通过互斥概率空间与局部相关假设探索图像生成
Exploring Image Generation via Mutually Exclusive Probability Spaces and Local Correlation Hypothesis
AI总结：
本文提出互斥概率空间和局部依赖假设两个理论框架，并设计BL-AE与γ-ARVM模型，揭示自回归图像生成中全局分布学习导致记忆化、局部依赖促进生成行为的机制。
摘要：
概率生成模型在图像生成中的一个常见假设是：学习全局数据分布足以通过采样生成新图像。我们研究这一核心假设的局限性，即学习全局分布会导致记忆化而非生成行为。我们提出两个理论框架用于研究：互斥概率空间（MEPS）和局部依赖假设（LDH）。MEPS源于以下观察：涉及随机变量的确定性映射（例如神经网络）倾向于降低所涉及随机变量之间的重叠系数，从而诱导互斥性。我们进一步提出一个以重叠系数表示的下界，并引入一种二值潜在自编码器（BL-AE），将图像编码为带符号的二值潜在表示。LDH将有限观测半径内的依赖关系形式化，这促使我们提出γ-自回归随机变量模型（γ-ARVM）。γ-ARVM是一种自回归模型，具有可变的观测范围γ，用于预测下一个token的直方图。使用γ-ARVM，我们观察到随着观测范围增大，自回归模型逐渐转向记忆化。在全局依赖的极限情况下，当模型在由我们的BL-AE生成的二值潜在表示上运行时，其行为表现为纯粹的记忆器。全面的实验和讨论支持我们的研究。
英文摘要：
A common assumption in probabilistic generative models for image generation is that learning the global data distribution suffices to generate novel images via sampling. We investigate the limitation of this core assumption, namely that learning global distributions leads to memorization rather than generative behavior. We propose two theoretical frameworks, the Mutually Exclusive Probability Space (MEPS) and the Local Dependence Hypothesis (LDH), for investigation. MEPS arises from the observation that deterministic mappings (e.g. neural networks) involving random variables tend to reduce overlap coefficients among involved random variables, thereby inducing exclusivity. We further propose a lower bound in terms of the overlap coefficient, and introduce a Binary Latent Autoencoder (BL-AE) that encodes images into signed binary latent representations. LDH formalizes dependence within a finite observation radius, which motivates our $γ$-Autoregressive Random Variable Model ($γ$-ARVM). $γ$-ARVM is an autoregressive model, with a variable observation range $γ$, that predicts a histogram for the next token. Using $γ$-ARVM, we observe that as the observation range increases, autoregressive models progressively shift toward memorization. In the limit of global dependence, the model behaves as a pure memorizer when operating on the binary latents produced by our BL-AE. Comprehensive experiments and discussions support our investigation.
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