arxiv: 2605.12651 · v2 · submitted 2026-05-12 · 💻 cs.LG

Recognition: 2 theorem links

· Lean Theorem

Runtime Monitoring of Perception-Based Autonomous Systems via Embedding Temporal Logic

Parv Kapoor , Abigail Hammer , Ashish Kapoor , Karen Leung , Eunsuk Kang

Authors on Pith no claims yet

Pith reviewed 2026-05-15 05:00 UTC · model grok-4.3

classification 💻 cs.LG

keywords runtime monitoringtemporal logicembedding spacesperception-based systemsautonomous systemsconformal calibrationmanipulation environments

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The pith

Embedding Temporal Logic monitors autonomous systems by defining predicates on distances between observed and reference embeddings.

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

The paper proposes Embedding Temporal Logic to perform runtime monitoring directly in learned embedding spaces rather than first mapping sensor data to discrete low-dimensional states. Traditional approaches need extra learned modules that tend to be costly, fragile, and semantically off. ETL instead treats predicates as distance comparisons between current embeddings and target embeddings taken from reference observations. These distance-based predicates combine with temporal operators to describe sequences of perceptual behaviors such as approaching a visual goal or staying away from certain semantic areas. Monitors for bounded traces plus conformal calibration give reliable predicate results, and tests in manipulation settings show close agreement with ground-truth labels.

Core claim

Embedding Temporal Logic (ETL) is a temporal logic that performs monitoring directly in learned embedding spaces. It defines predicates through distances between observed embeddings and target embeddings derived from reference observations. This formulation allows specifications to capture high-level perceptual concepts, such as similarity to visual goals or avoidance of semantic regions, that are difficult or impossible to express using traditional predicates. By composing these predicates with temporal operators, ETL naturally expresses temporally extended and sequential perceptual behaviors. Monitors evaluate specifications over bounded embedding traces, with a conformal calibration step,

What carries the argument

Embedding Temporal Logic (ETL), which defines predicates via distance comparisons between observed embeddings and reference-derived target embeddings to represent perceptual concepts.

If this is right

Specifications can now express temporally extended perceptual behaviors without requiring separate state-abstraction modules.
Conformal calibration supplies safety-oriented reliability guarantees for predicate satisfaction.
Evaluations demonstrate accurate monitoring of both atomic perceptual predicates and their temporal compositions in manipulation environments.

Where Pith is reading between the lines

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

Embedding-space monitoring could eliminate the need for separate perception-to-state translation layers in many autonomous pipelines.
If embedding distances prove consistent across environments, the same ETL formulas might transfer to new tasks without retraining the logic itself.
The distance-based predicate style might support natural-language-style task descriptions such as 'stay near objects like the training set' once reference embeddings are collected.

Load-bearing premise

Distances computed in the learned embedding space must align reliably with the intended perceptual meanings so that the predicates remain semantically valid.

What would settle it

An experiment showing an embedding distance that reports high similarity for two observations a human would judge as perceptually dissimilar, causing an ETL monitor to report false satisfaction of a specification.

Figures

Figures reproduced from arXiv: 2605.12651 by Abigail Hammer, Ashish Kapoor, Eunsuk Kang, Karen Leung, Parv Kapoor.

**Figure 2.** Figure 2: Qualitative and quantitative ETL results. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Figure 3: Dual-predicate Boolean timelines for mw-pick-place-wall. Top panels show distances to grasp (zA) and place (zB) embeddings with thresholds ϵ ∗ and ϵCP . Lower panels show ETL and ground-truth predicate activations. corresponding to a pick-and-place interaction. For tasks where proprioception is not sufficient to identify phase of tasks, we manually annotate the videos and generate the ground truth predicat… view at source ↗

read the original abstract

Runtime monitoring of autonomous systems traditionally relies on mapping continuous sensor observations to discrete logical propositions defined over low-dimensional state variables. This abstraction breaks down in perception-driven settings, where such mappings require additional learned modules that are often computationally expensive, brittle, and semantically misaligned. In this work, we propose Embedding Temporal Logic (ETL), a temporal logic that performs monitoring directly in learned embedding spaces. ETL defines predicates through distances between observed embeddings and target embeddings derived from reference observations. This formulation allows specifications to capture high-level perceptual concepts, such as similarity to visual goals or avoidance of semantic regions, that are difficult or impossible to express using traditional predicates. By composing these predicates with temporal operators, ETL naturally expresses temporally extended and sequential perceptual behaviors. We introduce ETL monitors for evaluating specifications over bounded embedding traces, along with a conformal calibration procedure that provides reliable and safety-oriented predicate evaluation. We evaluate our approach across multiple manipulation environments to show that ETL achieves strong empirical agreement with ground-truth semantics, including accurate monitoring of temporally composed behaviors.

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

ETL defines temporal predicates via distances to reference embeddings and adds conformal calibration, which is a clean way to monitor perceptual behaviors but rests on the embeddings actually lining up with the intended semantics.

read the letter

The main contribution is a temporal logic whose atomic predicates are distances in a learned embedding space to reference observations. This lets you write specs like “stay close to this visual goal” or “avoid that semantic region” directly on perception outputs, then wrap them in the usual until, eventually, and always operators. The conformal step gives finite-sample coverage guarantees on whether a predicate holds, which is a practical addition for safety monitoring in autonomous systems. On the manipulation tasks they show, the monitors track ground-truth semantics reasonably well across composed behaviors. That part is useful and not just a rehash of standard STL or embedding tricks. The approach avoids the brittle learned classifiers that usually sit between raw perception and logic. The soft spot is the embedding alignment assumption. Distances only mean what you want if the embedding model was trained in a way that preserves the perceptual distinctions you care about; nothing in the setup forces that, and conformal calibration only protects against statistical error once the distances are already meaningful. If the embedding has systematic gaps, the whole monitor can be confidently wrong. The paper treats this as an empirical matter rather than a theorem, which is honest but leaves the central claim dependent on the quality of the particular embedding. Minor implementation details on how bounded traces are handled and how expensive the distance computations get at runtime would also help. This is aimed at people doing runtime verification for perception-driven robotics. A reader working on autonomous manipulation or similar would get concrete value from the formulation and the calibration trick. It deserves a serious referee because the idea is new enough and the empirical check is there, even though the soundness case is still partly empirical.

Referee Report

3 major / 2 minor

Summary. The paper introduces Embedding Temporal Logic (ETL) for runtime monitoring of perception-based autonomous systems. ETL defines predicates directly in learned embedding spaces via distances between observed embeddings and target embeddings from reference observations, enabling high-level perceptual concepts such as visual similarity or semantic avoidance. These predicates are composed with standard temporal operators to express sequential behaviors. The work provides monitors for bounded embedding traces and a conformal calibration procedure to ensure reliable predicate evaluation with statistical guarantees. Empirical results on manipulation tasks show strong agreement with ground-truth semantics for both atomic and temporally composed specifications.

Significance. If the embedding-distance predicates prove semantically reliable and the conformal guarantees hold under the stated assumptions, ETL would offer a meaningful advance for runtime verification in perception-driven autonomy. It sidesteps brittle low-level state abstractions by operating natively in embedding spaces, which is practically relevant for vision-based systems. The combination of temporal logic with conformal prediction supplies a concrete path toward safety-oriented monitoring with finite-sample coverage, and the reported empirical agreement on manipulation tasks suggests immediate applicability if the gaps in metric detail and assumption analysis are addressed.

major comments (3)

[Conformal calibration] Conformal calibration section: the procedure claims finite-sample coverage for predicate reliability, yet the manuscript does not specify the nonconformity score (e.g., whether it is raw distance or a normalized variant) nor the calibration-set construction for embedding traces. This detail is load-bearing for the safety claims, as coverage can fail if the score does not satisfy exchangeability under perceptual distribution shift.
[Predicate definition] Predicate definition: the central claim that distances to reference embeddings capture perceptual concepts (e.g., 'similarity to visual goals') is presented as enabling high-level specifications, but no analysis is given of when the embedding metric aligns with human-interpretable semantics versus when it collapses under minor visual perturbations. This assumption directly affects whether the logic remains meaningful beyond the reported tasks.
[Empirical evaluation] Empirical evaluation: while agreement with ground-truth semantics is reported, the section provides no quantitative breakdown (e.g., precision/recall per temporal operator or false-positive rates on composed specifications), nor error analysis for cases where embedding distances deviate from intended predicates. These metrics are necessary to substantiate the claim of accurate monitoring of temporally extended behaviors.

minor comments (2)

[Abstract] The abstract refers to 'multiple manipulation environments' without naming them or providing links to datasets; adding this information would improve reproducibility.
[Notation] Notation for observed versus target embeddings is introduced but used inconsistently in the monitor pseudocode; a single clarifying table or definition box would help.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment below with clarifications drawn from the manuscript and indicate planned revisions to improve clarity and rigor.

read point-by-point responses

Referee: [Conformal calibration] Conformal calibration section: the procedure claims finite-sample coverage for predicate reliability, yet the manuscript does not specify the nonconformity score (e.g., whether it is raw distance or a normalized variant) nor the calibration-set construction for embedding traces. This detail is load-bearing for the safety claims, as coverage can fail if the score does not satisfy exchangeability under perceptual distribution shift.

Authors: We thank the referee for this important observation. The nonconformity score is the raw Euclidean distance between the observed embedding and the target reference embedding; no normalization is applied. The calibration set is formed from a held-out collection of reference observations drawn from the same perceptual distribution used for the test traces. We will revise the conformal calibration section to state these choices explicitly and add a paragraph discussing the exchangeability assumption together with its sensitivity to distribution shift. revision: yes
Referee: [Predicate definition] Predicate definition: the central claim that distances to reference embeddings capture perceptual concepts (e.g., 'similarity to visual goals') is presented as enabling high-level specifications, but no analysis is given of when the embedding metric aligns with human-interpretable semantics versus when it collapses under minor visual perturbations. This assumption directly affects whether the logic remains meaningful beyond the reported tasks.

Authors: The predicates rely on distances in the learned embedding space precisely because the embedding model is trained to encode perceptual similarity. While the current manuscript does not contain a dedicated robustness analysis, the reported experiments on manipulation tasks demonstrate close agreement with ground-truth semantics. In revision we will insert a short discussion of the conditions under which the embedding metric is expected to align with intended concepts and the risk of collapse under perturbations, together with guidance on embedding-model selection. revision: partial
Referee: [Empirical evaluation] Empirical evaluation: while agreement with ground-truth semantics is reported, the section provides no quantitative breakdown (e.g., precision/recall per temporal operator or false-positive rates on composed specifications), nor error analysis for cases where embedding distances deviate from intended predicates. These metrics are necessary to substantiate the claim of accurate monitoring of temporally extended behaviors.

Authors: We agree that finer-grained quantitative metrics would strengthen the evaluation. We will expand the empirical section to report precision and recall separately for atomic predicates and for each temporal operator, include false-positive rates on composed specifications, and add an error analysis highlighting cases where embedding distances deviate from the intended predicate semantics. revision: yes

Circularity Check

0 steps flagged

No significant circularity in ETL derivation chain

full rationale

The paper defines Embedding Temporal Logic (ETL) by introducing predicates as distances between observed embeddings and target embeddings from reference observations, then composes them with standard temporal operators and applies conformal calibration for predicate reliability. This construction draws on established embedding learning and conformal prediction frameworks with independent grounding outside the paper; the central claims do not reduce by the paper's own equations to self-referential definitions, fitted parameters renamed as predictions, or load-bearing self-citations. Empirical agreement with ground-truth semantics on manipulation tasks serves as external validation rather than internal forcing. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that learned embeddings provide a semantically meaningful metric space for perceptual predicates and that conformal calibration yields reliable safety-oriented evaluations.

axioms (1)

domain assumption Distances in learned embedding spaces align with perceptual semantic similarity
This underpins the predicate definitions for high-level concepts like visual goal similarity.

pith-pipeline@v0.9.0 · 5479 in / 1102 out tokens · 41898 ms · 2026-05-15T05:00:04.080641+00:00 · methodology

Review history (2 revisions) →

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

?

unclear
Relation between the paper passage and the cited Recognition theorem.

ETL defines predicates through distances between observed embeddings and target embeddings... δ_ap(z) = a({d(z, z_g) | z_g ∈ Z_target}) ... σ, i |= ap ⇔ δ_ap(z_i) ▷◁ ϵ
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

conformal calibration procedure that provides reliable and safety-oriented predicate evaluation... ϵ_CP = score_(k) with k=⌈(1−α)(n_cal+1)⌉

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

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