possible attack are major concerns. According to our experimental and theoretical analysis, existing methods are negatively impacted by the coarse measures for AFD/AC and the indiscriminate treatment for all constraints, particularly when there is no ideal solution. Hence, this study first develops a refined measure based on the Jaccard index appropriate for AFD and AC, distinguishing the failure degrees/costs of two possible attacks better than the existing indicator function-based scheme. Furthermore, we formulate novel optimization problems with the least constraint violation via new measures for AFD and AC, and theoretically demonstrate the effectiveness of weighting slack variables for constraints. Finally, a self-paced weighting strategy is proposed to assign different priorities to various constraints during optimization, resulting in larger attack gains compared to previous indiscriminate schemes. Meanwhile, our method avoids fluctuations during optimization, especially in the presence of highly conflicting constraints. Extensive experiments on four benchmark datasets validate the effectiveness of our method across different evaluation metrics.

‘‘Easy/hard sample” is a popular parlance in machine learning. Learning difficulty of samples refers to how easy/hard a sample is during a learning procedure. An increasing need of measuring learning difficulty demonstrates its importance in machine learning (e.g., difficulty-based weighting learning strategies). Previous literature has proposed a number of learning difficulty measures. However, no comprehensive investigation for learning difficulty is available to date, resulting in that nearly all existing measures are heuristically defined without a rigorous theoretical foundation. This study attempts to conduct a pilot theoretical study for learning difficulty of samples. First, influential factors for learning difficulty are summarized. Under various situations conducted by summarized influential factors, correlations between learning difficulty and two vital criteria of machine learning, namely, generalization error and model complexity, are revealed. Second, a theoretical definition of learning difficulty is proposed on the basis of these two criteria. A practical measure of learning difficulty is proposed under the direction of the theoretical definition by importing the bias-variance trade-off theory. Subsequently, the rationality of theoretical definition and the practical measure are demonstrated, respectively, by analysis of several classical weighting methods and abundant experiments realized under all situations conducted by summarized influential factors. The mentioned weighting methods can be reasonably explained under the proposed theoretical definition and concerned propositions. The comparison in these experiments indicates that the proposed measure significantly outperforms the other measures throughout the experiments.