We study high-dimensional inference problems with tensor-structured data and establish conditions under which their free energy can be approximated by that of a Gaussian comparison model. Our framework applies to models with independent observations and mismatch between the data-generating distribution and the statistical model. The results extend prior work beyond matrix settings and accommodate scaling regimes where the model parameters depend on the dimension. A key technical contribution is the use of generic chaining to control remainder terms arising from likelihood expansions over tensor-structured parameter spaces. As an application, we establish free energy universality for binary hypergraph models under the minimal assumption of diverging average degree, showing that their asymptotic behavior coincides with that of a Gaussian tensor model, even under model mismatch.

翻译：我们研究具有张量结构数据的高维推断问题，并建立了其自由能可被高斯比较模型近似成立的条件。该框架适用于包含独立观测数据且数据生成分布与统计模型存在失配的情形。研究结果将先前工作拓展至矩阵场景之外，并适用于模型参数随维度变化缩放的区域。关键技术贡献在于采用一般性链方法，控制来自张量结构参数空间似然展开的余项。作为应用实例，我们在平均发散度的最小假设下建立了二元超图模型的自由能普适性，证明即使在模型失配条件下，其渐近行为仍与高斯张量模型一致。