Guang Yang
Publications
Taming the Entropy Cliff: Variable Codebook Size Quantization for Autoregressive Visual Generation
Most discrete visual tokenizers rely on a default design: every position in the sequence shares the same codebook. Researchers try to scale the codebook size $K$ to get better reconstruction performance. Such a constant-codebook design hits a fundamental information-theoretic limit. We observe that the per-position conditional entropy of the training set decays so quickly along the sequence that, after a few positions, the conditional distribution becomes essentially deterministic. On ImageNet with $K=16384$, this happens within only 2 out of 256 positions, turning the remaining 254 into a memorization problem. We call this phenomenon the Entropy Cliff and formalize it with a simple expression: $t^{*} = \lceil \log_2 N / \log_2 K \rceil$. Interestingly, this phenomenon is not observed in language, as its natural structure keeps the effective entropy per position well below the codebook capacity. To address this, we propose Variable Codebook Size Quantization (VCQ), where the codebook size $K_t$ grows monotonically along the sequence from $K_{\min}=2$ to $K_{\max}$, leaving the loss function, parameter count, and AR training procedure unchanged. With a vanilla autoregressive Transformer and standard next-token prediction, a base version of VCQ reduces gFID w/o CFG from 27.98 to 14.80 on ImageNet $256\times256$ over the baseline. Scaled up, it reaches gFID 1.71 with 684M autoregressive parameters, without any extra training techniques such as semantic regularization or causal alignment. The extreme information bottleneck at $K_{\min}=2$ naturally induces a coarse-to-fine semantic hierarchy: a linear probe on only the first 10 tokens reaches 43.8% top-1 accuracy on ImageNet, compared to 27.1% for uniform codebooks. Ultimately, these results show that what matters is not only the total capacity of the codebook, but also how that capacity is distributed and organized.
Autoregressive Visual Generation Needs a Prologue
In this work, we propose Prologue, an approach to bridging the reconstruction-generation gap in autoregressive (AR) image generation. Instead of modifying visual tokens to satisfy both reconstruction and generation, Prologue generates a small set of prologue tokens prepended to the visual token sequence. These prologue tokens are trained exclusively with the AR cross-entropy (CE) loss, while visual tokens remain dedicated to reconstruction. This decoupled design lets us optimize generation through the AR model's true distribution without affecting reconstruction quality, which we further formalize from an ELBO perspective. On ImageNet 256x256, Prologue-Base reduces gFID from 21.01 to 10.75 without classifier-free guidance while keeping reconstruction almost unchanged; Prologue-Large reaches a competitive rFID of 0.99 and gFID of 1.46 using a standard AR model without auxiliary semantic supervision. Interestingly, driven only by AR gradients, prologue tokens exhibit emergent semantic structure: linear probing on 16 prologue tokens reaches 35.88% Top-1, far above the 23.71% of the first 16 tokens from a standard tokenizer; resampling with fixed prologue tokens preserves a similar high-level semantic layout. Our results suggest a new direction: generation quality can be improved by introducing a separate learned generative representation while leaving the original representation intact.