Paper Claims

A granular list of the empirical and conceptual claims the paper makes, with the figure or section that delivers each. This sits between the high-level pitch (contributions) and the per-figure design notes (figures) — it is the single place to scan "what does this paper actually claim, and where is each claim demonstrated?"

Status legend:

• core: load-bearing for the paper's thesis; corresponds to a body figure or a major textual finding.
• secondary: supporting evidence; appendix or short paragraph.
• deferred: noted but not yet pursued; flagged for future work.

Each claim entry follows the same shape: claim, significance, evidence/figure, placement, status.

C1 — Strategy is implicitly represented in the entangled LM but not separated

Claim. Latent reasoning strategies are present in the hidden states of an entangled language model — strategy classification from hidden states is decodable above chance, often early in generation — yet they are not exposed as a separable variable in the generative procedure $p(y|x)$.

Significance. Establishes that disentanglement can surface existing structure rather than being asked to invent it. Without this claim, the disentanglement target is ill-posed.

Evidence. Entanglement heatmap.

Placement. §4.2 Entanglement.

Status. Core.

C2 — Our methodology recovers a strategy-disentangled factorization

Claim. With our base-model-relative excess-reconstruction objective, samples $z \sim r(z|x)$ separate ground-truth strategies in latent space, and strategy-conditioned generation $g(y|x,z)$ produces the corresponding strategy-aligned outputs. Strategy decodability from $z$ approaches near-perfect by end of training.

Significance. Primary positive result — the methodology delivers what the problem statement asks for, on a controlled task suite.

Evidence. Latent dynamics and a now-deleted candidate qualitative strategy-conditioned generations note.

Placement. §4.3 Disentanglement.

Status. Core.

C3 — Base-normalized reconstruction and strategy disentanglement are correlated outcomes; ELBO sits in the collapsed corner

Claim. Strategy decodability from $z$ and the base-normalized reconstruction ratio $\rho_\mathrm{recon} = \bar{\ell}_\theta / c_\mathrm{base}$ are correlated across training runs. Here $\rho_\mathrm{recon}$ is a base-relative, fractional-fit metric: it is the leftover fraction of baseline surprisal after conditioning on $z$. Runs in which that leftover fraction is smaller — equivalently, runs in which $z$ explains a larger fraction of the residual surprise in $y$ beyond $x$ — also achieve higher strategy-decodability. Different methodology variants and $\beta$ values populate distinct regions of the $(\rho_\mathrm{recon}, \text{decodability})$ plane, tracing a frontier that characterizes the methodology's operating regime and exposes which variants are Pareto-dominant. The ELBO baseline sits in the collapsed corner: $\rho_\mathrm{recon} \approx 1$ — the factorized model matches the base on reconstruction, so it fits $p(y|x)$ trivially but $z$ is inert and strategy is not recovered.

Significance. Clarifies that ELBO's failure is not a failure to model $p(y|x)$ — ELBO succeeds at that, via the trivial factorization in which $z$ is ignored. The axis that separates trivial fit ($\rho_\mathrm{recon} \approx 1$, $z$ inert) from informative fit (\rho_\mathrm{recon} < 1, a smaller leftover fraction of baseline surprisal, and $z$ carrying information beyond $x$) is $\rho_\mathrm{recon}$ itself. Strategy disentanglement is downstream of $z$ being used; the correlation between lower leftover baseline surprisal and higher strategy-decodability is what makes our base-model-relative excess-reconstruction objective productive in this setting. The scatter also quantifies the gap between our variants and the ELBO baseline, supporting the Option A "characterized requirements / scaffolding for future work" posture.

Terminology. "Base-normalized reconstruction ratio" (symbol $\rho_\mathrm{recon}$) is the metric; "base-model-relative excess-reconstruction objective" is the umbrella name for the objective family that optimizes a variant of this quantity. See distribution-level z-free-relative reconstruction rescaling for the definition.

Evidence. Method metric bars.

Placement. §4.4 Ablations and analysis.

Status. Core.

C4 — Initialization at the base model induces a uniquely pathological optimization regime

Claim. Even with our modified objective, training a router-generator factorization initialized at the base model is harder than training one initialized from random weights. At matched objective and hyperparameter configurations, adapted-from-base runs exhibit posterior collapse and disentanglement failure more frequently than random-reinit runs; the adapted regime requires explicit objective tuning to succeed.

Significance. This is a separate claim from "standard ELBO fails" (C5). C5 is about the objective: standard ELBO does not place enough pressure on $z$ to encode information beyond $x$, so the factorization fits $p(y|x)$ but is not disentangled. C4 is about the optimization landscape under our modified objective: initializing at the base model places the parameters at the absorbing solution, making the basin of disentangled factorizations harder to reach. The adaptation regime is the practically important one — practitioners want to keep the pretrained backbone — so characterizing this difficulty is load-bearing for the paper's pretrained-LM relevance.

Evidence. Initialization pathology placeholder.

Placement. §4.4 Ablations and analysis (separate subsection or panel from C3).

Status. Core.

C5 — Standard ELBO is non-identifying in this setting

Claim. A naive-ELBO-trained factorization fits the base marginal $p_\theta(y|x)$ well but produces an entangled latent (strategy decodability near chance). Symbolically: any pair $(r, g)$ that marginalizes to $p_\theta(y|x)$ attains the same ELBO; the nearest gradient-descent solution from the pretrained initialization is the trivial one in which $z$ is ignored.

Significance. Justifies why a modified objective is required at all. Distinct from C4: this is about the objective, not about the initialization.

Evidence. ELBO failure dynamics for intuition; symbolic non-identifiability argument in §3.2 prose.

Placement. §3.2 The standard variational objective and why it fails.

Status. Core.

C6 — Lightweight LoRA adaptation is sufficient

Claim. A router-generator factorization parameterized as a lightweight LoRA adaptation of the pretrained base model is sufficient to obtain a strategy-disentangled factorization. Heavy retraining of the base model is not required.

Significance. Establishes computational tractability of the methodology. Practitioners can adapt an existing pretrained model rather than retrain. Implicit in the core results since they are obtained with LoRA, but worth stating explicitly so the reader does not miss the tractability point.

Evidence. Implicit in Latent dynamics and the pretrained-LM results in §4.3, which are themselves obtained with LoRA. Direct LoRA-vs-full-finetune ablation was previously tracked in the now-deleted appendix figure roster.

Placement. Brief paragraph in §4.3 stating the finding; appendix ablation supports.

Status. Secondary (stated explicitly; not headline).

C7 — The recovered latent exhibits cross-input semantic stability

Claim. Beyond separating strategies within a fixed input, the recovered latent exhibits cross-input semantic stability: when latent samples are compared across related inputs, the same latent value or region tends to correspond to the same high-level strategy. Analogical-agreement diagnostics therefore provide evidence that the latent is not merely an input-local partition, but a reusable strategy representation.

Significance. This is a stronger semantic notion of "strategy" than within-input separation alone. It connects the paper's factorization objective to the motivating applications in interpretation, intervention, and analogy-based strategy transfer: if latent semantics drift arbitrarily across inputs, then the latent is less useful as a controllable strategy variable even when it improves within-input decodability.

Evidence. Analogical-agreement diagnostics from the now-deleted cross-input semantic stability candidate note, motivated by the Apr 1 continuous-CVAE collection's analogical-agreement heatmap and router-probe-vs-agreement scatter.

Placement. §4.3 Disentanglement, as a stronger semantic follow-up to the within-input separation result.

Status. Core.

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Cross-references

• High-level pitch: contributions — the three headline contributions (problem formulation, methodology, benchmark + evaluation) under which these granular claims roll up.
• Arc placement: story boarding.
• Per-figure design: figures index.

Open meta-questions