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Transferable Evidence Reconstruction for Longitudinal Glucose Representations

Tian Zhou, Bingqing Peng, Linxiao Yang, Wenwei Wang, Mengni Ye, Beverly Jin, Zuyi Zhu, Jinjie Gu, Liang Sun

arXiv:2609.28199v1cs.LG

TL;DR

Long CGM recordings contain routine measurements alongside rare events, sustained burden, and recurring temporal patterns that can carry predictive information. TER trains representations by testing whether a reader fitted on one unlabeled group recovers structured evidence in another, then organizes glucose histories with clock-aware memory. It improves the strongest prior overall scores and sets a new best metric on 12 of 14 tasks.

  • Problem

    CGM recordings contain many routine measurements, while rare events, sustained burden, and recurring temporal patterns can carry more downstream information.

    Source: §1 · p. 1

  • Method

    TER fits a fresh reader on one unlabeled recording group and differentiates through its recovery of the same evidence on another, while the CGM encoder organizes multi-day history with clock-aware memory.

    Source: §1 · p. 2

  • Results

    TER exceeds GlucoFM’s published overall PR-AUC/ROC-AUC/Macro-F1 scores by 5.51/4.43/2.80 points and sets a new best metric on 12/14 tasks.

    Source: §1 · p. 2

  • Takeaways & Limitations

    Matched controls support combining structured evidence, cross-group reader fitting, and learned multi-day organization in a shared CGM representation.

    Source: §6 · p. 11

Abstract

from arXiv · show

Long physiological recordings contain many routine measurements, while predictive information is often concentrated in rare events, sustained burden, and recurring temporal patterns. Masked autoencoding recovers measurements; contrastive learning aligns views. We study self-supervision that explicitly prioritizes structured signal evidence. We introduce transferable evidence reconstruction (TER), which constructs evidence from unlabeled recordings, fits a fresh low-capacity reader on one recording group, and requires that reader to recover the same evidence in another group without refitting. Differentiating through this cross-group test learns representations with transferable evidence-decoding rules; the evidence guides self-supervision but is not used as a downstream feature. For continuous glucose monitoring (CGM), an observation-aware daily encoder and clock-aware multi-day memory bind glucose level and change to recorded time while organizing up to seven days of history. On the 14-task leaderboard, TER improves the strongest prior overall PR-AUC/ROC-AUC/Macro-F1 scores by 5.51/4.43/2.80 percentage points and sets a new best metric on 12/14 tasks. These leaderboard gains are 2.0-2.9 times the respective gaps between the two strongest baselines. With public pretraining data, folds, and the linear probe matched, TER outperforms our GlucoFM reproduction by 6.09/5.52/2.72 points. Target-reader ablations, same-history controls, and cross-person readouts support the combination of structured evidence, cross-group reader fitting, and learned multi-day organization.

1 Introduction

The introduction motivates self-supervision that prioritizes structured signal evidence and transfers its decoding rule across recording groups. It presents a clock-aware, multi-day CGM representation and reports broad gains across the evaluated tasks.

1 Introduction

  • CGM recordings contain unevenly informative measurements: brief lows, sustained highs, and recurring responses may matter more than ordinary stretches, even as waveforms vary across days.The introduction frames the challenge as choosing both what supervises the representation and how evidence is organized over time.Source: §1 · p. 1
  • Structured evidence trails raw-hourly recovery by 1.45 PR-AUC points with a persistent reader but leads by 2.88 points with fresh cross-group fitting, a 4.33-point interaction.Controlled timing changes indicate that evidence recovery preserves recurring response properties rather than exact event times.Source: §1 · p. 2
  • The direct seven-day raw encoder trails released TER by 7.25 PR-AUC points, while same-history mean–max and BiLSTM controls trail their aligned reference by 8.36 and 9.12 points.These controls support learned organization of history beyond longer input alone.Source: §1 · p. 2
  • TER reaches 64.31/71.13/62.70 overall PR-AUC/ROC-AUC/Macro-F1, exceeds GlucoFM’s published scores by 5.51/4.43/2.80 points, and sets a new best metric on 12/14 tasks.With public pretraining data and downstream evaluation matched, TER also leads the GlucoFM reproduction by 6.09/5.52/2.72 points.Source: §1 · p. 2

2 Related work

Related work spans view matching, measurement reconstruction, signal-derived targets, and episodic learning. TER instead uses fixed evidence coordinates and updates an encoder from a reader’s error on disjoint recorded identities.

Self-supervised targets and episodic learning

  • Contrastive learning matches constructed views and masked autoencoding reconstructs omitted observations, while video SSL has predicted signal-derived statistics.PULSE cross-reconstructs augmented physiological windows to retain shared dynamics (Chen et al., 2026).Source: §2 · p. 3
  • Differentiable Ridge readers appear in labeled meta-learning and self-supervised dataset distillation, whereas CACTUs and STUNT vary pseudo-tasks across unlabeled episodes (Hsu et al., 2019; Nam et al., 2023).TER fixes evidence coordinates and varies which recording identities fit a temporary reader; unlike dataset distillation, it updates an encoder on real recordings.Source: §2 · p. 3

Longitudinal health and CGM representations

  • Irregular-series models represent observation indices, missingness, or continuous-time dynamics, while CGM models use masked tokens, autoregressive prediction, latent prediction, or state–event separation (Muhammad et al., 2026; Li et al., 2026).This encoder aligns observation-supported daily content and forms glucose level/change–clock relations before multi-day aggregation.Source: §2 · p. 3

3 Transferable evidence reconstruction

TER makes cross-group recovery of fixed, unlabeled signal evidence the self-supervised objective. It fits a temporary reader on one recording group and tests its decoding rule on another, without retaining that reader as a model component.

3 Transferable evidence reconstruction

  • TER asks whether a mapping estimated from one unlabeled recording group can decode the same evidence on another, and tests target choice separately from reader training.The method treats transferable decoding relations, rather than equality between recordings’ representations, as the objective.Source: §3 · p. 3

3.1 Use evidence as supervision, not as exported features

  • The encoder maps the full history to a representation while fixed evidence functions compute label-free targets, including daily state and excursion summaries, longitudinal statistics, and low/high-event burden and persistence.Support-weighted burden and spread, together with recurrence of high-glucose days 24 hours apart, describe typical burden, variability, and persistence.Source: §3.1 · p. 3

3.2 Transfer the decoding relation, not a permanent decoder

  • A jointly trained persistent encoder–decoder can have low reconstruction loss without testing whether a newly fitted reader transfers to a disjoint group.TER removes the persistent reader from model state and evaluates the fitting procedure on groups with disjoint recorded identities.Source: §3.2 · pp. 3–4
  • Each update fits a fresh differentiable linear reader using only the fit group, applies it unchanged to the transfer group, and updates the encoder through the fit and transfer loss.The transfer evidence is not used to fit or recalibrate the reader, which is discarded before the next update.Source: §3.2 · p. 5

4 A clock-aware longitudinal glucose encoder

The CGM encoder first preserves observation-supported daily content, then organizes multi-day history and binds glucose level and change to recorded clock time. Its clock-aware path adds to the longitudinal base representation.

4 A clock-aware longitudinal glucose encoder

  • The CGM encoder preserves supported daily content, then binds glucose level and change to recorded time before aggregating days.The design addresses incomplete observations and loss of temporal arrangement; tasks share the resulting representation.Source: §4 · p. 5, Figure 3 · p. 5

4.1 Preserve what each day actually observes

  • The daily encoder uses glucose, observation masks, and sampling information, and aligns only jointly observable content while retaining signed excursions visible in denser views.Its daily representations feed a multi-day context encoder that describes what occurred across available history.Source: §4.1 · p. 5

4.2 Bind content to clock position before combining days

  • Because moving identical high-glucose values from morning to evening changes physiological evidence, the encoder forms glucose level/change–clock relations before day aggregation.A mask prevents changes across missing readings, and multiple harmonics retain within-day arrangement at several scales.Source: §4.2 · pp. 5–6

4.3 One representation, complementary information

  • The clock-aware representation adds an update to the longitudinal base, preserving that base and retaining it when history has insufficient support; evidence is not appended to the output.Training proceeds from local daily self-supervision to TER training of the longitudinal base, then the clock-aware memory; the table caption describes four cohorts and an equally weighted 14-task overall average.Source: §4.3 · p. 6, Table 1 · p. 6, §4.4 · p. 7

4.4 Training and downstream use

  • With public-only pretraining, the compared pair shares 2,283 pretraining windows and downstream evaluation.Table 1 also distinguishes published results, released checkpoints, and GlucoFM reproductions.Source: §4.3 · p. 6

5 Experiments

Across four cohorts, TER is evaluated on 14 tasks, alongside postprandial transfer, an independent-trial evaluation, and controlled ablations. It leads prior methods overall, while ablations and mechanism analyses examine evidence-reader fitting and longitudinal organization.

5.1 Datasets and evaluation

  • The fixed evaluation covers 14 tasks across four cohorts, using identity-grouped cross-validation and logistic-regression probes for PR-AUC, ROC-AUC, and Macro-F1.The cohorts contribute 855/609/994/250 processed windows from 45/65/37/56 recorded identity groups or visits, respectively.Source: §5.1 · p. 7

5.2 Phenotype prediction across four cohorts

  • TER ranks first in 30/42 cells across 12/14 tasks, exceeding GlucoFM’s Overall scores by 5.51/4.43/2.80 points; matched public-only TER improves our GlucoFM reproduction by 6.09/5.52/2.72 points.On common evaluation rows, folds, and a linear probe, TER exceeds the strongest released CGM checkpoint on each Overall metric by 8.26/8.99/5.15 points.Source: §5.2 · pp. 7–8

5.3 Postprandial response prediction

  • With frozen preceding-24-hour representations and common heads, TER has the lowest trajectory, positive-iAUC, and peak-rise errors among five CGM models, but peak-time error is 3.81% higher than X-CGM-JEPA’s.The separate meal–CGM cohort contains 1,705 meals from 409 people.Source: §5.3 · p. 8, Figure 4 · p. 8

5.4 Transfer to an independent cohort

  • In the independent AIDE T1D trial, TER has lower error on all seven outcomes; time-below-70-mg/dL MAE falls by 39.1% versus BiLSTM and 47.4% versus mean–max.The evaluation uses 81 participants and 236 treatment periods, with AIDE excluded from representation training and model selection.Source: §5.4 · p. 8

5.5 Ablations of evidence learning and longitudinal organization

  • With persistent readers, raw-hourly recovery beats structured evidence by 1.45 PR-AUC points; with fresh cross-group fitting, structured evidence leads by 2.88 points, a 4.33-point interaction.Holding structured evidence fixed, TER’s reader-training procedure gains 6.34 points, and its learned representation exceeds directly exported evidence by 5.82 points.Source: Evidence supervision and reader transfer · p. 9, Table 2 · p. 9
  • With complete causal histories, mean–max trails the aligned TER reference by 8.36/5.95/3.96 points and BiLSTM by 9.12/8.27/5.41; direct seven-day raw encoding trails released TER by 7.25/6.26/3.73.Reassigning level/change rows to different clock positions also lowers the aligned reference by 1.40/1.00/.86 points.Source: Evidence supervision and reader transfer · p. 9, Table 2 · p. 9

5.6 Mechanism analysis: what information is retained?

  • On synthetic signals with shifted event timing but unchanged response shapes and values, prediction drift is 6.92/2.64/1.49 minutes for masked-point, persistent-evidence, and TER readouts, respectively.TER retains correlation above .935 with the response parameter, while raw recovery predicts exact event timing better.Source: §5.6 · p. 10, Figure 5 · p. 10
  • Cross-person TER reduces held-out reconstruction error over persistent evidence recovery by 8.68% for longitudinal/event evidence versus 1.93% for current-day evidence; reader-transfer controls also lower drift and label error on 13/14 and 10/14 tasks.Across 136 people, centered distributions are more repeatable within a person than clock-aligned traces relative to matched between-person distances.Source: §5.6 · pp. 10–11

6 Conclusion

TER organizes multi-day CGM histories and exceeds GlucoFM’s published leaderboard scores, while controlled comparisons support the combination of structured targets, cross-group reader fitting, and temporal organization.

6 Conclusion

  • TER exceeds GlucoFM’s published PR-AUC/ROC-AUC/Macro-F1 by 5.51/4.43/2.80 points and sets a new best metric on 12/14 tasks.Matched controls support combining structured targets, cross-group reader fitting, and temporal organization.Source: §6 · p. 11

A Transferable evidence reconstruction: evidence and reader contract

  • The evidence inventory expands three families into ten rows totaling 336 scalar signal summaries, not phenotype labels or independent physiological measurements.The bank uses fixed domain rules, so the absence of phenotype labels does not make it knowledge-free.Source: Table 3 · p. 14, §A.1 · p. 15

A.1 Current evidence: four families of sixteen

  • The current bank has four 16-coordinate families, with state descriptors based on observed values and recorded clock time rather than inferred sleep or fasting annotations.Challenge proposals require observed start and endpoint conditions; they are candidate excursions, not identified meals.Source: §A.1 · pp. 14–15

A.2 Longitudinal and event evidence

  • Longitudinal evidence aggregates supported days in chronological order, while event descriptors summarize low/high burden and persistence across days.Event adjacency requires exactly 1,440 minutes between days; missing days are not made adjacent by interpolation.Source: §A.2 · p. 15

A.3 Sampling and numerics

  • Episodes use disjoint identity halves, fit a fresh reader on one side, and backpropagate transfer loss through both representations and the temporary Ridge fit.No reader state persists, and the final memory checkpoint is the last training step rather than the best audit loss or phenotype score.Source: §A.3 · p. 16

A.4 Auxiliary evidence-recoverability diagnostics

  • Explained-variance diagnostics use differing targets and protocols, so their values are not mutually comparable or comparable to Table 15’s q95 NMSE.These diagnostics do not define downstream model ranking or select the final checkpoint.Source: §A.4 · p. 17
  • Adding the complete longitudinal extension improves the three aggregate metrics by 9.443/7.467/4.579 points and 37 of 42 task–metric cells.This staged comparison jointly includes learned multi-day context and clock-aware memory; it does not isolate the final memory stage.Source: §A.4 · p. 17

A.5 Evidence-target and full-pipeline reader-training controls

The controls test how evidence targets, reader fitting, and identity grouping affect transferable readouts. Further analyses qualify the results by staged assembly, observation support, history length, and the limits of evidence-based downstream guarantees.

A.5 Evidence-target and full-pipeline reader-training controls

  • Fresh cross-group fitting favors structured evidence over raw hourly by +2.883/+3.234/+2.230 points, with a +4.333/+4.131/+3.680-point target-by-reader interaction.With persistent decoding, raw hourly exceeds structured evidence by +1.450/.897/+1.450 points.Source: §A.5 · p. 18

A.6 Does the target–reader contrast survive final-model assembly?

  • With structured evidence fixed, the aligned fresh-reader reference beats the persistent control by +8.841/+6.964/+4.943 percentage points; this is an assembled component contrast, not end-to-end retraining.The interaction is +3.806/+3.543/+3.076 points in the aligned assembly, versus +4.333/+4.131/+3.680 under the earlier daily representation.Source: §A.6 · p. 19

A.7 Recorded identity and source boundaries

  • Shanghai visit-based pretraining keys can place two visits from one participant in opposite episode roles; historical episode overlap was not replayed.The saved audits also do not establish biological-person linkage across independent sources.Source: §A.7 · p. 20

A.8 Shanghai biological-person regrouping sensitivity

  • After biological-person regrouping, TER stays ahead on Shanghai hyperlipidemia and hypoglycemia across metrics, but insulin resistance remains weak; this does not support a universal person-level claim.The sensitivity changes downstream grouping while keeping representations fixed.Source: §A.8 · p. 21, Table 8 · p. 21

B.2 Observation-fiber property and proof

  • Exact whole-view agreement forces constancy within each observation fiber, but does not imply that approximate agreement destroys useful information or predict residual distributions.The result concerns the realized residual under exact equality, not what sparse observations can predict.Source: §B.2 · p. 22

B.3 Clock-aware memory: implementation

  • Clock-aware memory binds recorded phase and elapsed age across up to seven days, activating only with at least three supported days; shorter histories retain the base representation.Missing or padded readings cannot supply innovations.Source: §B.3 · p. 23

C Limited mathematical links to downstream readout

  • The downstream-readout existence link applies only when targets are approximated by the evidence bank; it guarantees neither finite-sample reader selection nor PR-AUC or F1.Low empirical evidence risk and grouping alone also guarantee neither invariance nor population transfer.Source: C Limited mathematical links to… · p. 24

D Broad phenotype utility: full benchmark results

Across the 14-task benchmark, TER records 30/42 clear best-in-table cells across 12 tasks. The comparisons combine local runs and source-study scores, so their evaluation provenance matters.

D Broad phenotype utility: full benchmark results

  • The all-ten ranks combine local evaluations with published GlucoFM and generic-model scores, which were not rerun on the same folds.The published values come from Li et al. (2026); exact processed rows and fold assignments cannot be verified against the local evaluation.Source: D Broad phenotype utility: full… · pp. 24–25, Table 10 · p. 26, Table 11 · p. 26
  • TER leads in five of seven phenotype families, but each Figure 6 spoke has its own range, so polygon areas are not comparable.The published GlucoFM row is descriptive rather than a matched-fold comparison.Source: Figure 6 · p. 24
  • Public-only TER and the GlucoFM reproduction share 2,283 pretraining windows and downstream folds, but not architecture or optimization budget.The official GlucoFM code and checkpoint were unavailable.Source: D Broad phenotype utility: full… · pp. 24–25
  • 30/42 task–metric cells are clear best-in-table results across 12 tasks under a conservative comparison against all ten baselines.The rule accounts for publication precision; reported values remain benchmark point estimates, not evidence of statistical significance.Source: D Broad phenotype utility: full… · p. 25

E Clock-aware memory: full-budget controls

The full-budget controls test whether clock assignment, memory components, and longitudinal organization preserve useful signal structure under matched settings. Their results distinguish downstream predictive utility from reconstruction diagnostics and simple information containment.

E Clock-aware memory: full-budget controls

  • With matched values and capacity, true clock assignment raises dedicated EV from .0859481515 to .1227826755, while event EV and episode losses remain similar.The control permutes complete active rows before projection, changing physical assignment and within-day numerical order; the plotted comparison uses matched 6,960-step results.Source: E Clock-aware memory: full-budget… · p. 27, Figure 7 · p. 30
  • Harmonics 1 and 4 have the largest average removal losses, while day age and recency contribute smaller but consistently positive aggregate effects.Removing the internal causal mask changes aggregate scores little; these are conditional utility effects, not independent task-win claims.Source: E Clock-aware memory: full-budget… · p. 28, Table 12 · p. 28, Table 14 · p. 29

F Information preservation and arrangement illustration

  • The exact-prefix extension lowers the fixed fitted L2 reader’s macro PR-AUC/ROC-AUC/Macro-F1 by 1.579/.564/.228 percentage points despite preserving the complete TER representation.Information containment alone does not preserve the trained reader’s performance, and the control does not isolate a covariance or optimization cause.Source: F Information preservation and… · p. 30, Figure 7 · p. 30

G Observation-aware daily encoding: paired core control

  • Signed rather than unsigned targets change phenotype means by +.875/.654/.346 points and reduce dense-only q95 NMSE by 17.94% in the historical daily-core test.This paired core experiment isolates signed dense-only targets; it does not establish final-system ablation gains or additive attribution across stages.Source: G Observation-aware daily encoding:… · p. 31, Table 15 · p. 31
  • The signed-target comparison improves 26 task–metric cells and decreases 16, while common-view cosine distances are numerical zero in both arms.The q95 statistic identifies the tail-profile target, not an error quantile.Source: G Observation-aware daily encoding:… · p. 31

H Paired downstream improvement counts

I Pretraining corpus and downstream dataset inventory

The section documents how pretraining data and downstream cohorts were assembled and evaluated, then reports separate longitudinal and held-out hypoglycemia transfer tests in older adults with type 1 diabetes. The latter test supports transfer to unseen participants and a later period, with important cohort and comparator boundaries.

I Pretraining corpus and downstream dataset inventory

  • The public pretraining component contains 2,283 windows, while private rows are separately selected across stages and stage allocations are neither additive nor nested.The aggregate manifests do not establish per-source biological-participant counts, and raw or person-level private data are not distributed.Source: Table 17 · p. 32, I Pretraining corpus and downstream… · p. 32
  • History spans at most seven days and never crosses stored identity, cohort, split, cadence, or source; the audited build excludes identified downstream participants from Shanghai and Stanford.Because cross-source biological linkage is incomplete and those cohorts occur in both source collections and the benchmark, evaluation is not universally cohort-unseen.Source: I Pretraining corpus and downstream… · p. 32
  • Downstream scores use ten repeated five-fold recorded-identity splits, fold-fitted scaling and logistic regression, and equal weighting across 14 tasks.The processed records actually scored are recovered from fixed fold reports rather than raw-study enrollment.Source: I Pretraining corpus and downstream… · p. 33, Table 18 · p. 33

J Independent AIDE temporal and cohort validation

  • The AIDE seven-outcome comparison uses 81 participants and 236 treatment periods, matching 4–7 daily inputs and treatment covariates across arms.A fold-local StandardScaler and Ridge reader predicts future outcomes from Weeks 7–12; two of 238 eligible-history periods lack required future coverage.Source: J Independent AIDE temporal and cohort… · p. 34, Table 19 · p. 34
  • The held-out hypoglycemia test assigns 48/18/16 participants to discovery, validation, and private test before outcomes are read; all periods from each participant remain in one split.The study is absent from TER pretraining and public14 method selection, and the frozen input is the earliest eligible seven-calendar-day span in Weeks 5–6.Source: J Independent AIDE temporal and cohort… · p. 34, Table 20 · p. 34
  • On the private test, TER-minus-daily-code MAE is −.865 (95% interval [−1.381, −.329]), while TER-minus-physical-statistics MAE is +.006 (interval [−.179, +.180]).The latter interval includes zero and establishes neither a difference nor statistical equivalence; the result supports transfer to unseen participants and a later period, not treatment-effect estimation or superiority to clinical features.Source: Table 20 · p. 34, J Independent AIDE temporal and cohort… · p. 35

K Postprandial response transfer

The postprandial analyses test transfer from frozen CGM representations to meal-response outcomes, both alone and with shared recent-CGM and meal context. A separate reader-training audit compares TER with a matched persistent-reader arm.

K Postprandial response transfer

  • The postprandial benchmark retains 1,705 meals from 409 people after requiring a strictly causal 24-hour history and physical glucose measurements at all 24 target times.With one history day, the multi-day context and clock memory are inactive, so this benchmark evaluates the shared daily encoder rather than those longitudinal stages.Source: K Postprandial response transfer · p. 36
  • Representation-only TER is best on trajectory, positive iAUC, and peak rise, reducing error by 4.70%, 4.71%, and 4.02% versus the strongest non-TER mean.X-CGM-JEPA is best on peak time, where TER is 3.81% higher; TER’s trajectory difference from X-CGM-JEPA is below zero in paired subject bootstraps, while favorable iAUC and peak-rise intervals cross zero.Source: K Postprandial response transfer · p. 36, Table 21 · p. 36
  • With shared recent-CGM and meal context, X-CGM-JEPA is best on all four endpoints, while TER reduces GlucoFM errors on trajectory, positive iAUC, and peak rise by 6.71%, 12.34%, and 9.04%.The complete-predictor cohort may include identities contributing unlabeled pretraining CGM; a stricter identity-disjoint check leaves 130 meals from 39 people, where all four TER–GlucoFM mean differences favor TER but intervals cross zero.Source: K Postprandial response transfer · pp. 36–37, Table 21 · p. 36

L Reader-training audits

  • TER exceeds the matched persistent-reader arm in 34 of 42 task–metric cells and in at least two metrics for 12 of 14 tasks.The two task-level reversals are Shanghai insulin resistance and Shanghai hypoglycemia; the count is descriptive, not a second SOTA definition.Source: L Reader-training audits · p. 38
  • The matched controls support combining structured evidence with TER’s reader-training procedure, including differentiation through the temporary fit and recorded-identity separation.The reported interpretation is that the learned representation improves on direct evidence features and the tested persistent-head baseline.Source: L Reader-training audits · p. 38

M Label efficiency and observed history

The section tests label efficiency, longer-history use, and alternative longitudinal aggregators, then situates signal evidence within task definitions and prior learning approaches. The controlled comparisons characterize this TER procedure rather than establishing a universal ranking of self-supervised methods.

M Label efficiency and observed history

  • Across matched budgets, TER’s aggregate curve rises at every budget for all three metrics and exceeds the GlucoFM reproduction by +3.37/+2.66/+2.18 points on average.From one to five subjects per class, PR-AUC/ROC-AUC/Macro-F1 changes are +4.46/+5.68/+6.70 points; from 1% to 50% observations they are +3.74/+3.70/+3.44.Source: M Label efficiency and observed history · pp. 38–39, Table 22 · p. 38
  • Longer history improves PR-AUC in 11/13 units and ROC-AUC/Macro-F1 in 10/13, with mean gains of +5.94/+7.17/+7.93 points.Because the native-history protocol changes eligible start positions with history length, it measures the practical longer-history setting rather than a fixed-endpoint causal effect.Source: M Label efficiency and observed history · p. 39, Table 23 · p. 39
  • Against the same-history mean–max control, aligned TER gains 8.361/5.950/3.959 PR-AUC/ROC-AUC/Macro-F1 points and improves 37/42 paired cells.Corrected repeated-fold intervals remain significant after Holm correction; simple pooling extracts only a small portion of the longer record’s predictive signal.Source: M Label efficiency and observed history · pp. 39–40, Table 24 · p. 40
  • The aligned TER reference exceeds the trained BiLSTM by 9.118/8.270/5.414 PR-AUC/ROC-AUC/Macro-F1 points and improves 39/42 cells.All three corrected intervals remain significant after Holm correction; the BiLSTM’s label-free validation reconstruction loss fell from .2617 to .1441 by its preregistered final update.Source: M Label efficiency and observed history · p. 40
  • The released TER model exceeds the direct seven-day encoder by 7.248/6.255/3.735 PR-AUC/ROC-AUC/Macro-F1 points and raises task coverage from 5/14 to 12/14.The direct encoder improves over truncated current-day and mean–max controls, but does not substitute for evidence-trained multi-day organization.Source: M Label efficiency and observed history · pp. 39–40
  • The corrected repeated-CV direct-evidence differences remain significant for PR-AUC and ROC-AUC under the original conservative correction; the persistent-reader comparison is treated as an effect-size control.The repeated-CV test uses a two-sided Nadeau–Bengio corrected paired t-test with test/train ratio .25.Source: M Label efficiency and observed history · pp. 40–41, Table 25 · p. 40

N Task definitions and their relation to signal evidence

  • The task-definition audit groups 14 endpoints by their definitional relation to CGM, from CGM-derived patterns/events to more indirect anthropometric and lipid correlates.These groups are not an empirical ranking of task difficulty or measured correlation, and evidence examples are qualitative motivation rather than task-specific targets.Source: N Task definitions and their relation… · p. 41, Table 26 · p. 41

O Learning lineage and limits of interpretation

  • The controlled comparisons characterize the tested TER procedure, not a universal SSL ranking; broad contrastive and masked-autoencoding families are not exhaustively compared.Other signals may admit evidence and grouping rules, but non-CGM portability has not been demonstrated; retrospective prediction does not validate real-time diagnosis or treatment benefit.Source: O Learning lineage and limits of… · p. 43

P Multistage training contract

The section specifies a staged CGM representation pipeline and tests what its evidence-recovery objectives retain. Its analyses compare history lengths, real-recording repeatability, controlled timing changes, and readouts across independently observed days.

P Multistage training contract

  • Stage A fixes label-free daily encoders; Stage B trains a context encoder on histories of up to seven days, combining earlier-day clock-aware cell relations with daily and history summaries.The pipeline applies masks before attention and pooling and keeps histories within recorded identity, cohort, split, cadence, and source.Source: P Multistage training contract · pp. 44–45
  • Stage B differentiates through fresh Ridge readers fitted on one recording group and transferred without refitting, with a separate auxiliary episode recovering the observed last-day state.Stage C freezes the context encoder and inherited map while training clock-aware memory; final assembly retains those components and uses the prescribed downstream StandardScaler/logistic-regression protocol.Source: P Multistage training contract · pp. 44–45

Q Time interfaces in CGM encoders

  • The time-interface comparison concerns which objects encoders explicitly pass into aggregation, not whether other models can learn clock interactions.The table describes time of day as recorded time; the accompanying note says released-checkpoint use of calendar marks is unverified.Source: Q Time interfaces in CGM encoders · pp. 45–46, Table 27 · p. 46

R Performance across one to seven days of history

  • Across supported history lengths, PR-AUC and ROC-AUC peak at four days, while Macro-F1 is highest at seven.Longer K changes eligible start positions, while fixed-endpoint mean–max and BiLSTM controls separately test organization of the same available histories.Source: R Performance across one to seven days… · p. 47, Table 28 · p. 47

S.1 Real, nonoverlapping date blocks

  • Observed-only date blocks from 136 participants show repeatability measured relative to cohort-, source-, cadence-, and coverage-matched controls.The comparison uses separate between-person denominators for time-aligned and sorted-value distances, so a smaller ratio—not merely a smaller absolute sorted distance—indicates greater repeatability.Source: §S.1 · p. 47, Table 29 · p. 48

S.2 Matched recovery objectives on controlled signals

  • On controlled signals, timing shifts preserve the multiset of values and event properties, allowing evidence recovery to be tested for response information separately from exact event timing.The generated response target is a shape timescale, not a clinical recovery half-life.Source: §S.2 · p. 48
  • TER improves on persistent evidence recovery in all nine seed–condition pairs, while raw recovery predicts exact timing better in all nine.The response-error gap between raw recovery and TER grows by .3527/.3281/.4035 across seeds from zero- to 60-minute variation; direct evidence remains a stronger response-parameter reference in this constructed setting.Source: §S.2 · p. 48, Table 30 · p. 49

S.3 Fixed-model intervention shown in the main figure

  • After the intervention, TER’s response-prediction correlations with ground truth are .939/.939/.936; exact timing changes, so low timing-prediction drift would not itself be desirable.The encoder and readout are fixed before and after timing changes.Source: §S.3 · p. 49, Table 31 · p. 49

S.4 Readout on independently observed real days

The real-day readouts compare structured and raw targets alongside persistent and fresh readers, then assess performance and prediction changes on independently observed days. Additional figures describe phenotype-family PR-AUC differences and compare TER’s overall gains with released-checkpoint spread.

S.4 Readout on independently observed real days

  • With structured targets fixed, fresh versus persistent training improves drift on 13/14 and 12/14 tasks, B-label error on 14/14 and 12/14, and both on 13/14 and 10/14.Descriptive bootstrap intervals exclude zero for drift in 10/14 and 9/14 tasks and for B-label error in 5/14 and 6/14; they are not multiplicity-adjusted.Source: §S.4 · p. 50
  • Changing raw targets to evidence with fresh training improves B-label error on 9/14 and 7/14 tasks, but improves error and drift together on only 3/14 in either training set.Natural date changes can include genuine physiological changes, unlike the controlled timing intervention; normalized-change-profile readouts favor structured/fresh in mean across all eight cohort–set comparisons, but only the two Shanghai intervals exclude zero.Source: §S.4 · p. 50
  • The original full-history factorial favors structured/fresh over raw/fresh by 2.883/3.234/2.230 PR-AUC/ROC-AUC/Macro-F1 points, while the later daily-input comparison gives −.851/−.861/−1.495 points.These are distinct training trajectories, not repeated estimates of the released checkpoint.Source: §S.4 · p. 50

T Additional descriptive figures

  • Figure 8 compares TER’s PR-AUC with the highest family mean among four named baselines; Figure 9 contrasts released-checkpoint spread with TER’s gain over the strongest Overall metric.Figure 8’s published and local rows are not paired; Figure 9 matches evaluation rows, folds, and probe, but pretraining corpora differ.Source: Figure 8 · p. 51, Figure 9 · p. 51
  • MAE recovers masked measurements, whereas TER reconstructs structured evidence with a reader fitted on other recordings.Source: T Additional descriptive figures · p. 51

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