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Reasoning Denoiser: Denoising Reasoning Traces for Hallucination Detection in Large Reasoning Models

Junlin Fang, Do Nguyen-Thanh, Xiaogang Xu, Zhen Fang, Sean Du

arXiv:2607.22098v1cs.AIcs.LG

TL;DR

Long reasoning traces can contain irrelevant and repetitive steps that obscure signals for hallucination detection. REDE learns to identify and filter these steps using final-answer attention, consistently improving detection across benchmarks, models, and detector families, including 87.32% state-of-the-art performance on TruthfulQA.

  • Problem

    Irrelevant and repetitive reasoning steps obscure useful truthfulness signals, while existing confidence- and embedding-based filters do not reliably separate noisy from informative steps.

  • Method

    REDE uses final-answer attention to shape step-level representations, identify noisy steps, and filter them before downstream hallucination detection without human annotation.

  • Results

    87.32% state-of-the-art performance is achieved on TruthfulQA, while detection consistently improves across four tasks, datasets, LRM families, and detector types.

  • Takeaways & Limitations

    REDE is a lightweight, annotation-free module that can be plugged into diverse hallucination detectors to improve reasoning-trace-based assessment.

  • Takeaways & Limitations

    REDE may still make incorrect predictions, potentially over-trusting hallucinated answers or suppressing correct but unconventional reasoning traces.

Abstract

from arXiv · show

Large reasoning models (LRMs) generate long reasoning traces before producing final answers. While these traces may contain useful signals for hallucination detection, harnessing them is non-trivial because long trajectories often include noisy steps that obscure the cues relevant to truthfulness assessment. In this paper, we identify two prevalent forms of reasoning noises, i.e., irrelevant steps and repetitive steps, and show that both substantially degrade hallucination detection performance. Existing confidence-based scores and naive embedding-based filtering fail to reliably separate noisy from informative steps. To address this challenge, we propose REDE, a novel learning framework for denoising reasoning traces for hallucination detection. Specifically, REDE leverages final-answer attention as an automatic supervision signal to shape the step-level representation space, yielding refined embeddings in which noisy steps can be reliably identified and filtered. REDE can be readily plugged into diverse hallucination detectors by operating on the filtered reasoning trajectory after removing noisy steps. Extensive experiments on multiple reasoning benchmarks show that REDE consistently improves detection performance over competitive baselines.

1. Introduction

Long reasoning traces can aid hallucination detection but contain irrelevant and repetitive steps that substantially degrade performance. REDE addresses this problem by using final-answer attention to learn representations for reliably filtering noisy steps without human annotation.

  • Large reasoning models generate long traces before final answers, creating opportunities for hallucination detection but also introducing reliability challenges.
  • Irrelevant and repetitive steps are prevalent reasoning noises that substantially degrade hallucination detection performance.Irrelevant steps lack meaningful problem-specific information, whereas repetitive steps duplicate information covered later.
  • Confidence scores reflect generation certainty rather than a step’s usefulness for downstream hallucination detection, limiting their filtering reliability.Confidence-based methods are designed for improving reasoning-time generation, not identifying informative reasoning steps.
  • Naive kNN filtering can identify some irrelevant steps but fails to separate repetitive steps from informative ones in raw embedding space.Repetitive steps often remain close to informative steps because they are semantically similar.
  • REDE uses final-answer attention as annotation-free supervision to shape step representations and filter noisy reasoning steps before hallucination detection.The framework can plug into probing-based, uncertainty-based, and verbalized hallucination detectors operating on the filtered trajectory.

2. Problem setup

The problem setup models a large reasoning model’s response as variable-length reasoning steps followed by a final answer, then defines hallucination detection as binary truthfulness prediction. Because long traces contain weakly informative noise that can dilute relevant signals, the setup motivates denoising before detection.

  • Reasoning generation: A causal LRM decomposes each response into a reasoning trace C = (c_1, ..., c_K) and final answer a, with variable step counts and lengths.Each c_k is a contiguous token span representing one reasoning step.
  • Hallucination detection: Given prompt p, trace C, and answer a, a binary detector G(p, C, a) predicts whether a is truthful or hallucinated.The label is y = 0 for truthful answers and y = 1 for hallucinated answers.
  • Challenge of long reasoning traces: Long reasoning traces often include weakly informative noisy steps that dilute signals relevant to assessing final-answer truthfulness.Naively using the original trace may therefore hurt hallucination detection performance.

3. Understanding noisy reasoning steps for hallucination detection

The analysis identifies final-answer attention as a signal for distinguishing informative reasoning steps from irrelevant or repetitive noise. It also suggests that later steps among semantically similar steps better preserve information relevant to the final answer, motivating retention-based evaluation.

  • Final-answer attention reflects step informativeness: Final-answer attention provides a meaningful relevance signal because steps contributing more directly to the answer receive higher attention.This signal is examined as a way to identify useful reasoning steps for hallucination detection.
  • Final-answer attention reflects step informativeness: On annotated AIME 2024 examples with Qwen3-8B, irrelevant and repetitive steps receive low attention, while informative steps directly supporting the answer receive higher attention.The attention score is assigned by the final-answer token to each reasoning step.
  • Earlier semantically similar steps are often redundant: Low-attention steps include both irrelevant steps and repeated reasoning, so attention distinguishes noise without treating all low-attention steps as the same.Repetitive steps are effectively subsumed by later steps.
  • Earlier semantically similar steps are often redundant: Among semantically similar reasoning steps, the analysis investigates whether retaining the earliest or latest cluster member better preserves answer-relevant information.Steps are clustered by embedding similarity, and either the earliest or latest step is retained.
  • Earlier semantically similar steps are often redundant: Retention is evaluated by cosine similarity to the full-trace answer embedding and hallucination detection performance from a linear probe.The cosine criterion measures preservation of the original reasoning signal, while the probe measures detection performance.

4. Method

REDE denoises reasoning traces by using final-answer attention as annotation-free supervision to learn a representation space where informative and noisy steps separate. At inference, it filters noisy steps through distance-based scoring before passing the retained trace to any downstream hallucination detector.

  • Attention-based supervision: REDE scores each reasoning step by the final answer’s total attention mass, assigning lower scores to irrelevant or repetitive steps and higher scores to informative steps.Irrelevant steps receive weak query-key alignment, while repetitive content is typically subsumed by later occurrences.
  • Representation shaping: Because per-instance attention varies and requires test-time recomputation, REDE uses attention as supervision for learning a more stable step-level embedding space.A lightweight projection is trained over many examples rather than directly thresholding attention scores during inference.
  • Step embedding extraction: Step embeddings are formed with perplexity-weighted token aggregation, giving greater importance to less predictable tokens that typically carry richer semantic information.The representation combines token hidden states weighted by the LRM’s next-token probabilities.
  • Projection learning: REDE ranks attention scores to use the top-ρ% steps as informative proxies and bottom-ρ% steps as noisy proxies, then trains a projection while freezing the underlying LRM.The projection maps e_i to z_i and is optimized to shape the representation distribution for filtering.
  • Projection learning: The projection objective compacts informative steps, disperses noisy steps, and separates the two groups so noisy steps become identifiable by their distance from the informative region.This structure supports simple distance-based filtering while remaining detector-agnostic.
  • Inference-time filtering: At inference, REDE projects each step, computes its k-nearest-neighbor cosine distance within the trace, removes the top-ζ% highest-distance steps, and sends the filtered trace to a downstream detector.The procedure requires neither attention scores nor ground-truth labels at inference and is compatible with arbitrary downstream hallucination detectors.

5. Experiments

Experiments across four reasoning benchmarks and two LRM families show that REDE consistently improves hallucination detection by filtering noisy reasoning steps. Transfer, scaling, and ablation analyses further support the robustness and design of its learned representation-based selection.

  • Datasets and Models: REDE is evaluated on TruthfulQA, MATH, CODEELO, and MULTIHOPQA using Qwen3 and DeepSeek-R1-Distill LRM families.The benchmarks span open-domain question answering, mathematical reasoning, code generation, and multi-hop question answering; correctness labels use Qwen3-32B as an external judge.
  • Effect of reasoning step filtering: 87.32% AUROC versus 68.63 for CCS on Qwen3-8B TruthfulQA demonstrates the benefit of filtering the reasoning trace.Across all datasets and two LRMs, filtered traces substantially improve four representative detectors, indicating gains stem from removing noisy steps rather than a specific detector.
  • Comparison with competitive baselines: REDE achieves 87.06% on MATH, 87.19% on CodeElo, and 82.94% on MULTIHOPQA with Qwen3-8B supervised probing, while CCS reaches 87.32% on TruthfulQA without supervision.REDE delivers the best performance across nearly all settings and substantially outperforms unsupervised baselines with CCS.
  • Generalization across data distributions: 88.04% AUROC results when training on MULTIHOPQA and testing on CodeElo, slightly exceeding the 87.19% in-domain result.This cross-dataset evaluation uses Qwen3-8B with supervised probing as the downstream detector.
  • Scalability to larger LRMs: 90.87% AUROC on Qwen3-32B and 78.95% on DeepSeek-R1-Distill-Qwen-32B outperform RACE by 5.73% and 13.11%, respectively.Results are based on TruthfulQA with supervised probing, and REDE consistently outperforms the two strongest baselines across both larger models.
  • Ablation and robustness analyses: Removing any loss component degrades performance, direct attention filtering reaches 80.51 versus 87.32 for CCS with REDE, and performance peaks at a 70% drop ratio.Random or existing selection methods fail to consistently improve the original trace; alternative distance metrics remain comparable, while all layers exceed 82.58 versus 80.42 for the original trace.

6. Related work

Prior hallucination-detection methods span uncertainty, consistency, confidence, embedding, and mechanistic approaches, but are not designed for LRMs with long reasoning traces. Related work on reasoning-step selection uses measures such as perplexity shifts, surprisal, entropy, and hidden-state probes to improve generation quality and efficiency.

  • Hallucination detection methods include logit- and probability-based uncertainty, consistency scoring, verbalized confidence, embedding-based approaches, and mechanistic analyses.
  • Existing hallucination-detection methods effective for standard LLMs are not designed for LRMs, whose long reasoning traces introduce additional challenges.
  • Reasoning-step selection research targets generation quality and efficiency using perplexity shifts, first-token surprisal, step-level entropy, and hidden-state probes.Representative methods include SPIRIT, ASAP, Step Entropy, and STEP.

7. Conclusion · A. Additional experimental details · A.1. Input prompts

REDE filters noisy reasoning steps for hallucination detection by using final-answer attention to shape step representations. The paper also documents generation and correctness-evaluation prompts used in its experiments.

  • 7. Conclusion: REDE is a framework for filtering noisy reasoning steps to detect hallucinations in large reasoning models.It is presented as the paper’s central contribution.
  • 7. Conclusion: Final-answer attention shapes the step-level representation space, enabling reliable identification and removal of noisy reasoning steps.This provides the mechanism for denoising reasoning traces.
  • 7. Conclusion: REDE is lightweight, requires no human annotation, and can be plugged into diverse downstream hallucination detectors.The framework operates on filtered reasoning trajectories before downstream detection.
  • 7. Conclusion: REDE consistently improves hallucination detection performance across datasets, models, and detector families.The conclusion attributes this finding to extensive experiments.
  • A. Additional experimental details: The additional experimental details provide prompts for generating original reasoning traces and final answers and for evaluating answer correctness with an external judge model.These prompts support both data generation and correctness assessment.
  • A.1. Input prompts: For each dataset, generation prepends a task-specific system instruction before the question.The listed instructions cover TruthfulQA, MATH, CodeElo, and MULTIHOPQA.
  • A.1. Input prompts: Correctness is judged by Qwen3-32B, with answers graded INCORRECT or NOT_ATTEMPTED treated as hallucinations.The evaluation follows prior work and uses the prompt shown in Figure 9.

A.2. Dataset details … B. Additional ablation studies

The appendix evaluates REDE across four reasoning tasks, details its annotation, implementation, clustering, training, compute, and licensing procedures, and introduces additional ablations on TruthfulQA. The annotations show that noisy steps dominate the analyzed traces, while REDE remains more efficient than several comparison methods.

  • A.2. Dataset details: REDE is evaluated on TruthfulQA, MATH, CodeElo, and MULTIHOPQA, using task-specific datasets ranging from 408 Codeforces problems to 1,000 multi-hop questions.TruthfulQA contains 817 questions, while the MATH evaluation set contains 560 problems.
  • A.3. Annotation details on AIME 2024: On AIME 2024 traces generated by Qwen3-8B, repetitive steps are most common, and irrelevant plus repetitive steps comprise 73.0% of annotated steps.The annotation uses hybrid discourse-marker and formatting-based segmentation, with exactly one label per step.
  • A.4. Implementation details: REDE extracts perplexity-weighted step embeddings and trains a two-layer ReLU MLP projection, while downstream evaluation uses supervised probing, CCS, verbalized uncertainty, and perplexity detectors.The implementation uses final-layer hidden states unless otherwise specified.
  • A.5. Clustering details for Section 3: The clustering procedure assigns steps to centroid-based clusters when cosine similarity exceeds τ_c, then retains the earliest or latest representative from each cluster.Retained steps are concatenated in their original trace order for downstream use.
  • A.6. Training and inference algorithms of our REDE: During training, REDE uses final-answer attention as supervision for a projection module; during inference, it removes identified noisy steps without attention scores or ground-truth labels.The filtered reasoning trace is passed to a downstream hallucination detector.
  • A.7. Compute resources and time: 681 seconds is REDE’s training time and 49 seconds its TruthfulQA inference time on Qwen3-8B, compared with 1141, 1507, and 2077 seconds for Semantic Entropy, RACE, and SelfCheckGPT.All experiments use Python 3.10, PyTorch 2.3.1, and NVIDIA A100 GPUs with 80 GB memory.
  • A.8. Licenses of existing assets: The appendix lists dataset and pretrained-model licenses, including Apache 2.0, MIT, CC BY-SA 4.0, CC BY 4.0, and the Llama 3.1 Community License.The listed assets are used according to their respective licenses and intended research use.
  • B. Additional ablation studies: Additional ablations validate REDE’s design choices on TruthfulQA using Qwen3-8B and supervised probing as the downstream detector unless otherwise specified.The ablation section frames these experiments as tests of key design choices.

B.1. Effect of training selection ratio … C.1. Qualitative analysis

REDE’s ablations show that denoising remains effective across selection ratios, loss variants, distance metrics, neighborhood sizes, attention-score settings, embedding weights, and extraction locations. Qualitative examples further show that filtering can improve detection scores and separate truthful from hallucinated traces.

  • B.1. Effect of training selection ratio: Performance peaks at a moderate training selection ratio ρ because extreme ratios weaken contrastive supervision or reduce separation between attention-distribution ends.The top and bottom ρ% of steps form informative and noisy sets, respectively.
  • B.2. Visualization of loss ablation: The full model yields a compact informative-step cluster separated from scattered noisy steps, whereas removing any loss increases embedding overlap.This comparison uses t-SNE visualizations from the loss ablation.
  • B.3. Effect of different distance metrics: Cosine, Mahalanobis, and Euclidean distances all produce strong, comparable filtering results, indicating robustness to the distance metric.The comparison evaluates kNN-based filtering in REDE’s projected space.
  • B.4. Effect of loss weights: Detection performance remains stable across a moderate range of λ_disperse and λ_separate, showing limited sensitivity to their precise values.Setting either λ to 0 removes the corresponding loss component.
  • B.5. Effect of the number of nearest neighbors k: REDE consistently outperforms the unfiltered trace across k values, with performance peaking at k = 15 for all four downstream detectors.The learned projection provides a stable density structure for local-neighborhood filtering.
  • B.6. Effect of step score aggregation: Using the last answer token gives the best performance across downstream detectors, while the final transformer layer reaches 86.44% AUROC.Early layers generally achieve approximately 83% AUROC, and layers 27–28 decline to around 84.5% before recovery.
  • B.7. Effect of step embedding weighting: PPL-weighted step embeddings emphasize less predictable tokens because higher-perplexity tokens receive larger weights.The weighting is applied to token hidden states within each reasoning step.
  • B.8. Effect of embedding extraction location; C.1. Qualitative analysis: Block-output embeddings are favorable for hallucination detection across both LRM architectures, and filtering improves qualitative trace scores from 0.41 to 0.86 after removing 70% of steps.The case study concerns an incorrect answer whose 84-step trace contains repetitive and tangential content; REDE filtering makes the arithmetic error more salient.

C.2. Additional results on larger LRMs · C.3. Effect of sampling strategies · C.4. Accuracy of step selection

REDE remains effective on larger reasoning models and across diverse benchmarks, outperforming competitive baselines. Its gains depend on deterministic decoding and accurate identification of noisy reasoning steps.

  • C.2. Additional results on larger LRMs: REDE outperforms RACE and ARS across all evaluated benchmarks on both Qwen3-32B and DeepSeek-R1-Distill-Qwen-32B.The evaluation covers MATH, CodeElo, and MULTIHOPQA.
  • C.2. Additional results on larger LRMs: REDE filtering increases the supervised-probing detection score from 0.41 to 0.86 after removing 70% of steps for an incorrect MATH response.The filtered trace correctly flags the hallucinated response.
  • C.2. Additional results on larger LRMs: 14.63%, 4.27%, and 8.41% are REDE’s improvements over ARS on MATH, CodeElo, and MULTIHOPQA with Qwen3-32B, respectively.On DeepSeek-R1-Distill-Qwen-32B, the corresponding improvements are 2.99%, 3.55%, and 5.47%.
  • C.2. Additional results on larger LRMs: REDE’s reasoning-step denoising remains effective across diverse reasoning tasks as model scale increases.This conclusion follows from results on Qwen3-32B and DeepSeek-R1-Distill-Qwen-32B across the evaluated benchmarks.
  • C.3. Effect of sampling strategies: Greedy decoding consistently outperforms multinomial sampling with temperature 0.5 across all hallucination detectors.The improvement is particularly notable for the Perplexity and Verbalized detectors, indicating that deterministic traces provide more reliable downstream signals.
  • C.3. Effect of sampling strategies: REDE filtering decreases the supervised-probing detection score from 0.77 to 0.28 after removing 71% of steps for a correct MATH response.The filtering correctly reduces the false-positive rate.
  • C.4. Accuracy of step selection: 86.37% accuracy is achieved when REDE classifies AIME 2024 reasoning steps as informative versus noisy against human annotations.The result supports accurate identification of irrelevant and repetitive steps as the source of downstream detection gains.

C.5. Effect of truthfulness labeling methods … C.10. Results with additional metrics

Across truthfulness-labeling methods, datasets, filtering strategies, deployment settings, task accuracy, and evaluation metrics, REDE consistently strengthens hallucination detection while preserving practical applicability. The results support final-answer attention as a useful signal for selecting informative reasoning steps.

  • C.5. Effect of truthfulness labeling methods: REDE maintains strong detection performance across ROUGE-L, BLEURT, and DeepSeek-R1-Distill-Qwen-32B labeling methods, rather than depending on one judge or metric.ROUGE-L labels generations truthful above a similarity threshold of 0.3, while BLEURT uses the bleurt-base-128 variant.
  • C.6. Results on an additional dataset: On GSM8K, REDE-selected reasoning steps consistently outperform the original reasoning traces under the same experimental setup.The evaluation uses 7,473 training problems, reserves 25% for testing, and uses 100 validation examples.
  • C.7. Validating the attention signal: Dropping high-attention steps reduces detection quality, whereas dropping low-attention steps preserves or improves it, supporting final-answer attention as a usefulness signal.On TruthfulQA, AUROC falls from 80.42 to 57.18 when high-attention steps are dropped, but reaches 84.97 when low-attention steps are dropped.
  • C.7. Validating the attention signal: REDE outperforms position-based filtering under the same 70% drop ratio, while Drop-Latest performs worst and Drop-Earliest remains weaker.On TruthfulQA, REDE achieves 86.44% versus 77.53% for Drop-Earliest.
  • C.8. Applicability in a black-box setting: A proxy-based REDE variant consistently improves detection across four benchmarks and both target models in black-box settings.It improves over the original by 5.92% on MultiHopQA with DeepSeek and 8.04% on TruthfulQA with Qwen3-8B, recovering most white-box gains.
  • C.9. Impact of step filtering on downstream task accuracy: The downstream task-accuracy evaluation tests whether regenerating answers from REDE-retained steps preserves the LRM’s ability to produce correct answers.The evaluation uses Qwen3-8B reasoning traces on MATH and removes steps identified as noisy by REDE before answer regeneration.
  • C.10. Results with additional metrics: REDE-Filtered steps consistently improve Accuracy, F1, and AUROC over Original reasoning traces for both CCS and probing.Accuracy and F1 complement AUROC by evaluating additional aspects of detection performance.

D. Broader impact and limitations … E.3. 𝜅-NN distance separation from local density in the projected space

REDE is presented as a reliability-enhancing filtering component with limitations requiring human oversight and future integration into generation. The theoretical analysis formalizes its filtering setup, explains why noisy steps reduce discriminability, and shows when κ-NN distances separate informative from noisy steps.

  • D. Broader impact and limitations: REDE can improve reliability in applications such as question answering, educational assistants, and coding support by filtering noisy reasoning steps before detection.The paper frames REDE as a component that helps flag potentially hallucinated answers.
  • D. Broader impact and limitations: REDE may still over-trust hallucinated answers or suppress correct unconventional reasoning, so it is not a substitute for human oversight in high-stakes settings.The authors characterize REDE as reliability-enhancing rather than fully reliable.
  • D. Broader impact and limitations: REDE currently filters reasoning traces after generation rather than intervening during generation, motivating future training objectives that suppress noisy steps directly.The proposed direction integrates step-level informativeness into LRM training.
  • E. Theoretical analysis: The theoretical analysis studies REDE’s practical inference rule, which filters steps using intra-trace κ-NN distances in a shaped representation space.The framework formalizes oracle informative traces, full noisy traces, and filtered traces as objects for analysis.
  • E.1. Setup and definitions: The setup defines noisy-step retention and informative-step removal as filtering errors, while the score removes the M steps with the largest κ-NN distances at removal ratio ζ.The error rates are α for noisy steps erroneously retained and β for informative steps mistakenly removed.
  • E.2. Oracle informative traces are more discriminative: Under approximate label-uninformativeness, noisy steps reduce full-trace Fisher discriminability relative to the oracle informative trace up to slack controlled by (ε_μ, ε_c).The slack Δ(ε_μ, ε_c) decays continuously and vanishes as ε_μ, ε_c approach zero, recovering exact monotonicity in the strict-independence limit.
  • E.3. κ-NN distance separation from local density in the projected space: Assumption E.4 models informative steps as locally dense and noisy steps as sparse, with radii satisfying 0 < r_ℐ < r_𝒩.This geometry supports separating step types through local neighbor counts in the projected space.
  • E.3. κ-NN distance separation from local density in the projected space: Once the projection creates sufficiently dense informative and sparse noisy regions, the practical κ-NN distance separates the two step types at inference time.Proposition E.5 establishes this separation under the local density assumption using concentration bounds.

E.4. From 𝜅-NN score separation to rank-based filtering error … E.7. Connection to the shaping objective

The appendix formalizes how score separation governs rank-based filtering errors, representation distortion, and downstream hallucination-detection risk. It also connects the shaping objective to compact informative neighborhoods and sparse noisy regions that enable practical 𝜅-NN filtering.

  • E.4. From 𝜅-NN score separation to rank-based filtering error: On ℰsep, every noisy step has a larger practical 𝜅-NN score than every informative step, so rank-based removal prioritizes noisy steps.This separation event is the condition used to analyze the practical rule that removes the largest scores.
  • E.4. From 𝜅-NN score separation to rank-based filtering error: The rank-based filtering error equals the count mismatch between the removed steps M and the trace’s noisy-step count, while score overlap contributes an additional error source.Proposition E.6 gives the exact retained-noisy and lost-informative counts on ℰsep; the subsequent bounds separate count mismatch from score overlap.
  • E.4. From 𝜅-NN score separation to rank-based filtering error: Under local density separation, Corollary E.7 bounds practical filtering errors by combining score-separation guarantees with the rank-based error identities.The corollary follows by applying a union bound and Proposition E.5, then substituting the resulting separation bound into Proposition E.6.
  • E.5. Representation gap induced by imperfect filtering: Imperfect filtering creates a representation gap because some noisy steps are retained and some informative steps are removed; bounded step representations yield an expected gap bound.The analysis assumes separate norm bounds for informative and noisy step representations.
  • E.6. Detection risk on filtered traces: For a linear probe with Lipschitz loss, the filtered trace’s detection risk remains close to the oracle informative-trace risk, with the excess controlled by filtering quality.Theorem E.11 derives this relationship from the representation-gap lemma and extends it using the local-density-separation bounds.
  • E.6. Detection risk on filtered traces: Smaller slack parameters (𝜀𝜇, 𝜀𝑐) and smaller filtering errors (𝛼, 𝛽) produce larger improvement of the filtered trace over the unfiltered trace.The theorem controls risk relative to the oracle informative trace, while the slack parameters enter upstream through the full-to-informative trace risk gap.
  • E.7. Connection to the shaping objective: The shaping objective’s compactness term decreases informative-step 𝜅-NN distances, while its dispersion term increases noisy-step distances by respectively densifying and sparsifying local neighborhoods.This interpretation assumes attention-based proxy sets are reasonably aligned with latent informative and noisy step sets.
  • E.7. Connection to the shaping objective: Together, the shaping terms create compact high-density informative regions and sparse noisy regions, improving score separation, lowering filtering error, and tightening hallucination-detection risk.The appendix notes that the ablation study in Section 5.2 provides empirical support for this interpretation.
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