We study constrained versions of the Ingleton inequality in the entropic setting and quantify its stability under small violations of conditional independence. Although the classical Ingleton inequality fails for general entropy profiles, it is known to hold under certain exact independence constraints. We focus on the regime where selected conditional mutual information terms are small (but not zero), and the inequality continues to hold up to controlled error terms. A central technical tool is a structural lemma that materializes part of the mutual information between two random variables, implicitly capturing the effect of infinitely many non-Shannon--type inequalities. This leads to conceptually transparent proofs without explicitly invoking such infinite families. Some of our bounds recover, in a unified way, what can also be deduced from the infinite families of inequalities of Matúš (2007) and of Dougherty--Freiling--Zeger (2011), while others appear to be new.

翻译：我们研究了熵约束条件下英格尔顿不等式的受约束版本，并量化了其在条件独立性小幅违背下的稳定性。尽管经典英格尔顿不等式对一般熵轮廓不成立，但已知其在特定精确独立性约束下成立。我们聚焦于选定条件互信息项较小（但不为零）的情形，此时不等式在可控误差项内仍成立。一项核心技术工具是结构引理，该引理实现了两个随机变量间部分互信息的物质化，隐含地捕捉了无穷多个非香农型不等式的影响。这使我们无需显式调用此类无穷族即可获得概念上透明的证明。我们的一些界以统一方式复原了可从Matúš（2007）及Dougherty-Freiling-Zeger（2011）的无穷不等式族推导出的结果，而其他界则似乎是新的。