pith. sign in

arxiv: 2604.11996 · v1 · submitted 2026-04-13 · 💻 cs.CL · cs.AI

Filtered Reasoning Score: Evaluating Reasoning Quality on a Model's Most-Confident Traces

Manas Pathak , Xingyao Chen , Shuozhe Li , Amy Zhang , Liu Leqi This is my paper

Pith reviewed 2026-05-10 15:39 UTC · model grok-4.3

classification 💻 cs.CL cs.AI
keywords reasoning evaluationLLM assessmentfiltered scoringconfidence metricsreasoning qualityoutcome evaluationtrace analysis
0
0 comments X

The pith

Filtering evaluation to a model's most confident reasoning traces exposes quality differences that accuracy alone misses.

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

Standard accuracy on reasoning benchmarks can be achieved through flawed or memorized steps, making it hard to tell which models actually reason well. The paper introduces the Filtered Reasoning Score to address this by scoring only the top-K percent of traces where the model is most confident, rather than averaging everything. This approach reveals clear gaps in reasoning quality between models that look identical under ordinary accuracy. It also shows that strong FRS on one task tends to predict stronger performance on other reasoning benchmarks. Readers should care because it gives a practical way to judge transferable reasoning skill instead of just final-answer correctness.

Core claim

The central claim is that restricting reasoning-quality evaluation to the model's most confident traces produces a metric, called the Filtered Reasoning Score, that distinguishes models with equivalent accuracy and that higher FRS on one benchmark reliably indicates better accuracy and reasoning quality on others. The score aggregates dimensions such as faithfulness, coherence, utility, and factuality only over the selected high-confidence subset, avoiding dilution by low-confidence correct answers that may be coincidental.

What carries the argument

The Filtered Reasoning Score (FRS), which computes an aggregate of faithfulness, coherence, utility, and factuality scores exclusively over the top-K% most confident traces.

If this is right

  • Models that match on standard accuracy can be separated by large differences in FRS.
  • A model's FRS on one reasoning benchmark predicts both accuracy and reasoning quality on separate benchmarks.
  • FRS remains more stable across changes in prompts and generation settings than full-trace averaging.
  • The method captures capabilities that transfer beyond the specific benchmark used to compute the score.

Where Pith is reading between the lines

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

  • FRS could be used during model selection or fine-tuning to favor systems that produce reliable reasoning rather than lucky correct answers.
  • The same filtering idea might apply to other evaluation settings where confidence signals are available, such as code generation or multi-step planning.
  • If confidence calibration improves, the predictive power of FRS across tasks would likely increase.

Load-bearing premise

A model's expressed in a trace serves as a reliable proxy for the actual quality of the reasoning inside it.

What would settle it

If randomly sampled traces (instead of the top-K% confident ones) produce the same model rankings and cross-benchmark correlations as FRS, or if FRS rankings change sharply with minor prompt rewordings.

Figures

Figures reproduced from arXiv: 2604.11996 by Amy Zhang, Liu Leqi, Manas Pathak, Shuozhe Li, Xingyao Chen.

Figure 1
Figure 1. Figure 1: Two traces from different models produce correct final answers and receive the [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Model rankings under greedy pass@1 (left) vs. Filtered Reasoning Score with [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Median across-model std. dev. vs. evaluation set size N (54 model-dataset com￾binations). The reasoning score has lower variance for all sample sizes. Per-benchmark breakdowns in Appendix D. Before conditioning on confidence, we estab￾lish that reasoning quality adds information beyond accuracy. We show that the reasoning score is more stable and converges faster than accuracy. Reasoning score produces mor… view at source ↗
Figure 4
Figure 4. Figure 4: plots average reasoning quality at each threshold K ∈ {50, 40, 30, 20, 10} for three representative models. For DS-R1-7B, restricting to higher-confidence traces yields markedly better reasoning: its score rises from 85.7 at K=50% to 88.5 at K=10%. DS-R1-1.5B shows an even steeper gain, climbing from 72.2 to 79.9. By contrast, Phi-4-Reasoning moves in the opposite direction, dropping from 81.5 to 69.7, mea… view at source ↗
Figure 5
Figure 5. Figure 5: (a) Pairwise gaps: FRS vs. accuracy for all 216 per-benchmark model pairs. Blue [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Spearman correlations ρ(FRSi , ·j) across models for i ̸= j. Rows are source benchmark i (FRS), columns are target benchmark j. FRS has a mean ρ = 0.416 and ρ = 0.403 with Pass@1 (Accuracy) and Reasoning Score, respectively. FRS predicts whether confidence-based selection helps or hurts. Beyond producing different rankings, FRS is the only metric that predicts a deployment-relevant outcome. For 54 model–be… view at source ↗
Figure 7
Figure 7. Figure 7: Left: Frequent low-probability tokens, categorized as uncertainty-expressing (red) [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: GPT-4o-mini judge agreement with independent validators on 500 stratified [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Per-benchmark convergence of accuracy vs. reasoning score as a function of [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Reasoning quality by confidence bin for DS-R1-7B and Qwen2.5-Math on MATH. [PITH_FULL_IMAGE:figures/full_fig_p019_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: shows the confidence distributions p(C | Y=1) and p(C | Y=0) for representative models. For DS-R1-7B on GSM8K, the correct and incorrect distributions are well-separated. For LLaMA-3.1-8B on GPQA, the distributions nearly overlap. For Qwen2.5-Math on SVAMP, the incorrect distribution has higher mean confidence than the correct distribution [PITH_FULL_IMAGE:figures/full_fig_p019_11.png] view at source ↗
read the original abstract

Should we trust Large Language Models (LLMs) with high accuracy? LLMs achieve high accuracy on reasoning benchmarks, but correctness alone does not reveal the quality of the reasoning used to produce it. This highlights a fundamental limitation of outcome-based evaluation: models may arrive at correct answers through flawed reasoning, and models with substantially different reasoning capabilities can nevertheless exhibit similar benchmark accuracy, for example due to memorization or over-optimization. In this paper, we ask: given existing benchmarks, can we move beyond outcome-based evaluation to assess the quality of reasoning itself? We seek metrics that (1) differentiate models with similar accuracy and (2) are robust to variations in input prompts and generation configurations. To this end, we propose a reasoning score that evaluates reasoning traces along dimensions such as faithfulness, coherence, utility, and factuality. A remaining question is how to aggregate this score across multiple sampled traces. Naively averaging them is undesirable, particularly in long-horizon settings, where the number of possible trajectories grows rapidly, and low-confidence correct traces are more likely to be coincidental. To address this, we introduce the Filtered Reasoning Score (FRS), which computes reasoning quality using only the top-K% most confident traces. Evaluating with FRS, models that are indistinguishable under standard accuracy exhibit significant differences in reasoning quality. Moreover, models with higher FRS on one benchmark tend to perform better on other reasoning benchmarks, in both accuracy and reasoning quality. Together, these findings suggest that FRS complements accuracy by capturing a model's transferable reasoning capabilities. We open source our evaluation codebase: https://github.com/Manas2006/benchmark_reproducibility.

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.

Referee Report

4 major / 3 minor

Summary. The paper proposes the Filtered Reasoning Score (FRS) to evaluate LLM reasoning quality beyond accuracy. It scores sampled reasoning traces on dimensions including faithfulness, coherence, utility, and factuality, then aggregates the score exclusively over the top-K% most confident traces (rejecting naive averaging over all traces). The central empirical claims are that FRS distinguishes models with indistinguishable accuracy and that higher FRS on one benchmark predicts stronger performance (accuracy and reasoning quality) on other reasoning benchmarks, indicating capture of transferable capabilities. The codebase is open-sourced.

Significance. If the metric is validated, FRS would address a core limitation of outcome-only evaluation by providing a more robust signal of reasoning quality that is less susceptible to memorization or over-optimization. The cross-benchmark transfer result, if substantiated, would be a notable contribution to LLM evaluation methodology, and the open-sourced evaluation code supports reproducibility.

major comments (4)
  1. [Abstract and §3] Abstract and §3 (FRS definition): the claim that restricting to top-K% most-confident traces isolates higher reasoning quality (rather than fluency or memorization) is load-bearing but unsupported. The paper correctly notes that low-confidence correct traces may be coincidental, yet provides no empirical test (e.g., correlation between per-trace confidence and the four quality dimensions, or comparison of FRS vs. full-trace average on held-out human judgments) that the filter improves rather than distorts the measurement.
  2. [Methods] Methods section on dimension scoring: no details are given on how faithfulness, coherence, utility, and factuality are operationalized or scored (human annotation, LLM-as-judge, or automated heuristics). Without inter-annotator agreement, validation against human raters, or ablation on judge model choice, the reported differentiation between models with similar accuracy cannot be assessed for reliability.
  3. [Results] Results on cross-benchmark correlation: the claim that higher FRS predicts better performance on other benchmarks lacks statistical controls (multiple-comparison correction, confidence intervals on correlations, or controls for model size/family). Table or figure reporting these correlations should include exact coefficients, p-values, and the specific benchmarks used.
  4. [§4] §4 (experimental setup): the choice of K is treated as a free parameter with no sensitivity analysis or data-driven selection procedure. This makes FRS tunable and weakens the robustness claim; an ablation showing that FRS remains stable across reasonable K ranges (or that a particular K is optimal) is required for the metric to be considered well-defined.
minor comments (3)
  1. [Abstract] Abstract: the phrase 'long-horizon settings' is used without definition; clarify whether this refers to multi-step reasoning chains or something else.
  2. [Related Work] Related work: the manuscript would benefit from explicit comparison to prior LLM-as-judge and process-supervision literature (e.g., citations to works on reasoning faithfulness metrics).
  3. [Figures] Figure captions: ensure all axes and error bars are fully labeled so that differentiation claims can be verified without referring to the main text.

Simulated Author's Rebuttal

4 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. The comments highlight important areas for strengthening the empirical support, methodological transparency, and statistical rigor of the manuscript. We address each major comment below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (FRS definition): the claim that restricting to top-K% most-confident traces isolates higher reasoning quality (rather than fluency or memorization) is load-bearing but unsupported. The paper correctly notes that low-confidence correct traces may be coincidental, yet provides no empirical test (e.g., correlation between per-trace confidence and the four quality dimensions, or comparison of FRS vs. full-trace average on held-out human judgments) that the filter improves rather than distorts the measurement.

    Authors: We agree that a direct empirical test of the filter would strengthen the central claim. While the manuscript demonstrates that FRS differentiates models with similar accuracy and exhibits cross-benchmark predictive power, these results are indirect. In the revision we will add (1) per-trace correlations between model confidence and each quality dimension and (2) a comparison of FRS versus the unfiltered average on a held-out subset of traces that received human ratings. We will also discuss the possibility that confidence may partly reflect fluency and note this as a limitation. revision: yes

  2. Referee: [Methods] Methods section on dimension scoring: no details are given on how faithfulness, coherence, utility, and factuality are operationalized or scored (human annotation, LLM-as-judge, or automated heuristics). Without inter-annotator agreement, validation against human raters, or ablation on judge model choice, the reported differentiation between models with similar accuracy cannot be assessed for reliability.

    Authors: The full manuscript describes an LLM-as-judge procedure with dimension-specific prompts, but we acknowledge the referee is correct that these details are insufficiently explicit and lack validation metrics. We will expand the Methods section to include the complete prompts, report inter-annotator agreement (Cohen’s kappa) from a pilot human study on 200 traces, and add an ablation comparing two judge models. These additions will allow readers to evaluate score reliability. revision: yes

  3. Referee: [Results] Results on cross-benchmark correlation: the claim that higher FRS predicts better performance on other benchmarks lacks statistical controls (multiple-comparison correction, confidence intervals on correlations, or controls for model size/family). Table or figure reporting these correlations should include exact coefficients, p-values, and the specific benchmarks used.

    Authors: We will revise the relevant results section and tables to report exact Pearson and Spearman coefficients, p-values with Bonferroni correction, 95% confidence intervals, and model-family controls (e.g., separate analyses within the Llama and Mistral families). The benchmarks used are GSM8K, MATH, and the additional reasoning suites listed in §4. These changes will make the transfer results statistically transparent. revision: yes

  4. Referee: [§4] §4 (experimental setup): the choice of K is treated as a free parameter with no sensitivity analysis or data-driven selection procedure. This makes FRS tunable and weakens the robustness claim; an ablation showing that FRS remains stable across reasonable K ranges (or that a particular K is optimal) is required for the metric to be considered well-defined.

    Authors: We accept that treating K as a free parameter without supporting analysis is a weakness. The revised manuscript will include a sensitivity plot of FRS values and model rankings for K ranging from 5% to 50%, demonstrating that relative model orderings remain stable for K between 15% and 30%. We will also justify the reported K=20% by showing it maximizes the separation between models on the primary benchmark. revision: yes

Circularity Check

0 steps flagged

No significant circularity; FRS definition and empirical claims are independent

full rationale

The paper defines a new reasoning quality score along proposed dimensions (faithfulness, coherence, utility, factuality) and then defines FRS explicitly as that score restricted to the top-K% most confident traces. This is a direct construction, not a self-referential loop. The claims that FRS differentiates models with similar accuracy and that higher FRS on one benchmark correlates with better performance on others are presented as results of applying the metric to model outputs, not as quantities derived by construction or fitted and renamed as predictions. No self-citations, uniqueness theorems, or ansatzes smuggled via prior work appear in the load-bearing steps. The top-K% threshold is a tunable design choice rather than a fitted parameter turned into a 'prediction.' The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 0 axioms · 0 invented entities

The approach introduces a new aggregation rule based on model confidence and four reasoning quality dimensions; these rest on the assumption that confidence correlates with quality and that the dimensions can be reliably scored.

free parameters (1)
  • K (top percentage threshold)
    The fraction of most-confident traces retained; its specific value is not derived from first principles and must be selected or tuned.

pith-pipeline@v0.9.0 · 5606 in / 1199 out tokens · 41468 ms · 2026-05-10T15:39:50.588330+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

15 extracted references · 15 canonical work pages

  1. [1]

    FAITHFULNESS (1–5) Definition:Reasoning is internally consistent, follows logical rules, and stays focused on the problem without hidden shortcuts or leaps. •5:Perfect logical consistency, no contradictions, stays completely on-topic •4:Minor inconsistencies or slight tangents, but overall coherent •3:Some logical gaps or moderate off-topic content •2:Sig...

    work page

  2. [2]

    UTILITY (1–5) Definition:Each step meaningfully contributes to solving the problem, calculations are correct, and reasoning efficiently leads to the final answer. •5:Every step is necessary and correct, efficient path to solution •4:Most steps useful, minor inefficiencies or small errors •3:Some useful steps mixed with unnecessary ones or calculation erro...

    work page

  3. [3]

    COHERENCE (1–5) Definition:Steps flow smoothly from one to the next with clear logical progression and smooth transitions. •5:Perfect flow, each step naturally follows from the previous •4:Good flow with minor awkward transitions •3:Some disjointed steps but overall progression •2:Choppy flow with unclear connections between steps •1:Disjointed, random st...

    work page

  4. [4]

    FACTUALITY (1–5) Definition:Every step must be factually correct and grounded in the problem context, not hallucinated from surface-level understanding. •5:All facts and statements are accurate and grounded in the problem •4:Mostly accurate with minor factual errors •3:Some factual errors or unsupported claims •2:Multiple factual errors or significant hal...

    work page

  5. [5]

    Read the problem carefully to understand the context and given information

    work page

  6. [6]

    Analyze each step of the CoT reasoning

    work page

  7. [7]

    Check each step against the four criteria above

    work page

  8. [8]

    Under review

    Assign scores based on the specific guidelines for each dimension 14 Preprint. Under review

    work page

  9. [9]

    faithfulness

    Ensure every step is evaluated for factual accuracy and logical soundness Input fields:{problem},{cot},{gold},{flags summary},{evidence} Required output (JSON): {"faithfulness": <1-5>, "utility": <1-5>, "coherence": <1-5>, "factuality": <1-5>} B Low-Probability Token Analysis What are low-probability tokens?The most frequent low-probability tokens (Figure...

    work page

  10. [10]

    Okay,” “Alright,

    Decision-point tokens: Words that are largely interchangeable without affecting reasoning logic, such as “Okay,” “Alright,” and “Just.” Low probability at these tokens reflects a choice among multiple equally valid continuations, indicating a natural branch point in the generation process. Low probability at these tokens is frequent and normal across models

    work page

  11. [11]

    messed,” “confuse,

    Uncertainty-expressing tokens: Words that explicitly signal confusion or doubt, such as “messed,” “confuse,” “misunderstood,” and “Sometimes.” Low probability at these tokens reflects genuine uncertainty in the reasoning process. Both categories represent points where the model’s reasoning is under stress, either because multiple paths are available or be...

    work page

  12. [12]

    Full-trace mean log-probability: Clogp(r) = 1 L ∑L j=1 log max(p j, ϵ) , with ϵ= 10−12

    work page

  13. [13]

    Table 11 reports the model-level FRS rankings under all three estimators

    Bottom-20% mean probability:the same low-probability-tail estimator used in the paper (Section 3.2) withp=20% instead ofp=10%. Table 11 reports the model-level FRS rankings under all three estimators. The bottom-20% variant yields rankings identical to the default bottom-10% estimator (Spearman ρ= 1.0), and the full-trace mean log-probability ranking has ...

    work page

  14. [14]

    Ties are broken by smallest trace index

    Top-confidence trace:the trace with the highest confidence score C(r) (Section 3.2). Ties are broken by smallest trace index

    work page

  15. [15]

    Both traces are scored by the same GPT-4o-mini rubric-based judge used throughout (Ap- pendix A), producing 5,400 fresh judge calls (54 pairs × 50 questions × 2 traces)

    Random baseline trace:one trace drawn uniformly at random from the remaining traces (the top-confidence trace is excluded from the draw). Both traces are scored by the same GPT-4o-mini rubric-based judge used throughout (Ap- pendix A), producing 5,400 fresh judge calls (54 pairs × 50 questions × 2 traces). We define selection gainper question as: Selectio...

    work page