Failure overlap

Shared errors are the rule, not the exception

The benchmark's errors are far from randomly distributed. They repeatedly concentrate around the same structural bottlenecks: geometric reconstruction, circuit topology, global reasoning, missing solution branches and sign propagation.

The current analysis covers all 16 model-mode configurations and 60 exercises in the matched panel, corresponding to 1,600 distinct rubric locations. Repeated runs are first averaged within each configuration–exercise pair. A rubric criterion is then classified as substantially failed when the resulting credit is below 50%.

Under this definition, the panel contains 1,995 model–criterion failures. Of these, 1,686 occur on criteria also failed by a model from another provider.

84.5%of substantial criterion failures are shared across providers

The same exercise and rubric criterion is failed by at least one model from another provider.

The result remains strong when the analysis is restricted to the eight configurations whose current 60-exercise benchmark average is below 90.

1,734

Substantial failures below 90

1,430

Shared across providers

82.5%

Cross-provider overlap

Data & methodDownload the shared-failure summary CSV ↗ and the 1,600-location criterion-deficit CSV ↗. Thresholding and within-configuration repetition averaging follow the method ↗.

The automated analysis detects the same failed rubric criterion, not necessarily the same logical error. Manual examination is required before describing the underlying misconception as shared.

Observed versus independent

Models fail together more often than expected

For each configuration pair, the observed number of joint failures can be compared with the number expected if their errors were independent.

Configuration pairObservedExpectedCo-failure ratio
Grok 4.3 – DeepSeek no-thinking5213.13.96×
Haiku – DeepSeek no-thinking9330.93.01×
Sonnet – GPT-4.120468.82.97×
GPT-4.1 – Grok 4.39633.42.88×
Haiku – GPT-4.122178.72.81×

The expected count is computed from each model's marginal failure rate across the same 1,600 criterion locations. These models do not merely make many mistakes: they make them disproportionately often at the same points. Kim et al. (2025) ↗ report a related pattern across more than 350 language models, finding substantial error correlation even across different architectures and providers.

Model limit. The independence baseline uses marginal failure rates but does not control for criterion difficulty. Difficult criteria can increase overlap even without a shared mechanism.

Complete pairwise overlap

Observed joint substantial failures. Diagonal cells show each configuration's total failures.
ConfigurationFableHaikuSonnetDS-FDS-F directDS-ProSolGemini ProGemini FlashGemmaGrok 4.3Grok 4.5GPT-4.1o3Mistral MedMistral Small
Fable20151617171510171516201418151213
Haiku1539621325932613261992105442214778107
Sonnet162133462488271226208398372044985101
DS-F17252431242211231725271928242221
DS-F direct179388241252413242148523081374744
DS-Pro1526272224298232025252327242121
Sol101312111381610101116111491315
Gemini Pro17262623242310311725272230252121
Gemini Flash15192017212010172318191621171718
Gemma169283254825112518120433485404862
Grok 4.32010598275225162719431683796334560
Grok 4.514443719302311221634375143242533
GPT-4.1182212042881271430218596433185174112
o31547492437249251740332451603833
Mistral Med127885224721132117484525743810967
Mistral Small131071012144211521186260331123367152

Data & methodDownload the pairwise comparison CSV ↗ and the complete overlap-matrix CSV ↗. Expected counts use each pair's marginal failure rates across the same criterion locations.

Manual error analysis

Five recurring shared failure modes

01

Reconstructing the same wrong geometric object

In Geometric solid (A3-26-P4-E2) ↗, Claude Haiku, Claude Sonnet, GPT-4.1, Gemma 4 and DeepSeek V4 Flash no-thinking incorrectly reconstruct a three-dimensional solid. The correct horizontal section is an isosceles trapezoid; the models instead introduce a square, rectangle, Cartesian product or extrusion.

The answers differ in detail, but share one root failure: a complex geometric description is replaced with a simpler familiar structure.

02

Confusing a level set with a single orbit

In Phase portrait (A3-25-P3-E3) ↗, Gemma, Haiku, GPT-4.1, DeepSeek no-thinking and Grok 4.3 identify an algebraic set but fail to separate the zero level into its distinct invariant orbits.

level set ≠ single trajectory
03

Losing a constraint while transforming an equation

In Singular initial datum (A3-26-P1A-E3) ↗, the coefficient of y′ vanishes at the initial point while y² = 1. Grok 4.3, Gemma and DeepSeek no-thinking solve a transformed equation that is valid only away from that point.

The derivation can appear rigorous while solving a different problem.
04

Compressing a circuit into a familiar topology

Several DeepSeek and Grok configurations replace the actual parallel circuit with a familiar series equivalent, producing the wrong impedance, resonance and antiresonance. See the benchmark adjudication record ↗.

05

Propagating the same sign error

In an electromagnetic mechanics problem, Haiku, GPT-4.1, Gemma and DeepSeek no-thinking conclude that a mass moves downward; the correct result is that the rod moves left and the mass rises. See the benchmark adjudication record ↗.

Accuracy groups

More errors do not necessarily mean more correlated errors

Less accurate models make the patterns easier to observe because they generate more substantial criterion failures. Yet the rarer failures of stronger models are even more concentrated on shared rubric locations.

GroupShared substantial failuresShare
Configurations below 901,430 of 1,73482.5%
Configurations at or above 90256 of 26198.1%

Data & methodGroup totals are in the summary CSV ↗; the underlying criterion locations are in the criterion-deficit CSV ↗.

The 98.1% denominator is the 261 substantial failures made by configurations with an overall mean at or above 90; 256 occur at locations failed by another provider. This smaller denominator requires caution and still measures shared locations, not identical reasoning.

Weaker models reach shared failed criteria more frequently. Stronger models reach them less often, but their rarer failures cluster around the same exceptionally difficult rubric locations.

The most important convergences occur before most calculations begin: the wrong geometric object or circuit topology is constructed; a local result replaces a global classification; a branch, boundary or physical contribution is omitted; a singular constraint is lost; or an incorrect sign is propagated through the full solution.

Operational implication

Provider diversity is not automatically reasoning diversity

Agreement between models is often treated as independent confirmation. These results show why that assumption can be unsafe. Models from different providers may agree because they are correct, but they may also share the same failure attractor.

A useful benchmark should therefore measure not only accuracy, but also which criteria models fail together, whether they share the same root misconception, how overlap changes across providers and whether equivalent reformulations preserve or remove the error.

A better verification question

Which models fail differently enough to provide genuinely independent verification?

Conclusion

Model agreement can be a shared blind spot

Different wording, architectures and providers do not guarantee independent reasoning. The benchmark's most consequential failures repeatedly converge on a small set of structural simplifications.

Agreement is evidence only after we ask whether the underlying failure modes are independent.

This leaves a research question rather than an operational recommendation: can a pair selected for both accuracy and low residual error overlap provide safer verification than the two configurations with the highest individual means?

References

Sources and further reading