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

1. INTRODUCTION

• Paired ECG improves PPG-only representations, but prior work had not examined which ECG information the alignment transfers.Wearables are used to follow an individual over time, where changes such as blood-pressure trends can matter more than differences between people.Source: §1 · p. 1
• 40–59% of the teacher target energy lies in the per-recording trait, and pooled students fit this identity signal without carrying it to unseen recordings.A constant predictor reaches raw cosine 0.793, close to 0.823 for the best linear model, so raw alignment cosine obscures the distinction.Source: §1 · p. 1
• Fixed-effects distillation subtracts each recording’s mean from prediction and target, cancelling the trait exactly while a pooled anchor retains it.The change requires neither a new architecture nor additional data.Source: §1 · p. 1
• Across the reported protocol, state agreement more than doubles through the objective rather than the sampler, within-person labels improve while fixed labels do not, and gains hold on two further databases.The paper also reports that identity memorisation trades off against state learning.Source: §1 · p. 1

2.1. Setup and a decomposition of the teacher target

• The frozen ECG teacher maps each synchronous ECG window to a target embedding, while a bridge predicts intermediate teacher tokens from frozen PPG-backbone features.The PPG-only student reuses the teacher’s frozen upper layers as a decoder; ECG is used for training loss, not inference.Source: §2.1 · p. 1, Figure 1 · p. 2
• The target decomposes as z_ri = µ_r + δ_ri, with µ_r the recording-level trait and δ_ri the within-recording state.The trait contains 59% of centered target energy in raw coordinates and 40% in the standardized training coordinates.Source: §2.1 · p. 1

2.2. Why pooled objectives learn identity

• The state loss compares deviations from each recording’s batch mean, cancelling µ_r, while the raw anchor retains the recording-level trait.Figure 2 contrasts raw targets whose recording means separate the panels with centered within-recording variation whose means move to the origin.Source: §2.2 · p. 2, Figure 2 · p. 2
• 0.793 raw cosine comes from a constant predictor, versus 0.823 for the best linear model, leaving little raw-cosine range to assess useful alignment.The shared mean and per-recording offsets dominate the raw target.Source: §2.2 · pp. 1–2
• Trait agreement reaches 0.90 on training windows but only 0.33 on held-out recordings, as pooled regression fits identity-revealing PPG morphology.Between- and within-recording maps differ: their coefficient cosine is 0.15 for PaPaGei-S and 0.25 for AnyPPG; on PaPaGei-S, the within-recording map gives 0.26 state agreement versus 0.11 for the between-recording map.Source: §2.2 · p. 2
• Cross-recording InfoNCE negatives can be solved by identity alone and memorize the trait most strongly among the compared objectives.This objective uses negatives from other recordings, as is conventional for biosignals.Source: §2.2 · p. 2

3. CONDITIONING THE LOSS ON THE RECORDING

• The state term compares deviations from each recording’s batch mean using candidates from that same recording, while the pooled anchor retains recording-level information.The anchor also compares standardised embeddings and, with equal weight, logits from the teacher’s frozen classification head.Source: §3 · p. 2
• Adding a constant to every target in a recording leaves its state deviations unchanged, so the trait cancels from the state term.The conditional-likelihood formulation also eliminates incidental parameters.Source: §3 · pp. 2–3
• As λ increases, the linear analogue moves from the within ridge estimator toward the pooled ridge solution, with the ridge penalty held at the same relative weight.In the network, the anchor restores the trait and steadies the state, while most of the state gain remains without it.Source: Figure 3 · p. 3, §3 · p. 3

4.1. Data, backbones, and protocol

• Training uses 282 VitalDB recordings and selects on 174 held-out recordings, with 75 additional recordings never used for selection; experiments use two frozen PPG backbones.State agreement removes each recording’s mean and partials out heart rate, its square, and eight signal-quality descriptors; trait agreement is reported separately.Source: §4.1 · p. 3

4.2. Conditioning the loss raises state agreement

• State agreement rises from 0.136 ± 0.006 with pooled regression to 0.307 ± 0.001 with FE-COS on PaPaGei-S, with the same objective ordering and a 0.317 ± 0.000 endpoint on AnyPPG.Across 34 runs, trait and held-out state agreement trade off (Spearman ρ = −0.79).Source: §4.2 · p. 3
• The 0.206 state-agreement gain over the cross-recording sampler is attributed mainly to the objective (0.171), not the sampler (0.036), while FE-COS lowers trait agreement versus pooled loss.The linear analogue’s within-to-pooled state agreement falls from 0.130 to 0.093 on AnyPPG with fixed ridge penalty; penalty tuning shrinks the gap to 0.009.Source: §4.2 · pp. 3–4

4.3. The gain is state

• FE-COS lowers errors on within-recording blood-pressure and heart-rate labels on both backbones, while age and sex do not move; retrieval performance also separates person-finding from moment-finding objectives.mix-NCE is best for trait retrieval, while FE-COS+FE-NCE is best for state retrieval; the gain also persists under motion-like waveform tests and is concentrated in the repeating part of a window.Source: §4.3 · p. 4

4.4. Other sensors and another hospital

• On ECSMP, state agreement rises from 0.010 to 0.072 on PaPaGei-S and from 0.028 to 0.113 on AnyPPG; on MIMIC-III it rises from 0.049 to 0.129 and from 0.067 to 0.148, respectively.MIMIC-III heart-rate error falls by 19% and 13%; the bridge and objective did not see that hospital, though both backbones’ pretraining corpora included its PPG.Source: §4.4 · p. 4, Table 2 · p. 4

4.5. Limitations

• At 0.2 signal standard deviations of added white noise, FE-COS retains 0.058 and FE-COS+FE-NCE 0.093, versus 0.027 for pooled loss; blood-pressure read-outs remain worse than zero-prediction error.Mean RR is read equally well by every objective, while none reads the T/R amplitude ratio, to which PPG has no path.Source: §4.5 · p. 4

• Within-recording agreement with the teacher more than doubles on two backbones and holds on two further databases.Source: §5 · p. 4
• Making the loss relative to each recording’s own mean removes the identity component exactly, while a pooled anchor keeps it.Source: §5 · p. 4
• Pooled distillation spends much of its capacity on who wearers are, although wearables need to track how each wearer changes.Source: §5 · p. 4
• Raw alignment cosine cannot distinguish identity from state, so ECG-guided PPG models should report within-recording agreement.Source: §5 · p. 4

• The study was conducted retrospectively using de-identified human-subject data.Source: §6 · p. 5
• Data came from VitalDB and the MIMIC-III Waveform Database Matched Subset through PulseDB, and from ECSMP.Source: §6 · p. 5
• Ethical approval was not required, as confirmed by the open-access data licences.Source: §6 · p. 5