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Not All Error Yields to Scale: Where Scaling Stops in Vision-Language Inference

Xinye Zhao, Yunkai Dang, Yunchen Wu, Wenbin Li

arXiv:2610.01640v1cs.CVcs.AI

TL;DR

High-resolution VLM inference must divide fixed compute between visual tokens and language-backbone capacity, but prior studies do not characterize scaling as image size changes. We propose and fit a separable error law; results show architecture-dependent returns from visual tokens and a substantial fraction of questions that remain wrong across tested scales.

  • Problem

    Prior work does not characterize how to divide inference compute between backbone size and visual tokens as image resolution changes.

    Source: §1 · pp. 1–2

  • Method

    The Separable Law models VLM error as an error floor plus separate backbone-size and visual-token terms, fitted across 26 InternVL and QwenVL models and four high-resolution benchmarks.

    Source: §1 · p. 2, §2.3 · p. 4

  • Results

    Across tasks, many questions remain wrong at every tested scale, and visual-token gains differ sharply between model families despite similar backbone gains.

    Source: §1 · p. 2, §7 · p. 10

  • Takeaways & Limitations

    Combined with a cost law, the Separable Law directs fixed-budget compute toward larger InternVL backbones or more QwenVL visual tokens, and helps rank feasible deployment configurations.

    Source: §1 · p. 2, §5 · p. 8

    The allocation is optimal only under a language-side budget, because the vision encoder is excluded from the cost count.

    Source: §5.1 · p. 8

Abstract

from arXiv · show

Vision-language models (VLMs) face a fixed-budget trade-off between processing more visual information for fine-grained perception and using a larger language backbone for complex reasoning. Existing studies do not tell us which combination of backbone size and input resolution to deploy, especially in high-resolution deployments. To address this gap, we propose the Separable Law that describes how VLM performance changes with language backbone size and visual token count. We fit the law to measurements from 26 InternVL and QwenVL models, with language backbone sizes from 1B to 72B, on four high-resolution benchmarks with image sizes from 224 pixels to 8K. We find that the questions responding to scaling can be predicted from the skill they require, while a substantial fraction never responds at all. We also find that the two model families gain similarly from a larger backbone, while their gains from more visual tokens differ sharply. Combined with a cost law, the Separable Law gives a closed-form rule for allocating compute between backbone size and visual tokens. When deployment is limited to available configurations, the law identifies model and image sizes that perform close to the best feasible choice under the same budget. We hope our work offers a principled way to decide how much a model should be allowed to see at high resolution, given what it must reason about.

1 INTRODUCTION

High-resolution VLM inference must divide a fixed compute budget between visual tokens for fine-grained perception and backbone capacity for complex reasoning. The paper introduces a separable scaling law and reports how scaling behavior and budget allocation vary across questions and model families.

Research gap

  • Prior work leaves open how to divide a fixed inference budget across backbone size and visual tokens under high-resolution inputs and changing image-processing strategies.The motivating trade-off is between preserving fine visual details and providing capacity for complex reasoning.Source: §1 · pp. 1–2

Approach

  • The Separable Law describes VLM error as an error floor plus separate contributions from language-backbone size and visual-token count.It is fitted to 26 InternVL and QwenVL models, from 1B to 72B, on four high-resolution benchmarks spanning 224 pixels to 8K.Source: §1 · p. 2

Main findings

  • The model families gain similarly from a larger backbone but differ sharply in visual-token gains, and about a third of questions remain wrong at every tested scale.Persistent errors depend mainly on required skill, with the worst cases in particular skill-and-scene pairings; the preferred compute-allocation axis also reverses between families.Source: §1 · p. 2

Practical implications

  • Combining the Separable Law with a cost law yields a closed-form fixed-budget rule: use larger backbones for InternVL and more visual tokens for QwenVL.When deployment is restricted to available configurations, predicted-error selection identifies the best option on average, including when model and image sizes are held out from fitting.Source: §1 · p. 2

2 METHOD

The method adapts scaling-law analysis to VLM inference by modeling backbone capacity and visual evidence as separate contributors to error. Experiments cover multiple model series, benchmarks, and image sizes, and favor the separable form among the tested alternatives.

2.1 PRELIMINARIES

  • Chinchilla scaling represents training loss as an irreducible floor plus power-law terms for model capacity and training data [Hoffmann et al., 2022].The floor is e∞, while A, B, α, and β are fitted constants describing decay rates along the two axes.Source: §2.1 · p. 3

2.2 EXPERIMENTAL SETUP

  • Five QwenVL and InternVL model series from 1B to 72B were tested on four benchmarks, yielding 650 cells and 536,781 valid evaluations across 20 fitting groups.The visual input varies through preset image sizes while each model's visual processor remains unchanged.Source: §2.2 · p. 3

2.3 OUR SEPARABLE INFERENCE SCALING LAW

  • Prior VLM laws assume a multiplicative form and hold image resolution fixed, while changing token counts through compression or retraining [Li et al., 2025a; Wang et al., 2025b].The paper instead tests alternative forms on pretrained image VLMs as input image size changes.Source: §2.3 · p. 3, §2.1 · p. 3
  • The Separable Law models downstream error with an error floor and separate power-law terms for backbone size and visual-token count.The authors replace training-token count with visual tokens visible to the backbone, since high-resolution images expand into thousands of tokens and outweigh the textual query.Source: §2.3 · p. 4

2.4 VALIDATING THE SEPARABLE FORM

  • The pooled fit across 650 cells has R2 = 0.898 and residual standard deviation 0.041, with no region where the law clearly breaks down.Mean residuals rise from −0.037 in the lowest observed-error bin to +0.014 in the highest.Source: §2.4 · p. 4
  • The multiplicative law has 53.2% higher SSE than the separable form; the coupled form lowers SSE from 1.221 to 1.182 but raises BIC by 115.2.None of the other tested candidates earns its additional parameters, so the authors use the Separable Law throughout.Source: §2.4 · p. 4

3 FINDING 1: THE COGNITIVE CEILING

About a third of evaluated question trajectories remain ceiling-bound despite scaling; required skill explains more variation in fitted floors than domain, while severe ceilings depend on specific domain–skill pairings.

3 FINDING 1: THE COGNITIVE CEILING

  • Because e∞ averages error across questions, a task floor near zero can still hide individual questions that remain wrong at the largest evaluated model and token count.The analysis therefore examines floors at task-subset, individual-question, and visual-domain/required-skill levels.Source: §3 · p. 4
  • 20% of perception fits and 33% of reasoning fits meet Saturation (e∞≥0.20); mean fitted e∞ is 0.155 for reasoning versus 0.073 for perception.A high fitted floor means neither a larger backbone nor more visual tokens brings that task subset near zero error.Source: §3 · p. 5

3.2 SAMPLE-LEVEL REGIME DISCOVERY

  • 30.7% of question trajectories are CEILING BOUND (below 0.20 mean accuracy) and gain 0.014 across compute quartiles, versus 0.239 for SCALING BOUND trajectories.CEILING BOUND trajectories still move both ways: 32.1% gain more than 0.05, while 27.8% lose more than 0.05.Source: Figure 4 · p. 5, §3.2 · p. 6

3.3 DOMAIN AND SKILL GRANULARITY

  • Skill explains 36.67% of variance in the 33 fitted floors, versus 7.84% for domain, but the highest ceiling is specific to Aerial/Satellite–Scene Reasoning (0.780).That pairing's floor exceeds its domain and skill marginals (0.227 and 0.228); most Text Reading and Object Identification pairings reach 0.001.Source: Figure 4 · p. 5, §3.3 · p. 6

4 FINDING 2: ARCHITECTURAL DIVERGENCE

The two model families show similar capacity scaling but sharply different visual-token scaling, reflecting how their frontends convert image pixels into tokens. Their exponent balance reverses across architectures, so the axis with faster gains also reverses.

4 FINDING 2: ARCHITECTURAL DIVERGENCE

  • The families gain similarly from larger backbones but differ by more than an order of magnitude in visual-token scaling, reversing which axis pays off faster.The paper links this divergence to frontends that turn the same pixel budget into very different token counts.Source: §4 · p. 6

4.1 CAPACITY EXPONENTS AGREE ACROSS FAMILIES, VISUAL-TOKEN EXPONENTS DO NOT

  • Capacity-exponent medians are 0.19 for InternVL and 0.59 for QwenVL among the qualifying groups.Twelve InternVL groups and five of eight QwenVL groups qualify; including the three QwenVL fits at the upper bound raises its median to 0.78.Source: §4.1 · p. 6
  • β medians are 4.66 for InternVL and 0.17 for QwenVL, but the InternVL median covers only three of twelve groups.The other nine InternVL estimates reach the upper bound of 10, making the reported cross-family gap conservative.Source: §4.1 · p. 7, Figure 5 · p. 7

4.2 DISCRETE TILING AND CONTINUOUS RESIZING EXPOSE DIFFERENT TOKEN RANGES

  • InternVL tiling leaves token counts unchanged for 70.2% of questions as the pixel budget rises from 224 to 2048 px, yielding a median within-group token span of 1.22×.Its grid has at most twelve 448 × 448 tiles, each producing 256 visual tokens; the narrow span leaves nine β estimates at the upper bound.Source: §4.2 · p. 7
  • Across 224 to 2048 px, QwenVL’s within-group token count rises 34.09× to 87.79×, spanning roughly 37 to 15,000 tokens.Continuous resizing makes the decay visible; all eight groups have interior β estimates, with a median of 0.17.Source: §4.2 · p. 7
  • The median α/β ratio is 2.55 for QwenVL and 0.0395 for InternVL, indicating that capacity has the larger exponent in QwenVL and visual tokens in InternVL.The 0.0395 InternVL median is an upper bound because almost all excluded fits stop at the upper β bound.Source: §4.2 · p. 7

5 FINDING 3: FROM LAWS TO PRACTICE

The Separable Law and a fitted cost law guide compute allocation between backbone size and visual tokens. The resulting choices reflect architecture and perform close to the best feasible configuration, while the same analysis characterizes which benchmark questions distinguish models.

5.1 FROM LAWS TO A DEPLOYMENT DECISION

  • The cost law approximates prompt-processing FLOPs over the observed grid; its fitted values are p = 1.00, q = 0.77, and log-space R2 = 0.995.The vision encoder is excluded, so the allocation is optimal under a language-side budget; doubling R does not double cost because T0 is unchanged.Source: §5.1 · p. 8
  • The VPE allocation directs added compute toward a larger backbone for InternVL and more visual tokens for QwenVL as the budget grows.The faster-growing axis is determined by whether β or α is larger; the direction is more robust than the allocation’s starting point.Source: §5.1 · p. 8

5.2 CHOOSING AMONG AVAILABLE CONFIGURATIONS

  • Direct selection has 0.76 pp mean regret and 2.74 pp 90th-percentile regret, versus 2.33 pp and 7.71 pp for projection across 2,379 held-out decisions.Both methods outperform static rules, whose mean regrets range from 4.09 to 7.56 pp and 90th-percentile regrets from 12.23 to 20.14 pp.Source: Figure 6 · p. 9, §5.2 · p. 9

5.3 WHAT A BENCHMARK SEPARATES AND WHICH AXIS IT REWARDS

  • Only SCALING BOUND questions separate models; InternVL has a larger N-dominated share than QwenVL on every benchmark, yet both families rank the four benchmarks alike.A question is N-dominated when its accuracy moves further along the backbone axis than along the visual-token axis.Source: §5.3 · p. 9

6 RELATED WORK

Related work studies inference-compute allocation, visual-token efficiency, and finer-grained VLM failure analysis. This paper positions its contribution as fitting backbone size and the visual-token count induced by input size across different frontends.

6 RELATED WORK

  • Prior inference-scaling work reduces visual-token costs, adapts input resolution, requests sharper views, or spends compute on search, verification, and renewed looking.Related scaling analyses connect accuracy to model size and visual-token count, often with token counts set by compression, frame sampling, or retraining.Source: §6 · p. 9
  • Diagnostic benchmarks and adaptive perception methods study fine-grained failures, while question-level analyses track capability differences, difficulty, or gains and losses as compute grows.This work follows each question as backbone size and visual tokens grow together, relating persistent errors to required skill.Source: §6 · pp. 9–10

7 CONCLUSION

The Separable Law models how VLM error changes with language-backbone size and visual-token count. Across high-resolution evaluations, many questions remain wrong at every tested scale, while the two model families benefit differently from more visual tokens.

7 CONCLUSION

  • About a third of questions remain out of reach at every tested scale, and visual-token increases benefit QwenVL far more than InternVL.The paper presents the law as a principle for allocating limited inference compute in high-resolution settings.Source: §7 · p. 10
  • The work fits the Separable Law to four high-resolution benchmarks, with input sizes from 224 pixels to 8K.Source: §7 · p. 10
  • The Separable Law describes how VLM performance changes with language-backbone size and visual-token count.Source: §7 · p. 10

AI USE STATEMENT

This material states how generative AI was used and details the evaluated models, benchmarks, image sizes, and visual-token measurements. It covers 26 models from the InternVL and QwenVL families and four high-resolution benchmarks.

AI USE STATEMENT

  • GPT-4o-mini supported qualitative data labeling and paper editing; the authors reviewed all AI-assisted work and take responsibility for the final content.Source: AI USE STATEMENT · p. 10

A EXTENDED EXPERIMENTAL SETUP

  • The experimental setup traces each measurement from model and image through cell-level error, covering models, benchmarks, token counts, analysis units, decoding, and scoring.Source: A EXTENDED EXPERIMENTAL SETUP · p. 16

A.1 MODELS AND VISUAL FRONTENDS

  • The study covers 26 models in five InternVL and QwenVL series; InternVL uses fixed tokens per tile, while QwenVL varies token count with input size.The paper defines backbone size N as the language-backbone parameter count.Source: §A.1 · p. 16

A.1.1 INTERNVL FAMILY

  • InternVL 1.5 introduced dynamic tiling of up to 40 448×448 tiles and compressed each tile's 1,024 ViT tokens to 256; later versions retained this design.The evaluation allows at most 12 image tiles plus a whole-image tile, or 3,328 visual tokens.Source: §A.1.1 · p. 16

A.1.2 QWENVL FAMILY

  • Qwen2-VL introduced dynamic resolution, making visual-token counts change in smaller patch-grid steps than InternVL's whole-tile increments; later QwenVL versions retained this frontend.Qwen2.5-VL reduced large-input ViT cost with window attention; Qwen3-VL retained dynamic resolution and the 2×2 MLP merger.Source: §A.1.2 · p. 17

A.1.3 EVALUATED MODELS

  • N is the exact language-backbone parameter count, excluding the vision encoder and projector, although model sizes within a series may differ in those components and training.Source: §A.1.3 · p. 17

A.2 BENCHMARKS

  • The four benchmarks cover fine-grained perception, real-world high-resolution scenes, grounded visual reasoning, and tiny details in crowded scenes.The evaluation uses the Lite split of MME-RealWorld, 405 TreeBench questions, and 191 V* Bench questions.Source: §A.2 · pp. 17–18

A.3 INPUT SIZES AND VISUAL TOKEN COUNTING

  • The shared input sizes are 224–2048 px, with HR-Bench additionally evaluated at 4096 px; visual-token counts are measured at the language-backbone input.QwenVL counts come from processed image tokens, while InternVL counts use inserted placeholders or tile counts multiplied by 256.Source: §A.3 · pp. 18–19

A.4 UNITS OF ANALYSIS AND SCALE OF THE STUDY

The study organizes evaluations into cells and groups, scores model answers, and fits the Separable Law to the resulting errors. It also describes the robustness checks used to validate the fits.

A.4 UNITS OF ANALYSIS AND SCALE OF THE STUDY

  • The study contains 650 cells across 20 series–benchmark groups and 19,890 question trajectories, derived from 515,938 scored observations.Source: §A.4 · p. 19

A.5 DECODING AND SCORING

  • Text accuracy is the main signal because text and logit predictions agree on 96.6% of records; cell error is one minus text accuracy.The question-level robustness analysis also uses normalized correct-option probability without assuming it is calibrated.Source: §A.5 · p. 19

B FITTING AND VALIDATING THE SEPARABLE LAW

B.1 FITTING PROCEDURE

  • Each group is fitted separately by minimizing unweighted squared error over cells, with exponents optimized numerically and nonnegative amplitudes solved in closed form.The baseline objective weights configurations equally and supports the uncertainty and sensitivity analyses.Source: §B.1 · p. 20

B.2 PER-GROUP FITS AND DIAGNOSTICS

Across the tested functional forms, the Separable Law balances fit and parameter count, and it predicts held-out configurations as well as or better than Coupled at the group level. Robustness checks preserve its main allocation and scaling conclusions, while residual diagnostics and parameter estimates identify qualifications.

B.2 PER-GROUP FITS AND DIAGNOSTICS

  • R² is 0.898 pooled across 650 cells, and 17 of 20 groups reach R² ≥0.65; the three weaker groups are InternVL on V* Bench, where token ranges are narrow.Residuals are centered near zero overall, but their tails are heavier than a matched Gaussian and the mean trend shifts from −0.037 in the lowest error bin to +0.014 in the highest.Source: §B.2 · pp. 20–21, Table 7 · p. 21, Figure 7 · p. 22

B.3 COMPARISON OF FUNCTIONAL FORMS

B.4 SAMPLING UNCERTAINTY AND PRECISION WEIGHTING

  • Paired image bootstraps retain the preference for Separable: Coupled's 3.15% unweighted SSE reduction accompanies a BIC difference of 115.23, with a 95% interval of [93.95, 123.10].Precision weighting gives the same preference, with a 106.91 BIC difference and 95% interval [89.65, 116.90].Source: §B.4 · p. 25, Table 10 · p. 25

B.5 HELD-OUT PREDICTION

  • On held-out configurations, group-specific Separable has lower RMSE on all-cell backbone holdouts and matches Coupled on input-size holdouts; interior differences are only −0.012 and −0.011 percentage points.Unclipped predictions outside [0, 1] occur only in endpoint folds.Source: §B.5 · p. 25, Table 11 · p. 26, Figure 10 · p. 26

B.6 A BOUNDED VERSION OF THE LAW

  • Bounded outputs leave allocation decisions nearly unchanged: the laws agree on 100.0% of backbone, 99.3% of input-size, and 98.3% of joint holdouts, while interior RMSEs differ by at most 0.12 percentage points.The bounded law keeps predictions in [0, 1].Source: §B.6 · p. 27, Table 12 · p. 27, Table 14 · p. 27

B.7 PARAMETER UNCERTAINTY AND SEARCH BOX

  • Bootstrap estimates resolve QwenVL visual-token exponents below 0.51, while InternVL fits frequently hit the upper bound; narrowing the exponent range preserves the family contrast but raises pooled SSE to 1.400.Four InternVL group floors shift by more than 0.02 under the narrower range.Source: §B.7 · p. 28, Table 15 · p. 28

B.8 SENSITIVITY TO THE LARGEST INPUT SIZE AND TO VISUAL-TOKEN AGGREGATION

  • Removing HR-Bench's 4096 px setting preserves exponent ordering and allocation direction; exact question-level token aggregation also preserves ordering and 79 of 80 configuration choices while lowering pooled RMSE from 4.092 to 3.077 percentage points.The aggregation alternative removes all upper-bound β solutions.Source: §B.8 · pp. 28–29, Table 17 · p. 29

C FINDING 1: THE COGNITIVE CEILING

C.1 TASK-LEVEL FLOORS

Reasoning tasks have higher fitted error floors than perception tasks across all five model series, but high floors are concentrated in a minority of task subsets. Regime proportions remain stable across cutoff choices, and regime labels distinguish held-out accuracy and scaling response.

C.1 TASK-LEVEL FLOORS

  • Reasoning has a higher mean fitted floor than perception in all five series, with pooled means of 0.155 and 0.073.The comparison uses 40 matched task-level fits across model series, benchmarks, and task subsets.Source: §C.1 · pp. 29–30, Table 18 · p. 30
  • Ten of 40 task-level fits meet the saturation threshold e∞≥0.20, while most fits approach a near-zero floor.Saturation occurs in 20% of perception fits and 33% of reasoning fits; 18 perception fits and 8 reasoning fits meet the floor criterion e∞≤0.01.Source: §C.1 · p. 30

C.2 SENSITIVITY OF THE REGIME CUTOFFS

  • Across cutoff sweeps, the CEILING BOUND share stays between 25.2% and 33.2%, with default cutoffs yielding 30.7%.The sweep varies τeasy over {0.85, 0.90, 0.95} and τcog over {0.15, 0.20, 0.25}.Source: §C.2 · p. 30
  • On held-out configurations, CEILING BOUND accuracy is 7.08%–8.85% and SCALING BOUND accuracy is 50.53%–54.79% across five series.Their held-out slopes are 0.13–1.24 and 3.13–4.55 percentage points per doubling of NR, respectively; 17.95% of questions shared by all series are CEILING BOUND in every series.Source: §C.2 · p. 30

C.3 PERSISTENCE AT HIGH COMPUTE

At the highest observed compute, many questions remain low-accuracy, though individual scaling responses vary. A smaller response-based persistent-error core is stable across definitions, and question labels organize error floors by visual scene and required skill.

C.3 PERSISTENCE AT HIGH COMPUTE

  • At the highest-compute quartile, 4,602 of 5,392 CEILING BOUND trajectories (85.3%) remain below 0.20 accuracy, with mean accuracy of 8.6%.From Q1 to Q4, 32.1% gain more than 0.05 in correct-option probability, while 27.8% lose more than 0.05; the analysis covers 15,830 trajectories from 3,166 questions.Source: §C.3 · pp. 30, 32
  • The joint response rule selects 1,502 trajectories (9.5%) on raw probability and 1,296 (8.2%) after chance normalization; 98.9% and 97.1% lie inside CEILING BOUND.The stricter response-based criteria isolate a smaller persistent-error core while capturing nearly all of it within CEILING BOUND.Source: §C.3 · p. 32, Table 22 · p. 32
  • Under stricter persistent-error criteria, MME-RealWorld and TreeBench retain higher rates than HR-Bench and V* Bench, and reasoning exceeds perception at 11.1% versus 6.7%.The benchmark and task contrasts persist across the compared definitions on the same observations.Source: §C.3 · pp. 32–33, Table 23 · p. 33
  • A small-response core persists across threshold sweeps, selecting 4.2%–18.4% of trajectories on raw probability and 3.5%–15.5% after normalization.Using mean configuration token counts gives 9.7% and 8.4%, close to defaults of 9.5% and 8.2%; a stricter quartile-mean condition leaves 970 candidates (6.1%).Source: §C.3 · p. 33
  • High-compute difficulty replicates across configuration halves: 65.0% and 69.8% of selected candidates meet the rule in the other half, and 96.8%–98.2% retain high-compute difficulty.The experiments establish persistence over the evaluated grid, without extrapolating to unseen architectures or configurations beyond that grid.Source: §C.3 · p. 33

C.4 TAXONOMY OF DOMAIN AND SKILL

  • The shared taxonomy separates each question’s visual-scene domain from its required skill, enabling fitted floors to be compared across benchmark-specific labels.GPT-4o-mini assigned one domain and one skill to 3,178 questions; the fits use six shared input sizes, excluding HR-Bench records available only at 4096 px.Source: §C.4 · pp. 33–34

C.5 FITS FOR EACH DOMAIN–SKILL PAIRING

Fitted error floors vary most across particular domain–skill pairings, with skill accounting for more broad variation than domain. Resampling supports that ordering, while most pairing-level exponent fits avoid their search bounds.

C.5 FITS FOR EACH DOMAIN–SKILL PAIRING

  • The 33 pairing-level floors are fitted under a common protocol that pools five series and weights eligible benchmark–configuration–domain–skill subcells equally.The fits use six shared input sizes and retain subcells with at least five questions, yielding 10,135 subcells across 624 configurations.Source: §C.5 · p. 34
  • Across 33 supported pairings, fitted floors of at least 0.30 occur in ten pairings; the highest is Aerial/Satellite with Scene Reasoning at e∞=0.780.Marginal means range from 0.001 for Text Reading to 0.432 for Attribute Recognition, and from 0.041 for Documents/Charts/Slides to 0.272 for People/Surveillance.Source: §C.5 · p. 34, Table 25 · p. 35, Table 24 · p. 35
  • Skill accounts for 36.67% of fitted-floor variance and domain for 7.84%, a ratio of 4.68.The decomposition explains 9.26%, 38.09%, and 44.51% with domain alone, skill alone, and both factors together, respectively; factor shares average over both entry orders.Source: §C.5 · p. 34
  • Image-cluster resampling preserves the skill-dominant ordering in 82.6% of ordinary-bootstrap replicates and 81.6% of positive-weight replicates.The ratio intervals cross one, so the resampling supports the ordering but does not pin down the point-estimate ratio of 4.68.Source: §C.5 · p. 35, Table 26 · p. 35
  • β is interior in 29 of 33 pairing fits, and both exponents are interior in 28, though interior estimates alone do not establish statistical identification.Several β estimates reach the lower bound, and zero fitted amplitudes leave matching α values undetermined for two pairings.Source: §C.5 · pp. 35–36

D FINDING 2: ARCHITECTURAL DIVERGENCE

  • The architectural-divergence analysis compares fitted exponents by family and series, then examines visual-token movement, effective pixels, and image quality at fixed token sequences.The section introduces these checks because β reaches the upper bound in most InternVL groups.Source: D FINDING 2: ARCHITECTURAL DIVERGENCE · p. 36

D.1 EXPONENTS BY FAMILY, SERIES, AND TASK

This section examines visual-token scaling across model families and frontends, then combines the fitted performance and FLOPs-based cost laws to derive a continuous compute allocation. It checks the allocation’s algebra and evaluates held-out rules against static baselines, while distinguishing continuous allocation from selection among feasible configurations.

D.1 EXPONENTS BY FAMILY, SERIES, AND TASK

  • InternVL backbone-capacity exponent α has median 0.19 versus QwenVL’s 0.59 (0.78 including boundary fits), while task-level α/β medians reverse: 0.0395 versus 2.55.On reasoning tasks, the QwenVL and InternVL medians are 14.47 and 0.0685. These ratios use fits with both exponents interior; one QwenVL fit has An = 0 and an undetermined α.Source: §D.1 · pp. 36–37
  • Nine of 12 InternVL visual-token exponents β hit the upper bound of 10, while all eight QwenVL fits are interior with median 0.17; this ordering repeats across every series.Each InternVL series has one interior estimate, its HR-Bench fit, between 3.87 and 4.93; the two QwenVL series have medians 0.155 and 0.173. The series pattern is reported in the prose and summarized by Table 27.Source: §D.1 · p. 36, Table 27 · p. 36

D.2 TOKEN RANGES OF THE TWO FRONTENDS

  • InternVL’s token span is only 1.07–1.55× within groups (median 1.22), whereas QwenVL spans 34–360× across full grids and 34.09–87.79× across shared input sizes.For InternVL, 69.9% of questions keep the same tile count at all six sizes; QwenVL token counts vary at finer patch-grid granularity and need not rise at every step.Source: §D.2 · p. 37
  • Replacing token count R with effective pixels Peff raises InternVL R2 from 0.594/0.548/0.515 to 0.943/0.940/0.963 across its three series.For InternVL3.5, held-out-backbone RMSE falls from 8.95 to 3.32 points and held-out-input-size RMSE from 10.50 to 3.16; Qwen2.5-VL is essentially unchanged, while Qwen3-VL R2 drops from 0.959 to 0.914. Adding R after Peff adds almost no InternVL R2 and fails to separately identify conditional effects.Source: §D.2 · p. 37, Figure 11 · p. 38
  • Controlled native-image sweeps show endpoint gains of 30.37 points for InternVL on V* Bench and 30.00, 17.00, and 42.41 points for QwenVL on HR-Bench, MME-RealWorld, and V* Bench.On InternVL V* Bench, native-source accuracy rises from 53.40% to 83.77% across token limits, versus 46.07% to 52.88% for 224-pixel sources; the interaction is 23.56 points (95% interval [14.66, 32.46], Holm-adjusted p = 4.32×10−6). Identical token counts and input-sequence hashes across source-quality conditions isolate the effect of available pixel information.Source: §D.2 · pp. 38–39, Table 28 · p. 38, Figure 13 · p. 39
  • The fitted family contrast is grid-specific rather than an intrinsic architectural exponent reversal, because the frontends traverse different token and image-information ranges.Fixed-8B sweeps vary visual tokens but not backbone size, so they cannot recover the ordering of α and β across model sizes; the VPE allocation rates are conditional on the evaluated grids.Source: §D.2 · p. 39

E.1 COST MEASURES AND COST-LAW FITS

  • The FLOPs cost law fits all five series with log-space R2 of 0.986–1.000, p = 1.00, q = 0.96 for InternVL, and q = 0.75–0.78 for QwenVL.The allocations use the pooled FLOPs fit; latency is unstable across families, with R2 from 0.019 to 0.764. Adding visual-side cost preserves the family-level allocation direction, although budgets and some individual choices require recalibration.Source: §E.1 · pp. 40–41, Table 29 · p. 40

E.2 DERIVATION OF THE VPE ALLOCATION

  • Under positive coefficients and exponents, the continuous allocation has a unique optimum, and its budget elasticities depend only on α, β, p, and q.The derivation concerns the fitted laws and does not establish fit quality or behavior outside the observed grid; its algebraic core is independently formalized in Lean 4.Source: §E.2 · pp. 41–42
  • The certificate machine-checks that the closed form satisfies the budget and balance equations, their intersection is unique, and the log-budget responses have the stated slopes.It does not establish fitted parameter values, convexity or global optimality, or which configuration is best in a finite set; discrete selection is evaluated separately.Source: §E.2 · p. 45

E.3 HELD-OUT ALLOCATION

  • The evaluation refits on 650 folds from 20 groups, holding out a backbone-size row and input-size column, and retains 2,379 of 2,600 planned decisions.Regret is selected-configuration error minus the lowest feasible-candidate error; budgets use the 25th, 50th, 75th, and 90th percentiles of language-side cell costs.Source: §E.3 · p. 45
  • Direct selection has 0.76 pp mean regret and 2.74 pp 90th-percentile regret, below all three static baselines on both measures.Projection has 2.33 pp mean regret and 7.71 pp 90th-percentile regret; static rules range from 4.09 to 7.56 pp in mean regret and 12.23 to 20.14 pp at the 90th percentile.Source: §E.3 · p. 45
  • Direct selection’s worst-case regret is 19.37 pp; projection reaches 34.55 pp, while bounded-law direct selection has 0.75 pp mean and 2.74 pp 90th-percentile regret.Projection’s worst case exceeds the 27.00 pp of the largest-visual-token static rule; the projection/direct gap arises from the projection step, not the fitted law.Source: §E.3 · p. 45

E.4 IN-SAMPLE ALLOCATION AND BREAKDOWN BY SERIES

The in-sample allocation projection outperforms static resource rules and stays near the best feasible choice across most decisions. Benchmark profiles also differ by model family: QwenVL is more often separated by visual-token scaling, while InternVL is more often separated by backbone size.

E.4 IN-SAMPLE ALLOCATION AND BREAKDOWN BY SERIES

  • 1.98 pp mean regret for projection, versus 6.51 pp for the best static rule, the largest-token-count rule, across 80 in-sample decisions.Projection also has 0.00 pp median regret and 11.52 pp worst-case regret.Source: Table 31 · p. 46, §E.4 · p. 46
  • InternVL has 2.16 pp mean regret and QwenVL 1.71 pp, but their regret distributions cross, so family ordering depends on the threshold.Both families have 0.00 pp median regret; the 90th percentiles are 7.06 pp for InternVL and 4.70 pp for QwenVL.Source: §E.4 · p. 47
  • 77 of 80 projection decisions (96.25%) fall within 8 pp of the optimum, including all 32 QwenVL decisions and 45 of 48 InternVL decisions.52 decisions (65.00%) fall within 2 pp; 41 select the designated best cell and 42 reach the lowest feasible error, with one tied decision explaining the difference.Source: §E.4 · p. 46, Table 33 · p. 47
  • Three decisions exceed 8 pp regret, all from InternVL2.5; the largest is 11.52 pp on V* Bench.The other two are 9.74 pp on MME-RealWorld and 8.63 pp on HR-Bench; the text does not identify an architectural cause for these cases.Source: §E.4 · p. 48

E.5 BENCHMARK PROFILES BY FAMILY

  • On every benchmark, QwenVL has a larger R-dominated share than InternVL, while InternVL is more often N-dominated; benchmark profiles should therefore be read with the frontend in view.For example, R-dominated shares range from 31.6% versus 6.7% on HR-Bench to 72.6% versus 38.5% on V* Bench for QwenVL versus InternVL.Source: §E.5 · p. 48

F CASE STUDIES

Selected Qwen3-VL cases illustrate that answers can change with input size or model size. These examples show both non-monotonic input-size behavior and errors that persist in smaller models, but they are individual questions rather than averages.

F CASE STUDIES

  • These are selected individual questions, not averages, and the fixed-input comparisons cannot show how the gap between model sizes changes with input size.The outputs also leave open why an answer changes.Source: F CASE STUDIES · pp. 48–49

Sensitivity to input size across model sizes

  • Across five selected questions, larger inputs make the answer correct in four cases, while the 2B example switches from correct to incorrect and back to correct as resolution rises.The 8B example becomes correct at 1024 px; the two 32B examples at 768 and 512 px, and the two 4B examples at 512 and 768 px.Source: F CASE STUDIES · p. 49, Figure 14 · pp. 50–51

Sensitivity to model size across input sizes

  • At fixed input sizes, the 8B and 32B models answer correctly while 2B and 4B do not in five examples; at 336 px, the 4B model also answers correctly.The examples span 224 to 2048 px and concern different questions at each size.Source: F CASE STUDIES · p. 49, Figure 15 · p. 53

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