Eight dimensions, 2.3 degrees of freedom: the correlation matrix behind 32 Chinese multimodal models

Eight boxes, maybe two and a half votes

This 2026 China native multimodal LLM tier list scores 32 models across eight dimensions: visual perception, document OCR, chart reasoning, video timing, GUI agents, generation, Chinese context and ecosystem/cost. The weights are 20, 18, 14, 14, 14, 6, 6 and 8.

One question has never been tested: are these eight dimensions actually measuring eight different things?

If two dimensions move together across 32 models, weighting them separately is effectively voting twice for the same thing. The ranking does not become “more comprehensive”; it becomes more precise at repeating one preference.

We computed Pearson correlations across all eight scores for all 32 models, then eigen-decomposed the correlation matrix. The headline: the first principal component explains 62.9% of variance; the first four explain 90.5%; by participation ratio, the scorecard has only 2.33 effective dimensions. You think you are selecting on eight axes. Most of the weight goes to one general-capability axis.

The 8×8 correlation matrix

Method: standardise each dimension across 32 models, then compute pairwise Pearson correlations. The sample is every listed model; every score is public in the model library and can be recomputed.

	Perception	Document	Chart	Video	Agent	Generation	Chinese	Ecosystem
Perception	1.00	0.52	0.61	0.43	0.67	0.29	0.67	0.59
Document	0.52	1.00	0.94	0.19	0.68	0.25	0.72	0.72
Chart	0.61	0.94	1.00	0.38	0.81	0.45	0.70	0.79
Video	0.43	0.19	0.38	1.00	0.53	0.52	0.29	0.36
Agent	0.67	0.68	0.81	0.53	1.00	0.53	0.73	0.79
Generation	0.29	0.25	0.45	0.52	0.53	1.00	0.32	0.41
Chinese	0.67	0.72	0.70	0.29	0.73	0.32	1.00	0.69
Ecosystem	0.59	0.72	0.79	0.36	0.79	0.41	0.69	1.00

Three pairs deserve attention.

Document × chart = 0.94. Shared variance 88%. Across these 32 models, “good at documents” almost automatically means “good at charts”. The two dimensions together carry 32% of the weight, but they behave like two ticks on one axis.

Chart × agent = 0.81, agent × ecosystem = 0.79. Shared variance 66% and 62%. The agent–ecosystem link is especially counterintuitive: whether a model can call tools moves with its price, licence, context and community support. Not because “good ecosystem causes good agents”, but because both are pushed by the same underlying capability — model scale and engineering maturity.

The lowest correlations are document × video = 0.19, document × generation = 0.25, video × Chinese = 0.29 and perception × generation = 0.29. These four pairs are the genuinely independent axes. Video, generation and perception (relative to documents) each carry information the others do not.

PC1: one all-positive “general capability” axis

Eigen-decomposition of the correlation matrix gives eight eigenvalues. Sorted:

Component	Eigenvalue	Variance explained	Cumulative
PC1	5.03	62.9%	62.9%
PC2	1.17	14.6%	77.5%
PC3	0.63	7.9%	85.4%
PC4	0.41	5.2%	90.5%
PC5–PC8	0.76	9.5%	100%

All eight PC1 loadings are positive, between 0.24 and 0.41: perception 0.34, document 0.37, chart 0.41, video 0.24, agent 0.41, generation 0.25, Chinese 0.37, ecosystem 0.39. In plain language: a model that is “generally stronger” tends to score higher on all eight. The axis is not a specific skill; it is the water level raised by scale, training data and engineering investment.

PC2 explains 14.6%: video +0.65, generation +0.59, document −0.38. This is the “temporal/generative versus static document” axis. Models good at moving things are often bad at reading a receipt cleanly, and vice versa. DeepSeek-OCR 2 and Emu3.5 sit at opposite ends.

PC3 explains 7.9%: perception −0.67, generation +0.51. This is “seeing versus making”. A strong perception model is not necessarily a strong generator; a strong generator is not necessarily good at grounding. InternVL 4.0 and BAGEL-2 sit at opposite ends.

The three axes together explain 85.4%. The remaining 14.6% is where dimensions are genuinely independent — and PC4 (5.2%) is mostly video and generation residual.

How “2.33 degrees of freedom” is computed

The eigenvalues sum to the number of dimensions, 8. The participation ratio is:

effective dimensions = (Σλ)² / Σλ²

Substituting the eight eigenvalues: 64 / (5.03² + 1.17² + 0.63² + 0.41² + 0.30² + 0.27² + 0.17² + 0.01²) ≈ 2.33.

This does not mean the world contains only 2.33 skills. It means: within the actual score distribution of these 32 models, the eight dimensions provide about 2.3 independent directions of discrimination. With 320 models, or 20 finer-grained dimensions, the number would change. It describes this scorecard, not the nature of multimodal capability.

But it answers a practical question: is your weighted table double-counting? Yes.

Three places where the weights repeat

Put weights and correlations side by side:

Weight block	Total weight	Correlation	What it actually does
Document + chart	32%	0.94	Nearly two votes for one axis
Agent + ecosystem	22%	0.79	Two names for engineering maturity
Perception + Chinese + agent	40%	0.67–0.73	Three projections of the general factor
Video	14%	average 0.39	A genuinely independent vote
Generation	6%	average 0.40	A genuinely independent vote

Video and generation have the lowest average correlations (0.39 and 0.40), yet receive 14% and 6% of the weight. Document and chart average 0.58 and 0.67, yet receive 32%. This is not an argument for raising the video weight. It is an argument that the current table hands most decisions to “general capability” while pretending to balance eight directions.

If your work is video moderation, long-video timing or creative generation, selecting off this composite will systematically underrate specialists. The fix is not to change the total; it is to read model shapes and the residuals below.

Residuals: who is still a specialist after controlling for general capability

A high raw score may just be a high water level. To see genuine specialisation, subtract the general factor.

Method: z-standardise each dimension, then subtract the model’s average z-score on the other seven dimensions. A positive residual means “this is more prominent than the model’s own overall level”; negative means “this drags”. It is relative shape, not absolute capability.

Dimension	Strongest residual (model / score / rank)	Weakest residual
Perception	Cloudwalk Congrong 2 +12.8 (91 / #32); Hikvision Guanlan 3 +12.1 (92 / #27)	GLM-5.3 −5.0 (93 / #4)
Document	DeepSeek-OCR 2 +17.7 (99 / #20); InternVL 4.0 +7.0 (93 / #16)	NetEase Fuxi 2 −13.5 (70 / #29)
Chart	DeepSeek-OCR 2 +8.9 (88 / #20); InternVL 4.0 +7.3 (90 / #16)	NetEase Fuxi 2 −11.9 (68 / #29)
Video	Hikvision Guanlan 3 +19.6 (91 / #27); WITA-Omni +17.6 (92 / #23)	JD Yanxi 2 −22.9 (55 / #28)
Agent	Kimi K3 +7.5 (95 / #5); GLM-5.3 +6.6 (95 / #4)	BAAI Emu3.5 −9.3 (70 / #24)
Generation	BAAI Emu3.5 +25.0 (98 / #24); BAGEL-2 +20.2 (90 / #31)	DeepSeek-OCR 2 −17.0 (60 / #20)
Chinese	Ant Ling 2 +8.8 (92 / #22); NeuroXess-N1 +8.6 (88 / #30)	DeepSeek-V4.1-Flash −5.9 (86 / #12)
Ecosystem	Qwen3.8-Flash +14.8 (97 / #13); DeepSeek-V4.1-Flash +13.3 (95 / #12)	WITA-Omni −17.9 (60 / #23)

This table explains why overall and single-dimension boards disagree:

• Emu3.5 is #1 on generation at 98, but its agent score is 70, a −9.3 residual. It is not “unbalanced”; it is a world model that does one thing. Putting it in a general-assistant seat is a procurement error, not a model error.
• DeepSeek-OCR 2 has document 99 and a +17.7 residual, but generation 60 and a −17.0 residual. It is a pure document component. Rank #20 does not mean weak; it means narrow.
• Cloudwalk Congrong 2 has the highest perception residual (+12.8) and ranks #32 overall. Almost all of its score comes from face, ID and receipt recognition — scenario exclusivity by another name (see the industry exclusivity map).
• The top three overall have the flattest shapes. Qwen3.8-Max spreads 7 points, Doubao 10 and Qwen3.5 8. They are not exceptional at one thing; they have no hole. The overall board rewards balance; single-dimension boards reward extremes — two different products.

Three fixes for three readers

Fix one: merge redundant dimensions. For general selection, collapse document and chart into “static documents”, and agent and ecosystem into “engineering usability”. That leaves perception, video, generation and Chinese as independent axes. Eight dimensions become five; the ranking barely moves, but the weights finally correspond to independent information.

Fix two: read residuals, not raw scores. If you need “especially strong at one thing”, use the residual table. Raw scores mix in the water level; residuals isolate how much a model stands out relative to its own other abilities.

Fix three: use scenario gates, not weighted sums. In enterprise procurement, document 99 cannot compensate for agent 72. Instead of tuning weights, set gates first (see the five veto gates), then compare totals among survivors. Gates handle “must have”; weights handle “better”.

Boundaries

• This is descriptive statistics, not a theory of capability. With 32 samples and eight coarse scores, the matrix depends on sample composition; another set of models would produce different r values.
• Correlation is not causation. Document and chart correlate at 0.94, but that does not mean “fix documents and charts follow”; more likely they share the same visual encoder and language decoder.
• PCA does not prove the dimension definitions are wrong. It shows that, in this score distribution, the dimensions overlap linearly. Capability may be eight-dimensional; our measurement mixes several of them.
• The scores carry error. Grade B is ±1.5 points, grade C wider; the matrix does not fold that in. With error included, effective dimensionality would be lower, not higher.

Reproduction

The matrix is computed directly from the eight scores in src/data/models.ts: standardise → Pearson correlation → eigen-decomposition → participation ratio. No rotation, no imputation, no tuning. Scripts and intermediate tables ship with the site data; rerun after every expansion, and the numbers update in the changelog.

If this essay leaves one sentence: eight dimensions are not eight votes; they are about two and a half. Next time you see an “eight-dimension weighted” board, ask for its correlation matrix. If the author has never computed one, the “comprehensive” score is probably just repetition.