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arxiv: 2606.21255 · v1 · pith:34HIIUSUnew · submitted 2026-06-19 · 💻 cs.CL

SCOPE: Sequential Conformal Probing for Reliable OOD Rejection in LLM Services

Zhuoyun Li , Boxuan Wang , Changshun Wu , Xiaowei Huang , Yi Dong This is my paper

Pith reviewed 2026-06-26 14:35 UTC · model grok-4.3

classification 💻 cs.CL
keywords OOD rejectionconformal predictionLLM serviceshidden layerssupermartingale e-processout-of-distribution detectionconformal gate
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The pith

SCOPE selects a readable hidden layer and applies sequential conformal probing with a supermartingale e-process to reject out-of-distribution inputs more reliably than final-layer detectors.

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

The paper introduces SCOPE to improve out-of-distribution rejection for LLM services by probing inside the model rather than at the output. It selects a readable hidden layer where service-boundary signals are clearest, builds a conformal gate calibrated on in-distribution data, and uses a supermartingale e-process to provide theoretical guarantees for held-out inputs. Experiments on multiple backbones and six boundary conditions demonstrate better gate-level rejection performance. The approach also shows that different types of OOD boundaries appear as distinct geometric patterns in the hidden space. This matters because reliable filtering of unsupported requests is essential before full generation in deployed LLM services.

Core claim

SCOPE is a framework that selects a readable hidden layer, constructs a conformal gate with IND calibration, and uses a supermartingale e-process to certify persistent service-boundary evidence, leading to improved rejection over standard final-layer detectors across multiple LLM backbones and six boundary conditions, while revealing geometric forms of OOD boundaries in hidden space.

What carries the argument

The conformal gate at a selected hidden layer combined with a supermartingale e-process for certifying boundary evidence.

If this is right

  • Gate-level rejection improves compared to final-layer detectors.
  • Different OOD boundaries manifest as distinct geometric forms in hidden space.
  • The supermartingale e-process provides a theoretical guarantee for held-out inputs.
  • Service-boundary signals are most clearly encoded at a selectable hidden layer.

Where Pith is reading between the lines

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

  • SCOPE could be adapted to other sequential models beyond LLMs for OOD detection.
  • Selecting different layers might allow tuning for specific types of boundary conditions.
  • Integrating this into production LLM services might reduce unnecessary computation on invalid inputs.

Load-bearing premise

Service-boundary signals are most clearly encoded at a selectable readable hidden layer and the supermartingale e-process supplies a valid theoretical guarantee for held-out inputs under the chosen calibration.

What would settle it

A new set of OOD boundary conditions where the selected hidden layer does not show clearer signals than the final layer, or where the e-process fails to certify evidence on held-out data.

Figures

Figures reproduced from arXiv: 2606.21255 by Boxuan Wang, Changshun Wu, Xiaowei Huang, Yi Dong, Zhuoyun Li.

Figure 1
Figure 1. Figure 1: Examples for Service-scope OOD rejection before generation. A task-specific LLM service should answer inputs within its IND scope and reject or route unsupported inputs before full generation. SCOPE pro￾vides a reliable gate for pre-generation rejection. for frozen LLM backbones, which are attractive in deployment because they offer cost-efficiency, controllability, and easy integration into existing servi… view at source ↗
Figure 2
Figure 2. Figure 2: Overview of SCOPE. The framework first selects a readable hidden layer from frozen LLM representa￾tions, then calibrates the selected score into an IND-controlled rejection gate, and finally accumulates the held-out rejection stream with an e-process to obtain an anytime-valid service-boundary certificate. conformal pipelines (Gibbs et al., 2025; Kato et al., 2023). In SCOPE, conformal calibration serves a… view at source ↗
Figure 3
Figure 3. Figure 3: shows the same gate after confor￾mal calibration. The score is converted into bi￾nary rejection decisions and accumulated by the e-process. Far-OOD traffic accumulates evidence rapidly, near-OOD traffic grows more gradually, and the IND-only stream stays below the certifi￾cation threshold. Thus, the certificate is driven by repeated IND-calibrated rejections rather than by an uncalibrated confidence score.… view at source ↗
Figure 4
Figure 4. Figure 4: Cross-model service-boundary certification. Each cell reports CLG on one backbone and one bound￾ary. Color shows AUROC; markers show e-process certificate rate over shuffled held-out streams. threshold, and e-process parameters are fixed be￾fore the held-out stream is evaluated. Thus, the heatmap does not merely report offline OOD rank￾ing; it tests whether a development-selected gate continues to produce … view at source ↗
Figure 5
Figure 5. Figure 5: Selected-layer representation geometry. PCA projections illustrate separable and overlapping IND/OOD hidden-state patterns at the selected layer. shows that service-boundary definition is not a sec￾ondary detail: fine-grained intent splits and intent￾preserving rewrites induce different hidden-state signals. This motivates the readout-geometry anal￾ysis in Sec. 4.4. 4.4 Geometry of Selected-Layer OOD Signa… view at source ↗
Figure 6
Figure 6. Figure 6: provides two useful checks. First, AUROC generally improves and Tα decreases as model size increases, suggesting that larger backbones tend to encode more readable service￾boundary signals. Second, the relative depth of the selected layer remains qualitatively stable across the QWEN2.5 family for the same boundary type. This supports the use of a one-time layer-selection step and reinforces the main claim … view at source ↗
Figure 7
Figure 7. Figure 7: Sensitivity to the conformal threshold. Smaller ϵ gives a stricter threshold, reducing IND false rejections but also lowering OOD-TPR and certificate rate. Larger ϵ increases OOD rejection and certification by spending more IND false-rejection budget. The main experiments use ϵ = 0.05 as a balanced operating point. P1 P2 P3 P4 P5 P6 0.0 0.2 0.4 0.6 0.8 1.0 IND false rejection CP tau fixed 0.5 P1 P2 P3 P4 P… view at source ↗
Figure 9
Figure 9. Figure 9: Sensitivity to the e-process parameters. Vary [PITH_FULL_IMAGE:figures/full_fig_p013_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: Additional PCA examples of selected￾layer IND/OOD geometry. Broad OOD boundaries show clearer separation in the selected representation, while tight near-intent boundaries remain more entan￾gled. These examples complement the main geometry analysis by illustrating why calibrated rejection is eas￾ier for broad service shifts than for fine-grained intent splits. C.3 Directional gate e-process We also examin… view at source ↗
Figure 12
Figure 12. Figure 12: E-process trace for the conformal direc￾tional gate. The directional gate accumulates strong ev￾idence on broad far-OOD streams, but produces weaker evidence on tighter near-OOD streams. This supports the use of CLG as the main gate: a one-dimensional direction can capture coarse shifts, while a richer linear boundary is more effective for finer service-boundary signals [PITH_FULL_IMAGE:figures/full_fig_… view at source ↗
read the original abstract

Rejecting inputs outside the defined in-distribution (IND) service scope is critical for large language model (LLM) services, where unsupported requests should be filtered before full generation. Existing out-of-distribution (OOD) detectors often rely on final outputs or final-layer representations, leaving unclear where service-boundary signals are most clearly encoded inside the model; they also lack a theoretical guarantee for held-out inputs. In this paper, we introduce SCOPE (Sequential Conformal OOD Probing and Evaluation), a framework that selects a readable hidden layer, constructs a conformal gate with IND calibration, and uses a supermartingale e-process to certify persistent service-boundary evidence. Experiments across multiple LLM backbones and six carefully designed boundary conditions show that SCOPE improves gate-level rejection over standard final-layer detectors, while revealing how different OOD boundaries take different geometric forms in hidden space.

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

1 major / 0 minor

Summary. The paper introduces SCOPE (Sequential Conformal OOD Probing and Evaluation), a framework that selects a readable hidden layer in LLMs, constructs a conformal gate using IND calibration data, and applies a supermartingale e-process to certify persistent service-boundary evidence for OOD rejection. Experiments on multiple LLM backbones under six boundary conditions demonstrate improved gate-level rejection compared to standard final-layer detectors and provide insights into the geometric forms of different OOD boundaries in hidden space.

Significance. If the theoretical guarantees hold, the work could advance reliable OOD rejection for LLM services by moving beyond final-layer heuristics to layer-selected conformal gates with e-process certification. The multi-backbone experiments and six boundary conditions constitute a strength in empirical coverage.

major comments (1)
  1. [the section describing the supermartingale e-process construction and conformal gate] The central claim that SCOPE certifies persistent service-boundary evidence rests on the supermartingale e-process supplying a valid theoretical guarantee after conformal calibration at a selected hidden layer. No explicit derivation is provided showing that the filtration and the layer-selection step preserve the supermartingale property when hidden-layer scores are high-dimensional and token-sequence dependent (which can violate exchangeability or filtration conditions even under exchangeable calibration data). This is load-bearing for the certification claim for arbitrary held-out inputs.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback and for recognizing the potential impact of the work on reliable OOD rejection in LLM services. We address the major comment below.

read point-by-point responses

  1. Referee: [the section describing the supermartingale e-process construction and conformal gate] The central claim that SCOPE certifies persistent service-boundary evidence rests on the supermartingale e-process supplying a valid theoretical guarantee after conformal calibration at a selected hidden layer. No explicit derivation is provided showing that the filtration and the layer-selection step preserve the supermartingale property when hidden-layer scores are high-dimensional and token-sequence dependent (which can violate exchangeability or filtration conditions even under exchangeable calibration data). This is load-bearing for the certification claim for arbitrary held-out inputs.

    Authors: We appreciate the referee pointing out the need for a more rigorous justification of the theoretical guarantees. The construction relies on the fact that the calibration data is exchangeable, and the conformal scores at the selected layer are used to form the e-process. The layer selection is performed using a validation set from the IND data, which maintains exchangeability. However, we agree that an explicit derivation showing preservation of the supermartingale property under layer selection and for high-dimensional, sequence-dependent scores is missing from the manuscript. In the revised version, we will add a new subsection or appendix providing this derivation, including how the filtration is defined over the sequence of tokens and why the property holds for held-out inputs under the standard assumptions of conformal prediction. We will also discuss potential limitations when strong dependencies violate exchangeability. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on external conformal and e-process methods

full rationale

The paper introduces SCOPE by selecting a hidden layer, building a conformal gate via IND calibration, and applying a supermartingale e-process for certification. These steps invoke standard techniques from conformal prediction literature rather than reducing any prediction or guarantee to fitted quantities by construction within the paper. No equations are exhibited that equate outputs to inputs via self-definition, renaming, or self-citation chains. The abstract and description present the framework as an application of existing tools to LLM hidden representations, with experimental validation on multiple backbones. This is self-contained against external benchmarks and does not meet the criteria for any enumerated circularity pattern.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract only; ledger is necessarily incomplete. Standard conformal prediction assumptions and the validity of supermartingale e-processes for boundary certification are invoked without further detail.

axioms (2)
  • standard math Conformal prediction yields valid coverage under exchangeability of calibration and test points.
    Core to the conformal gate construction mentioned in the abstract.
  • domain assumption Supermartingale e-process can certify persistent service-boundary evidence for held-out inputs.
    Invoked to provide the theoretical guarantee stated in the abstract.

pith-pipeline@v0.9.1-grok · 5685 in / 1260 out tokens · 23220 ms · 2026-06-26T14:35:08.064569+00:00 · methodology

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