# 教会 PPG 「怎么做」而非「是谁」：来自 ECG 的固定效应蒸馏

# TEACHING PPG HOW, NOT WHO: FIXED-EFFECTS DISTILLATION FROM ECG
Source: [https://arxiv.org/html/2610.10662](https://arxiv.org/html/2610.10662)
Zhongli Wu1, Zhuangzhi Gao2, Yuankai Wang1, Gregory Y\.H\. Lip1, Bilal H\. Kirmani4, Yalin Zheng3\\sthanksCorresponding author: Yalin\.Zheng@liverpool\.ac\.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, holds4040–59%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 scores0\.7930\.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\.

###### Index Terms:

photoplethysmography, cross\-modal distillation, wearable monitoring, foundation models, contrastive learning

††address:1Liverpool Centre for Cardiovascular Science, University of Liverpool, UK
2Shanghai Artificial Intelligence Laboratory, Shanghai, China
3Department of Eye and Vision Sciences, University of Liverpool, UK
4Liverpool Heart and Chest Hospital, Liverpool, UK## 1Introduction

Wearables are worn to follow one person over time\. What makes a PPG trace useful is often less how it differs from other people’s than how it has changed since an hour ago, such as a blood\-pressure trend or a haemodynamic response during surgery\. The per\-person offset is the hard part, which is why cuff\-less blood\-pressure estimation is calibrated per user\[[10](https://arxiv.org/html/2610.10662#bib.bib1)\]\. ECG carries much of the relevant information, and a growing body of work uses synchronous ECG as a privileged training signal for PPG\-only models: a PPG encoder is aligned to an ECG model, trained to reconstruct ECG, or coupled to ECG\-linked codes\[[11](https://arxiv.org/html/2610.10662#bib.bib2),[6](https://arxiv.org/html/2610.10662#bib.bib3),[15](https://arxiv.org/html/2610.10662#bib.bib4),[14](https://arxiv.org/html/2610.10662#bib.bib5)\]\. Paired ECG does improve PPG\-only representations\[[14](https://arxiv.org/html/2610.10662#bib.bib5)\], but which part of the ECG information the alignment transfers has not been examined\.

Much of it, we find, is identity: the part a deployment calibrates away, and the part that does not carry to new people\. 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*; the trait holds4040–59%59\\%of the target energy\. A 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; an InfoNCE whose negatives come from other recordings, as is conventional for biosignals\[[5](https://arxiv.org/html/2610.10662#bib.bib6)\], only has to tell people apart\. The usual metric does not reveal this: a constant predictor already reaches a raw cosine of0\.7930\.793with the target, against0\.8230\.823for the best linear model\.

The problem has a classical form\. Each recording’s mean is an incidental parameter in the sense of panel data\[[1](https://arxiv.org/html/2610.10662#bib.bib7)\], and the fixed\-effects remedy, conditioning on the unit\[[2](https://arxiv.org/html/2610.10662#bib.bib8)\], carries over directly: we subtract the recording’s mean from prediction and target before comparing them, so the trait cancels exactly, and keep a pooled anchor that retains it\. The change needs no new architecture and no extra data\.

Our contributions are: \(i\) a diagnosis: pooled distillation learns who rather than how, the raw alignment cosine cannot tell the two apart, and the identity a student memorises trades off against the state it learns; \(ii\) fixed\-effects distillation, a state loss conditioned on the recording under which the trait cancels exactly, with a pooled anchor that keeps it; and \(iii\) a within\-recording protocol and evidence: state agreement more than doubles through the objective, not the sampler, each loss term does its own job, within\-person labels improve while fixed ones do not, and the gain holds on two other databases\.

Figure 1:\(a\) Training\. The frozen ECG teacherTTis split after its fourth stage: its lower layersTloT\_\{\\mathrm\{lo\}\}map ECG to400400\-channel tokenshr​ih\_\{ri\}, and the bridgefθf\_\{\\theta\}predicts these tokens ash^r​i\\hat\{h\}\_\{ri\}from multi\-scale features of the frozen PPG backbone\. The upper layersThiT\_\{\\mathrm\{hi\}\}maphr​ih\_\{ri\}andh^r​i\\hat\{h\}\_\{ri\}tozr​iz\_\{ri\}andz^r​i\\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 traitμr\\mu\_\{r\}; the state loss compares deviations from the mean over the windows of recordingrrin the batch, whereμr\\mu\_\{r\}cancels, with candidatesCrC\_\{r\}from the same recording\. \(b\) Inference needs PPG only \(about3939M parameters with PaPaGei\-S,28\.628\.6M of them inThiT\_\{\\mathrm\{hi\}\}\); a linear read\-out fitted once mapsz^r​i\\hat\{z\}\_\{ri\}to downstream tasks\.
## 2What distillation transfers

### 2\.1Setup and a decomposition of the teacher target

Letrrindex a recording andiia 10 s window within it\. Each window carries a PPG segmentxr​ix\_\{ri\}and a synchronous ECG segmentyr​iy\_\{ri\}\. A frozen single\-lead ECG foundation modelT=Thi∘TloT=T\_\{\\mathrm\{hi\}\}\\circ T\_\{\\mathrm\{lo\}\}supplies the targetzr​i=Thi​\(hr​i\)∈ℝDz\_\{ri\}=T\_\{\\mathrm\{hi\}\}\(h\_\{ri\}\)\\in\\mathbb\{R\}^\{D\},hr​i=Tlo​\(yr​i\)h\_\{ri\}=T\_\{\\mathrm\{lo\}\}\(y\_\{ri\}\)\. A bridgefθf\_\{\\theta\}, the only trained module, sees PPG only: it predictsh^r​i=fθ​\(xr​i\)\\hat\{h\}\_\{ri\}=f\_\{\\theta\}\(x\_\{ri\}\)from frozen PPG\-backbone features\. The student is the whole PPG\-only path \(backbone, bridge, and the teacher’s frozen upper layers reused as a decoder\), and its output is the predictionz^r​i=Thi​\(h^r​i\)\\hat\{z\}\_\{ri\}=T\_\{\\mathrm\{hi\}\}\(\\hat\{h\}\_\{ri\}\); ECG is used in the loss and is never required at inference\.

Because every recording contributes many windows, the target splits into a recording\-level and a within\-recording part,

zr​i=μr\+δr​i,μr=𝔼i​\[zr​i∣r\],𝔼i​\[δr​i∣r\]=0\.z\_\{ri\}=\\mu\_\{r\}\+\\delta\_\{ri\},\\qquad\\mu\_\{r\}=\\mathbb\{E\}\_\{i\}\\\!\\left\[z\_\{ri\}\\mid r\\right\],\\qquad\\mathbb\{E\}\_\{i\}\\\!\\left\[\\delta\_\{ri\}\\mid r\\right\]=0\.\(1\)We callμr\\mu\_\{r\}the*trait*component \(who is recorded\) andδr​i\\delta\_\{ri\}the*state*component \(how they are doing\)\. The trait holds59%59\\%of the centred target energy in the teacher’s raw coordinates and40%40\\%in the standardised coordinates used for training \(282 training recordings; Fig\.[2](https://arxiv.org/html/2610.10662#S2.F2)\)\. The state is what changes while the sensor stays on the same person, and it is what continuous monitoring needs\.

![Refer to caption](https://arxiv.org/html/2610.10662v1/fig_pca.png)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 meansμr\\mu\_\{r\}\(×\\times\) set the recordings apart; the trait holds59%59\\%of the centred energy, here as over all training recordings\. Right: the state loss compareser​ie\_\{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 itsμr\\mu\_\{r\}lies between them\.
### 2\.2Why pooled objectives learn identity

The raw metric is dominated by the recording level\.The shared mean and the per\-recording offsets dominate the raw target: the constant predictor \(the training mean ofzz\) reaches a raw cosine of0\.7930\.793against the true target, and the best linear model only0\.8230\.823, so the usable range is about0\.030\.03\.

Pooled students memorise the trait\.μr\\mu\_\{r\}isDD\-dimensional and appears once per recording, so the number of unknowns grows with the data, as for an incidental parameter\[[1](https://arxiv.org/html/2610.10662#bib.bib7)\]\. Minimising∥z^−z∥2\\lVert\\hat\{z\}\-z\\rVert^\{2\}forces the student to fit it, and on training recordings it succeeds by reading identity\-revealing PPG morphology: with the batch composition a cross\-recording objective would use, trait agreement reaches0\.900\.90on training windows but only0\.330\.33on held\-out recordings\.

The two levels need different maps\.A pooled least\-squares fit is a matrix\-weighted average of the between\- and within\-recording maps\[[9](https://arxiv.org/html/2610.10662#bib.bib9)\], so it is a compromise whenever they differ\. Here they do: their coefficient cosine is0\.150\.15\(PaPaGei\-S\) and0\.250\.25\(AnyPPG\)\. On PaPaGei\-S a map fitted between recordings predicts trait nearly as well as the pooled fit \(0\.310\.31vs0\.340\.34on held\-out recordings\) but reaches only0\.110\.11on state, against0\.260\.26for a map fitted within recordings\.

Cross\-recording negatives reward identity\.An InfoNCE whose negatives come from other recordings can be solved by identity alone; at the same batch composition it memorises the trait most strongly of all objectives \(Fig\.[3](https://arxiv.org/html/2610.10662#S2.F3)a\)\.

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±\\pmsd over three seeds where available \(Sec\.[4\.1](https://arxiv.org/html/2610.10662#S4.SS1)\), and in grey the pooled loss on batches of96×196\\times 1and24×424\\times 4windows\. \(b\) The same objectives on ECSMP, an external database with chest ECG and wrist PPG \(seed mean±\\pmsd\)\. \(c\) Theλ\\lambdapath 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\.

## 3Conditioning the loss on the recording

We condition the state term on the recording, which removesμr\\mu\_\{r\}, and keep a pooled anchor that carries it \(Fig\.[1](https://arxiv.org/html/2610.10662#S1.F1)\):

ℒ=λ​Huber⁡\(z^,z\)⏟anchor\+ℒstate\.\\mathcal\{L\}=\\lambda\\,\\underbrace\{\\mathrm\{Huber\}\(\\hat\{z\},z\)\}\_\{\\text\{anchor\}\}\\;\+\\;\\mathcal\{L\}\_\{\\text\{state\}\}\.\(2\)The anchor is taken on the standardised embedding and, with equal weight, on the logits of the teacher’s frozen classification head\. Writingdr​i=z^r​i−z^¯rd\_\{ri\}=\\hat\{z\}\_\{ri\}\-\\bar\{\\hat\{z\}\}\_\{r\}ander​i=zr​i−z¯re\_\{ri\}=z\_\{ri\}\-\\bar\{z\}\_\{r\}for the deviations from the mean over the windows of recordingrrpresent in the batch, the state term is

fe\-cos:\\displaystyle\\text\{\{fe\-cos\}\}:1−cos⁡\(dr​i,er​i\),\\displaystyle\\quad 1\-\\cos\(d\_\{ri\},e\_\{ri\}\),\(3\)fe\-nce:\\displaystyle\\text\{\{fe\-nce\}\}:−log⁡exp⁡\(si​i/τ\)∑j∈Crexp⁡\(si​j/τ\),\\displaystyle\\quad\-\\log\\frac\{\\exp\(s\_\{ii\}/\\tau\)\}\{\\sum\_\{j\\in C\_\{r\}\}\\exp\(s\_\{ij\}/\\tau\)\},\(4\)whereCrC\_\{r\}holds the windows of the anchor’s own recording,i∈Cri\\in C\_\{r\}, andsi​j=cos⁡\(dr​i,er​j\)s\_\{ij\}=\\cos\(d\_\{ri\},e\_\{rj\}\)\.fe\-cosis our objective; the conditional logitfe\-nceis reported as a variant, in the unweighted sumfe\-cos\+\+fe\-nce\.

Why the trait cancels\.Adding a constantcrc\_\{r\}to every target of recordingrrleaveser​ie\_\{ri\}unchanged, soμr\\mu\_\{r\}never reaches either state term, and it would drop out of Eq\.[4](https://arxiv.org/html/2610.10662#S3.E4)even without centring: with inner\-product logits⟨z^r​i,zr​j⟩/τ\\langle\\hat\{z\}\_\{ri\},z\_\{rj\}\\rangle/\\tauover candidates from one recording, the softmax is unchanged when all logits shift by⟨z^r​i,cr⟩/τ\\langle\\hat\{z\}\_\{ri\},c\_\{r\}\\rangle/\\tau\. This is how a conditional likelihood eliminates incidental parameters\[[1](https://arxiv.org/html/2610.10662#bib.bib7),[2](https://arxiv.org/html/2610.10662#bib.bib8)\]\. Restricting the comparison to one subject follows the subject\-aware contrastive loss of\[[3](https://arxiv.org/html/2610.10662#bib.bib10)\]and conditional contrastive learning\[[8](https://arxiv.org/html/2610.10662#bib.bib11)\]; we apply it to a frozen cross\-modal teacher and pair it with an anchor that keeps the removed component\.

Role of the anchor\.In the linear case, letX,YX,Ystack the inputs and targets of all windows,Xw,YwX\_\{w\},Y\_\{w\}their within\-recording deviations, andWWa coefficient matrix\. Minimising\(1\+λ\)−1​\(∥Yw−Xw​W∥F2\+λ​∥Y−X​W∥F2\)\+α​∥W∥F2\(1\+\\lambda\)^\{\-1\}\(\\lVert Y\_\{w\}\-X\_\{w\}W\\rVert\_\{F\}^\{2\}\+\\lambda\\lVert Y\-XW\\rVert\_\{F\}^\{2\}\)\+\\alpha\\lVert W\\rVert\_\{F\}^\{2\}moves from the within ridge atλ=0\\lambda=0to the pooled ridge asλ→∞\\lambda\\to\\infty, with the penaltyα\\alphakeeping the same weight relative to the data term throughout\. In the network the two terms split the work \(Table[1](https://arxiv.org/html/2610.10662#S3.T1)\): without the anchor the trait vanishes but most of the state gain remains, and the anchor restores the trait and steadies the state\.

Table 1:Held\-out agreement on PaPaGei\-S without and with the anchor \(three seeds\)\.
## 4Experiments

### 4\.1Data, backbones, and protocol

We train on 282 VitalDB recordings from PulseDB\[[13](https://arxiv.org/html/2610.10662#bib.bib12)\]\(10 s windows at 125 Hz, synchronous finger PPG and ECG, intraoperative\) and select on 174 held\-out recordings; 75 further recordings are reported but never selected on\. The teacher is the frozen single\-lead ECGFounder\[[7](https://arxiv.org/html/2610.10662#bib.bib13)\]\. We use two frozen PPG backbones: PaPaGei\-S\[[12](https://arxiv.org/html/2610.10662#bib.bib14)\], which has never seen ECG, and AnyPPG\[[11](https://arxiv.org/html/2610.10662#bib.bib2)\], which was itself aligned to the same teacher, so it shows whether the effect persists after such alignment\. The bridge is a 4\.7–4\.8 M\-parameter cross\-attention module that predicts the teacher’s stage\-4 tokens from multi\-scale backbone features \(Fig\.[1](https://arxiv.org/html/2610.10662#S1.F1)a\); the teacher embedding hasD=1024D=1024dimensions\. All runs use 12 k steps, batches of 6 recordings×\\times16 windows, and three seeds for every objective except cross\-recording negatives, withτ=0\.1\\tau=0\.1, a smooth\-ℓ1\\ell\_\{1\}Huber of unit cutoff, andλ=1/9\\lambda=1/9forfe\-cosandλ=1\\lambda=1otherwise\.

State agreement\.Since the raw cosine is saturated \(Sec\.[2\.2](https://arxiv.org/html/2610.10662#S2.SS2)\), we remove each recording’s own mean from prediction and target and, as the primary metric, also partial heart rate, its square, and eight signal\-quality descriptors out within each recording \(cospartialstate\\cos^\{\\mathrm\{partial\}\}\_\{\\mathrm\{state\}\}\)\. Trait agreementcostrait\\cos\_\{\\mathrm\{trait\}\}, the cosine between predicted and true recording means, is reported separately; on training windows it gauges memorisation\. Because this metric is close to whatfe\-cosoptimises, Sec\.[4\.3](https://arxiv.org/html/2610.10662#S4.SS3)turns to read\-outs that no objective was trained on\.

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±\\pmsd over three seeds; mix\-NCE: InfoNCE with negatives from all recordings; best objective per backbone in bold\.
### 4\.2Conditioning the loss raises state agreement

Fig\.[3](https://arxiv.org/html/2610.10662#S2.F3)\(a\) places every run by the identity it memorises on training recordings and the state it learns on held\-out ones\. The two trade off across all 34 runs \(Spearmanρ=−0\.79\\rho=\-0\.79\), and the objectives order themselves by how much of the state term is conditioned on the recording\. State agreement rises along that order on both backbones: from0\.136±0\.0060\.136\\pm 0\.006for the pooled regression, through0\.1950\.195for cross\-recording negatives and0\.240±0\.0020\.240\\pm 0\.002for mixed negatives \(mix\-NCE\), to0\.307±0\.0010\.307\\pm 0\.001forfe\-cos\(PaPaGei\-S\); the AnyPPG backbone gives the same order and ends at0\.317±0\.0000\.317\\pm 0\.000\. Seed spread is at most0\.0060\.006, against steps of0\.050\.05–0\.080\.08between rungs and0\.170\.17in total\.

The gain comes from the objective, not from the batch sampler\. Drawing batches of 96 different recordings with one window each, the composition a cross\-recording alignment loss would use, leaves the pooled objective at0\.1000\.100, and 24 recordings of 4 windows at0\.1120\.112\(grey in Fig\.[3](https://arxiv.org/html/2610.10662#S2.F3)a\); the6×166\\times 16sampler alone moves it to0\.1360\.136\. Of the0\.2060\.206between the cross\-recording sampler with a pooled loss andfe\-cos, the sampler accounts for0\.0360\.036and the objective for0\.1710\.171\. Conditioning also cuts memorisation: trait agreement on training windows drops from0\.490\.49–0\.690\.69for the pooled loss to0\.230\.23–0\.320\.32forfe\-cos\(range over three seeds and both backbones\), as Eq\.[1](https://arxiv.org/html/2610.10662#S2.E1)predicts onceμr\\mu\_\{r\}leaves the state gradient\.

Nor is it a matter of regularisation strength\. In the linear analogue of Sec\.[3](https://arxiv.org/html/2610.10662#S3)on ECSMP, with the ridge penalty held fixed along the wholeλ\\lambdapath \(Fig\.[3](https://arxiv.org/html/2610.10662#S2.F3)c\), state agreement falls monotonically from the within estimator to the pooled solution, from0\.1300\.130to0\.0930\.093on AnyPPG, a paired difference of\+0\.037\+0\.037\[0\.033,0\.040\]\[0\.033,0\.040\]\. Tuning each endpoint’s penalty by cross\-validation shrinks the gap to0\.0090\.009, so regularisation masks part of the effect rather than creating it\.

### 4\.3The gain is state

Labels that vary within a recording improve; labels fixed per person do not\.Table[2](https://arxiv.org/html/2610.10662#S4.T2)reads the predicted embedding out with linear probes against public labels, divided in advance into those that vary within a recording \(blood pressure, heart rate\) and those fixed per person \(age, sex\)\. The decomposition predicts a gain on the first group only, and that is what we observe\.fe\-coslowers the error of every within\-recording label on both backbones \(systolic pressure from8\.938\.93to8\.778\.77mmHg on PaPaGei\-S and from8\.218\.21to7\.837\.83on AnyPPG, heart rate from2\.502\.50to2\.292\.29bpm and from2\.672\.67to2\.382\.38\), while age and sex do not move\. mix\-NCE leaves blood pressure where the pooled loss left it and raises the heart\-rate error, so the gain comes from conditioning, not from contrast\.

Retrieval splits people from moments\.mix\-NCE is best at trait retrieval, finding the right person among 75 \(0\.2180\.218top\-1 against0\.1160\.116forfe\-coson PaPaGei\-S\);fe\-cos\+\+fe\-nceis best at state retrieval, finding the right moment among 256 windows of one person \(0\.1960\.196, against0\.1230\.123for mix\-NCE and0\.0320\.032for the pooled loss\)\.

It is not shared artefact, and it is repeatable\.On 60 validation recordings \(one seed\), injecting one band\-limited0\.10\.1–22Hz motion\-like waveform into both the PPG and the ECG of a window leaves the gain offe\-cosover the pooled baseline at\+0\.166\+0\.166, against\+0\.169\+0\.169clean and\+0\.165\+0\.165with independent waveforms; corrupting only the ECG leaves it at\+0\.159\+0\.159\. On 150 validation recordings, encoding each half of a window separately splits the target into a part that repeats within the window and a part that does not:\+0\.122\+0\.122\[0\.116,0\.129\]\[0\.116,0\.129\]of the gain lies on the first against\+0\.022\+0\.022\[0\.019,0\.025\]\[0\.019,0\.025\]on the second, andfe\-cosreaches94%94\\%of the teacher’s agreement with itself \(0\.2430\.243against0\.2600\.260, same covariates removed\)\.

### 4\.4Other sensors and another hospital

ECSMP\[[4](https://arxiv.org/html/2610.10662#bib.bib15)\]is an independent database with chest ECG and wrist PPG from different devices, in no pre\-training corpus, aligned per recording with a fitted clock model \(52 recordings, 78 h\)\. Fig\.[3](https://arxiv.org/html/2610.10662#S2.F3)\(b\) shows the same ladder:0\.010→0\.0720\.010\\rightarrow 0\.072on PaPaGei\-S and0\.028→0\.1130\.028\\rightarrow 0\.113on AnyPPG\. The gap between backbones is a domain\-shift effect: PaPaGei\-S reaches a within\-recording heart\-rate tracking correlation of only0\.320\.32on wrist PPG against0\.780\.78for AnyPPG, and the objective helps on both\.

On 60 recordings of MIMIC\-III, a second hospital that the bridge never saw, state agreement rises from0\.0490\.049to0\.1290\.129on PaPaGei\-S and from0\.0670\.067to0\.1480\.148on AnyPPG, and the heart\-rate error falls by19%19\\%and13%13\\%\(Table[2](https://arxiv.org/html/2610.10662#S4.T2)\)\. MIMIC\-III PPG, like VitalDB PPG, is part of both backbones’ pre\-training corpora\[[12](https://arxiv.org/html/2610.10662#bib.bib14),[11](https://arxiv.org/html/2610.10662#bib.bib2)\], so this test is external to the bridge and to the objective, not to the backbones\.

### 4\.5Limitations

White noise on the PPG lowers every objective, but the conditioned ones stay ahead: at0\.20\.2of the signal’s sd,fe\-coskeeps0\.0580\.058andfe\-cos\+\+fe\-nce0\.0930\.093against0\.0270\.027for the pooled loss \(same 60 recordings\), so the conditional\-logit form suits noisy input best\. The gain lies beyond heart rhythm and within what PPG can observe: mean RR is read equally well by every objective \(ρ=0\.69\\rho=0\.69–0\.700\.70\), and the T/R amplitude ratio, to which PPG has no path, by none \(ρ=0\.04\\rho=0\.04–0\.050\.05\)\. On MIMIC\-III every blood\-pressure read\-out stays above the zero\-prediction error of8\.268\.26mmHg, while state agreement and heart rate transfer\.

## 5Conclusion

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, so ECG\-guided PPG models should report within\-recording agreement\.

## 6Compliance with Ethical Standards

This study was conducted retrospectively using de\-identified human subject data made available in open access by VitalDB and the MIMIC\-III Waveform Database Matched Subset, both through PulseDB\[[13](https://arxiv.org/html/2610.10662#bib.bib12)\], and by ECSMP\[[4](https://arxiv.org/html/2610.10662#bib.bib15)\]\. Ethical approval was not required, as confirmed by the licences attached to the open\-access data\.

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