This research concerns Learned Data Structures, a recent area that has emerged at the crossroad of Machine Learning and Classic Data Structures. It is methodologically important and with a high practical impact. We focus on Learned Indexes, i.e., Learned Sorted Set Dictionaries. The proposals available so far are specific in the sense that they can boost, indeed impressively, the time performance of Table Search Procedures with a sorted layout only, e.g., Binary Search. We propose a novel paradigm that, complementing known specialized ones, can produce Learned versions of any Sorted Set Dictionary, for instance, Balanced Binary Search Trees or Binary Search on layouts other that sorted, i.e., Eytzinger. Theoretically, based on it, we obtain several results of interest, such as (a) the first Learned Optimum Binary Search Forest, with mean access time bounded by the Entropy of the probability distribution of the accesses to the Dictionary; (b) the first Learned Sorted Set Dictionary that, in the Dynamic Case and in an amortized analysis setting, matches the same time bounds known for Classic Dictionaries. This latter under widely accepted assumptions regarding the size of the Universe. The experimental part, somewhat complex in terms of software development, clearly indicates the nonobvious finding that the generalization we propose can yield effective and competitive Learned Data Structural Booster, even with respect to specific benchmark models.

翻译：本研究关注学习型数据结构，这是一个在机器学习与经典数据结构交叉领域新兴的研究方向，具有重要的方法论意义和极高的实践价值。我们聚焦于学习型索引，即学习型有序集合字典。现有的方案具有特化性，它们只能显著提升基于有序布局的表查找过程（例如二分查找）的时间性能。我们提出了一种全新范式，作为已知特化方法的补充，能够为任意有序集合字典（例如平衡二叉搜索树或基于非有序布局（如Eytzinger布局）的二分查找）生成学习型版本。从理论上讲，基于这一范式，我们获得了若干有意义的成果，包括：(a) 首个学习型最优二叉搜索森林，其平均访问时间受限于字典访问概率分布的熵；(b) 首个学习型有序集合字典，在动态场景和摊销分析框架下，其时间界限与经典字典的已知界限相匹配，且这一结果基于关于宇宙规模广泛接受的假设。实验部分虽在软件开发方面较为复杂，但明确揭示了一个非平凡的发现：我们提出的泛化方法能够生成有效且具有竞争力的学习型数据结构增强器，即便与特定的基准模型相比亦如此。