HCE Accuracy: Metrics & Applications

• HCE accuracy is a family of metrics that quantifies measurement fidelity across domains such as astrophysical detectors, cold electronics, and image segmentation.
• It employs specialized methodologies like glitch detection, degradation modelling, region-based correction, and entropy-based causal inference to assess performance.
• The metrics have practical implications for optimizing detector noise, prolonging device lifetimes, reducing user correction effort, and aligning machine outputs with human evaluations.

High Coincidence Event (HCE) accuracy encompasses a family of concepts and metrics that quantify the fidelity, reliability, and interpretability of “HCE” phenomena or methodologies across diverse scientific disciplines. Historically, the term originates from astrophysical instrumentation, but by 2025 it spans applications from cosmic ray impact analysis and device lifetime projections to advanced evaluation criteria in image segmentation, neural modeling, hierarchical clustering, ensemble learning, retrieval, and natural language understanding.

1. HCE Accuracy in Low-Temperature Detector Physics

In the context of the Planck/HFI instrument, HCEs (High Coincidence Events) refer to nearly simultaneous glitches across many sub-Kelvin bolometers, triggered by a cosmic ray shower impacting the focal plane (Miniussi et al., 2014). Accurate HCE identification is fundamental for correct astrophysical data analysis. The process involves:

• Glitch detection algorithmically binned at 15 ms resolution.
• Histogram analysis: Coincident events above a threshold (∼15 bolometers per bin) are attributed statistically to “true” HCEs.
• Extrapolation of the high-coincidence histogram tail estimates HCE rates (∼100/hour).
• Classification into “fast” (rise ∼5 s) and “slow” (rise ∼30 s) HCEs, in part by stacking time-series bolometer responses.

The accuracy of HCE identification directly impacts the noise model, sensitivity, and systematic error assessment for sky signals. For example, even a microkelvin-scale temperature spike influences data at the level of the detector’s NEP (∼10⁻¹⁷ W/Hz^{1/2}). Distinguishing fast/slow types and quantifying their rates is essential for both current mission data correction and future mission design.

2. HCE Accuracy as a Device Degradation Metric in Cold Electronics

Here HCE denotes “Hot Carrier Effects,” describing performance degradation in CMOS devices exposed to high electric fields, most notably in cold ADC electronics for cryogenic neutrino detectors (Chen et al., 2018). HCE accuracy is quantified through:

• Precision current degradation measurements (I_VDD) under accelerated stress.
• Definition of degradation criteria (e.g., 1% drop in I_VDD).
• Model: lifetime T scales exponentially in 1/V_ds (T ∝ exp(β/V_ds)), allowing accurate projection from stress tests to operational voltages.
• Differential/Integral Non-Linearity metrics (DNL, INL) are continuously tracked for non-monotonic drift.

Lifetime projection for a candidate ADC (ADI AD7274) yields ∼6.1 × 10⁶ years at the operative 2.5 V, demonstrating that—on the relevant timescale—HCE-induced accuracy losses are negligible.

3. HCE Accuracy in Segmentation and Interactive Correction

In high-precision image segmentation, HCE stands for Human Correction Effort (Qin et al., 2022) and reflects the expected number of user interactions (typically mouse clicks) needed to correct a segmentation mask’s errors:

• Computation is based on extracting connected false-positive/false-negative regions, extracting dominant points along their boundaries using algorithms such as Ramer-Douglas-Peucker, applying region relaxation (tolerance γ), and tallying the minimal necessary intervention.
• The metric is practical: A low HCE signifies direct deployability in user-facing applications (art, 3D design). In benchmarking, HCE discriminates models that may be indistinguishable under IoU, F₁, or MAE but differ greatly in real-world post-processing cost.

HCE accuracy here defines a model’s proximity to “plug-and-play” readiness—critical where small errors are costly to correct.

4. HCE Accuracy in Statistical Causality and Hierarchical Clustering

In time-series causal inference, HCE refers to Higher-order Causal Entropy, an algorithmic framework for discovering unique, non-Markov-equivalent causal structures in nonstationary data (Kang et al., 2022):

• Accuracy is measured by the area under the ROC curve (AUC), true positive rates (TPR), and false positive rates (FPR), comparing inferred causal edges to ground truth.
• The acceptance of an edge depends on statistical tests of conditional entropy differences, estimated with nearest-neighbor algorithms.
• The decomposability property of the underlying model allows distributed estimation, substantially improving algorithmic accuracy and scalability.

For hierarchical community detection (Armas, 6 Aug 2025), HCE (Hierarchical Clustering Entropy) accuracy is quantified by the Adjusted Mutual Information (AMI) between detected partitions and ground truth. The HCE measure scans dendrogram levels to maximize:

$$\text{HCE}(K) = \frac{N - K}{N - 1} \sum_{c=1}^{K} p_c \log \left(\frac{1}{p_c}\right)$$

with $p_c = (n_c - 1)/(N - K)$, favoring balanced, nontrivial partitions. Accuracy is then the empirical alignment (as measured by AMI) between HCE-derived levels and planted or reference structures.

5. HCE Accuracy in Language Understanding and Computational Human Calibration

In natural language understanding, HCE accuracy (“Human Calibration Envelope accuracy”) assesses how closely a model’s outputs align with human rater variability (Acharjee et al., 15 Sep 2025):

$$\mathcal{E}_i = [\bar{s}_i^{\text{human}} - \sigma_i^{\text{human}},\; \bar{s}_i^{\text{human}} + \sigma_i^{\text{human}}]$$

$$\text{HCE}_i = \begin{cases} 1, & s_i^{\text{LLM}} \in \mathcal{E}_i \ 0, & \text{otherwise} \end{cases}$$

$$\text{HCE}_{\text{accuracy}} = \frac{1}{N} \sum_{i=1}^N \text{HCE}_i$$

A high HCE accuracy means the model’s predictions fall within human annotators’ standard deviation for a large fraction of items, reflecting a human-like tolerance to interpretative uncertainty—a property unattainable with simple correlation or mean error metrics.

6. HCE and Accuracy in Ensemble, Compression, and Retrieval Models

In neural network ensemble methods, specifically the Heterogeneously Compressed Ensemble (HCE) (Zhang et al., 2023), ensemble accuracy is improved by combining models pruned and quantized from the same baseline. The diversity-aware training objective ensures the ensemble (Q for quantized, S for sparse/pruned):

$$\text{Loss}(S) = \alpha L_{CE}(S) + (1 - \alpha) L_{KL}(S, O - Q)$$

maximizing coverage of the baseline’s decision boundary. Efficiency-accuracy tradeoffs are empirically verified via standard classification metrics, with HCE approaches achieving higher accuracy at lower FLOPs compared to either ensemble or compression in isolation.

In retrieval, Hierarchical Corpus Encoder (HCE) (Chen et al., 26 Feb 2025) accuracy is measured by recall@k, MRR, and NDCG on standard datasets. HCE’s innovation—contrastive sibling-level training in a document hierarchy—enables index updates without retraining, maintaining accuracy comparable to or exceeding generative approaches.

7. HCE Accuracy in Multimodal and Visualization Contexts

In multimodal video colorization (AnimeColor) (Zhang et al., 27 Jul 2025), the High-level Color Extractor (HCE) distills semantic color tokens from references to guide a diffusion transformer. Ablation studies show that the inclusion of HCE sharply boosts color accuracy (e.g., measured by PSNR, SSIM, and perceptual metrics) relative to architectures without it.

In clinical trials with hierarchical composite endpoints, accuracy of HCE analysis is augmented by sophisticated visualization—maraca, mosaic, sunset, and Dustin plots—each ensuring that the calculated statistical measures (e.g., win odds) are interpretable and directly linked to the raw endpoint distribution (Karpefors et al., 2 Jun 2025).

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Table: HCE Variants and Accuracy Dimensions

Context	HCE Expansion	Accuracy Definition / Impact
Planck/HFI Detectors	High Coincidence Event	Thermal spike classification, noise modeling
Cold Electronics (CMOS)	Hot Carrier Effect	Device degradation/lifetime projection
Segmentation	Human Correction Efforts	Pixel/region correction effort estimation
Time Series Causality	Higher-order Causal Entropy	ROC/TPR/FPR/AMI for causal structure
LLM Evaluation	Human Calibration Envelope	Model-human tolerance overlap
Clustering/Community Detection	Hierarchical Clustering Entropy	AMI/community structure recovery
Neural Ensembles	Heterogeneously Compressed Ensemble	Classification accuracy vs. efficiency
Dense Retrieval	Hierarchical Corpus Encoder	Recall@k, MRR, NDCG; retrieval robustness
Video Colorization	High-level Color Extractor	PSNR/SSIM/LPIPS; semantic color consistency
Clinical Trials	Hierarchical Composite Endpoint	Visualization-driven statistical accuracy

Summary

HCE accuracy encapsulates diverse and domain-specific notions of model or measurement reliability, grounded variously in rigorous statistical estimation, physical modeling, usability-driven evaluation, and human-model alignment. The analytic paradigms used—statistical extrapolation, Bayesian inference, entropy maximization, formal calibration envelopes—reveal the foundational principle: HCE accuracy is achieved not solely by maximizing pointwise performance but by quantifying, controlling, and communicating the relevant uncertainty and effort required for real-world interpretability, whether in fundamental science, engineering systems, or machine intelligence.