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arxiv: 2604.27914 · v1 · submitted 2026-04-30 · 💻 cs.CL · cs.LG

Recognition: unknown

Geometry-Calibrated Conformal Abstention for Language Models

Rui Xu , Yi Chen , Sihong Xie , Hui Xiong
Authors on Pith no claims yet

Pith reviewed 2026-05-07 05:51 UTC · model grok-4.3

classification 💻 cs.CL cs.LG
keywords conformal predictionabstentionlanguage modelshallucinationselective answeringrepresentation geometryuncertainty estimationfinite-sample guarantees
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The pith

Conformal Abstention adapts conformal prediction to give language models finite-sample guarantees on when their answers are reliable

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

The paper proposes Conformal Abstention (CA), a post-hoc method that lets language models decide when to abstain from a query rather than risk generating a hallucination. It adapts conformal prediction but replaces intractable non-conformity scores with prediction confidence calibrated by the geometry of the model's internal representations. This calibration is intended to align confidence with the model's actual ignorance, delivering finite-sample guarantees on both the rate at which the model chooses to answer and the correctness of those answers. Experiments report that the approach reaches 75 percent conditional correctness on selective answering tasks. Readers should care because it offers a way to control hallucinations in deployed generative systems without retraining or depending on scarce benchmarks for ignorance.

Core claim

Conformal Abstention (CA) is a post hoc framework adapted from conformal prediction (CP) to determine whether to abstain from answering a query. CA provides finite-sample guarantees on both the probability of participation (i.e., not abstaining) and the probability that the generated response is correct. The abstention decision relies on prediction confidence rather than the non-conformity scores used in CP, which are intractable for open-ended generation. To better align prediction confidence with the model's ignorance, we introduce a calibration strategy using representation geometry within the model to measure knowledge involvement in shaping the response. Experiments demonstrate that we

What carries the argument

Geometry-calibrated prediction confidence, which uses the model's internal representation geometry to measure knowledge involvement and thereby enables conformal prediction guarantees for abstention decisions in open-ended generation

If this is right

  • Language models can be made to answer only when a user-specified correctness probability is guaranteed by finite-sample bounds
  • The method operates post hoc and requires no retraining or access to scarce ignorance benchmarks
  • Abstention becomes practical for open-ended generation tasks where traditional non-conformity scores cannot be computed
  • Selective answering reaches high conditional correctness, reported at 75 percent in the experiments
  • The approach avoids the overly conservative behavior that can arise from retraining models to admit ignorance

Where Pith is reading between the lines

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

  • The geometry-based calibration may extend naturally to other generative domains such as code or image synthesis where internal representations also encode task knowledge
  • If the alignment between geometry and ignorance proves stable across model scales, the method could serve as a lightweight uncertainty signal for very large foundation models
  • Combining the abstention rule with retrieval-augmented generation might tighten the effective guarantees by reducing the incidence of knowledge gaps
  • A direct test would be to measure whether the geometry signal improves abstention decisions on domain-specific queries known to lie outside the model's training distribution

Load-bearing premise

Calibrating prediction confidence via representation geometry successfully aligns those scores with the model's true ignorance, allowing finite-sample conformal guarantees to transfer when confidence is used in place of non-conformity scores

What would settle it

An experiment on a held-out set in which the observed correctness rate among answered queries falls below the target level guaranteed by the conformal procedure after geometry calibration would falsify the central transfer claim

Figures

Figures reproduced from arXiv: 2604.27914 by Hui Xiong, Rui Xu, Sihong Xie, Yi Chen.

Figure 1
Figure 1. Figure 1: Token representation geometry captures how the model’s internal knowledge shapes its response. view at source ↗
Figure 2
Figure 2. Figure 2: Participation and conditional correctness are ensured. view at source ↗
Figure 3
Figure 3. Figure 3: (a) Information flow and contribution matrices of layer view at source ↗
Figure 4
Figure 4. Figure 4: The relation between direct knowl￾edge contribution and embedding rotation. The relation between direct knowledge contribution ω l dir and its corresponding embedding rotation θ l dir is shown in view at source ↗
Figure 5
Figure 5. Figure 5: Dynamic rotation and static align￾ment are complementary but independent characterizations of prediction reliability. Analogous to Eq. (16), for alignment to dominant in￾distribution directions, we define ϕ l,in dir as the angle between η l in and e l [T], and ϕ l,in prop as the angle between η˜ l+1 in and e˜ l+1[T]. Similarly, we define ϕ l,out dir and ϕ l,out prop with respect to η l,out and η˜ l+1 out .… view at source ↗
Figure 6
Figure 6. Figure 6: Separation of generated tokens from correct and incorrect predictions using dcorr and dinc. Tokens from correct predictions should exhibit small dcorr and large dinc, while the opposite is expected for incorrect predictions. We empirically evaluate this separability using Gemma-3-4B-Instruct on Simple-Questions-Wikidata. A reference set is used to estimate µcorr, µinc and Σcorr, Σinc. Similarly, we treat c… view at source ↗
Figure 7
Figure 7. Figure 7: Knowledge interaction strength and relative angular dis￾tance between correct and incorrect predictions. We validate Hypotheses 1 and 2 on reference sets using correct and incorrect predictions, with results averaged across datasets. For each sample, we compute the knowledge interaction strength and relative angular distance by layer-wise averaging Ω ⊙ Θ ∈ R 2L−1 and Φ in − Φ out ∈ R 2L−1 , respectively, a… view at source ↗
Figure 8
Figure 8. Figure 8: Conditional correctness using different UQ methods as uncertainty scoring functions, with Gemma-3- view at source ↗
Figure 9
Figure 9. Figure 9: Impact of signal permuta￾tion on AUROC and AUPRC. We conduct an importance analysis of the proposed geometry sig￾nals (Ω, Θ, Φ in , Φ out) by randomly permuting each component during inference and measuring the resulting drop in AUROC and AUPRC. We report the average performance across all in￾ference models and datasets view at source ↗
Figure 10
Figure 10. Figure 10: Conditional correctness using different UQ methods as uncertainty scoring functions, with LLaMA view at source ↗
Figure 11
Figure 11. Figure 11: Conditional correctness using different UQ methods as uncertainty scoring functions, with LLaMA view at source ↗
read the original abstract

When language models lack relevant knowledge for a given query, they frequently generate plausible responses that can be hallucinations, rather than admitting being agnostic about the answer. Retraining models to reward admitting ignorance can lead to overly conservative behaviors and poor generalization due to scarce evaluation benchmarks. We propose a post hoc framework, Conformal Abstention (CA), adapted from conformal prediction (CP) to determine whether to abstain from answering a query. CA provides finite-sample guarantees on both the probability of participation (i.e., not abstaining) and the probability that the generated response is correct. Importantly, the abstention decision relies on prediction confidence rather than the non-conformity scores used in CP, which are intractable for open-ended generation. To better align prediction confidence with the model's ignorance, we introduce a calibration strategy using representation geometry within the model to measure knowledge involvement in shaping the response. Experiments demonstrate that we improve selective answering significantly with 75 percent conditional correctness.

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

3 major / 2 minor

Summary. The paper proposes Conformal Abstention (CA), a post-hoc framework adapted from conformal prediction (CP) for deciding when language models should abstain from answering queries. It claims finite-sample guarantees on both the probability of participation (not abstaining) and the conditional probability that generated responses are correct. The abstention decision uses prediction confidence calibrated via representation geometry (to measure knowledge involvement) rather than intractable non-conformity scores. Experiments are reported to show significant improvement in selective answering, achieving 75% conditional correctness.

Significance. If the finite-sample guarantees survive the substitution of geometry-calibrated confidence for standard non-conformity scores, the work would provide a practical, training-free method for controlling abstention and reducing hallucinations in open-ended generation with theoretical backing. The geometry calibration step is a novel attempt to operationalize model ignorance in representation space and could extend to other selective prediction settings. The emphasis on finite-sample validity and open-ended text addresses a genuine limitation of classical CP, making the contribution potentially significant for reliable deployment of LLMs if the transfer of guarantees is established.

major comments (3)
  1. [Abstract] Abstract: The central claim asserts finite-sample guarantees on participation rate and conditional correctness when thresholding geometry-calibrated confidence instead of non-conformity scores. No derivation, theorem, or proof sketch is referenced showing that the representation-geometry metric preserves the exchangeability and monotonic ranking (higher score implies greater strangeness/lower correctness) required for marginal coverage to transfer. This is load-bearing for the theoretical contribution.
  2. [Method] Method (Geometry Calibration section): The geometry calibration is motivated as aligning confidence with ignorance via representation-space distances or involvement metrics. However, no analysis or worst-case argument is given that this metric ranks errors correctly (i.e., incorrect responses receive systematically lower calibrated confidence), which is necessary for the chosen threshold on the calibration set to deliver the advertised coverage guarantee. If monotonicity fails, the finite-sample claim does not hold.
  3. [Experiments] Experiments: The 75% conditional correctness figure is presented as empirical support for the framework. The manuscript does not specify how response correctness is defined (exact match, entailment, human judgment) or confirm that the calibration set construction maintains exchangeability with test points. These details are required to assess whether the experiments validate the transferred guarantee or only demonstrate heuristic improvement.
minor comments (2)
  1. [Abstract] Abstract: The distinction between the theoretical finite-sample guarantee and the empirical 75% conditional correctness could be stated more explicitly to avoid conflating the two.
  2. [Method] Notation: The paper should clarify whether the geometry calibration introduces any additional fitted parameters beyond the standard CP threshold, as this affects the 'parameter-free' flavor of the guarantees.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We are grateful to the referee for their insightful comments that identify key areas for improving the clarity of our theoretical claims and experimental setup. We respond to each major comment below and outline the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim asserts finite-sample guarantees on participation rate and conditional correctness when thresholding geometry-calibrated confidence instead of non-conformity scores. No derivation, theorem, or proof sketch is referenced showing that the representation-geometry metric preserves the exchangeability and monotonic ranking (higher score implies greater strangeness/lower correctness) required for marginal coverage to transfer. This is load-bearing for the theoretical contribution.

    Authors: We acknowledge that the abstract does not explicitly reference a theorem or proof sketch. The guarantees derive from the exchangeability of the data points under the i.i.d. assumption, which holds independently of the specific score function as long as it is computed consistently. The geometry calibration is designed to provide a monotonic ranking by measuring knowledge involvement in the representation space, with lower involvement indicating higher likelihood of incorrect responses. To address this, we will include a dedicated theorem with a proof sketch in the revised Method section and update the abstract to reference it. revision: yes

  2. Referee: [Method] Method (Geometry Calibration section): The geometry calibration is motivated as aligning confidence with ignorance via representation-space distances or involvement metrics. However, no analysis or worst-case argument is given that this metric ranks errors correctly (i.e., incorrect responses receive systematically lower calibrated confidence), which is necessary for the chosen threshold on the calibration set to deliver the advertised coverage guarantee. If monotonicity fails, the finite-sample claim does not hold.

    Authors: The geometry calibration uses distances in representation space to quantify how much the model's internal knowledge is engaged in producing the response. We agree that a formal worst-case analysis of the ranking property would strengthen the theoretical foundation. While we provide empirical support through experiments showing improved selective performance, we will add a discussion in the revised manuscript analyzing the conditions for monotonicity and include additional experiments validating the correlation between the calibrated confidence and response correctness on the calibration set. revision: partial

  3. Referee: [Experiments] Experiments: The 75% conditional correctness figure is presented as empirical support for the framework. The manuscript does not specify how response correctness is defined (exact match, entailment, human judgment) or confirm that the calibration set construction maintains exchangeability with test points. These details are required to assess whether the experiments validate the transferred guarantee or only demonstrate heuristic improvement.

    Authors: We will revise the Experiments section to explicitly define response correctness as determined by human judgment for open-ended responses, supplemented by automatic metrics where appropriate. The calibration set is randomly held out from the same dataset distribution as the test queries, preserving exchangeability. We will add a statement confirming this and report the exact construction procedure to allow readers to verify the validity of the empirical results. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation of conformal abstention guarantees

full rationale

The paper adapts standard conformal prediction (CP) to language models by replacing intractable non-conformity scores with geometry-calibrated prediction confidence scores for abstention decisions. Finite-sample guarantees on participation rate and conditional correctness are claimed to transfer from CP theory, with a new post-hoc calibration step using representation geometry to measure knowledge involvement and align confidence with ignorance. No load-bearing step reduces the result to its inputs by construction: there are no self-definitional quantities (e.g., a score defined in terms of the coverage it guarantees), no fitted parameters renamed as independent predictions, and no self-citation chains justifying uniqueness or ansatzes. The geometry calibration is presented as an empirical alignment strategy rather than a tautological redefinition. The derivation remains self-contained against external CP benchmarks and standard exchangeability assumptions, with the transfer of ranking properties treated as an assumption rather than derived internally. No quoted equations or text exhibit the specific reductions required for a positive circularity finding.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the transferability of conformal prediction guarantees when the non-conformity score is replaced by prediction confidence, plus the validity of using representation geometry to measure knowledge involvement. These are domain assumptions and an ad-hoc calibration strategy introduced by the paper.

free parameters (1)
  • geometry calibration parameters or confidence threshold
    The abstention decision depends on a calibrated confidence measure whose exact fitting or selection procedure is not detailed in the abstract.
axioms (2)
  • domain assumption Finite-sample guarantees of conformal prediction continue to hold when abstention is based on prediction confidence rather than non-conformity scores
    The paper explicitly changes the score type used for the decision while claiming the same guarantees.
  • ad hoc to paper Representation geometry within the model measures the degree of knowledge involvement in shaping the response
    Introduced as the calibration strategy to align confidence with ignorance.

pith-pipeline@v0.9.0 · 5460 in / 1443 out tokens · 45761 ms · 2026-05-07T05:51:13.961111+00:00 · methodology

discussion (0)

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