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An Interpretable Evaluation of Entropy-based Novelty of Generative Models (2402.17287v2)

Published 27 Feb 2024 in cs.LG, cs.CV, and stat.ML

Abstract: The massive developments of generative model frameworks require principled methods for the evaluation of a model's novelty compared to a reference dataset. While the literature has extensively studied the evaluation of the quality, diversity, and generalizability of generative models, the assessment of a model's novelty compared to a reference model has not been adequately explored in the machine learning community. In this work, we focus on the novelty assessment for multi-modal distributions and attempt to address the following differential clustering task: Given samples of a generative model $P_\mathcal{G}$ and a reference model $P_\mathrm{ref}$, how can we discover the sample types expressed by $P_\mathcal{G}$ more frequently than in $P_\mathrm{ref}$? We introduce a spectral approach to the differential clustering task and propose the Kernel-based Entropic Novelty (KEN) score to quantify the mode-based novelty of $P_\mathcal{G}$ with respect to $P_\mathrm{ref}$. We analyze the KEN score for mixture distributions with well-separable components and develop a kernel-based method to compute the KEN score from empirical data. We support the KEN framework by presenting numerical results on synthetic and real image datasets, indicating the framework's effectiveness in detecting novel modes and comparing generative models. The paper's code is available at: www.github.com/buyeah1109/KEN

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Citations (5)
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Summary

  • The paper introduces the kernel-based entropic novelty (KEN) score, using spectral properties of kernel covariance matrices to measure novelty in model outputs.
  • It employs Cholesky decomposition to reduce computational complexity while accurately detecting underrepresented modes in both synthetic and real image datasets.
  • Extensive experiments validate the approach, establishing an interpretable benchmark for assessing the creative fidelity of generative models.

A Spectral Method for Evaluating Novelty in Generative Models

Introduction

In the landscape of deep generative models, such as Variational Autoencoders (VAEs), Generative Adversarial Networks (GANs), and denoising diffusion models, significant strides have been made in rendering realistic and diverse images and speech data. Prudent evaluation of these models is essential to uncover the nuances of their learning capabilities, particularly their novelty generation prowess. The paper introduces a spectral approach to assess the novelty of generative models by explicitly quantifying the modes present in a test distribution more prominently than in a reference dataset.

Novelty Evaluation Framework

The cornerstone of this work is the Kernel-based Entropic Novelty (KEN) score, a metric devised to measure the novelty of a generative model’s output relative to a reference data distribution. This spectral method capitalizes on the eigenspace of kernel covariance matrices, correlating the principal eigenvectors with the mean centers of significant modes in mixture distributions. The KEN score, derived from the entropy of the positive eigenvalues of a difference covariance matrix, precisely quantifies the relative frequency of novel modes in the generated data.

Theoretical Analysis and Methodological Development

Analytical underpinnings of the KEN score are explored through the lens of mixture distributions with sub-Gaussian components. A methodological breakthrough is achieved by employing the Cholesky decomposition, reducing the computational complexity of evaluating novelty in high-dimensional feature spaces. This reduction not only facilitates efficient computation of the KEN score but also circumvents the challenges associated with non-Hermitian matrices intrinsic to original matrix-based approaches.

Empirical Validation

A series of numerical experiments underscore the efficacy of the proposed methodology. Applying the KEN score to synthetic and real image datasets, the paper demonstrates its potent capability in detecting unexpressed or underrepresented modes in reference datasets. The flexibility and adaptability of the KEN score are evidenced by its application to substantive generative models, offering an interpretable benchmark for enhancing the creative fidelity of these models.

Implications and Future Prospects

This work fills a critical gap in the generative models' evaluation by providing a principled approach to novelty assessment. It paves the way for refining training paradigms to encourage the discovery of novel data representations. The introduction of the KEN score enhances our toolkit for a deeper dive into the capabilities and limitations of generative models, setting a new precedent for future developments in the field. It raises intriguing questions about the bounds of novelty generation and opens avenues for exploring other significant traits of generative models such as coherence and contextual relevance.

Conclusion

The proposed spectral method for evaluating novelty injects a new dimension into the analysis of generative models. By spotlighting the importance of novelty alongside quality and diversity, this paper contributes a critical perspective to the discourse on generative model evaluation. As we venture into uncharted realms of artificial creativity, tools like the KEN score will be indispensable in shaping the evolution of generative models to generate not just data that mimics reality but also data that enriches it with novelty.

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