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.

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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 familyPrimary object of changeStability notionUses measured signal energy?What it cannot do (gap PECT fills)
Concept-drift / distributional drift [ 3 , 7 ]Input/label distributions ( P(X)P(X) , P(Y)P(Y) , P(Y∣X)P(Y|X) )Detect/track distribution change; trigger adaptationNoNo 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 changeNoPerturbations are abstract (e.g., norm-bounded); does not relate drift to a physiologically interpretable quantity like ΔEphys\Delta E_{\text{phys}} .
Invariance / equivariance (group-based) [ 11 , 12 ]Transformation structure (symmetries)Representation should be invariant/equivariant to certain transformsNoSpecifies 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 configurationsLow learned energy for plausible statesNo (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/trajectoriesSometimes (via equations)Typically constrains outputs, not latent drift geometry ; does not define a runtime criterion separating virtual drift from real drift via ∥δz∥\|\delta z\| and ∣ΔE∣|\Delta E| .
Continual learning / representation-drift penalties [ 16 , 17 ]Feature/parameter drift across tasks or timeReduce forgetting; stabilize features across domains/tasksNoTargets 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.
Fig. 1: Multimodal ECG architecture showing encoder pathways, fusion, and the integration of physiologic drift and energy analysis for ECRL.
ModelAcc cleanAcc pertRobustness Deg.
M1 1D-CNN (baseline)0.93550.39250.5430
M1 1D-CNN (BIT+PECT)0.94090.88170.0591
M2 2D-CNN (baseline)0.91940.90860.0108
M2 2D-CNN (BIT+PECT)0.90320.90320.0000
M3 Transformer (baseline)0.87630.84410.0323
M3 Transformer (BIT+PECT)0.88710.88710.0000
TABLE II: Unimodal ECG Models: Baseline vs. BIT+PECT.
ModelAcc cleanAcc pertRobustness Deg.
M4 1D+TR (baseline)0.93000.76880.1612
M4 1D+TR (BIT+PECT)0.92470.80650.1183
M5 2D+TR (baseline)0.93000.25270.6773
M5 2D+TR (BIT+PECT)0.93010.92470.0054
M6 1D+2D (baseline)0.94000.72580.2142
M6 1D+2D (BIT+PECT)0.93010.90860.0215
TABLE III: Multimodal Late-Fusion ECG Models: Baseline vs. BIT+PECT.
ModelClean Δ%\Delta\%Pert Δ%\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.
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