Base-Directed Reconstruction Variants

This note records the paper-facing terminology for the objective variants, baselines, and ablations used when reporting experiments on base-directed reconstruction. It complements Base-directed reconstruction objective, which records the formal objective and notation; this note records the variant taxonomy and compact labels for text, captions, tables, and figures.

Family Structure

Use base-directed reconstruction family for the objective family whose reconstruction pressure is defined using fixed base-model quantities from $p_\theta$ .

Reference phrasing:

The base-directed reconstruction family has two $p_\theta$ -dependent mechanisms: a global $p_\theta$ surprisal scale, which measures reconstruction in base-model reference units, and token-level $p_\theta$ surprisal weighting, which allocates reconstruction pressure across response tokens.

Use global $p_\theta$ surprisal scale for the global reference-scale mechanism. In equations, this corresponds to measuring reconstruction relative to the z-free base-model reference scale such as $c_\theta$ or its empirical estimate $\widehat c_\theta$ .

Use token-level $p_\theta$ surprisal weighting for the token-allocation mechanism. This names the use of z-free base-model token surprisal $b_{\theta,t}(x,y)$ to allocate reconstruction pressure across response tokens.

Use global scale + token-level weighting for the combined variant in prose. Avoid using base-directed reconstruction as the label for only the combined variant, because all variants in this family are base-directed in the broader sense.

Reported Comparison Set

The default reported comparison set contains standard variational baselines, base-directed reconstruction variants, and an inverse-surprisal ablation.

Role	Figure label	Paper-facing name	Reference description
Standard variational baseline	ELBO	standard conditional ELBO	Standard conditional ELBO baseline with uniform reconstruction pressure and the usual variational regularizer.
Reduced-KL variational baseline	$\beta$ -ELBO	$\beta$ -ELBO or low- $\beta$ conditional ELBO	Same uniform reconstruction term as ELBO, but with $\beta<1$ on the KL term. Captions should specify that $\beta<1$ .
Global base-directed variant	global scale	global $p_\theta$ surprisal scale	Uses the global z-free base-model surprisal scale to measure reconstruction in base-model reference units.
Token-level base-directed variant	token weighting	token-level $p_\theta$ surprisal weighting	Uses token-level z-free base-model surprisal to allocate reconstruction pressure across response tokens.
Combined base-directed variant	global + token	global scale + token-level weighting	Combines the global $p_\theta$ surprisal scale with token-level $p_\theta$ surprisal weighting.
Reversed token-direction ablation	token inverse	inverse-surprisal ablation	Ablation that reverses the token-level direction by placing reconstruction pressure inversely with respect to base-model token surprisal.

The figure labels should stay concise. Captions and surrounding text should expand global scale as global $p_\theta$ surprisal scale and token weighting as token-level $p_\theta$ surprisal weighting.

Baseline Language

Use ELBO as the figure label for the standard baseline. At first mention in prose, write standard conditional ELBO. When discussing the minimized loss rather than the bound itself, standard negative conditional ELBO is acceptable.

Use $\beta$ -ELBO as the figure label for the reduced-KL baseline. Captions should make clear that this is a low- $\beta$ setting with $\beta<1$ . In prose, low- $\beta$ conditional ELBO is useful when the sentence needs to emphasize the intervention.

Avoid standard cVAE and $\beta$ -cVAE as primary figure labels. They are familiar to ML readers, but they label a model class rather than the objective comparison. The experiment compares objective variants within the router-generator setup, so objective labels are more precise.

Variant Language

Use global scale only as a compact figure label. In prose and captions, expand it to global $p_\theta$ surprisal scale or global base-model surprisal scale.

Use token weighting only as a compact figure label. In prose and captions, expand it to token-level $p_\theta$ surprisal weighting.

Use global + token only as a compact figure label. In prose and captions, expand it to global scale + token-level weighting or the combined base-directed variant.

Use token inverse only as a compact figure label. In prose and captions, expand it to inverse-surprisal ablation.

Reference Language

Short method-set description:

We compare ELBO and $\beta$ -ELBO baselines against three base-directed reconstruction variants: a global-scale variant, a token-weighting variant, and a combined global + token variant. We also include a token-inverse ablation that reverses the surprisal direction of token-level reconstruction pressure.

More explicit version:

The base-directed variants isolate two $p_\theta$ -dependent mechanisms: a global $p_\theta$ surprisal scale and token-level $p_\theta$ surprisal weighting. The global scale variant measures reconstruction in base-model reference units; the token weighting variant allocates reconstruction pressure by base-model token surprisal; and the global + token variant combines both mechanisms.

Caption-style expansion:

global scale uses the global $p_\theta$ surprisal scale; token weighting uses token-level $p_\theta$ surprisal weighting; global + token combines both; token inverse is the inverse-surprisal ablation.

Relationship To Neighboring Concepts

Formal notation for $\mathcal R_\theta$ , $c_\theta$ , $b_{\theta,t}(x,y)$ , and the token weights belongs in Base-directed reconstruction objective.

Metric and plot language for $\mathcal R_\theta$ , residual surprise explained by $z$ , and alignment-reconstruction frontiers belongs in Metrics and frontier language.

The reason ELBO baselines can land in the collapsed corner connects to ELBO under-specification and the z-ignoring solution.