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VLM accuracy can be predicted from a scalar capability score derived from LLM text benchmarks plus multimodal data volume via a fitted transfer-absorption scaling law.

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arxiv 2608.00013 v1 pith:DAZQVSOR submitted 2026-06-24 cs.CL cs.AIcs.CV

What Transfers from Text to Vision? Capability Scaling Laws and Transfer Dynamics for VLMs

classification cs.CL cs.AIcs.CV
keywords modelfamiliesframeworkscalingtextualbenchmarkscapabilitymultimodal
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors trained over 150 vision-language models by combining 34 different open-source text-only language models with the same vision encoder, projector, and training data. They then measured each language model on dozens of text benchmarks and used principal component analysis to compress those scores into a single "capability score" S. Their proposed scaling law is P = A*S + (B0 - Bm*S)*ln(D) + P0, where P is average VLM accuracy, D is multimodal training tokens, and A, B0, Bm, P0 are constants fitted to the training runs. The formula says a stronger text backbone helps at the start, but stronger backbones absorb less benefit from additional multimodal data.

The paper validates the formula by predicting the performance of Qwen2.5-72B, a backbone much larger than any used in fitting, and by leaving entire model families out of the fit. It also reports that some text benchmarks seem to hurt VLM performance ("transfer tax") and that base models are more data-efficient VLM backbones than instruction-tuned ones.

The empirical effort is large and the cross-family results are suggestive. But the law is a fitted linear model rather than a derivation, the out-of-sample evidence is thin (two 72B models; a few families), and some claims in the abstract do not match the tables. The GitHub link is provided but no commit hash or raw trajectories are in the paper.

Core claim

Eq. 7 is the load-bearing assertion: P = A_hat*S + (B0 - Bm*S)*ln(D_mm) + P0, with fitted constants, predicts VLM benchmark accuracy from a scalar capability score S extracted from LLM textual benchmarks, and generalizes to 72B-scale backbones and held-out model families. If true, practitioners can predict VLM performance and optimal hyperparameters before training.

Load-bearing premise

That a single scalar S = w^T (top-K PCA components of the text-benchmark matrix) is a sufficient cross-family proxy for the LLM properties that determine multimodal transfer, so that e^S can stand in for parameter count N in Eq. 6 and P is linear in S and ln(D_mm). This enters at Eqs. 3-5 and is not derived; if the PCA basis estimated on training families does not capture the capability axes of held-out families or 72B models, the framework's extrapolations fail.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Axiom & Free-Parameter Ledger

6 free parameters · 5 axioms · 1 invented entities

The central claim depends on fitted constants (w, A_hat, B0, Bm, P0) and on the assumption that PCA of text benchmarks captures the LLM properties relevant to multimodal transfer. No new physical entities are introduced.

free parameters (6)
  • A_hat (transfer rate) = not reported for global fit; type/family fits 0.212-0.361 (Tables 2, 3)
    Linear coefficient of S in Eq. 7; fitted jointly with w via Algorithm 1.
  • B0 (baseline absorption rate) = Base 1.60e-2, Chat 1.49e-2 (Table 2); family 0.28e-2 to 2.46e-2 (Table 3)
    Intercept of the ln(D_mm) coefficient in Eq. 8; fitted.
  • Bm (absorption decay rate) = Base 0.78e-2, Chat 1.04e-2 (Table 2); family up to 4.55e-2 (Table 3)
    Interaction coefficient on S * ln(D_mm); fitted.
  • P0 (benchmark baseline) = not reported
    Additive offset in Eq. 7; fitted.
  • w (capability aggregation weights) = not reported
    Projection of K PCA components onto scalar S; jointly optimized in Algorithm 1 and used to define transfer coefficients lambda_i.
  • K (number of PCA components) = K=3 for loss fit; not stated for Eq. 7
    Number of components chosen to explain >=95% variance in X; a modeling choice.
axioms (5)
  • domain assumption Benchmark-model matrix X has low-rank structure (Eq. 3)
    Imported from Ruan et al. 2024; needed for PCA to yield a meaningful capability vector.
  • ad hoc to paper S ∝ log C_text (Eq. 5)
    Follows from Eq. 3 only if the linear projection does not cancel the log-compute relation; used to justify substituting e^S for N in Eq. 6.
  • ad hoc to paper P is linear in S and ln(D_mm) with interaction (Eq. 7)
    Phenomenological ansatz, not derived from Eq. 6 or from a learning-theoretic model.
  • domain assumption Power-law data term B/D^β_mm holds for multimodal training
    Borrowed from Kaplan/Hoffmann text scaling laws; assumed without re-derivation for VLM training.
  • domain assumption Unified LLaVA-OneVision recipe with frozen SigLIP is a representative base case
    The Limitations section explicitly restricts the framework to late-fusion, frozen-encoder settings.
invented entities (1)
  • Capability score S (latent vector S_m) independent evidence
    purpose: Compress many text benchmark scores into a scalar predictor of VLM accuracy
    S_new is computable from a new LLM's text benchmarks and yields falsifiable VLM accuracy predictions, but the projection w and PCA basis are fit on the training models, so it is not independently measured.

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Choosing the right large language model (LLM) backbone is the most consequential decision when building a vision-language model (VLM), yet it remains fundamentally unprincipled: compute-based scaling laws fail to generalize across model families, and no framework exists for directly predicting VLM performance before training begins. We propose the Capability-Driven Multimodal Scaling Law, the first cross-family framework that predicts VLM benchmark accuracy from directly observable textual capability. Given a low-dimensional capability score $S$ extracted from LLM textual benchmarks via PCA, we model VLM performance as a function of $S$, with a per-backbone transfer rate and an absorption rate that quantifies data-scaling efficiency. To fit and validate the framework, we train over 150 VLMs on 34 LLMs spanning 7 model families under a strictly controlled recipe. Evaluations on more than 200 textual and 50 multimodal benchmarks show that the law accurately extrapolates transfer rate from models up to 8B parameters to 72B-scale backbones, predicts full VLM training trajectories with high fidelity, and generalizes to entirely held-out model families. Beyond the scaling law, our analysis surfaces actionable insights: certain textual benchmarks negatively correlate with multimodal performance, exposing latent benchmark-gaming behavior; base LLMs outperform instruction-tuned counterparts as VLM backbones due to higher absorption rates and lower data-scaling decay; and different model families occupy distinct positions in the transfer--absorption space. The framework turns backbone selection from costly empirical sweeps into a principled, quantitative decision. Code and data are available at https://github.com/wangq-dev/CDMScaling.

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