The Oscillome›Programs›F · Learned representations
Program F · Learned representations · page 2 of 3
Five neural-mass models fitted to every window of the archive, then representations learned from the raw waveform with nobody saying what to look for — judged on the same terms; and the equations read as dynamical systems, to ask where the alpha system changes character and whether the recordings go there.
Supported associationA frozen EEG foundation model separates the session labels in 39 of 40 held-out sessions, but setting, posture and eye behavior remain entangled with the label: recognition, not yet prediction.
Program F in three pages · Neural-mass models · Learned representations · Brain states and phase diagrams
21 — Learned representations Retrospective · exploratory
Analysis basis 42 recordings, 40 session groups, 1,630 two-minute windows (54.3 h); all 58 standing representations scored on the 15 post-freeze recordings (615 windows) for Results 22 and 23 · dataset release 2026.09.16 · left out: windows under 50 % usable; psilocybin (one session) from the class probes · last recomputed in analysis release 4.24 · current
Every measure above was chosen by a person. These were not. The same 1,630 two-minute windows of raw EEG were given to networks of six kinds:
Every representation is read by one calibrated, tuned read-out, a gradient-boosted tree ensemble, with whole sessions held out, on the session label and on three open-ended targets no network was trained on. The first result is about the archive, not the networks: the time of day alone, with no EEG, places 27 of 40 sessions (log loss 0.57), and the time of day with the eye-state estimate 31 (0.50).
In-house transformer. The factorized spatial-temporal network of earlier versions (5.4 million weights, 256 dimensions, VICReg22: two augmented views of one window must agree), trained from scratch on all 42 recordings. A second training configuration changes one thing: the two views are two different windows of the same recording, at most ten minutes apart.
It learns without labels and is the network earlier versions of this page reported. It appears here as trained, with neighboring windows as the two views, and trained with the fitted neural-mass model constants of §20 as inputs; it is joined by a fourth in-house network, a replica of REVE.
A foundation model is a network pretrained on a large body of other people's EEG, released with its weights. Each is used here as a fixed feature extractor: every two-minute window is resampled to the network's rate, cut into four-second segments, and its embedding is the mean of the segment embeddings. Not one weight is changed. All five are given the same fourteen channels by name and the same read-out afterwards.
| Model | Published | Weights | Pretraining | How it reads EEG |
|---|---|---|---|---|
| LaBraM | ICLR 2024 | 5.8 M | about 2,500 hours from 20 public datasets | Each channel is cut into one-second patches; a learned tokenizer turns each patch into a code, and a transformer is trained to predict the codes of masked patches. Channels are named by 10–20 position. |
| CBraMod | ICLR 2025 | 5.0 M | 9,000 hours (Temple University corpus) | One-second patches embedded from their spectrum; a criss-cross transformer alternates attention across channels with attention along time; masked patches are reconstructed. |
| BIOT | NeurIPS 2023 | 3.2 M | several clinical and sleep corpora, five-second segments | Every channel becomes a sequence of spectral tokens, so any montage can be fed in; contrastive pretraining between views of one segment. |
| EEGPT | NeurIPS 2024 | 25.3 M | about 250 hours, five datasets, 62 channels | Four-second segments, spatial and temporal attention; pretrained by masked reconstruction together with alignment to a slowly updated copy of itself. |
| REVE | 2025 (IMT Atlantique) | 69.2 M | 60,000 hours, 25,000 people, 92 datasets | One token per channel per second, with a four-dimensional positional code built from each electrode's coordinates and time, so any layout works; masked patches reconstructed in space–time blocks. The largest EEG network with released weights. |
Low-rank adapters23 (rank 8, α = 16, on every attention and feed-forward layer of the transformer blocks; 1.4 M trainable weights of 70.6 M for REVE) are trained by masked reconstruction: half of the fourteen-electrode × four-second patch grid of each segment is hidden, two whole electrodes among them, and a small decoder must reconstruct every hidden patch's waveform and log-amplitude spectrum. The optimizer (AdamW, one-cycle schedule) changes only the adapter weights and the decoder; the pretrained weights stay frozen underneath. For REVE, LaBraM and CBraMod each hidden patch is reconstructed from the network's own token at that electrode and moment (the objective these networks were pretrained with); EEGPT and BIOT expose only a pooled vector, so their decoder reads that. No label enters. Every fine-tuned network passes a label-free health check before it is evaluated (Result 5): its effective dimensionality, and the shares of its variance explained by recording identity and by eye state, against the frozen network. The learning rate is the strongest hyperparameter setting that passes: 1e-3 for 30 epochs for REVE and LaBraM, 1e-4 for 15 epochs for CBraMod, which collapses at the higher rate; the other setting is scored as a sensitivity check.
As inputs, during fine-tuning. Each electrode's 41 fitted constants are encoded by a small shared network and added to that electrode's tokens (or to the pooled embedding, for EEGPT and BIOT), with electrodes dropped and the constants jittered during training so the network cannot copy them, and the same reconstruction objective; the evaluation embedding then contains them. Line 4 does this from the pretrained weights; line 5 starts from the adapters of line 3, so it is fine-tuned on the EEG and then with the constants. At the read-out, not by fine-tuning. The 574 constants are concatenated with the embedding and the same read-out is fitted on both, which trains no network and is the only way a frozen network can be joined with them. Frozen beside fine-tuned. The frozen and fine-tuned embeddings are concatenated, so fine-tuning can only add to what the frozen network already gives the read-out; this is the comparison that makes "fine-tuning cannot hurt" true by construction. The constants are estimated from the EEG itself, so none of these routes uses a label.
A replica of REVE. REVE's released code was read and its design rebuilt at a size this archive can fill (9 million weights instead of 69): one token per channel per one-second patch, a four-dimensional positional code from the electrode's coordinates and time, RMSNorm and GEGLU blocks, and masked-patch reconstruction in space-time blocks with a global-token loss. It was trained from scratch on these recordings only, once as is and once with the fitted constants as inputs to its tokens, and its result with the constants is replicated over three training seeds.
Four references go through the identical read-out. Time of day (no EEG at all: the hour the session began), because psychedelic-labeled sessions are evenings and workdays are daytime. The clock with the eye-state estimate of §16, because eye closure is the largest effect in the archive. Sixteen hand-built spectral features of each window (band shares, alpha frequency and power, the 1/f exponent, the 2α harmonic, asymmetry, frontal slow share, amplitude), which is what a person would compute. And the 41 × 14 fitted neural-mass model constants of §20 on their own.
The sixteen were chosen because they are what a conventional EEG report computes by hand: the band composition, the 1/f background, the alpha peak and its harmonic, the front–back and left–right balance of alpha, a blink proxy and the amplitude. That makes them the plain baseline every learned representation has to beat, keeps the space small enough for 1,630 windows, and gives the attribution of Result 11 dimensions with names.
| Hand-built feature | What it is | Computed from |
|---|---|---|
| rel_delta, rel_theta, rel_alpha, rel_beta, rel_gamma | share of the 1–45 Hz power in the band (1–4, 4–8, 8–13, 13–30, 30–45 Hz) | each electrode's share, averaged over the fourteen |
| aperiodic_exponent, aperiodic_offset | slope and intercept of the 1/f line fitted to the log spectrum over 2–40 Hz, leaving out 6–14 and 17–24 Hz | the mean posterior spectrum (P7, O1, O2, P8) |
| alpha_freq_hz | frequency of the largest peak above the 1/f line between 7 and 13 Hz | the mean posterior spectrum |
| alpha_power_db | height of that peak above the 1/f line, in dB | the mean posterior spectrum |
| harmonic_power_db | height above the 1/f line within 1 Hz of twice the alpha frequency | the mean posterior spectrum |
| alpha_post_front_db | posterior alpha power over frontal alpha power, in dB | posterior (P7, O1, O2, P8) against frontal (AF3, F3, F4, AF4) means |
| alpha_asym_rl | log of right-hemisphere over left-hemisphere alpha power | the seven right against the seven left electrodes |
| theta_beta_ratio | log of the theta share over the beta share | the head-averaged shares above |
| frontal_slow_share | share of 1–3 Hz in the frontal spectrum, a proxy for blinks and saccades | the mean frontal spectrum |
| alpha_mean_abs_corr | mean absolute zero-lag correlation of the 8–13 Hz-filtered signals | all 91 electrode pairs |
| log_rms | log of the broadband amplitude | every electrode and segment |
Each feature is one number per two-minute window, from Welch spectra on 4-s Hann segments (half overlap, only segments free of artifact, at least six of them); none is a per-electrode value. The same names label the bars of the attribution in Result 11.
The unit is the session, never the window. Each representation is read by CatBoost71, a gradient-boosted tree ensemble, with five folds by session group: inside each training fold its hyperparameters are chosen by Bayesian optimization with Hyperband early stopping72 (30 trials), its scores are calibrated to probabilities by Platt scaling73 fitted on the training sessions' inner out-of-fold scores, and the held-out session's windows are combined by their mean log-odds. Decisions use the calibrated probability at 0.5; no threshold is tuned. The scores are log loss (0.66 is a read-out that knows only the base rate), Brier score and AUC; representations are compared pairwise on their per-session log losses with a 10,000-draw session bootstrap. A permutation control (session labels shuffled, the whole pipeline re-run) scores at the base rate. The same read-out, as a regressor, predicts three open-ended targets chosen because no network was trained on them and none is a spectral quantity the networks already encode: alpha phase coupling between electrode pairs (weighted phase-lag index74) with alpha strength regressed out, the long-range memory of the alpha envelope (detrended fluctuation exponent over 2–30 s75), and signal complexity (Lempel–Ziv14 of the fourteen-electrode binary matrix, surrogate-normalized). Results 7 to 15 characterize every standing representation without the session label (what each space contains, how its geometry sits, what it listens to, how it degrades) and, where a score is needed, use the same read-out with fixed hyperparameters.
Read across a row to see what each step does for one foundation model; read down a column to compare the foundation models at the same step. Each cell is held-out sessions on the correct side of the label, of 40, then the log loss (lower is better; 0.66 is a read-out that knows only the base rate, 0.57 the time of day). The in-house models are the second table.
Line 2, frozen. LaBraM is the best single representation in the study: 39 of 40 (log loss 0.15), AUC 1.00. It misses only DMT experiment 001, the recording first archived as a baseline and reclassified in September, which every representation misses. REVE follows at 37 of 40 (log loss 0.24), EEGPT at 37 of 40 (log loss 0.26), CBraMod and BIOT at 36 and 36. Under the linear read-out of earlier releases REVE led LaBraM; the order of the two best frozen networks depends on the read-out, and both are within a session of each other.
Line 3, LoRA fine-tuned on the EEG. Fine-tuning without labels adds nothing beyond the frozen network: REVE 0.24 → 0.23 (paired difference -0.009 [-0.046, +0.024], p = 0.628), EEGPT 0.26 → 0.28, BIOT 0.28 → 0.31. Where the fine-tuning narrows the representation it costs: LaBraM 0.15 → 0.22 (+0.067 [+0.015, +0.128], p = 0.022), CBraMod 0.28 → 0.34. Kept beside the frozen embedding (the "frozen beside fine-tuned" column) every network ties its frozen version (LaBraM 0.16, p = 0.70; REVE 0.23, p = 0.26), which says the same thing from the other side: the fine-tuned embeddings carry no label information the frozen ones lack.
Lines 4 and 5, with the fitted constants. As inputs during fine-tuning the constants help the networks that knew least: CBraMod 0.28 → 0.23 (-0.052 [-0.102, -0.006], p = 0.034) and REVE 0.24 → 0.19 (-0.050 [-0.104, -0.004], p = 0.059), and leave LaBraM, EEGPT and BIOT where they were. Concatenated at the read-out they do the same job with no fine-tuning at all: BIOT 0.28 → 0.23, CBraMod → 0.23, REVE → 0.22, LaBraM 0.15 → 0.16. The fitted constants are complementary information where a network is weak and redundant where it already encodes what a resonator measures.
Line 1, in-house. The REVE replica trained on these recordings alone reaches 36 of 40 (log loss 0.31); trained with the fitted constants as inputs to its tokens 38 of 40 (log loss 0.24) (-0.067 [-0.122, -0.019], p = 0.013; the same gain in three training seeds, pooled p = 0.009), and with the constants concatenated at the read-out 0.27. The original in-house transformer places 31 of 40 (log loss 0.43), between the clock's 27 and the hand-built features' 35; the neighbor-positive version 31 (0.49), 33 trained with the constants. Nine million weights, 54 hours of one person's EEG and a resonator's fitted constants get within a session or two of a network pretrained on thousands of hours, on an archive the replica had seen and the pretrained networks had not.
AUC ranks sessions and ignores how confident or how wrong a read-out is. Log loss and Brier score after calibration reward a read-out for being confidently right and punish it for being confidently wrong; the decisions are the calibrated probability against 0.5, so "sessions right" follows from the same numbers rather than from a tuned threshold.
Every representation of the standing set, sorted by log loss; the alternative learning-rate configurations and the pooled-decoder REVE side comparison are in the sensitivity table below. Data (CSV) Per-session probabilities (CSV)
What the top of the table has in common. The best representations get every ordinary session right and miss one psychedelic-labeled session, DMT experiment 001. Below them the errors are ordinary sessions with much eyes-closed time (Resting baseline 003 part 1, the 14 September home session) and the 19 August home session whose context was originally uncertain: the eye-state overlap of §16, seen through the read-out.
The baselines. Time of day places 27 of 40 under this read-out (AUC 0.78); with the eye-state estimate 31. Sixteen hand-built features reach 35 (0.26); the 41 × 14 fitted constants alone 38 (0.21, AUC 0.99), the second tier of the whole table on their own.
The size of the evidence, plainly. 12 sessions more than a clock, out of forty, and about half the clock's log loss. Only four ordinary sessions were recorded in the evening, so "beyond time of day" rests on them.
Sensitivity. The other learning-rate configuration for LaBraM and CBraMod, and REVE fine-tuned with the pooled-decoder objective, are scored the same way; none changes the reading above.
The session label is entangled with the evening and the eyes. These three window-level quantities are not: alpha phase coupling between electrode pairs with alpha strength regressed out, the long-range memory of the alpha envelope, and signal complexity. Each is computed from the raw EEG of each window and predicted from every representation by the same read-out as a regressor, R² on windows of held-out sessions (1,630 windows; 858 with enough clean signal for the memory exponent): one minus the residual variance over the total variance of the held-out windows, so it is negative when the read-out predicts worse than the archive mean, which happens for phase coupling in a few spaces.
Complexity is read almost perfectly from REVE and EEGPT, frozen or fine-tuned (REVE 0.90 frozen, 0.92 fine-tuned; EEGPT 0.88), less well from LaBraM (0.76) and least from BIOT (0.55); the fitted constants alone give 0.53. The constants as inputs lower complexity for the small-token networks (LaBraM 0.79 → 0.70; CBraMod 0.73 → 0.45): the constants code displaces the fine waveform detail complexity depends on.
Long-range memory is hard for everything (R² 0.20–0.23 for the frozen networks). The fitted constants alone reach 0.29, above every frozen network; the best representation is EEGPT, frozen | constants at the read-out at 0.32. Adding the constants as inputs improves every foundation model on this target (LaBraM 0.22 → 0.27, CBraMod 0.20 → 0.26, BIOT 0.24 → 0.26).
Phase coupling with alpha strength removed is where the learned representations are weakest: the fitted constants alone reach 0.30, frozen EEGPT 0.25, and frozen LaBraM, CBraMod and BIOT sit near zero (-0.00, -0.01, 0.10); the best representation is In-house transformer, neighbor positives | constants at the read-out at 0.30. Fine-tuning on the EEG alone does not change that; the constants as inputs lift LaBraM and CBraMod to 0.18 and 0.20.
Why it matters. On the label the frozen networks win and the fitted constants are redundant for the strong ones; on the two targets that look beyond the spectrum the fitted constants carry the information, alone or joined with an embedding. Forty-one interpretable numbers per electrode carry information about the envelope's memory and about coupling between electrodes that 60,000 hours of pretraining did not put into a pooled embedding. That is the case for keeping the mechanistic description beside the learned ones rather than as a stepping stone to them.
Label-free fine-tuning optimizes reconstruction, not the read-out's question, so nothing in it preserves what the frozen network's read-out used. Three quantities, computed on the fine-tuned embedding over all 1,630 windows and compared with the frozen network, say what changed: the effective dimensionality (entropy of the variance spectrum), the share of variance explained by which recording a window came from, and the share explained by eye state. A rise in the recording share of more than 0.05 is flagged: a network that has learned to recognize sessions cannot help on sessions held out. The reconstruction loss (L1 on hidden patches; a waveform loss near 0.79 is what predicting zero gives) says how much the objective was learned.
Why the earlier fine-tuning was withdrawn. Releases 4.5 to 4.23 fine-tuned the networks by segment agreement (VICReg on two segments of one window). On one person's recordings the easiest way to make two segments agree is to recognize the recording, and that is what happened: REVE's recording-identity share 0.45 → 0.82, effective dimensions 28 → 13, and every downstream score fell. The health check was built to catch this, and the objective was replaced by masked reconstruction. A pooled-decoder version of it collapsed LaBraM and CBraMod to a few dimensions; reconstructing each hidden patch from the network's own token, above, keeps REVE intact (20 of 28 dimensions, recording share 0.49 against 0.45) and LaBraM acceptable (8 of 18, recording share unchanged, eye-state share up).
CBraMod is the network no objective fine-tunes well. At learning rate 1e-3 it collapses to 3 of 39 dimensions with half its variance on recording identity; at 1e-4 it keeps 23 but its recording share still rises by 0.07, and its waveform loss never leaves the trivial level: the objective does not take hold, the representation drifts anyway. Its fine-tuned versions are reported as flagged, and Result 1 shows what the collapse costs.
Rank does not matter. The adapters' rank was set at 8 by convention, so REVE's fine-tuning was repeated at 4, 16 and 32 with α = 2r. Eight times the adapter capacity lowers the reconstruction loss by two per cent and moves none of the health measures beyond noise.
Every member's held-out probability comes from a read-out that never saw the session, and the member sets were fixed in advance with equal weights, so nothing is selected on held-out sessions. Two aggregations: the mean probability and the mean log-odds.
Result. No ensemble beats the best single representation: the five frozen networks combined reach 38 of 40 at log loss 0.21 against frozen LaBraM's 0.15, and adding the fitted constants or every standing representation does not change that. The foundation models are largely interchangeable on this label, and the networks trained here add nothing to them. An earlier release reported a greedy ensemble that ranked all fifteen labeled sessions above all twenty-five ordinary ones; it selected its members on the same sessions it was scored on and is not part of the standing results. Data (CSV)
On the three open-ended targets. The same sets, with each member's held-out prediction of the target in place of its probability: on complexity the best ensemble is the greedy of every standing label-free EEG representation at R² 0.925, above the best single representation (REVE fine-tuned, 0.916) and +0.009 over its own best member (REVE fine-tuned), an interval that excludes zero; on the memory of the alpha envelope the best ensemble is the greedy of trained here only (in-house networks, fitted constants, hand-built features) at R² 0.297, below the best single representation (EEGPT frozen | constants read-out, 0.320) and +0.004 over its own best member (Constants 41 × 14), within the bootstrap interval; on alpha phase coupling with alpha strength removed the best ensemble is the greedy of every standing label-free EEG representation at R² 0.336, above the best single representation (In-house (nbr) | constants read-out, 0.301) and +0.037 over its own best member (Constants 41 × 14), an interval that excludes zero. Over the 36 set-by-target-by-aggregation cells the ensemble beats its best member with an interval that excludes zero in 7 and is worse in 5. Equal weights are the wrong choice on the targets: the mean is worse than its best member in 4 of 12 cells, because one member is usually far ahead of the rest and averaging dilutes it; the stack and the greedy selection recover it and, on complexity and on phase coupling, go a little past it (best aggregation per set and target: greedy 10, stack 1, mean 1). So the ensembles do more on the targets than on the label, but the gains are small next to the choice of the single best representation. Data (CSV)
These networks were trained without labels, so their quality should not rest on one. The scorecard uses measures from the self-supervised-learning literature: how many dimensions carry variance (participation ratio) and how fast the variance spectrum decays (α; near zero is noise spread thin, above about one is structure); uniformity of the points on the sphere and alignment, here the distance between adjacent two-minute windows relative to two random windows (near 1: the network sees no continuity in time); autocorrelation; how much variance belongs to the recording; whether a window's neighbors are its neighbors in the other representations too; and how far an embedding moves when nothing physiological has changed (the amplitude doubled; a little noise added), in units of the distance between two windows of the same recording.
The scorecard shows the fault in the original in-house transformer without a single label. Its variance spectrum is flat (α = 0.19: variance spread thin over a hundred directions), adjacent windows are 0.92 times as far apart as two random windows (it sees no continuity in time), and it shares 4% of a window's neighbors with the other representations. The same network trained with neighboring windows as positives has α = 2.95 and an adjacent-to-random ratio of 0.05. The frozen foundation models sit between (α 0.81–2.40, ratio 0.22–0.66, 10%–28% of neighbors shared), which is what a representation of slowly varying state should look like. LoRA fine-tuning on the EEG leaves those numbers roughly where they were (α 1.04–2.19, ratio 0.20–0.61, 13%–35% shared); with the fitted constants as inputs they are α 1.16–2.14, ratio 0.20–0.52. The 574 fitted constants alone sit at α = 0.92, ratio 0.65 and 10% shared, near CBraMod, and concatenating them at the read-out pulls every frozen network towards that geometry (ratio 0.48–0.66 against 0.22–0.66 frozen).
The last two columns are a warning about the foundation models. Doubling the amplitude of the input — which changes nothing physiological — moves a LaBraM embedding by 1.9 and an EEGPT embedding by 2.4 within-recording distances; BIOT (which normalizes its input) and REVE do not move at all. On a headset whose contact impedance drifts, that sensitivity is a confound waiting to happen. Data (CSV)
Four networks pretrained on different corpora with different objectives agree with each other (mean CKA 0.67) and with sixteen hand-built numbers (0.66–0.75) far more than the in-house model agrees with anything, itself included (≤ 0.20). Language models show the same convergence, and the reading is the same: what they share is the structure of the data. Here that structure is mostly the power spectrum. LaBraM is the one that keeps something after the spectrum is removed.
In word vectors a relation is a direction. Here: the offset of each class from ordinary days. In LaBraM the four offsets are only weakly parallel (cosines 0.23–0.36, every session-bootstrap interval above zero): a small shared component, and mostly class-specific directions. No space contains a single “psychedelic axis”. A held-out session's offset points towards its own class's offset, built without it, in 11 of 14 sessions (chance 1 in 3), and LaBraM names LSD, DMT or ayahuasca correctly for 12 of 15 held-out sessions (time of day: 7) — though both ayahuasca nights are called DMT.
The eye-closure offset is a second analogy test. Within a recording, closed minus open is a fairly consistent direction across ordinary sessions in the foundation-model spaces (cosine 0.36–0.41) and a much less consistent one across psychedelic-labeled sessions (0.15–0.22), at equal size; in the hand-built features the gap is smaller (0.55 against 0.45). Eye closure does not mean the same thing in those sessions — or the classifier that defines it does not.
No space has discrete states: in the frozen and in-house spaces the best clustering beats a Gaussian null by 0.07–0.21 in silhouette and the two- or three-way splits follow eye state.
The standing representations of Result 1 sit where their construction predicts. Every network LoRA fine-tuned on the EEG stays close to its frozen parent (linear CKA 0.74–0.97); with the fitted constants as inputs it moves further (0.56–0.89). The read-out concatenations are the frozen space with something added: frozen beside fine-tuned agrees with frozen at 0.91–0.99, frozen with the constants at 0.92–0.97. The 574 fitted constants themselves agree with the frozen networks at 0.53–0.69 and with the hand-built features at 0.70, so the constants describe the windows in a way no learned space already contains, which is what Results 3 and 4 found from the read-out side.
A t-SNE map of each label-free representation, all 1,630 windows, drawn with the same coloring. The maps preserve neighborhoods, not distances (trustworthiness in each corner), so read them for structure — do psychedelic-labeled windows form a region, does the space split by eye state — and take every number in this section from the full space, not from the picture. The large map below can be switched to any representation.
Method. Of the three standard tools, permutation importance is the one that fits. LIME fits a local surrogate around one example and is unstable when inputs are as correlated as neighboring EEG frequencies; SHAP needs named input features, which a raw-waveform model does not have; permutation importance needs only a way to scramble one interpretable component and a score to watch. The component here is a frequency band in a scalp region: for each test window, that component is cut out and replaced by the same component from another window, so its statistics stay realistic while its link to the label is broken. The window is re-embedded and scored by read-outs trained on clean data from other sessions (223 windows, 40 sessions). The same procedure runs unchanged on every standing representation: the in-house networks, every foundation model frozen and LoRA fine-tuned, the read-out concatenations, the hand-built features and the fitted constants. For the two spaces whose dimensions have names, SHAP values are given as well: for the hand-built features, read linearly, they are closed-form, φi = ci(xi − E[xi]), so nothing is approximated; for the 41 × 14 fitted constants they are the exact SHAP values of their CatBoost read-out, summed over electrodes, the same values as in §20.
Everything reads alpha for eye state. Scrambling 8–13 Hz over the whole scalp lowers eye-state AUC by 0.43–0.54 in every network and in the hand-built space; no other band costs any of them more than 0.02. That is the confound of §16 seen from inside the networks.
For the session label the networks part company. The in-house transformer, CBraMod and the hand-built features depend on alpha and on almost nothing else (log-loss increase 0.5–0.8 for alpha, under 0.2 for any other band). LaBraM is different: beta costs it more than alpha (+0.54 against +0.38; its single most important component is posterior beta, +0.72), and it is the only network hurt about equally by scrambling any region (+1.3 to +1.6), so it is using relations between regions and not one site. Beta is also what its class read-out needs (+0.61 for LSD / DMT / ayahuasca, against +0.24 for alpha). This is the clearest lead in the study for what LaBraM knows that the hand-built description does not: the 13–30 Hz range, where the 2α harmonic of §11 lives.
Across the whole standing set the picture holds: scrambling alpha over the scalp costs the label read-out 0.11–0.39 of session AUC in the frozen networks, 0.11–0.39 in the networks LoRA fine-tuned on the EEG, 0.14–0.38 in those fine-tuned with the fitted constants as inputs, and 0.26 for the 574 fitted constants alone; alpha is the costliest band for 53 of the 55 standing representations.
The same bands with their phases randomized. Scrambling swaps a band for another window's, which also breaks its relations with the other bands and channels; a phase-randomized surrogate keeps every channel's amplitude spectrum in the band exactly and destroys only its waveform and phase relations. Under that intervention alpha costs the frozen networks -0.02–0.10 of session AUC against 0.11–0.39 for the scramble, and the fitted constants 0.03 against 0.26: most of what the scramble cost was the hybrid signal, not alpha's waveform, and the label read-outs rest mainly on the power spectrum. Randomizing the phases of the whole signal in every channel, which leaves every power spectrum intact, then separates the networks by what they read (REVE 0.44, EEGPT 0.29, LaBraM 0.10, CBraMod 0.05, BIOT -0.01; the fitted constants 0.03 and the hand-built features 0.03, both spectral by construction): 16 of the 55 standing representations lose 0.10 or more, REVE and its fine-tuned versions most. Where that waveform dependence sits is the telling part: randomizing the frontal channels alone costs frozen REVE 0.08 against 0.06 for the posterior channels, its fine-tuned version 0.35 against 0.07, and EEGPT 0.23 against 0.03. The artifact screen excludes every sample the headset flags as a blink, wink or lateral eye movement, padded by 0.75 s, and the masked stretches stay masked under every intervention here; what the frontal phases carry is therefore what survives the screen: eye and eyelid activity below the device's detection threshold, slow drifts of eye position, forehead muscle, and any genuine frontal waveform. The phase test cannot tell those apart; an independent eye-state recording could. What it does establish is that these networks read frontal waveform shape, which the constants and the hand-built features, being descriptions of spectra, do not.
BIOT leans on beta and gamma (+0.89, +0.99), which on this headset is where muscle lives; EEGPT leans on the frontal channels (+2.0 for the region, +1.3 for frontal alpha alone), where the eyes are. REVE, the best network, is the hardest to read: no single band matters much (1–4 Hz most, +0.47; alpha +0.25), and scrambling any one region costs about +2.0, so it depends on the relations between regions more than on any one oscillation — and 1–4 Hz is also where eye movements live. High scores reached by routes a physiologist would distrust are a reason to keep the mechanistic and hand-built descriptions beside the learned ones.
The named features say the same in plainer words. In the hand-built space the session-label read-out is mostly alpha power (mean |SHAP| 2.2 log-odds), then lower alpha coherence, a less posterior alpha distribution, a steeper 1/f slope and larger amplitude. Eye state is read from low delta share and high alpha. LSD windows are picked out by amplitude, little frontal slow activity and more gamma share; DMT windows by high alpha power with low gamma and low amplitude — two quite different signatures, which is why the class offsets of this section are not parallel.
In the space of the 41 × 14 fitted constants the session label is read, by its CatBoost read-out, above all from L1 peak gain db (1.21), L1 aperiodic exponent (1.18), L2 t0 ms (0.58), N2 p mean (0.41) (mean |SHAP| summed over electrodes), and from the F3, F8, T7 electrodes most; sessions with the label have a sharper, taller alpha resonance. The compound-by-compound version is in §20.
Every read-out reads alpha: removing 8–13 Hz lowers the read-out's log-odds more in psychedelic-labeled windows than in ordinary ones in 55 of the 55 standing spaces (frozen LaBraM -6.2 against -1.7; frozen BIOT -2.0 against +2.1). LoRA fine-tuning on the EEG leaves that in place (alpha removal -6.8 to -1.7 in psychedelic-labeled windows for the fine-tuned networks, -7.7 to -2.1 for those fine-tuned with the fitted constants as inputs), and the 574 fitted constants themselves move 1.38 within-recording distances when alpha is removed against 0.58 when the frontal channels are. Alpha on this headset is largely eye state, so part of what separates the labels is likely to be eye behavior — screen work against evenings with eyes closed — rather than cortex; that is a confound the eye-state estimate does not remove, because it is built from posterior alpha. The original in-house transformer barely moves under any deletion — at most 0.53 of the distance between two windows of the same recording — which is what a representation of window-specific detail would do. The frontal channels matter, but not in one direction: removing them changes the frozen foundation models' log-odds by -5.4 to +2.7 in psychedelic-labeled windows and -3.8 to +8.0 in ordinary ones, and after alpha LaBraM leans most on 30–45 Hz, where this headset records muscle.
The same test windows were perturbed at five increasing amplitudes in six ways — white noise, 1/f noise, muscle-band noise (20–45 Hz) and slow frontal noise (0.5–3 Hz, the eyes), each as a multiple of the window's own RMS; a change of gain; and lost channels — and scored with the read-outs fitted on clean data, exactly as a deployed network would meet them.
No representation is robust to everything, and the failures are specific. With white noise equal to the signal's own RMS, frozen LaBraM keeps a session AUC of 0.79 (from 0.99) and CBraMod 0.92; hand-built features fall to 0.86, EEGPT to 0.77, and BIOT to 0.66. At four times the RMS every network is at or below 0.89.
Gain. Invariant, because their inputs are normalized: REVE and BIOT. LaBraM's AUC runs from 0.81 to 0.91 when the amplitude is halved, doubled or multiplied by eight (clean 0.99); EEGPT falls to 0.72 and CBraMod to 0.50 at eight times the amplitude. Those three were pretrained on signals in fixed units and carry that assumption with them. The network most robust to muscle-band noise is EEGPT, LoRA fine-tuned on the EEG (0.93 at the signal's RMS, 0.88 at four times); frozen REVE keeps 0.84 under white noise at the signal's RMS, against LaBraM's 0.79.
Each family has its own weak point. Hand-built features keep 0.81 under muscle-band noise at four times the RMS and 0.66 under broadband noise at the same level. Losing four of fourteen channels hurts BIOT, LoRA fine-tuned on the EEG most (0.55) and CBraMod, frozen | constants at the read-out least (0.97). Slow frontal noise, the stand-in for eye movements, at four times the signal leaves LaBraM at 0.75 and BIOT at 0.72. A deployed pipeline on this headset would want LaBraM for clean data, a hand-built cross-check for noisy stretches, and amplitude normalization in front of all of them.
The fitted constants, measured. The 41 × 14 constants were refitted on every perturbed window, so their robustness is measured rather than assumed. A doubling of the gain moves them by 0.12 within-recording distances — the estimators fit the spectral shape, but the fit bounds and the ABC summary statistics are not perfectly scale-free — while the label read-out is unchanged (0.98 at twice the gain, 0.99 at eight times, against 0.98 clean); they keep a session AUC of 0.92 under white noise at the signal's RMS and 0.81 at four times, 0.57 under muscle-band noise at four times, and 0.96 with four of fourteen channels lost (clean 0.98); concatenated with frozen LaBraM at the read-out the pair keeps 0.91 under white noise at the signal's RMS and 0.93 with four channels lost. LoRA fine-tuning keeps the profile of its frozen parent in the typical condition (median gap 0.02 of AUC over every network and condition) but not in every one: the largest gap is 0.39, LaBraM under a quarter of the gain; and the networks fine-tuned with the fitted constants as inputs are the more gain-robust for it, their AUC at eight times the amplitude sitting -0.01 to +0.49 relative to the frozen network's.
The session-level scores of Result 2 hide what happens inside a session. Here every two-minute window of a session is scored on its own by the standing read-out, from the fold that never saw that session, and the calibrated probability is drawn against time for frozen LaBraM, frozen REVE, the hand-built features, the fitted constants. The sessions are the five with the lowest session log loss under frozen LaBraM and the five with the highest, among the 36 sessions with at least 10 valid windows. Surest: Workday recording 016 (ordinary), LSD experiment 011 (psychedelic-labeled), LSD experiment 015 (psychedelic-labeled), Workday recording 006 (ordinary), DMT experiment 012 (psychedelic-labeled). Least sure: DMT experiment 001 (psychedelic-labeled), Workday recording 002 (ordinary), Workday recording 017 (ordinary), DMT experiment 013 (psychedelic-labeled), Workday recording 008 (ordinary). The read-outs were rerun to keep each window's probability; their session probabilities reproduce the standing ones to within 0.07 (LaBraM), 0.05 (REVE), 0.06 (hand-built), 0.13 (constants), the hyperparameter search being stochastic; the session values in the table are the standing ones.
The surest sessions. In the five surest sessions the LaBraM read-out keeps 95 %–100 % of the windows on the correct side from the first minute to the last, the spread of the window probabilities is 0.02–0.16, and the other three read-outs land on the same side in 75 %–100 % of the windows. Each of these sessions reads as one state throughout; nothing inside it changes the read-out's mind.
The least sure sessions, one by one. Only 55 %–68 % of the windows fall on the correct side, and the probability moves within the session (spread 0.27–0.35) rather than sitting near 0.5. The patterns differ: 2 follow eye state (Workday recording 017: 0.53 with eyes closed against 0.21 open; DMT experiment 013: 0.90 with eyes closed against 0.49 open); 1 drifts through the session (Workday recording 002: 0.61 in the first half, 0.31 in the second); 2 alternate between windows with no eye-state or time structure (DMT experiment 001: 55 % of the windows on the correct side, spread 0.27; Workday recording 008: 60 % of the windows on the correct side, spread 0.28). In the sessions that follow eye state the eyes-closed windows read as more psychedelic than the eyes-open ones, the direction in which the psychedelic-labeled sessions, mostly recorded with eyes closed, differ from the ordinary ones; the read-out leans on what eye closure does to the spectrum, which Result 11 measures directly. Two sessions (Workday recording 002, Workday recording 008) have no eyes-closed windows, so eye state cannot be what moves them.
What this says. The other three read-outs agree with LaBraM window by window at r = 0.25–0.76 in the least sure sessions against 0.08–0.69 in the surest, and all four land on the same side in 27 %–71 % of the windows against 75 %–100 %. Where the read-outs disagree window by window, the uncertainty belongs to the representations, not to the recording: the windows are not intrinsically ambiguous, the representations read different things in them. Where they agree and are wrong together, the recording itself carries the other state's signature in those windows. The session-level scores of Result 2 cannot make this distinction; the window-level traces can, and they say that the hard sessions fail for different reasons, the eye-state dependence being the one that a change of protocol (a fixed eyes-closed block in every session) would remove.
A learned representation has no nameable dimensions, so what it reads has to be measured at its input. For every standing network, each of five frequency bands in each of three groups of electrodes was scrambled in turn, and the change in each compound’s read-out was recorded (the scrambling design of Result 11). A read-out here is a CatBoost read-out with fixed hyperparameters for one compound against every other session, ordinary days included, scored only on sessions it never saw. Importance is how much the read-out’s separation between the compound’s sessions and all others shrinks — not how much the compound’s own score falls, because every scramble moves all windows at once and that shift has to be canceled. Each network’s importances are expressed as shares of its total, so networks with different scales can be pooled, and only read-outs that genuinely find the compound are pooled: a session-level AUC of at least 0.75, which 24 of the 25 standing networks reach for LSD, 16 for DMT and 7 for ayahuasca.
Five frequency bands — delta 0.5–4 Hz; theta 4–8 Hz; alpha 8–13 Hz; beta 13–30 Hz; gamma 30–45 Hz — in three groups of electrodes: frontal (AF3, F7, F3, F4, F8, AF4); central–temporal (FC5, T7, T8, FC6); posterior (P7, O1, O2, P8). Scrambling replaces that band in those electrodes with the same band from another recording window, so the signal keeps its power but loses any relation to the compound.
LSD. The band carrying most of its evidence is alpha (0.43 of the total, positive in 100% of networks), then delta (0.29); by region, frontal electrodes carry 0.31, the others 0.30 and 0.25. The single largest cell is alpha over the frontal electrodes (+0.18).
DMT and ayahuasca. For DMT the largest cell is alpha over the frontal electrodes (+0.20); its frontal electrodes carry 0.41 of its evidence. For ayahuasca, which rests on 7 networks and two sessions, the largest cell is alpha over the posterior electrodes (+0.13).
A caution the frontal result needs. The frontal electrodes are the ones nearest the eyes and the forehead muscles. Slow activity there is where blinks and eye movements appear, and gamma there is where muscle tension appears; Result 11 already found one foundation model, EEGPT, leaning on the frontal electrodes, and REVE leaning most on 1–4 Hz activity. DMT and ayahuasca sessions are also the ones with the most eyes-closed time. So a frontal reading may be partly how the eyes and face behave under those compounds rather than what cortex does.
What this does not license. Knowing what each read-out uses does not make the compounds easy to tell apart; ayahuasca rests on 2 sessions. Dose, timing and eye closure differ between compounds, nothing was blinded, and no subjective ratings were recorded, so this is what the networks attend to, not what the compounds do or how they feel. The fitted constants' own account of the same question is in §20.
Results 1, 3, 4 and 21 show that the 41 × 14 fitted constants help a network trained here. A reviewer's alternative reading is that any good per-electrode summary of the spectrum would have done the same, because the constants are a deterministic function of the same EEG. This result tests that with five controls computed from the same clean samples, without labels: the six constants of the L1 damped oscillator on their own (the coordinates the recovery test identifies); six principal components of the log power spectrum; six conventional descriptors (alpha peak frequency and power, the 1/f exponent and offset, the theta-to-alpha ratio, the beta share); six fixed random projections of the log spectrum; and the 41 constants with their association to the windows permuted, which keeps every number and removes every relation to the signal. Each is read alone, concatenated with frozen LaBraM at the read-out, and given to the base replica as inputs to its electrode tokens over three training seeds, all by the standing read-out. (Read-outs after the first of each route were warm-started from its tuned hyperparameters, with a narrowed twelve-trial search.)
Result. As inputs, the constants lower the replica's log loss from 0.30 to 0.25. The informative controls reach the six PSD components 0.27, the six random projections 0.28, the six spectral descriptors 0.30, against 0.27 for the permuted constants, so none of them adds usable information beyond what any extra input adds. The six L1 constants alone reach 0.25, all of the gain of the full 41. The constants beat every matched control as inputs by more than two seed standard deviations (0.002), so the gain is not that of a good summary of the spectrum in general; it follows the particular coordinates the equations define. The permuted constants carry no information about the window, yet they too lower the loss, from 0.30 to 0.27: about 55% of the constants' gain is what any noisy extra input does for a network trained on 54 hours (the inputs are dropped and jittered during training, which regularizes), and the remaining 45% is information about the window.
The other two routes. Read alone, the ranking is the 41 constants 0.22, the six L1 constants 0.23, the six PSD components 0.28, the six spectral descriptors 0.29, the six random projections 0.46, the permuted constants 0.69. Beside frozen LaBraM at the read-out every summary lands between 0.16 and 0.21, the permuted constants included, so that route measures LaBraM and not the summary; it is reported for completeness.
Two of the review's objections are answered by rerunning the key fine-tuned rows. Seeds. Every fine-tuned foundation-model row of Result 1 rests on one training seed; here the three LoRA rows of REVE and LaBraM are trained at five seeds and scored by the standing read-out. Folds. The fine-tuned rows and the in-house replicas were trained on the unlabeled signal of every recording before the read-out held sessions out, which makes them transductive; here each is refitted five times with the read-out's held-out sessions excluded from its training, and the read-out then scores each fold with the network that never saw it. (Read-outs after the standing seed of each row were warm-started from its tuned hyperparameters.)
Seeds. Over 5 training seeds the session log loss of a fine-tuned row moves by 0.007–0.018 (one s.d.; ranges 0.02–0.04), and between-seed variation is below one percent of the variance of session losses: which session is being scored matters far more than which seed trained the adapters. The constants-as-inputs gain seen at one seed holds over the seeds (fine-tuned on the EEG against with the constants: REVE: 0.24 ± 0.01 against 0.21 ± 0.02; LaBraM: 0.19 ± 0.01 against 0.19 ± 0.01), which is the uncertainty the single-seed rows of Result 1 carry.
Folds. Refitting the representation inside each outer fold, so that no held-out session ever enters the fine-tuning or the replica's training, changes the log loss by -0.017 to +0.008 across the 8 rows (largest: REVE replica, EEG alone, +0.008); the fold-wise numbers are the ones to quote for these rows, the frozen rows and the constants needing no such correction because nothing in them was trained on the archive.
A 2026 report found that reconstruction-trained EEG networks encode the aperiodic, low-frequency part of the spectrum and recording identity more strongly than the oscillations. Here every standing representation is probed for four quantities of this archive's own spectral fits, with whole sessions held out: the alpha peak frequency and the alpha power (the oscillation), and the 1/f exponent and offset (the aperiodic background). The probe is a ridge regression on the standardized embedding, reported as held-out R² (below zero means worse than predicting the mean); the last column is the alpha-frequency R² over the exponent R², the two quantities that separate the oscillation from the background. The hand-built features contain all four targets among their sixteen inputs, so their row reads 1.00 by construction and is not ranked.
Result. Alpha power is read by every network (0.69–0.98). The alpha peak frequency is the hard quantity, and it is where the representations part: the frozen foundation models read it at R² 0.09–0.27 and LoRA fine-tuning on the EEG leaves that at 0.09–0.32, while the same networks fine-tuned with the fitted constants as inputs reach 0.15–0.44 and the constants concatenated at the read-out 0.36–0.40; the 574 constants alone read it at 0.38 (LaBraM 0.21 frozen, 0.44 with the constants). The 1/f exponent, by contrast, is read well by nearly every network (0.55–0.75 frozen, 0.65–0.84 fine-tuned): the background is carried far more faithfully than the oscillation's frequency, which is the report's finding, reproduced here on one person's archive. The graph transformers of Result 19 read alpha frequency at 0.02–0.28 and the exponent at 0.29–0.67.
Reading it. The original in-house transformers read neither quantity (alpha frequency -0.27 to 0.09, exponent -1.77 to 0.05), which is what a representation settled on eye state should look like. The fitted constants are, by construction, a description of the oscillation, and giving them to a network is what lifts its reading of the alpha frequency; nothing in the reconstruction objective does that on its own. A representation that reads alpha frequency poorly cannot be carrying the alpha-frequency result of §06 and §17, whatever else it reads, so this table also says which representations are candidates for that result and which are not.
The replica of Result 1 treats every electrode-second as an interchangeable token. Two graph transformers were trained here to ask whether representing the EEG as a network of electrodes gives a better representation. The replica with a graph prior keeps the replica exactly and adds, to the attention between any two tokens, a bias computed from the edge between their electrodes: scalp distance and hemisphere, and in the dynamic variants this window's alpha phase coupling (wPLI) and signed phase lag. Every bias weight starts at zero, so at the start the network is the replica and it is free to ignore the graph. The hierarchical graph transformer reads time within an electrode, then space across electrodes, then time again: each electrode's half-second patches within a four-second segment pass through a local temporal encoder to one vector; the fourteen vectors are the nodes of a graph transformer with full attention plus the same bias, each node made of its EEG embedding, the electrode's 41 fitted constants (in the variants that have them) and its position; a temporal transformer then reads the successive segments. Both have eight encoder blocks at the replica's width (8.4 to 8.6 M weights) and the replica's objective, crop, optimizer and epochs: masked reconstruction with 55 % of the signal hidden, three training seeds each.
What each architecture assumes. The ordinary transformer assumes nothing about the scalp beyond a position code: any electrode-second may attend to any other, so cross-electrode phase relations are computed from the raw patches, and every spatial regularity has to be learned from 1,630 windows. The graph prior keeps that function class and adds a soft preference, from fixed geometry, for which pairs of tokens interact; its dynamic form adds the one thing the crop cannot contain, a statistic of the whole two-minute window (alpha coupling and lag), as a bias the network can weight or ignore. The hierarchy is a hard prior: each electrode's four seconds are summarized into one vector before the electrodes meet, so fine-timescale phase relations between electrodes survive only if the local encoder keeps them (which is why the measured coupling is taken up several times more strongly there); the electrodes interact only within one moment; and the long timescales see summaries of segments, not patches. It is also the reading of each electrode's own dynamics, which is what makes its embeddings so much more organized by recording than the ordinary transformer's.
The replica with a graph prior.
The hierarchical graph transformer.
Together. The best graph network is the replica trained with the constants, the scalp graph and alpha coupling as its prior, and the forecast objective, at 0.256, 37 of 40; the ordinary transformer stands at 0.307 without the constants and 0.239 with them, frozen REVE at 0.242 and frozen LaBraM at 0.152. Over three training seeds the graph networks' mean log loss runs from 0.229 to 0.343 (standard deviations 0.007–0.046), the replica's 0.298 ± 0.015 and 0.244 ± 0.004 with the constants. On the question asked, whether a network of electrodes gives a better representation than interchangeable tokens: a scalp-graph prior improves the ordinary transformer; the hierarchical graph transformer reads the label as well as the ordinary transformer, within the bootstrap interval; no graph network given the constants improves on the ordinary transformer trained with them.
Where each does better, and why. The graph prior's gain is broad and small: 15 sessions read better and 4 worse of 40, psychedelic-labeled sessions by -0.043 and ordinary ones by -0.026, and the change is unrelated to what a session is (no rank correlation with its properties beyond 0.18): it behaves as a regularizer, the same help everywhere. The hierarchy splits the sessions: -0.081 on the psychedelic-labeled sessions and +0.031 on the ordinary ones (17 better, 9 worse). Its gains go to sessions with more eyes-closed windows and more alpha power (rank correlations the share of eyes-closed windows -0.30, alpha power -0.29), its losses to long eyes-open recordings (the number of windows +0.31); the sessions it reads best are DMT experiment 009 (-0.69), Resting baseline 002 (-0.45), Resting baseline 003 (part 1) (-0.33), the ones it reads worst Workday recording 003 (+1.06), Workday recording 014 (+0.69), Workday recording 001 (+0.55). Without any graph bias the split is the same (-0.079 and +0.026), so it comes from the hierarchy, not from the graph. That is the prior at work: a network that reads each electrode's own oscillatory dynamics first is at its best where the state is written in those dynamics, eyes closed with a strong alpha, and at its worst in long, eyes-open working sessions whose signal is broadband and drifting. The forecast objective repairs exactly those: its largest gains are Workday recording 003 (-0.54), Workday recording 001 (-0.37), Workday recording 014 (-0.36) (13 sessions better, 5 worse; the gain is largest where alpha coupling is low, rank correlation -0.33). What predicts the next second of an eyes-open recording is the slow, broadband structure the masked objective under-weights, and asking for it puts that structure into the embedding.
Did the networks use the graph? Every bias weight starts at zero, so a network that has no use for an edge feature leaves its weight there. After training the mean absolute weight over the eight heads is in the replica with a graph prior 0.16 for scalp distance and 0.20 for hemisphere, 0.04 for the measured alpha coupling and 0.05 for its signed phase lag, so the coupling carries about 24 % of the weight of the geometry; the read-out with the coupling changes by -0.004 [-0.022, +0.013], p = 0.695; in the hierarchical graph transformer 0.04 for scalp distance and 0.05 for hemisphere, 0.17 for the measured alpha coupling and 0.19 for its signed phase lag, so the coupling carries about 4.2 times the weight of the geometry; the read-out with the coupling changes by +0.014 [-0.022, +0.055], p = 0.502 (edge features in standard units). Taking a feature up and gaining from it are separate things: the weights say what the reconstruction objective found useful, the read-outs say what that did for the representation.
What the embeddings carry. By the label-free health check of Result 7: the replica with a graph prior 7.1–10.5 effective dimensions, recording identity 38–45 % of the variance and eye state 19–22 %; the hierarchical design 5.8–8.8 effective dimensions, recording identity 70–74 % of the variance and eye state 15–20 %; the ordinary transformer 7.6, 39 % and 20 %; frozen REVE 28.2, 45 % and 18 %. The hierarchical embeddings are organized by recording far more than the ordinary transformer's.
Which features each reads. On the spectral probe of Result 18, the alpha peak frequency at R² 0.12–0.30 for the ordinary transformer, 0.11–0.28 with the graph prior, 0.02–0.26 for the hierarchy; the 1/f exponent at R² 0.49–0.68 for the ordinary transformer, 0.52–0.67 with the graph prior, 0.29–0.62 for the hierarchy; alpha power at R² 0.88–0.95 for the ordinary transformer, 0.88–0.95 with the graph prior, 0.81–0.95 for the hierarchy. The graph prior leaves what the replica reads unchanged, as a bias on attention should; the hierarchy reads the within-electrode quantities, the peak frequency and the exponent, less well than the ordinary transformer, the price of summarizing each electrode before the electrodes meet. On the three open-ended targets the table above tells the same story.
The three open-ended targets (held-out R²). Complexity: the graph prior 0.83–0.87, the hierarchy 0.79–0.83, the ordinary transformer 0.81–0.86; the memory of the alpha envelope: the graph prior 0.19–0.27, the hierarchy 0.08–0.24, the ordinary transformer 0.22–0.25; alpha phase coupling with alpha strength removed: the graph prior 0.05–0.13, the hierarchy -0.01–0.25, the ordinary transformer 0.15.
Result 19 shows where the graph transformer's attention goes; this result asks how far it reaches, and what the predictions rest on: the electrode itself and its neighbors, or the whole scalp. Four routes. Reach. For every head of every graph block the attention-weighted mean scalp distance from the attending electrode to the attended ones, in cm, over all 1,630 windows; a head that attends everywhere equally has a reach of 11.8 cm, one that attends only to its own electrode a reach of 0. For the joint-token transformers, where a token is an electrode at a time step, the same in space and in time. Restriction at inference. A trained network is left as it is and, when the windows are embedded, every electrode is allowed to attend only to itself and the electrodes within r cm (or only to those beyond r); a CatBoost read-out fitted on the unchanged embeddings then scores the changed ones, as in Results 12 and 13, so nothing is refitted on them. Single heads are silenced the same way, then the most local and the most global heads together. Training under constraint. The same networks trained from scratch with attention confined to the three nearest electrodes, or freed of geometry (no graph bias and no electrode coordinates), read by the standing read-out. The archive's own correlation length. For every window and band, the correlation of each electrode pair against its distance, fitted as an exponential decay: its length ξ is what the data offer, to set beside what the networks chose.
Reach. Without the constants at the nodes the hierarchical graph transformer's heads reach 9.8–10.1 cm on average (uniform 11.8), 5–7 of its 24 heads put more than half their attention on the electrode itself and its three nearest, and the first two graph blocks are the local ones (8.8–9.3 and 8.9–9.3 cm against 11.4–11.6 in the third); with the constants at the nodes the attention goes nearly uniform: reach 11.2 cm, 1–2 local heads, the same at every seed (seed spread 0.01–0.13 cm). A node that already carries its own oscillator description has less to fetch from its neighbors, and the graph transformer stops routing by geometry once the constants are there. Eye closure lengthens the reach by 0.07–0.29 cm in every variant.
The joint-token transformers. The ordinary transformer (the replica) reaches 9.4 cm in space and 3.53 s in time (uniform 11.8 cm and 5.07 s), keeps 17 % of its attention on the token's own electrode (7 % would be uniform) and 27 % on the same time step; 20 of its 64 heads are local in space, and its heads spread from 0.5 to 13.2 cm and from 0.06 to 4.92 s. With the constants as inputs its reach is 9.1 cm and 3.09 s, shorter in time. The replica with a graph prior reaches 9.2–9.4 cm. In the joint stack the electrodes and the time steps compete for the same attention, and the network spends most of it within the electrode and within a few seconds: the ordinary transformer is a local network in both senses, with a minority of heads that span the scalp or the crop.
What the data offer. The zero-lag correlation between electrodes falls with distance on a length of 10.1 cm for the broadband signal (8.0 cm for theta, 14.0 cm for alpha, median over windows), and alpha's length depends on the eyes: 34.8 cm with them closed against 10.6 cm open, 16.2 cm in the psychedelic-labeled sessions against 9.9 in the ordinary ones. The lag-blind coupling (wPLI, which ignores zero-lag mixing) does not fall with distance at all at this spacing (fitted length 111.5 cm, a flat line), and gamma's is long only because its correlations are small everywhere (29.1 cm). So the short correlation length is largely volume conduction, and the coupling that survives it has no characteristic length that fourteen electrodes could resolve. The networks' reach without the constants (about 9–10 cm) sits at the broadband and theta lengths; with the constants they read past it.
Restricting the routing. Session log loss under the frozen read-out, by network:
With the constants at the nodes the label survives each electrode being left to itself (0.272) and is read best within 8 cm; without them the network needs the whole scalp (0.434 alone, 0.213 whole) because each electrode's description is assembled from its neighbors. The two cross-electrode targets need the routing whatever the inputs: complexity and phase coupling fall to 0.49 and 0.09 with attention confined to the electrode, and keep rising to the full scalp, while the memory of the alpha envelope, a quantity of one electrode's own time course, is read as well or better alone (0.21 against 0.14). Attention kept only beyond a distance costs little or nothing on the label (0.166–0.206 over the tested distances): the nearest neighbors are the dispensable ones once the electrode has its own constants.
The joint-token transformer under the same restriction. For the ordinary transformer, attention confined to the token's own electrode gives 1.028 against 0.259 unrestricted, and complexity R² falls from 0.86 to -1.51; confined in time to the same patch it gives 0.427, and to ±1.8 s 0.265 with complexity at 0.81: the ordinary transformer needs the whole scalp and about two seconds of time. Silencing its eight most time-local heads adds +0.957 [+0.494, +1.388], its eight most time-global +0.268 [+0.061, +0.454].
Heads silenced.
No single head carries the label; the local heads as a group matter more than the global ones in the network without the constants, and neither group in the network with them until half the heads are gone.
Trained under the constraint. The restriction at inference can only remove what a trained network happens to use; a network trained under the constraint says whether the routing is needed.
Of the 9 constrained networks read so far, 1 is worse than the base beyond the bootstrap interval on the label and 0 are better. The targets say the opposite: alpha phase coupling is read worse by 3 of the 9 constrained networks beyond the interval, most by replica, no electrode coordinates (0.15 → -0.04), and complexity by 2 of 9: the label can be learned within a neighborhood, the coupling cannot.
What it says. Where the attention reaches is a choice the network makes from its inputs, not a property of the architecture: the same hierarchy is local without the constants and global with them. What the predictions rest on depends on the quantity: the session label is carried by each electrode's own description and a neighborhood of a few centimeters, and reads best when the attention is confined there; the cross-electrode targets, complexity and alpha phase coupling, need the whole scalp. The archive's own correlation length agrees: the zero-lag correlation falls off over 8–14 cm, mostly by volume conduction, while the coupling that survives it has no characteristic length at this spacing, which is why a network reading it must attend everywhere. For this archive and this headset, then, there is an optimal integration length for the label, about 6–8 cm once each electrode carries its own constants, and none for the coupling.
REVE was pretrained on about 60,000 hours of EEG and has 69 M weights; LaBraM on about 2,500 hours with 5.8 M. Can the fitted constants of §20 stand in for scale? The same REVE-style architecture was trained from scratch on this archive alone, in a grid that changes one thing at a time: four sizes (0.4 M to 22.0 M weights), three shares of the session groups available for self-supervised training (a quarter, a half and all: 15, 24, 54 hours of EEG), with and without the 41 × 14 fitted constants given to the electrode tokens as inputs, and three training seeds for every cell: 60 networks, the largest size at the full share only. Every cell is read by the standing CatBoost read-out with whole sessions held out and the same folds, so any two cells are compared like for like, and a cell and its twin with the constants share their seeds and are compared session by session.
Size. With every session available, the log loss without the constants runs 0.32 → 0.35 → 0.29 → 0.29 from 0.4 M to 22.0 M weights, and with them 0.24 → 0.22 → 0.24 → 0.24. A tenfold increase in weights lowers the log loss by 0.024 without the constants and makes no measurable difference with them; the 54-fold range of sizes buys less than the constants do at any one size. The tiny network at 50 % with the constants, 0.238 at 0.4 M weights, is ahead of the large network without them, 0.293 at 22.0 M.
Data. More of the archive did not lower the log loss reliably. Of the 6 size-and-input series that run from a quarter of the sessions to all of them, 3 fall step by step, and in 3 the quarter-share cell is the best of the three: at 8.4 M weights, 0.27 → 0.33 → 0.29 without the constants and 0.20 → 0.26 → 0.24 with them. The fractional cells say why: the held-out sessions divide into those the network trained on and those it never saw, and in 6 of the 6 cells the sessions it trained on are read worse than the sessions it never saw, by 0.02 to 0.19 of log loss without the constants. Self-supervised training on a session does not make that session easier to read; the label read-out holds sessions out either way, so this is not leakage but the reverse of it. With all sessions in training there are no never-seen sessions left, which is the full-share cells' handicap.
The constants. Against its twin, the constants lower the log loss in 9 of the 10 matched cells and the interval excludes zero in 7; over the 30 size-share-seed triplets the mean effect is -0.066 (95 % interval -0.084 to -0.049), +2.3 sessions of 40. The effect does not shrink with size (tiny -0.077, small -0.060, base -0.067, large -0.051) and grows with the share of sessions (25 % -0.035 (interval crosses zero), 50 % -0.083, 100 % -0.078); the one cell where it fails is small at 25 % (+0.028, interval -0.031 to +0.099), the strongest small at 100 % (-0.130). On the never-seen sessions alone the constants change the log loss by -0.057 (-0.083 to -0.031), on the sessions the network trained on by -0.061: the gain is the same for sessions the network never saw, which answers the transductive objection inside the grid.
Against the released networks and the constants alone. 5 of the 10 cells with the constants read the label better than frozen REVE (0.242 at 69 M weights, pretrained elsewhere), against 0 without them. The best cell, base at 25 % with the constants, stands at 0.197 ± 0.047 (37.7 of 40), ahead of the 574 constants read alone (0.210) and of the hand-built features (0.260), behind frozen LaBraM (0.152, 39 of 40). The smallest network that matches the best one trained without the constants (base at 25 %, 0.269) is tiny at 50 % with them, 0.238 with 21 times fewer weights. The replicas saw this archive's unlabeled recordings in training; the released networks saw none of it.
What it says, and what limits it. Within one family of architectures on one person's archive, the fitted constants move the whole curve and size moves little of it: the question the study was built to ask, whether a mechanistic description can stand in for scale, is answered in the constants' favor at every size and at the 50 % and 100 % shares of the sessions, with the interval crossing zero at the 25 % share, with the released networks as the outside reference. What it cannot say: whether the same holds for a second person, for a network pretrained elsewhere and then given the constants (Results 3 and 5 say it does not for the strongest of them), or beyond forty held-out sessions, where the session count is near its ceiling and the log loss carries the comparison. Result 16 asks whether the constants beat an equally informative summary that is not mechanistic.
Every earlier result in this section is retrospective: the sessions were in hand when the read-outs were fitted, and whole sessions were held out in turn. The site has said since release 4.5 that the decisive test is a different one, to fix the models and predict sessions recorded later. That test has now been run once. The frozen LaBraM and REVE representations, the sixteen hand-built features and the 41 × 14 neural-mass model constants, with the standing CatBoost read-outs fitted on the 40 published sessions and nothing else, were asked for the probability that each of thirteen later sessions was a psychedelic session: the twelve ordinary additions of this release (Workday recordings 009 and 020 to 028, Daily-life recordings 004 and 005) and Ayahuasca experiment 019. The two other new psychedelic sessions, Ayahuasca experiment 018 and Psilocybin experiment 017, were kept out of the test and retained for the model analyses of §20; their frozen read-outs are listed for information and were not scored. The unit of scoring is the session (the mean window log-odds), the loss is the per-session log loss against the confirmed label, and the no-EEG references are the time of day alone and the time of day with the eye-state estimate.
| Read-out (frozen) | Sessions right | Ayahuasca 019: probability, rank of 13 | Mean log loss (session bootstrap) | Published, 40 sessions |
|---|---|---|---|---|
| LaBraM | 13 / 13 | 0.90, 1 | 0.063 (0.028–0.107) | 39 / 40, 0.152 |
| REVE | 12 / 13 | 0.62, 1 | 0.181 (0.070–0.334) | 37 / 40, 0.242 |
| 16 hand-built features | 13 / 13 | 0.80, 1 | 0.076 (0.033–0.132) | 35 / 40, 0.260 |
| 41 × 14 model constants | 13 / 13 | 0.76, 1 | 0.070 (0.036–0.114) | 38 / 40, 0.210 |
| Time of day alone (no EEG) | 8 / 13 | 0.51, 6 | 0.624 (0.441–0.800) | 27 / 40, 0.570 |
| Time of day + eye-state estimate | 9 / 13 | 0.62, 3 | 0.547 (0.338–0.781) | 31 / 40, 0.502 |
| Eye-state estimate alone | 13 / 13 | 0.61, 1 | 0.210 (0.139–0.291) | – |
Result. LaBraM, the hand-built features and the model constants called all thirteen sessions and ranked the ayahuasca session first; REVE called twelve, placing one evening office session (Workday recording 025) at 0.61. Paired session by session against the time of day, every EEG read-out was better by 0.44 to 0.56 nats (sign-flip p = 0.0006), and against the time of day with the eye-state estimate by 0.37 to 0.48 (p ≤ 0.002). The two sessions the clock cannot call, the evening at home (Daily-life recording 004) and the evening office session, were called correctly by every EEG read-out. Removing the flicker-sweep windows changes nothing (REVE then recovers Workday recording 025); reading only the eyes-open windows, LaBraM, the hand-built features and the constants still call every session and still rank the ayahuasca session first, while the eye-state estimate alone falls to 0.49 for it. By the rule written down beforehand, LaBraM, the hand-built features and the constants are successes and REVE a partial success.
| Session | Label | LaBraM | REVE | Hand-built | Constants | Time of day |
|---|---|---|---|---|---|---|
| Workday recording 009 | ordinary | 0.009 | 0.078 | 0.009 | 0.032 | 0.629 |
| Daily-life recording 004 | ordinary | 0.028 | 0.021 | 0.023 | 0.009 | 0.588 |
| Workday recording 020 | ordinary | 0.062 | 0.075 | 0.076 | 0.081 | 0.638 |
| Workday recording 021 | ordinary | 0.010 | 0.039 | 0.054 | 0.032 | 0.198 |
| Workday recording 022 | ordinary | 0.026 | 0.049 | 0.033 | 0.038 | 0.464 |
| Workday recording 023 | ordinary | 0.015 | 0.116 | 0.033 | 0.017 | 0.623 |
| Workday recording 024 | ordinary | 0.023 | 0.097 | 0.023 | 0.033 | 0.213 |
| Psilocybin experiment 017 (retained) | psychedelic | 0.885 | 0.949 | 0.947 | 0.973 | 0.678 |
| Daily-life recording 005 | ordinary | 0.009 | 0.026 | 0.024 | 0.012 | 0.241 |
| Workday recording 025 | ordinary | 0.168 | 0.605 | 0.076 | 0.155 | 0.670 |
| Workday recording 026 | ordinary | 0.070 | 0.120 | 0.046 | 0.056 | 0.174 |
| Workday recording 027 | ordinary | 0.023 | 0.029 | 0.017 | 0.038 | 0.241 |
| Workday recording 028 | ordinary | 0.221 | 0.226 | 0.289 | 0.102 | 0.464 |
| Ayahuasca experiment 018 (retained) | psychedelic | 0.903 | 0.604 | 0.892 | 0.777 | 0.528 |
| Ayahuasca experiment 019 | psychedelic | 0.901 | 0.616 | 0.800 | 0.761 | 0.505 |
What limits it. One psychedelic session supports a rank, not a rate: the read-outs placed it first of thirteen, and nothing more can be said about sensitivity from one case. The eye-state estimate alone also separates the thirteen sessions (log loss 0.210), and against the resting-block convention the frozen eye-state read-out finds no eyes-closed block in the three psychedelic sessions (0.00 in both blocks, against 0.71–0.83 in the closed block of the office sessions), so either the convention was not followed there or the read-out, built on posterior alpha, does not see the closed eyes under the compound; the recordings cannot say which. Part of what the read-outs see therefore remains entangled with eye behavior, which is why the eyes-open sensitivity set matters: it is the half of the evidence that is not eye behavior. Within the ayahuasca session the window probability rose through the session, from 0.58 in the first twenty minutes to 0.97 after minute 45, in parallel with the eye-closed share, and the eyes-open windows at minutes 10 to 18 already scored 0.84 to 0.99. Added for information, the two retained sessions were read at 0.90 (Ayahuasca experiment 018) and 0.88 (Psilocybin experiment 017) by LaBraM. The next round needs what this one lacked: several psychedelic sessions, ordinary evening sessions made the way the dosed ones are, and the labels sealed until the predictions are filed. The pre-specified plan, the frozen artifacts' hashes and every prediction are in the archive. Data (CSV)
Result 22 scored the four representations named in the pre-specified plan. The same test can be put to every standing representation, provided nothing is retrained: each network was run on the new windows with its saved weights (two published recordings re-embedded with the same code reproduce the stored embeddings of every family to a cosine of at least 0.9999), and each read-out was fitted on the published sessions alone. Because the read-outs here use one fixed set of hyperparameters rather than the tuned heads of the pre-specified test, the four named representations score slightly differently than in Result 22; the ordering is the point.
Psychedelic or not. 49 of the 55 EEG representations call all thirteen prospective sessions correctly, and the same 49 call all fifteen when the two retained psychedelic sessions are added. Every one of them beats the time of day alone (log loss 0.73). The eye-state estimate alone reaches 0.21 on all windows and 0.17 on eyes-open windows; reading only the eyes-open windows, 52 of the 55 EEG representations still do better than it, so what they read is not the eyelids alone. The best are BIOT, frozen (0.016) and Neural-mass model constants, 41 × 14 electrodes (0.019); the weakest are the label-free in-house transformers (0.28 and 0.42). How well a representation did on the published sessions predicts how well it does here only loosely (rank correlation 0.5): the published ranking of Result 1 is a guide, not a forecast.
What each representation predicts about a new window. The same read-out design, as regressions, asks what each representation carries about seventeen measures of the window, the open targets of Result 10 among them. R² is computed on the new windows against the variance of the published windows; the hand-built features are left out of the medians because they contain most of these measures by construction. Signal diversity transfers almost perfectly: spatiotemporal Lempel–Ziv complexity is predicted at a median R² of 0.87 (best 0.95, REVE, frozen | constants at the read-out). Two measures transfer poorly from every representation: the long-range memory of the alpha envelope (DFA; median 0.25, best 0.37) and frontal–posterior alpha phase coupling with its dependence on alpha strength removed (median 0.34, best 0.49). On both the 41 × 14 constants carry more than the median learned network (0.36 against 0.24 to 0.27 for DFA, 0.42 against 0.30 to 0.35 for the coupling), and they are the best single predictor of the alpha center frequency (0.65 against a median of 0.44). Timing over tens of seconds and phase relations between distant electrodes are what no representation here has learned to keep.
| Measure of the window | Median R², new windows | Median R², published (out of fold) | Frozen | Fine-tuned | In-house | Constants | Best |
|---|---|---|---|---|---|---|---|
| eye-state estimate (probability closed) | 0.97 | 0.93 | 0.97 | 0.97 | 0.96 | 0.97 | 0.98 |
| posterior alpha power | 0.95 | 0.92 | 0.96 | 0.97 | 0.93 | 0.98 | 0.98 |
| gamma share | 0.94 | 0.85 | 0.95 | 0.96 | 0.92 | 0.93 | 0.98 |
| beta share | 0.94 | 0.89 | 0.94 | 0.95 | 0.92 | 0.95 | 0.97 |
| theta share | 0.90 | 0.80 | 0.91 | 0.92 | 0.87 | 0.94 | 0.95 |
| alpha harmonic power | 0.90 | 0.83 | 0.91 | 0.91 | 0.87 | 0.94 | 0.94 |
| alpha correlation between electrodes | 0.89 | 0.83 | 0.90 | 0.90 | 0.87 | 0.88 | 0.94 |
| spatiotemporal Lempel–Ziv complexity | 0.87 | 0.79 | 0.89 | 0.88 | 0.83 | 0.77 | 0.95 |
| theta/beta ratio | 0.85 | 0.66 | 0.88 | 0.88 | 0.81 | 0.90 | 0.93 |
| aperiodic exponent | 0.80 | 0.49 | 0.82 | 0.84 | 0.75 | 0.91 | 0.92 |
| frontal slow share | 0.80 | 0.71 | 0.79 | 0.78 | 0.80 | 0.86 | 0.88 |
| signal amplitude (log RMS) | 0.74 | 0.67 | 0.82 | 0.78 | 0.66 | 0.59 | 0.93 |
| posterior-to-frontal alpha | 0.65 | 0.36 | 0.71 | 0.69 | 0.56 | 0.62 | 0.87 |
| alpha asymmetry, right over left | 0.59 | 0.50 | 0.64 | 0.60 | 0.59 | 0.64 | 0.73 |
| alpha center frequency | 0.44 | 0.27 | 0.38 | 0.50 | 0.33 | 0.65 | 0.65 |
| frontal–posterior alpha phase coupling (wPLI, adjusted) | 0.34 | 0.13 | 0.34 | 0.35 | 0.30 | 0.42 | 0.49 |
| long-range memory of the alpha envelope (DFA) | 0.25 | 0.22 | 0.24 | 0.27 | 0.21 | 0.36 | 0.37 |
Medians over the 54 representations other than the hand-built features and the no-EEG references; family columns are medians within the family (the constants are one representation). Data (CSV)
Compute. Everything in this section and §20 ran on one laptop: Intel Core Ultra 9 185H (22 threads), 32 GB, NVIDIA GeForce RTX 4080 Laptop GPU, 12 GB, PyTorch 2.13, CatBoost 1.2.10, Optuna 4.9; no cloud compute was used, and jobs often shared the machine, so these are upper bounds.
A single-subject EEG archive: 56 recordings, 100.1 hours, 19 acute sessions, four psychedelic classes, 34 photic resonance sweeps, thirteen light-noise runs, one brain, February to October 2026. All 56 recordings form the analysis cohort.