arxiv: 2605.07096 · v1 · submitted 2026-05-08 · 💻 cs.LG · cs.AI· stat.ME

Recognition: 2 theorem links

· Lean Theorem

Query-efficient model evaluation using cached responses

Ben Johnson, Carey Priebe, Hayden Helm

Authors on Pith no claims yet

Pith reviewed 2026-05-11 00:50 UTC · model grok-4.3

classification 💻 cs.LG cs.AIstat.ME

keywords query-efficient evaluationcached responsesmodel benchmarkingperformance predictionData Kernel Perspective Spaceblack-box modelskernel perspective

0 comments

The pith

DKPS with cached responses allows benchmark evaluation of new models using far fewer queries while matching baseline accuracy.

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

The paper introduces a method to predict how a new model will perform on a benchmark by using responses already obtained from other models. It uses the Data Kernel Perspective Space to capture relationships between these models without needing to inspect their internal workings. This enables query-efficient evaluation, where the new model is only run on a subset of the test cases. Theory establishes conditions under which this saves queries, and experiments show the prediction error stays as low as running the full set. The work further suggests selecting the queries in advance based on how well they fit known models.

Core claim

The authors claim that DKPS-based methods achieve the same mean absolute error as baselines with a substantially decreased query budget by leveraging cached model responses. They provide theoretical results on query-efficiency under certain conditions and empirical validation on benchmarks, plus an offline query selection method that improves accuracy over random choice.

What carries the argument

The Data Kernel Perspective Space (DKPS), which quantifies relationships between models in the black-box setting to leverage cached responses for performance prediction.

If this is right

Benchmark performance can be estimated accurately without querying every test case.
Existing caches of model responses become a resource for reducing evaluation costs of future models.
Query selection can be done offline to maximize prediction quality based on reference models.
The approach applies when theoretical conditions on model similarities hold in practice.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Shared evaluation caches could become standard in model development to speed up testing.
The method might extend to selecting minimal query sets for entire model families.
It suggests potential for dynamic evaluation strategies that adapt based on observed similarities.

Load-bearing premise

The Data Kernel Perspective Space reliably quantifies black-box relationships between models, allowing the theoretical query-efficiency conditions to hold in actual benchmark evaluations.

What would settle it

An experiment on a standard benchmark where the DKPS method requires the same or more queries than a non-DKPS baseline to achieve equivalent mean absolute error in performance prediction.

Figures

Figures reproduced from arXiv: 2605.07096 by Ben Johnson, Carey Priebe, Hayden Helm.

**Figure 1.** Figure 1: Example d = 2-dimensional Data Kernel Perspective Spaces (DKPS) for models publicly evaluated on HELM-Lite’s MATH counting and probability subtask. Each panel includes the DKPS representations for different (n, m) = (number of models, number of queries) pairs induced by a random query set of size m. Each dot is a model colored by its score on the subtask. As the number of queries increases (left to right),… view at source ↗

**Figure 2.** Figure 2: Regression in the Data Kernel Perspective Space (DKPS) provides query-efficient benchmark prediction relative to using the sample score across the representative HELM-Lite subtasks. Lines represent the average mean absolute error across leave-one-family-out and 512 randomly sampled query sets. Lower is better. Actual query-efficiency depends on the number of models used to induce DKPS and train the regress… view at source ↗

**Figure 3.** Figure 3: Choice of embedding function can have a large effect at small m. For small m, the best performing embedding model (gemini-embedding-001) improves upon the worst performing (all-minilm-l6-v2) by ≈ 20% (from MAE ≈ 0.15 to MAE ≈ 0.12) at m = 1. For large enough m, any modern sentence embedding function is sufficient. into model-specific benefits, such as predicting the suitability of DKPS-based methods for … view at source ↗

**Figure 4.** Figure 4: Performance gain (MAE of Sample Score minus MAE of Ensemble regressor) on a per model basis (top) and a per query set basis (bottom) for the four representative subtasks. Each dot represents the average difference in performance across query sets (top) or across models (bottom). A A dot above 0 indicates that the Ensemble regressor is better than just using Sample Score. The majority of the mass of the dis… view at source ↗

**Figure 5.** Figure 5: Active query selection can improve query-efficiency of DKPS-based prediction methods. Top left. Relationship between MAE and linear goodness-of-fit (R 2 ) between DKPS representations of reference models and full benchmark score for m = 8 queries on the MATH counting and probability subtask. The highest R 2 (lowest 1 − R 2 is highlighted with a red ×. Top center. Histogram of MAE for different query subset… view at source ↗

read the original abstract

Evaluating a new model on an existing benchmark is often necessary to understand its behavior before deployment. For modern evaluation frameworks, generating and evaluating a response for all queries can be prohibitively expensive. In practice, responses from previously-evaluated models are often cached -- creating a potential opportunity to use this additional information to decrease the number of queries required to accurately evaluate a new model. In this paper, we introduce an approach for predicting benchmark performance that leverages cached model responses based on the Data Kernel Perspective Space (DKPS), a method for quantifying the relationship between models in the black-box setting. Theoretically, we show that DKPS-based methods are query-efficient under certain conditions. Empirically, we demonstrate that DKPS-based methods achieve the same mean absolute error as baselines with a substantially decreased query budget. We conclude by proposing an offline method for selecting a set of queries that maximizes the goodness-of-fit on reference models, improving prediction accuracy over random query selection.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

DKPS gives a workable way to cut queries for new model eval using cached responses, but the span assumption looks untested for dissimilar models.

read the letter

The core takeaway is that this paper shows how to predict a new model's benchmark score from a small subset of queries by projecting onto the Data Kernel Perspective Space built from cached reference responses, and they back the claim with both theory and experiments that match full-evaluation error at lower cost. They also add an offline query-selection step that picks queries to maximize fit on the references rather than using random ones. That combination is the actual new piece; prior work on model similarity or active evaluation does not seem to frame it exactly this way. The theory section establishes query-efficiency under stated conditions on the kernel, and the empirical results report the same mean absolute error with a substantially smaller query budget, which is the practical point if it holds up. The math and citation pattern look solid on a first pass, with no obvious circularity or missing priors on kernel methods for black-box models. The soft spot is the one you flagged: the method assumes the new model's response vector lies close enough to the span of the cached references for the DKPS coordinates to stay well-conditioned. The experiments appear to use models already represented in the cache, with no reported tests on qualitatively different architectures or training regimes. If that assumption breaks, the reduced-budget MAE guarantee does not follow. The theory conditions are also somewhat restrictive and may not map cleanly to messy real benchmarks. This is aimed at groups that run repeated evaluations on the same large benchmarks and want to trim compute or API spend. A reader focused on efficient benchmarking or model comparison would get usable ideas from it. The work is coherent enough and has enough grounding to deserve a serious referee, though the review should press for out-of-distribution checks and clearer discussion of when the span condition fails. I would send it to peer review with those requests.

Referee Report

2 major / 2 minor

Summary. The paper introduces DKPS (Data Kernel Perspective Space) as a black-box method to leverage cached responses from previously evaluated models, enabling query-efficient prediction of a new model's full benchmark score. It provides theoretical conditions under which DKPS-based predictors are query-efficient, demonstrates empirically that they match baseline mean absolute error at substantially lower query budgets, and proposes an offline procedure that selects a fixed query subset by maximizing goodness-of-fit on a reference model cache.

Significance. If the central claims hold, the work offers a practical route to amortize the cost of large-scale benchmarking by reusing cached model outputs, which is increasingly relevant as evaluation budgets grow. The offline query-selection method and the explicit statement of kernel-span conditions are concrete strengths that could be built upon.

major comments (2)

[Experiments] The empirical protocol (Experiments section) evaluates only models whose response vectors lie inside the linear/kernel span of the cached reference set; no out-of-distribution trials are reported in which the target model belongs to a qualitatively different architecture family or training regime. Because the DKPS coordinate estimation and the claimed MAE preservation both rely on the new model remaining well-conditioned within that span, the absence of such tests makes the general query-efficiency claim load-bearing and unverified.
[§3] §3 (theoretical analysis): the query-efficiency guarantee is stated to hold “under certain conditions” on the kernel matrix and the target response vector, yet the manuscript does not quantify how often these conditions are satisfied for realistic model caches or provide a diagnostic that practitioners could use to check them before deployment.

minor comments (2)

[§2] Notation for the DKPS kernel and the projection operator is introduced without an explicit comparison table to standard kernel ridge regression or Nyström approximations; a short side-by-side would clarify the novelty.
[Abstract] The abstract claims “substantially decreased query budget” but supplies neither the exact reduction factor nor the identity of the strongest baseline; these numbers should appear in the abstract or a prominent table.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive review and for recognizing the practical relevance of amortizing benchmark costs via cached responses. We address each major comment below and commit to revisions that strengthen the manuscript without altering its core claims.

read point-by-point responses

Referee: [Experiments] The empirical protocol (Experiments section) evaluates only models whose response vectors lie inside the linear/kernel span of the cached reference set; no out-of-distribution trials are reported in which the target model belongs to a qualitatively different architecture family or training regime. Because the DKPS coordinate estimation and the claimed MAE preservation both rely on the new model remaining well-conditioned within that span, the absence of such tests makes the general query-efficiency claim load-bearing and unverified.

Authors: We agree that the reported experiments focus on in-span models, which is the setting in which the theoretical guarantees of DKPS hold. The method is explicitly intended for cases where the target response vector lies in the kernel span of the reference cache; out-of-span models are expected to exhibit higher error, consistent with the analysis in §3. To clarify the scope of the query-efficiency claim, we will add a new subsection in the Experiments section that includes out-of-distribution trials using models from qualitatively different architecture families and training regimes. These results will show the anticipated degradation in MAE when the span condition is violated, together with a discussion of how practitioners can detect such cases. This addition will make the boundaries of the method explicit rather than leaving the claim unverified. revision: yes
Referee: [§3] §3 (theoretical analysis): the query-efficiency guarantee is stated to hold “under certain conditions” on the kernel matrix and the target response vector, yet the manuscript does not quantify how often these conditions are satisfied for realistic model caches or provide a diagnostic that practitioners could use to check them before deployment.

Authors: We will expand §3 with a new subsection that empirically quantifies the prevalence of the required conditions across the reference caches used in the paper. Concretely, we will report the distribution of kernel-matrix condition numbers, effective ranks, and residual norms of the projection of held-out target vectors onto the span for each benchmark and cache size. In addition, we will define and validate a simple, computable diagnostic: the normalized residual norm of the target response vector after projection onto the cached kernel span (which can be evaluated using only the existing cache before any new queries are made). This diagnostic will be presented with threshold guidelines derived from the empirical distributions, enabling practitioners to decide whether DKPS is likely to be query-efficient for a given new model. revision: yes

Circularity Check

0 steps flagged

No significant circularity; DKPS derivation and query selection remain independent of target predictions

full rationale

The paper introduces DKPS as a black-box quantification of model relationships, derives query-efficiency under stated theoretical conditions, and empirically shows equivalent MAE at lower query budgets. The offline query-selection procedure optimizes goodness-of-fit explicitly on reference models before applying the reduced set to new models; this is presented as an engineering improvement rather than a statistical tautology. No equations or claims reduce a prediction to a fitted quantity by construction, no load-bearing self-citations close the central argument, and the derivation chain does not rely on renaming or smuggling an ansatz. The result is therefore self-contained against external benchmarks and receives only a minor score for the inherent reference-set dependence of any caching method.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no free parameters, axioms, or invented entities are identifiable from the provided text.

pith-pipeline@v0.9.0 · 5458 in / 906 out tokens · 42030 ms · 2026-05-11T00:50:12.566768+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
DKPS representations … argmin … (||zi − zj|| − Dii′)² … nearest neighbor regression … Assumption 1 (Lipschitz Score Function)
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear
Theorem 2 … MSE(ŷNN) ≤ ε … query-efficient relative to ŷQ

Reference graph

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