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

The gist The fixed-effects distillation method improves PPG-only models by conditioning on the recording to cancel out identity effects, leading to more accurate state learning.

What is being taught and why it matters

ECG is widely used to teach PPG-only models, yet what it teaches is unexamined The raw alignment cosine misses this, since a constant predictor scores 0.793. Wearables are valued for tracking how a person’s cardiovascular state changes, but ECG-to-PPG distillation mostly learns who the person is. The trait holds 40–59% of a frozen ECG teacher’s target.

The decomposition of the teacher target

Every recording, one monitoring session of one person, contributes many windows, so a frozen ECG teacher’s embedding splits into a per-recording mean, the trait, and a within-recording deviation, the state. We call µr the trait component (who is recorded) and δri the state component (how they are doing), where µr = Ei[zri r]. The trait holds 59% of the centred target energy in the teacher’s raw coordinates and 40% in the standardised coordinates used for training.

Why pooled objectives learn identity

The raw metric is dominated by the recording level, as the shared mean and per-recording offsets dominate the raw target. A pooled student that regresses the pooled target fits the trait on training recordings by reading identity-revealing PPG morphology, and does not carry it to unseen ones. Minimising∥zˆ − z∥2 forces the student to fit it, and on training recordings it succeeds by reading identity-revealing PPG morphology. The cross-recording negative objective rewards identity, as an InfoNCE whose negatives come from other recordings can be solved by identity alone.

Fixed-effects distillation protocol

The fixed-effects remedy, conditioning on the unit carries over directly, as we subtract the recording’s mean from prediction and target before comparing them, so the trait cancels exactly. The change needs no new architecture and no extra data. The objective is defined as L = λ Huber(ˆz, z) anchor + Lstate, where the state term is conditioned on the recording, which removes µr. This conditional likelihood eliminates incidental parameters.

The resulting gains and findings

State agreement more than doubles through the objective, not the sampler, as state agreement rises along that order on both backbones. The gain comes from the objective, not from the batch sampler. FE-COS lowers the error of every within-recording label on both backbones (systolic pressure from 8.93 to 8.77 mmHg on PaPaGei-S and from 8.21 to 7.83 on AnyPPG). Retrieval splits people from moments, as FE-COS+FE-NCE is best at state retrieval, finding the right moment among 256 windows of one person. The raw alignment cosine cannot see this, so ECG-guided PPG models should report within-recording agreement.

The study concludes that making the loss relative to each recording’s own mean removes that component exactly, a pooled anchor keeps it, and within-recording agreement with the teacher more than doubles on two backbones and holds on two further databases. The raw alignment cosine cannot see this.

How it works

The setup involves a frozen single-lead ECG foundation model T = Thi ◦ Tlo supplying the target zri = Thi(hri) ∈ R D, hri = Tlo(yri). A bridge fθ, the only trained module, sees PPG only and predicts hˆri = fθ(xri) from frozen PPG-backbone features. The student is the whole PPG-only path (backbone, bridge, and the teacher’s frozen upper layers reused as a decoder).

Key objectives and metrics

The primary objective is L = λ Huber(ˆz, z) anchor + Lstate. The state term uses FE-COS: 1 − cos(dri, eri), where dri = ˆzri − ¯zˆr and eri = zri − z¯r for the deviations from the mean over the windows of recording r present in the batch. The anchor is taken on the standardised embedding and, with equal weight, on the logits of the teacher’s frozen classification head.

Experimental validation

State agreement rises along that order on both backbones from 0.136 ± 0.006 for the pooled regression. The gain comes from the objective, not from the batch sampler. FE-COS lowers the error of every within-recording label on both backbones (systolic pressure from 8.93 to 8.77 mmHg on PaPaGei-S and from 8.21 to 7.83 on AnyPPG). The gain lies beyond heart rhythm and within what PPG can observe.

Limitations

White noise on the PPG lowers every objective, but the conditioned ones stay ahead at 0.2 of the signal’s sd, FE-COS keeps 0.058 and FE-COS+FE-NCE 0.093 against 0.027 for the pooled loss. The gain lies beyond heart rhythm and within what PPG can observe.

Conclusion

A wearable is calibrated to its wearer and needs from an ECG teacher how that wearer changes, yet pooled distillation spends much of its capacity on who they are. Making the loss relative to each recording’s own mean removes that component exactly, a pooled anchor keeps it, and within-recording agreement with the teacher more than doubles on two backbones and holds on two further databases. The raw alignment cosine cannot see this.

References

[1] Ramakrishna Mukkamala, Jin-Oh Hahn, Omer T. Inan, Lalit K. Mestha, Chang-Sei Kim, Hakan Toreyin, and Survi Kyal, “Toward ubiquitous blood pressure monitoring via pulse transit time: Theory and practice,” IEEE Transactions on Biomedical Engineering

[2] Guangkun Nie, Xiaocheng Fang, Gongzheng Tang, Yujie Xiao, Jun Li, Bo Liu, Hongyan Li, and Shenda Hong, “AnyPPG: An ECG-guided PPG foundation model trained on over 100,000 hours of recordings for holistic health profiling,” in Proceedings of the 32nd ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.2

[3] Chenqi Li, Yu Liu, Timothy Denison, and Tingting Zhu, “BioXBridge: Model bridging for unsupervised cross-modal knowledge transfer across biosignals,” in The Fourteenth International Conference on Learning Representations

[4] Hao Zhou, Simon A.

1. The improved system can perform state-aware prediction by conditioning distillation on individual recordings, as Conditioning on the recording turns distillation toward the within-person changes that wearables monitor. This allows for tracking how a person’s cardiovascular state changes over time rather than just learning who they are.

2. Fixed-effects distillation enables exact cancellation of identity components in the prediction loss by subtracting the recording’s mean from both prediction and target, as we subtract the recording’s mean from prediction and target before comparing them, so the trait cancels exactly. This ensures that models focus on state information that changes within a session.

3. The system can achieve significantly improved state agreement by using conditional contrastive losses like FE-COS, which is shown to have an effect of state agreement more than doubles compared to other objectives. This leads to better performance on held-out recordings for intra-person labels while age and sex do not improve.

4. The system can utilize a pooled anchor that keeps it [the trait] while the state loss focuses on deviations, as the paper demonstrates that the anchor sees row mean and state loss sees = -̄trait removed. This dual approach allows the model to retain identity information while learning dynamic physiological changes.

5. The system can improve performance on external or unseen databases by leveraging a pooled anchor, as evidenced by state agreement rising on the second database (MIMIC-III) when using FE-COS and FE-NCE objectives, showing state agreement rises from 0.049 to 0.129 on PaPaGei-S and from 0.067 to 0.148 on AnyPPG.

6. The system can be more robust to noise in PPG signals by using the conditional-logit form of loss, as the conditioned ones stay ahead: at 0.2 of the signal’s sd, FE-COS keeps 0.058 and FE-COS+FE-NCE 0.093 against 0.027 for the pooled loss. This makes it better suited for real-world noisy wearable data where white noise on the PPG lowers every objective, but the conditioned ones stay ahead.