WEBVTT

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An encoder turns an image into continuous feature vectors.
编码器把图像转成连续特征向量。

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Vector quantization gives each vector a discrete address:
向量量化为每个向量赋予离散地址：

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find the nearest entry in a learned codebook,
找到学习得到的码本中最近的条目，

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replace the feature with that entry, and let the decoder
reconstruct from the selected entries.
用它替换特征，再让解码器根据所选条目重建图像。

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Here is an original two-dimensional illustration.
这里是一个原创二维示意。

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Small dots represent encoder outputs; large colored dots
represent code vectors.
小点代表编码器输出，大的彩色点代表码向量。

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The connecting lines show nearest-neighbor choices.
连线表示最近邻选择。

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The counts on the right are computed from this small cloud, not
copied from a tokenizer benchmark.
右侧计数由这片小点云计算得出，并不是视觉标记化模型基准的结果。

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Keep the feature cloud, but place the codebook entries down one
side.
保持特征点云不变，但把码本条目放在一侧。

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Several entries attract no points at all. Other entries collect
many assignments, including points a long way away.
有些条目完全没有点选择，另一些条目获得许多分配，其中包括距离很远的点。

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Adding entries has not automatically supplied useful
representatives for this cloud.
增加条目并不自动为这片点云提供有用的代表。

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That picture captures the motivation behind these two papers.
这幅图体现了两篇论文的动机。

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They study a mismatch between feature and code-vector
distributions.
它们研究特征分布与码向量分布之间的不匹配。

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Codebook collapse means many entries remain unused;
码本坍塌意味着许多条目未被使用；

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a bad geometric fit also creates substantial distortion when
features are replaced by distant codes.
几何匹配不好时，用远处码向量替换特征会引入较大失真。

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The earlier, twenty twenty-five paper already combines three
criteria.
较早的二零二五年论文已经把三个指标结合起来。

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Quantization error asks how far each feature travels to its
selected code.
量化误差衡量特征到所选码向量的距离。

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Utilization asks whether each code was selected at least once.
利用率衡量每个码向量是否至少被选择过一次。

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Codebook perplexity asks how evenly assignments are spread
across the entries.
码本困惑度衡量分配在各条目之间是否均衡。

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Coverage and balance are different.
覆盖与均衡是不同的。

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A code used once and a code used repeatedly both count as used.
只使用一次和反复使用的码向量都算被使用。

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So a fully occupied codebook can still have heavily concentrated
assignments.
因此，一个所有条目都被用到的码本，仍可能存在高度集中的分配。

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The three questions should be read together, rather than
treating one percentage as the whole story.
这三个问题应该一起看，而不是用一个百分比概括全部表现。

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The earlier method adds a distribution-matching objective.
较早的方法加入分布匹配目标。

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Under a Gaussian approximation, its Wasserstein distance can be
computed
在高斯近似下，Wasserstein 距离可以计算，

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from the two clouds' estimated means and covariance matrices.
依据是两片点云估计的均值和协方差矩阵。

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The mean describes location; covariance captures spread and
orientation.
均值描述位置，协方差描述扩散程度和方向。

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Matching only the center would leave the shape unchecked.
仅匹配中心，仍不能检查分布形状。

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This auxiliary objective complements nearest-code assignments.
这个辅助目标补充最近码向量分配。

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The later paper explicitly keeps its matching gradients on the
codebook, with encoder gradients detached for that term.
后来的论文明确让匹配项的梯度只更新码本，并截断该项对编码器的梯度。

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It encourages the representatives to fit the feature
distribution;
它鼓励代表向量贴合特征分布；

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it does not force the encoder itself to generate a Gaussian
cloud.
并不是强迫编码器生成高斯点云。

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The twenty twenty-six record broadens this framework with
maximum mean discrepancy, or MMD.
二零二六年的记录通过最大均值差异，也就是 MMD，扩展了这个框架。

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It compares samples through a kernel without choosing a Gaussian
distributional form.
它用核函数比较样本，不需要指定高斯分布形式。

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Both matching methods update codebook parameters through their
auxiliary loss,
两种匹配方法的辅助损失都更新码本参数，

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while keeping encoder gradients detached for that term.
同时截断该项对编码器的梯度。

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This matters when a cloud has multiple separated modes.
当点云存在多个分离的模式时，这一点尤其相关。

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In the later work's bimodal synthetic experiment, the methods
are comparable near Gaussianity;
后来论文的双峰合成实验中，接近高斯时两方法表现相近；

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as mode separation increases, MMD obtains better error and
utilization.
模式间距增大后，MMD 获得更好的误差和利用率。

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Pairwise kernel comparisons also cost more computation in their
timing study.
其计时研究也显示，样本两两核比较需要更多计算。

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There is an important experimental detail inside the method.
方法中有一个重要的实验细节。

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Raw quantization error depends on the feature distribution's
variance.
原始量化误差依赖特征分布的方差。

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If two encoders produce differently scaled clouds,
如果两个编码器产生不同尺度的点云，

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their raw errors do not isolate which quantizer represents its
own cloud better.
直接比较误差不能单独反映量化器对自身点云的表示能力。

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The later paper therefore studies controlled synthetic features
when comparing the criterion triple.
因此，后来论文在比较三个指标时使用受控的合成特征。

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In our teaching picture, we also hold the small dots fixed while
changing codebook locations.
教学示意保持小点不变，只改变码本位置。

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That makes the geometric comparison readable.
这样使几何比较更容易理解。

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Image reconstruction is then evaluated separately in the actual
trained models.
实际训练模型的图像重建表现则另行评估。

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Now separate the drawing from a measured result.
现在把示意图与测量结果分开。

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In the later paper's FFHQ VQ VAE table, both selected rows use
two hundred fifty-six tokens
后来论文的 FFHQ VQ-VAE 表中，两行都使用二百五十六个 token，

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and a codebook of sixteen thousand three hundred eighty-four
entries.
码本含一万六千三百八十四个条目。

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Vanilla vector quantization reports PSNR of twenty-seven point
eight three decibels.
普通向量量化的 PSNR 为二十七点八三分贝。

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Wasserstein quantization reports twenty-nine point zero three.
Wasserstein 量化为二十九点零三分贝。

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The same block reports codebook use of three point eight percent
for Vanilla
同组中，普通方法的码本利用率为百分之三点八，

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and one hundred percent for Wasserstein.
Wasserstein 方法为百分之一百。

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These are results for this dataset and configuration.
这些结果对应这一数据集和配置。

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PSNR measures reconstruction fidelity; it is not the raw
quantization error,
PSNR 衡量重建保真度，不是原始量化误差，

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and the illustrative cloud does not stand in for this
experiment.
教学点云也不代表这个实验。

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These are two distinct arXiv records.
这是两个不同的 arXiv 记录。

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The earlier one develops the distribution-matching perspective,
the criterion triple, and a Wasserstein-based method.
较早的记录建立分布匹配视角、三个评价指标和基于 Wasserstein 的方法。

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The later one presents a broader framework that also includes
MMD
后来的记录提出更广泛框架，也包含 MMD，

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and explicitly compares their behavior across feature
distributions.
并明确比较两方法在不同特征分布下的表现。

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Read them as a connected research story while preserving their
dates and evidence.
阅读时可以把它们看作相互联系的研究故事，同时保留各自的日期与证据。

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The extension is not that coverage suddenly becomes measurable
in twenty twenty-six.
扩展不是二零二六年才突然能测量覆盖率。

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It is that the matching objective is considered more broadly,
而是更广泛地考虑匹配目标，

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with efficiency and distribution shape entering the choice of
method.
把效率和分布形状纳入方法选择。

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Return to our dots.
回到这些点。

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When code vectors sit near the regions occupied by features,
码向量靠近特征占据的区域时，

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the assignment lines become short and the usage counts become
less concentrated.
分配连线变短，使用计数更均衡。

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Those computed counts explain the geometry; they are not a
promised result of running a training algorithm.
计算出的计数是在解释几何关系，而不是承诺某个训练算法一定达到这种结果。

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The useful question is bigger than whether an image has been
assigned token IDs.
有用的问题不仅是图像是否已经获得 token 编号。

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Are the representatives close, are the entries covered, and is
their use balanced?
代表向量是否接近特征？条目是否被覆盖？使用是否均衡？

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Distributional matching gives these papers a common language for
improving all three aspects of the codebook.
分布匹配为两篇论文提供了共同语言，用于改善码本的这三个方面。