Learning Deep Representations of Data Distributions

The book uses channels-first ordering for all image dimensions.

• Standard: (C, H, W) (Channels, Height, Width).
• Action: Convert any (H, W, C) orderings (e.g., \x \in \mathbb{R}^{H \times W \times 3}) to the (C, H, W) format (e.g., \mathbb{R}^{c \times h \times w}).

% Correct (Channels-first)
\mathbb{R}^{c \times h \times w}

% Incorrect (Channels-last)
\mathbb{R}^{h \times w \times c}

The chapter uses various symbols for definitional equality (such as := or \triangleq).

Resolution: Standardize all instances to use \doteq throughout the chapter.

Sync regions are defined by LaTeX labels that act as anchors between English and Chinese files. Labels use prefixes such as ch:, sec:, sub:, eqn:, fig:, thm:, and ex:.

To find a sync region for a changed line range in an English file:

1. Upper Bound: Search upward from the first changed line to find the nearest \label{...} line. If none exists, use the beginning of the file.
2. Lower Bound: Search downward from the last changed line to find the nearest \label{...} line. If none exists, use the end of the file.
3. Extraction: The sync region includes all content between these two labels (inclusive of the label lines).

Note: If multiple changed regions share the same bounding labels, they should be merged into a single sync region.

Chapter 8 establishes a primary notation of f_{\theta} for the encoder and g_{\eta} for the decoder. Several sections deviate from this:

• VAE section: Uses \mathcal{E} and \mathcal{D}.
• RAE section: Uses f and g without subscripts.
• Michelangelo section: Uses \mathcal{E}_{\mathrm{s}}, \mathcal{D}_{\mathrm{s}}, \mathcal{E}_{\mathrm{i}}, \mathcal{E}_{\mathrm{t}}.
• Conditional generation section: Uses \mathcal{E} and \mathcal{D}.

Resolution: If the VAE encoder/decoder are architecturally distinct from the transformer-based f_{\theta}/g_{\eta}, calligraphic notation is acceptable but must be acknowledged as distinct. At a minimum, convert \mathcal{E} to \cE and \mathcal{D} to \cD to maintain distinction.

When performing a translation sync, be aware of the following edge cases:

• Missing Labels: If a changed region lacks an upper label, use the start of the file. If it lacks a lower label, use the end of the file.
• Merged Regions: If multiple changed regions are bounded by the same set of labels, merge them into one single sync region for translation.
• Missing Translation Files: If the corresponding _zh.tex file for an English file does not exist, the process should skip that file and issue a warning.

In Chapter 8, the symbol heta is primarily used for neural network parameters. However, conflicts arise in specific sections:

• Cupid section: Redefines heta as camera pose ( heta = \boldsymbol{\theta}).
• EgoAllo section: Uses heta for both SMPL joint rotations and network parameters.

Resolution: Use a different symbol for pose or joint rotations (e.g., \vxi) or use clear subscripts to distinguish them from network parameters.

There is a notation conflict regarding the symbol \mathcal{D}:

• Overall setup: \cD represents the set of possible data (the dataset).
• VAE section: \mathcal{D} is used to represent both the dataset AND the decoder.

Resolution: Use \cD exclusively for datasets. Use a different symbol or a subscripted version for the decoder to avoid ambiguity.

When using ordinals:

• Prefer "first" over "firstly".
• Prefer "second" over "secondly".
• In bulleted or itemized lists, avoid using ordinals if they are unnecessary.

When citing sources, use specific LaTeX citation commands instead of the bare \cite{...} command:

1. Parenthetical citations: Use \citep{...} when the citation should appear in parentheses within the sentence (e.g., "...as shown previously \citep{smith2020}.").
2. Textual citations: Use \citet{...} when the author's name is part of the sentence flow (e.g., "As \citet{smith2020} showed...").

% Parenthetical
...as shown previously \citep{smith2020}.

% Textual
As \citet{smith2020} showed...

When referencing structural elements like figures, tables, sections, chapters, theorems, or remarks, always use the \Cref{...} command (with a capital 'C').

Do not use:

• Bare \ref{...}
• Manual labels like Figure~\ref{...} or Section~\ref{...}
• Lowercase \cref{...}

Note that \Cref{...} automatically includes the type name (e.g., \Cref{ch:foo} produces "Chapter ##"), so you should not manually add the word "Chapter" or "Figure" before the command.

% Correct
\Cref{fig:example}
\Cref{ch:intro}

% Incorrect
\ref{fig:example}
\cref{fig:example}
Figure~\ref{fig:example}