intrinsic representation analysis

该研究提出一种在Mapper诱导的结构化表示上进行学习的框架，解决传统方法可能忽略数据多尺度结构的问题。

Conventional entropy-based diversity metrics fail to capture the intrinsic geometric and topological structure of high-dimensional training data, limiting their ability to assess data quality and predict model performance. Method: This work introduces persistent homology—a tool from topological data analysis—to quantify structural properties such as connected components, holes, and higher-order voids, thereby jointly characterizing data richness and redundancy through both topological and geometric lenses. Contribution/Results: Experiments demonstrate that the proposed topological metrics exhibit strong correlation with model generalization performance and serve as effective predictors of data quality. The framework enables principled data selection and efficient training, offering a novel paradigm for dataset curation. By leveraging topological signatures, it enhances training efficiency and robustness of AI systems without requiring model retraining or architectural modification. The approach is broadly applicable across domains where data geometry and topology critically influence learning dynamics.

Conventional dimensionality reduction (DR) evaluation suffers from systematic bias due to the frequent adoption of highly correlated metrics, leading to overemphasis on specific structural properties. Method: We propose an empirically grounded metric redundancy reduction framework: first computing Pearson correlation matrices across diverse datasets and DR algorithms; then applying clustering to identify functionally redundant metric groups; and finally retaining only the most representative metric per group—replacing subjective, intent-driven metric selection with objective, behavior-based clustering. Contribution/Results: Our approach significantly improves cross-dataset and cross-algorithm stability of DR evaluations, effectively mitigating structural biases inherent in traditional assessment protocols. Experimental validation demonstrates enhanced reproducibility and generalizability, establishing a principled, data-driven framework for fair and robust comparative evaluation of DR methods.

This paper addresses the challenges of evaluating dimensionality reduction (DR) effectiveness and estimating intrinsic data dimensionality. We propose a geometric profiling method based on sectional curvature in discrete metric spaces, which characterizes large-scale data geometry via metric relationships among point triplets. For the first time, this approach systematically introduces differential-geometric curvature into quantitative DR quality assessment and intrinsic dimension estimation—without requiring embedded coordinates or manifold assumptions, thus ensuring both theoretical rigor and computational feasibility. Experiments across diverse synthetic and real-world datasets demonstrate that our method robustly discriminates DR algorithm performance, achieves significantly lower intrinsic dimension estimation error than state-of-the-art methods (e.g., MDS- and PCA-based estimators), and successfully uncovers latent negative curvature in empirical networks—including social and biological networks.

Existing evaluation metrics for deep generative models (e.g., VAEs, GANs, diffusion models, Transformers) in engineering design—largely borrowed from statistical likelihood-based measures—fail to capture design-critical properties such as constraint satisfaction, functional performance, and design value. Method: We propose the first multidimensional evaluation framework tailored to engineering design, comprising four orthogonal dimensions: constraint compliance, functional effectiveness, novelty, and conditional controllability. We further develop an open-source, reproducible benchmark suite and software toolkit to bridge machine learning theory and design practice. Contribution/Results: The framework is rigorously validated on 2D visualization case studies and real-world engineering tasks—including bicycle frame and structural topology generation. Experiments demonstrate substantial improvements in alignment between automated evaluation and human-assessed design value: target achievement rate (+23.6%), geometric constraint compliance (+31.4%), and design novelty (+18.9%).

Existing neural representational similarity measures focus solely on the extrinsic geometry of state space, limiting their ability to reveal the essential intrinsic differences among neural network solutions. This work proposes Metric Similarity Analysis (MSA), which introduces Riemannian geometry into representational similarity research for the first time. Grounded in the manifold hypothesis, MSA characterizes the geometric structure of neural representations through intrinsic metrics defined on statistical manifolds. The method effectively distinguishes computational mechanisms of deep networks trained under different learning paradigms, enables precise comparison of nonlinear dynamical behaviors, and successfully extends to the analysis of diffusion models. Empirical validation demonstrates its broad applicability across diverse settings and its mathematical rigor.

This work proposes the first projective-geometric framework for measuring representational drift, grounded in the Fubini–Study metric, which treats high-dimensional representations as points in projective space and quantifies their geometric evolution along trajectories. Conventional metrics—such as Euclidean or cosine distance—are prone to conflating genuine structural changes in data with artifacts induced by parametrization ambiguities, such as global scaling or sign flips. In contrast, the proposed approach is gauge-invariant, effectively disentangling intrinsic representational dynamics from spurious perturbations due to parameterization freedom. It further introduces a computable, monotonic quantity to rigorously quantify representational churn. Experiments on real high-dimensional data demonstrate that this framework avoids the systematic overestimation of drift inherent in traditional measures, yielding stable and interpretable diagnostics suitable for general-purpose empirical analysis pipelines.

This work addresses the systematic misjudgments of existing identifiability evaluation metrics—such as MCC, DCI, and R²—arising from mismatches between their implicit assumptions and either the true data-generating process or the encoder’s geometric structure. Through theoretical analysis and synthetic benchmarking, we develop a stress-testing framework and introduce, for the first time, a taxonomy that disentangles the roles of data-generation assumptions and encoder geometry in determining metric validity. This classification clarifies the failure mechanisms of current metrics under both classical and post-hoc identifiability settings. Accompanying this analysis, we release a reproducible evaluation suite that delineates the valid applicability domains of each metric, thereby providing reliable tools and principled guidelines for assessing identifiability in representation learning.

Existing dataset characterization methods—statistical, structural, and model-driven—lack sufficient interpretability and deep structural insight. To address this, we propose a novel tensor-based representation paradigm that transcends conventional two-dimensional assumptions. Our approach leverages high-order tensor decomposition, multilinear modeling, and cross-modal joint representation to explicitly capture high-dimensional, nonlinear, and multi-source relational structures inherent in complex data. Extensive experiments demonstrate that the proposed method significantly outperforms baseline approaches in three key aspects: (i) disentangling intricate data structures, (ii) enhancing feature interpretability, and (iii) enabling traceable downstream task reasoning. This work establishes a unified tensor modeling framework for dataset representation and pioneers a data-driven discovery pathway tailored for explainable AI. It contributes both theoretical advances—through formalizing multilinear structure learning—and practical utility—by providing an interpretable, computationally grounded toolkit for transparent data analysis.

研究探讨了模型素养作为视觉分析性能的额外评价因素，通过控制实验发现模型-任务准确性和视觉分析任务准确性之间存在正相关关系。