Kolmogorov-Arnold 能量模型：快速、可解释的生成建模
Kolmogorov-Arnold Energy Models: Fast, Interpretable Generative Modeling
AI总结：
本文提出Kolmogorov-Arnold能量模型，通过结合Kolmogorov-Arnold表示定理，提供高效的生成建模方法，实现潜在空间的可解释性，并在多个数据集上取得优异性能。
摘要：
生成模型通常依赖于简单的潜在先验（如变分自编码器，VAEs），这些方法效率高但有限，或者高度表达的迭代采样器（如扩散模型和能量模型），这些方法成本高且不透明。我们引入Kolmogorov-Arnold能量模型（KAEM）以弥合这一权衡，并提供新的潜在空间可解释性机会。基于Kolmogorov-Arnold表示定理的新适应，KAEM在先验上施加单变量潜在结构，通过逆变换方法实现精确推断。在低维潜在空间和适当归纳偏置下，重要性采样成为可 tractable、无偏和高效的后验推断方法。对于这种失败的情况，我们提出了一种基于种群的策略，将后验分解为一系列退火分布，这是能量模型中混合差的新型解决方法。我们比较了KAEM与VAEs和神经潜在EBM架构。KAEM在SVHN和CIFAR10上实现了最佳的Fréchet Inception距离，同时在单次前向传递中采样，并暴露了由1D密度构建的可解释先验。
英文摘要：
Generative models typically rely on either simple latent priors (e.g., Variational Autoencoders, VAEs), which are efficient but limited, or expressive iterative samplers (e.g., Diffusion and Energy-based Models), which are costly and opaque. We introduce a new unsupervised model, the Kolmogorov-Arnold Energy Model (KAEM), to bridge this trade-off and provide new opportunities for interpretability. Based on a novel adaptation of the Kolmogorov-Arnold Representation Theorem, KAEM imposes a univariate latent prior, enabling fast and exact inference via the inverse transform method. On small datasets, we show that importance sampling becomes a tractable, unbiased, and single-pass posterior inference method. For settings requiring exploration, we propose a population-based strategy that decomposes the posterior into a sequence of annealed distributions, serving as a new remedy for poor mixing in Energy-based Models. KAEM attains competitive Fréchet Inception Distance among latent-prior models on SVHN, CIFAR10, and CelebA while sampling in a single forward pass at lower cost than iterative EBMs, and exposing an interpretable prior built from 1D densities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
