Teaching PPG How not Who: Fixed-Effects Distillation from ECG

Zhongli Wu; Zhuangzhi Gao; Yuankai Wang; Gregory Y. H. Lip; Bilal H. Kirmani; Yalin Zheng

cs.LGOct 7, 2026

Teaching PPG How not Who: Fixed-Effects Distillation from ECG

Authors: Zhongli Wu, Zhuangzhi Gao, Yuankai Wang, Gregory Y. H. Lip, Bilal H. Kirmani, Yalin Zheng

Organizations: Liverpool Centre for Cardiovascular Science, University of Liverpool, UK · Shanghai Artificial Intelligence Laboratory, Shanghai, China · Liverpool Heart and Chest Hospital, Liverpool, UK · Department of Eye and Vision Sciences, University of Liverpool, UK

Abstract

ECG is widely used to teach PPG-only models, yet what it teaches is unexamined. Wearables are valued for tracking how a person's cardiovascular state changes, but ECG-to-PPG distillation mostly learns who the person is. A per-recording mean, the trait, holds 40-59% of a frozen ECG teacher's target, and pooled students memorise it without carrying it to new recordings. The raw alignment cosine misses this, since a constant predictor scores 0.793. Across 34 runs, the more identity a student memorises, the less state it learns. Fixed-effects distillation subtracts each recording's mean from prediction and target, so the trait cancels exactly, while a pooled anchor keeps it. State agreement more than doubles, within-person labels improve while age and sex do not, and the gain holds on two backbones and two further databases. Conditioning on the recording turns distillation toward the within-person changes that wearables monitor.

Figures & tables

Figure 1: (a) Training. The frozen ECG teacher

T

is split after its fourth stage: its lower layers

T_{\mathrm{lo}}

map ECG to

400

-channel tokens

h_{ri}

, and the bridge

f_{\theta}

predicts these tokens as

\hat{h}_{ri}

from multi-scale features of the frozen PPG backbone. The upper layers

T_{\mathrm{hi}}

map

h_{ri}

and

\hat{h}_{ri}

z_{ri}

and

\hat{z}_{ri}

. The anchor compares raw embeddings, and with equal weight the logits of the teacher’s frozen classification head, so it keeps the trait

\mu_{r}

; the state loss compares deviations from the mean over the windows of recording

r

in the batch, where

\mu_{r}

cancels, with candidates

C_{r}

from the same recording. (b) Inference needs PPG only (about

39

M parameters with PaPaGei-S,

28.6

M of them in

T_{\mathrm{hi}}

); a linear read-out fitted once maps

\hat{z}_{ri}

to downstream tasks.

Figure 2: Teacher targets of four training recordings (360 windows each); no model is involved. Each panel uses its own principal axes, both at one scale, and each ellipse covers two standard deviations of one recording. Left: the anchor compares raw targets, where the row means $\mu_{r}$ ( $\times$ ) set the recordings apart; the trait holds $59\%$ of the centred energy, here as over all training recordings. Right: the state loss compares $e_{ri}$ , where every row mean moves to the origin and only the shape of each recording’s own variation remains. The pink recording visits two states, and its $\mu_{r}$ lies between them.

Figure 3: Colour marks the objective and marker shape the backbone in every panel. (a) Every run: trait agreement on training windows, which gauges memorised identity, against state agreement on held-out recordings; seed mean

\pm

sd over three seeds where available (Sec. 4.1 ), and in grey the pooled loss on batches of

96\times 1

and

24\times 4

windows. (b) The same objectives on ECSMP, an external database with chest ECG and wrist PPG (seed mean

\pm

sd). (c) The

\lambda

path of the linear analogue on ECSMP with one ridge penalty held fixed along the path, relative to the within estimator; both backbones decay monotonically towards the pooled solution.

		state agreement $\uparrow$	trait agreement	raw cosine
pooled		0.136 $\pm$ 0.006	0.316 $\pm$ 0.003	0.798 $\pm$ 0.002
fe-nce	w/o anchor	0.210 $\pm$ 0.021	0.003 $\pm$ 0.002	0.109 $\pm$ 0.073
	with anchor	0.268 $\pm$ 0.000	0.220 $\pm$ 0.031	0.797 $\pm$ 0.005
fe-cos	w/o anchor	0.249 $\pm$ 0.012	0.013 $\pm$ 0.007	0.174 $\pm$ 0.040
	with anchor	0.307 $\pm$ 0.001	0.219 $\pm$ 0.026	0.795 $\pm$ 0.007

Table 1: Held-out agreement on PaPaGei-S without and with the anchor (three seeds).

held-out recordings: labels that vary within a recording
		PaPaGei-S				AnyPPG
	none	pooled	mix-NCE	fe-cos	+fe-nce	pooled	mix-NCE	fe-cos	+fe-nce
SBP error (mmHg)	10.97	8.93 $\pm$ 0.03	8.86 $\pm$ 0.02	8.77 $\pm$ 0.05	8.63 $\pm$ 0.06	8.21 $\pm$ 0.01	8.16 $\pm$ 0.09	7.83 $\pm$ 0.04	7.79 $\pm$ 0.03
DBP error (mmHg)	5.48	4.81 $\pm$ 0.02	4.80 $\pm$ 0.00	4.73 $\pm$ 0.02	4.69 $\pm$ 0.03	4.50 $\pm$ 0.02	4.45 $\pm$ 0.04	4.25 $\pm$ 0.02	4.22 $\pm$ 0.02
HR error (bpm)	5.90	2.50 $\pm$ 0.02	2.62 $\pm$ 0.02	2.29 $\pm$ 0.01	2.50 $\pm$ 0.01	2.67 $\pm$ 0.02	2.84 $\pm$ 0.03	2.38 $\pm$ 0.00	2.62 $\pm$ 0.02
state retrieval top-1	0.004	0.032 $\pm$ 0.001	0.123 $\pm$ 0.001	0.112 $\pm$ 0.001	0.196 $\pm$ 0.003	0.040 $\pm$ 0.001	0.138 $\pm$ 0.001	0.137 $\pm$ 0.001	0.221 $\pm$ 0.001

Table 2: Public labels and a second database. Linear read-outs of the predicted embedding, fitted on training recordings and scored on 75 held-out recordings never used for selection and on 60 MIMIC-III recordings the bridge never saw. Errors of labels that vary within a recording are taken after removing each person’s mean; ‘none’ is the no-information reference. Mean

\pm

sd over three seeds; mix-NCE: InfoNCE with negatives from all recordings; best objective per backbone in bold.

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Cross-Modal Representation Learning Joint-Embedding Predictive Architecture Multimodal Foundation Models

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Electrocardiography (ECG), photoplethysmography (PPG), and phonocardiography (PCG) provide complementary views of the same cardiac cycle, yet existing cardiac foundation models are trained for a single sensing modality, leaving the shared physiology across sensors unexploited. We introduce CardioState-JEPA, a cardiac foundation model to learn a single shared representation jointly across ECG, PPG, and PCG, built on a physiology-aware joint-embedding predictive architecture. The model maps heterogeneous waveforms into a common token space, processes them with a single shared Transformer encoder, and learns by predicting masked latent cardiac states, placing the pretraining target on shared physiology rather than sensor-specific waveform appearance. To handle the temporal offsets between electrical, mechanical, and hemodynamic events, cross-modal prediction uses a learned delay aligner that matches signals at the corresponding cardiac time. Because synchronized multi-sensor recordings are scarce, CardioState-JEPA first learns within-modality structure from abundant unimodal data and then uses paired data to align modalities in latent cardiac time. Evaluated as a frozen encoder across 25 downstream tasks spanning ECG, PPG, and PCG, our encoder improves average PPG classification by 8.2 AUROC points, PCG murmur detection by 18.8 AUROC points, and ECG classification by 15.5 AUROC points over the best self-supervised signal baseline and matches or exceeds cardiac models trained with privileged clinical text or supervised labels on several ECG benchmarks. These results establish that heterogeneous cardiac signals can mutually supervise a single foundation model of cardiac physiology.

Abstract

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