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Development case · blind model judgment pending independent human review; not a formal Benchmark conclusion.
AutocompleteEvidence version preferred91 / 162 · e63057eb341f2997

Quantum Computational Complexity -- From Quantum Information to Black Holes and Back

Astrophysics · 2110.14672v1

FLOWING EVIDENCE BENCHMARK

How do we tell whether Evidence helps?

At the same writing position, with the same model and task, how does supplying retrieved paper passages change the first output? We compare matched versions and retain ties, unusable outputs and incomplete reviews.

SAME DRAFT · EVIDENCE ON OR OFF

01 · FIXED WRITING POSITION

MANUSCRIPT

Same writing position ▌

Matched autocomplete at the same draft position

02 · TWO MATCHED INPUTS

SHARED BY BOTH

Manuscript context, model, task and prompt

A · With Evidence

Retrieved paper passages supplied

B · Without Evidence

No retrieved passages supplied

LLM

Same model and version

A → first output

B → first output

Blind judge agent

First outputs are anonymized as X and Y

Continuation review: accuracy, fit to the writing task and usability
Returns: X preferred / tie / Y preferred / both unusable

Order check: X / Y → Y / X

HOW DOES BLIND JUDGING WORK?

① Anonymize both outputs
The judge sees the same draft and both first outputs without knowing which received Evidence.

② Compare and swap order
The judge applies task-specific criteria in X/Y and then Y/X order.

③ Review disagreements
A third pass resolves disagreements. Incomplete reviews remain in the denominator.

How are autocomplete positions stratified?

Before seeing generation outcomes, we check whether a retrieved passage contains a specific proposition that directly supports the next writing move. Those positions appear in the left opportunity group; the rest are ordinary positions on the right. We select a balanced sample from admitted papers in each field. The 50/50 split is experimental, not a measure of how often either type occurs in writing.

AUTOCOMPLETE · 110

Biology, statistics and astrophysics

55 positions on each side; statistics uses the ten-paper rerun.

AUTOCOMPLETE · 52

Psychology and climate science

26 positions on each side; psychology includes nine papers and climate science four.

How are the table percentages calculated?

Across five fields there are 81 source-opportunity positions. The original blind review preferred Evidence in 51; a task check moved one empty Evidence continuation to both unusable, leaving 50 in public counts. In the ordinary group, another pair of empty outputs moved from no winner to both unusable. Original verdicts remain visible on case pages.

50Evidence version preferred
÷
81All positions in this group
=
62%Evidence preference in this group

Source contribution is a separate review: 16 of 21 Evidence wins entered into source review directly used retrieved papers; another 29 wins await review.

These are development-stage model judgments pending independent human review. They are not formal Benchmark conclusions and do not, on their own, establish causality.

Manuscript writing position

Text excerpt · not a PDF page

Research manuscript · excerpt

Quantum Computational Complexity -- From Quantum Information to Black Holes and Back

9 Summary and Outlook

…lained, the computations are manageable only when one can exploit a symmetry of the system; for this reason it seems promising to consider CFTs, but for the moment it is not known how to compute the relative complexity of two states that do not belong to the same conformal family. As we have seen, in free theories the complexity can be found in terms of the spectrum of the theory. Presumably in a CFT there will be some dependence on the OPE coefficients as well. It would be interesting to understand this dependence, and to determine whether some part of complexity has universality properties.

…ry. As we have seen in the single qubit case, but is true more generally, their effect is to create negative sectional curvature, which in turn is associated to diverging geodesics and chaotic behavior (notice however that in the case of coherent states we found a section with the geometry of hyperbolic space even without any penalty factors). It is therefore important to try and understand how the complexity in QFT is affected by penalty factors (see [ 141 , 142 ] for some work in this direction). This would also help in understanding better the relation between complexity and chaos [ 32 ] .

↓ Next paragraph was generated here

The highlighted text is near the writing position. This is a layout of the evaluation input, not a PDF screenshot.

A matched comparison at the same writing positionJudgment: Evidence version preferred

Both arms use the same model, task and manuscript context. Only the retrieved passages differ. The first recorded output from each arm is shown below.

Evidence

Same model and position · retrieved passages supplied · first output

Preferred by blind review

A related open question concerns the geometry of the complexity metric itself: while uniform penalty factors yield a positively curved metric whose geodesic flow is not ergodic, non-uniform penalty factors can render some sectional curvatures negative, though not all of them.

Passages supplied to the Evidence version

On the geometry of quantum complexity ↗

Another desirable property of complexity metric is the ergodicity of geodesics, which is important to apply thermodynamical arguments to complexity evolution [ 47 , 48 , 49 ] . Ergodicity in this context refers to the general idea that the trajectory of a generic state along a geodesic will eventual…

Read full passage excerpt

Another desirable property of complexity metric is the ergodicity of geodesics, which is important to apply thermodynamical arguments to complexity evolution [ 47 , 48 , 49 ] . Ergodicity in this context refers to the general idea that the trajectory of a generic state along a geodesic will eventually visit all the allowed portions of the unitary space. There are classical mathematical results (see e.g. [ 51 ] ) showing that the geodesic flow on a manifold with all negative sectional curvatures is ergodic. The complexity metric with uniform penalty factors is positively curved in all the directions and does not have an ergodic geodesic flow. The introduction of non-uniform penalty factors can make some of the sectional curvatures negative [ 5 ] , but not all of them.

No Evidence

Same model and position · no retrieved passages · first output

Not preferred in this comparison

The product produced no insertable continuation text.

The model explicitly returned a no-completion marker.

Judgment and task check

The blinded model review preferred the Evidence version. Its original rationale appears below.

Read the original model judgment

In this rationale, Output A = No Evidence; Output B = Evidence.

Output A is empty and provides no completion, which violates the task requirement to continue the manuscript with one coherent academic paragraph. Output B provides a grounded continuation that connects to the draft's discussion of penalty factors and negative sectional curvature. The B output is directly supported by the source snippet, which states that 'The complexity metric with uniform penalty factors is positively curved in all the directions and does not have an ergodic geodesic flow. The introduction of non-uniform penalty factors can make some of the sectional curvatures negative, but not all of them.' B preserves the factual content (positive curvature with uniform penalties, partial negative curvature with non-uniform penalties, non-ergodic flow) without adding unsupported claims. The B output also coherently bridges from the draft's preceding discussion of penalty factors creating negative curvature and chaos to the source's discussion of ergodicity, making it a natural continuation.

Source review confirmed that this continuation directly used specific, verifiable information from the retrieved paper.

The passages are input material; their presence does not mean an output used them or that they support every claim. Draft and source passages are excerpted; no simulated scores or PDF appear here.