When Should a Model Change Its Mind? An Energy-Based Theory and Regularizer for Concept Drift in Electrocardiogram (ECG) Signals

Timothy Oladunni; Blessing Ojeme; Kyndal Maclin; Clyde Baidoo

cs.LGFeb 25, 2026

When Should a Model Change Its Mind? An Energy-Based Theory and Regularizer for Concept Drift in Electrocardiogram (ECG) Signals

Authors: Timothy Oladunni, Blessing Ojeme, Kyndal Maclin, Clyde Baidoo

Organizations: Department of Computer Science, Morgan State University, Baltimore, MD, USA.

Abstract

Models operating on dynamic physiologic signals must distinguish benign, label-preserving variability from true concept change. Existing concept-drift frameworks are largely distributional and provide no principled guidance on how much a model's internal representation may move when the underlying signal undergoes physiologically plausible fluctuations in energy. As a result, deep models often misinterpret harmless changes in amplitude, rate, or morphology as concept drift, yielding unstable predictions, particularly in multimodal fusion settings. This study introduces Physiologic Energy Conservation Theory (PECT), an energy-based framework for concept stability in dynamic signals. PECT posits that under virtual drift, normalized latent displacement should scale proportionally with normalized signal energy change, while persistent violations of this proportionality indicate real concept drift. We operationalize this principle through Energy-Constrained Representation Learning (ECRL), a lightweight regularizer that penalizes energy-inconsistent latent movement without modifying encoder architectures or adding inference-time cost. Although PECT is formulated for dynamic signals in general, we instantiate and evaluate it on multimodal ECG across seven unimodal and hybrid models. Experiments show that in the strongest trimodal hybrid (1D+2D+Transformer), clean accuracy is largely preserved (96.0% to 94.1%), while perturbed accuracy improves substantially (72.6% to 85.5%) and fused representation drift decreases by over 45%. Similar trends are observed across all architectures, providing empirical evidence that PECT functions as an energy-drift law governing concept stability in continuous physiologic signals.

Figures & tables

Framework family	Primary object of change	Stability notion	Uses measured signal energy?	What it cannot do (gap PECT fills)
Concept-drift / distributional drift [ 3 , 7 ]	Input/label distributions ( $P(X)$ , $P(Y)$ , $P(Y\|X)$ )	Detect/track distribution change; trigger adaptation	No	No principled bound on how much latent space may move under label-preserving physiologic variability.
Robustness / Lipschitz / margin bounds [ 8 , 9 , 10 ]	Model mapping sensitivity (input $\rightarrow$ features/logits)	Small input change $\Rightarrow$ bounded output/feature change	No	Perturbations are abstract (e.g., norm-bounded); does not relate drift to a physiologically interpretable quantity like $\Delta E_{\text{phys}}$ .
Invariance / equivariance (group-based) [ 11 , 12 ]	Transformation structure (symmetries)	Representation should be invariant/equivariant to certain transforms	No	Specifies which transforms should preserve outputs, but not the magnitude law governing admissible latent motion under physiologic variability.
Energy-Based Models (EBMs) [ 13 , 14 ]	Learned scalar energy function over configurations	Low learned energy for plausible states	No (learned energy)	“Energy” is a learned potential, not physical/physiologic waveform energy; no energy–drift consistency constraint in representation space.
Physics-informed learning (PINNs, mechanistic constraints) [ 15 ]	Outputs constrained by known physics (often PDEs)	Physical consistency of outputs/trajectories	Sometimes (via equations)	Typically constrains outputs, not latent drift geometry ; does not define a runtime criterion separating virtual drift from real drift via $\\|\delta z\\|$ and $\|\Delta E\|$ .
Continual learning / representation-drift penalties [ 16 , 17 ]	Feature/parameter drift across tasks or time	Reduce forgetting; stabilize features across domains/tasks	No	Targets task/domain shifts rather than benign within-class physiologic variability; no physically grounded admissible-drift rule.

TABLE I: How PECT/ECRL differs from existing stability and drift frameworks. PECT uniquely ties measured physiologic signal energy to latent representation drift and uses energy–drift consistency to separate virtual drift from real concept change.

Panel of Figure 2 — Fig. 1: Multimodal ECG architecture showing encoder pathways, fusion, and the integration of physiologic drift and energy analysis for ECRL.

Model	Acc clean	Acc pert	Robustness Deg.
M1 1D-CNN (baseline)	0.9355	0.3925	0.5430
M1 1D-CNN (BIT+PECT)	0.9409	0.8817	0.0591
M2 2D-CNN (baseline)	0.9194	0.9086	0.0108
M2 2D-CNN (BIT+PECT)	0.9032	0.9032	0.0000
M3 Transformer (baseline)	0.8763	0.8441	0.0323
M3 Transformer (BIT+PECT)	0.8871	0.8871	0.0000

TABLE II: Unimodal ECG Models: Baseline vs. BIT+PECT.

Model	Acc clean	Acc pert	Robustness Deg.
M4 1D+TR (baseline)	0.9300	0.7688	0.1612
M4 1D+TR (BIT+PECT)	0.9247	0.8065	0.1183
M5 2D+TR (baseline)	0.9300	0.2527	0.6773
M5 2D+TR (BIT+PECT)	0.9301	0.9247	0.0054
M6 1D+2D (baseline)	0.9400	0.7258	0.2142
M6 1D+2D (BIT+PECT)	0.9301	0.9086	0.0215

TABLE III: Multimodal Late-Fusion ECG Models: Baseline vs. BIT+PECT.

Model	Clean $\Delta\%$	Pert $\Delta\%$	Robust. Red.%
M1 1D-CNN	+0.58%	+124.6%	89.1%
M2 2D-CNN	-1.75%	-0.6%	100%
M3 TR	+1.24%	+5.1%	100%
M4 1D+TR	-0.6%	+4.9%	26.6%
M5 2D+TR	+0.01%	+266%	99.2%
M6 1D+2D	-1.06%	+25.2%	89.9%

TABLE IV: Percentage improvement introduced by BIT+PECT.

Concept Drift

Concept drift is change over time in the relationship between data and target outcomes, which can erode the accuracy of deployed models.

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CFD-Guided Detection of Concept Drift in Multimodal Physiologic Signals

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Concept Drift Electrocardiography Wearable Health Monitoring Drifting Models Multimodal Sensor Fusion

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Cardiovascular AI models can classify clean elec- trocardiogram (ECG) signals, but real wearable signals change because of motion, breathing, posture, sensor contact, and true clinical deterioration. This paper asks when a model should keep its prediction, change it, or flag uncertainty. We propose a physiologic stability framework, called PECS, that compares changes inside the model with measurable changes in the signal. ECG is treated as the main cardiac signal, photoplethysmography (PPG) adds pulse and vascular information, and respiration is used only when ECG and PPG disagree. We test the framework on PTB-XL at pilot and full scales and on synchronized BIDMC and MIMIC waveform cohorts. The PTB-XL pilot and full- scale analyses selected different domain pairs, and the strongest cross-modal pair also changed across BIDMC and MIMIC, showing that adding every available signal is not always the best choice. PECS outperformed the evaluated drift-detection baseline implementations, reaching drift classification accuracy (DCA) of 0.8786 on expanded BIDMC and 0.9560 on MIMIC. The MIMIC results also showed that respiration can help during disagreement cases, but it should be used selectively rather than as an automatic override. Overall, the results support PECS as a candidate monitoring framework for wearable cardiovascular AI while highlighting the need for scale-aware domain selection and interpretable trust routing

Abstract

Concept Drift

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