What lets a decoder answer an SSVEP frequency it never trained on?

Question

Asked with the spectrum of CCA’s own reference signals, does the head do better on frequencies it never trained on?

What changed

How each frequency is asked: the reference spectrum in place of the numeric code or the question number, read by the FiLM head on the same features and splits.

Matched control

The same FiLM head asked with the numeric code on held-out frequencies and with the question number on seen ones; CCA and a fixed spectrum match, neither of them trained, score the same windows.

Result

Asked with the spectrum of CCA’s own reference signals (sine and cosine at the frequency and its second and third harmonics), the head reached 39.00% (36.07%–41.78%) on frequencies it never trained on. The numeric code reached 41.46% and CCA 80.90%. Paired with the numeric code, the reference spectrum differed by −2.46 pp (−3.47 to −1.52). On the seen 32-way task it reached 31.48% balanced accuracy, against 32.06% for the question number: the paired difference, −0.57 pp (−1.06 to −0.05), is equivalent within the ±2-point margin and is also a small difference below zero.

On frozen CBraMod features the reference spectrum was again below the numeric code on unseen frequencies (−2.35 pp, −3.16 to −1.57). On seen frequencies it was within the margin, with the direction unresolved (+0.44 pp, −0.01 to +0.92). This question changes the harmonics, the shape and size of the query and the size of the head together, so the result describes the recipe as a whole.

95% intervals from 2,000 hierarchical paired bootstrap draws over people and fold-shared seed indices (seed 20261007). Four primary contrasts on the plain spectrum and four secondary on frozen CBraMod features, with no multiplicity correction. A fixed spectrum match against the same reference, with no training, reached 28.84% on unseen frequencies. Its scores do not depend on the rotation, so its generalisation cost is zero by construction, as is CCA’s.

Limit. Not run in this round: the matching (bilinear) head and a fundamental-only reference; card 2 runs both.

Question

What holds the head back: the head itself, the spectrum it reads, or the way a frequency is asked? And does a plain softmax do better on seen frequencies?

What changed

One named part per contrast: the head (a matching head in place of the FiLM head), the features (the complex spectrum, which keeps phase, in place of the plain spectrum), the question (the reference with stimulus phase, or the reference without its second and third harmonics) and, in a separate run, the output (a softmax with no question, or route 3’s head trained with a softmax loss).

Matched control

The same arm without that change, paired on the same people, folds, rotations and seeds; card 1’s reference spectrum, numeric code and CCA sit beside them as levels.

Result

A plain 32-way softmax on the same spectrum reached 35.90% seen balanced accuracy (32.30%–39.32%). The head with one output per question, trained with the same softmax loss, reached 31.45%; trained one-vs-rest, as in route 3, it reached 32.16%. The paired difference, −0.71 pp (−1.01 to −0.41), is small, below zero and inside the ±2-point margin.

On the plain spectrum, a matching head in place of the FiLM head changed seen balanced accuracy by −3.60 pp with the reference spectrum (−4.37 to −2.73) and by +2.54 pp with question numbers (+1.74 to +3.37); the protocol counts a head gain as meaningful when its lower bound is above +2 points, and neither lower bound is. With question numbers, the complex spectrum, which also keeps phase, changed seen balanced accuracy by +18.03 pp for the FiLM head (+14.13 to +21.77), to 50.08%, and by +21.53 pp for the matching head (+17.25 to +25.63), to 56.14%. It also changes size, scaling and the head’s size, so these figures describe the feature recipe as a whole.

On held-out frequencies, a question carrying each target’s stimulus phase changed the complex-spectrum FiLM head’s accuracy by +16.30 pp against the magnitude question (+13.36 to +19.32), to 24.97%, and the matching head’s by +15.95 pp (+13.38 to +18.45), to 22.47%. Read side by side, both stay below the reference spectrum on the plain spectrum (39.00%), the numeric code (41.46%) and CCA (80.90%); the matching head’s paired difference from CCA is −58.43 pp (−62.10 to −54.83).

The stimulus phases come from the BETA authors’ corrigendum, converted to the cosine convention with zero latency; equal amplitudes across harmonics, with harmonic h at h times the stimulus phase, are modelling assumptions. They are the phases of the stimulus as displayed, and the question carries no phase measured on the scalp.

Dropping the second and third harmonics from the reference spectrum changed the plain-spectrum FiLM head’s held-out accuracy by −13.27 pp (−15.04 to −11.45), to 25.73%, and its seen balanced accuracy by −3.12 pp (−3.65 to −2.57).

95% intervals from 2,000 hierarchical paired bootstrap draws over people and fold-shared seed indices (seed 20261007). Twelve planned contrasts in the main run, all primary, and one primary and one secondary in the softmax run, with no multiplicity correction.

Limit. Each arm is one fixed recipe: the matching head is one bilinear design, and the softmax run changes the whole training objective or several parts of the architecture at once. These contrasts compare the recipes; how much frequency information the plain spectrum holds stays open. Both runs were designed with route 3’s results known.

During training only, each window’s complex spectrum got a random delay common to all channels, drawn either from 0–125 ms or from 0 to one period of the training label’s frequency. The head was the FiLM head on the complex spectrum, asked with the reference with stimulus phase, the phase-carrying query (526,465 parameters, trained from scratch); queries and test windows were unchanged. On held-out frequencies the 0–125 ms arm reached 12.51% (11.93%–13.13%) and the one-period arm 13.13% (12.61%–13.68%). The same head without the delay reached 24.97% (22.60%–27.44%). Primary change, 0–125 ms minus no delay: −12.46 pp (−14.84 to −10.25). Seen balanced accuracy fell from 49.24% to 15.70% and 15.28%.

Only the 0–125 ms minus no-delay contrast is primary; the others are descriptive. 95% intervals from 2,000 hierarchical paired bootstrap draws over people and training seeds (seed 20261007), conditional on the fixed person folds and three seeds; the five fixed rotations are averaged first. None of the 6 contrasts is adjusted for multiplicity. The delay multiplies already-windowed coefficients by one phase ramp, which approximates an onset shift. The one-period range is drawn from the training label’s frequency; the 0–125 ms range ignores the label and equals one period only at the lowest stimulus frequency, so its phase spread differs by target. BETA assigns each target its own stimulus phase, in equal steps between neighbouring frequencies, so the delay also removes information tied to the label. The magnitude-reference head on the plain spectrum (39.00%) differs in features, query and size. All 4 randomized-label checks passed (40 fits); a training-only shortcut through the label-dependent delay remains possible.

During training only, each window’s complex spectrum got a random delay of up to one stimulus period, applied as one phase ramp across all channels. Queries and test windows were unchanged. With the magnitude reference as the query, the FiLM head reached 30.56% on held-out frequencies (27.81%–33.22%). Against the same head and query on the plain spectrum the change was −8.45 pp (primary; −10.14 to −6.69); against the same head and query on the complex spectrum without the ramp, which reached 8.67%, it was +21.88 pp (secondary; +18.78 to +25.00). Seen balanced accuracy fell from 47.29% to 15.03%. The matching head ended at chance on both tasks. CCA reached 80.90% on the same held-out task. The bet in the thread was that held-out accuracy would clear 39%; the FiLM head reached 30.56% with the magnitude reference and 28.10% with the numeric code.

Of the 13 contrasts, six are primary (P1–P6) and seven secondary (S1–S7); none is adjusted for multiplicity. 95% intervals from 2,000 hierarchical paired bootstrap draws over people and training seeds (seed 20261007), conditional on the fixed person folds and three seeds; the five fixed rotations are averaged first. CCA has no training and a single seed axis; its only contrast is S7 (−67.97 pp). Held-out scores choose among 8 candidates and seen scores among 32, so the two are different tasks; m8 is the matched comparison for a held-out score, and there the FiLM head with the magnitude reference reached 42.86%. The contrasts against the plain spectrum (P1, P2, S3, S4) compare two feature recipes as well as the ramp: the complex and plain spectra differ in normalisation, size and capacity. The delay range is drawn from each window’s training label. The FiLM and matching heads start from different initial scores, so head comparisons are not initialisation-matched. BETA assigns each target its own stimulus phase, so phase carries real label information. The ramp acts on already-windowed coefficients, keeps magnitudes and the phase between channels, rotates the phases of the harmonics together, and approximates a time shift. All 10 randomized-label checks passed (120 fits); a training-only shortcut through the label-dependent delay remains possible.

On the same splits, CCA on the raw two-second window reached 80.90% on held-out frequencies (76.80%–85.13%, person bootstrap). Tapering the window with a Hann function changed it by −7.95 pp (−9.07 to −6.78), to 72.96%. A cropped-spectrum match with no training reached 73.20% on held-out frequencies (68.62%–78.13%), +0.24 pp from Hann-tapered CCA (−0.12 to +0.64). It works on the complex spectral coordinates that the earlier complex-spectrum heads read before their fitted scaling; asked with the reference with stimulus phase, those heads reached 24.97% (FiLM head) and 22.47% (matching head) on card 2, quoted here with no paired contrast. The match fits channel and reference weights for each window without labels.

Averaging each channel’s energy in the reference span reached 55.21% (49.99%–60.90%). One ridge scorer trained on the source people over each channel’s energy fraction at each of the 3 harmonics reached 57.45% (53.20%–62.14%): +2.23 pp over that average (+0.13 to +4.37) and −23.46 pp from CCA (−26.64 to −20.45). On the seen 32-way task it was −0.82 pp from the same average (−2.86 to +1.18).

Every method is given all 40 candidate frequencies; held-out means left out of supervised fitting. The study has 6 training-free scorers and 35 ridge fits, and seven prespecified contrasts on each task. 95% percentile intervals from 2,000 paired person bootstrap draws (seed 20261015); no multiplicity correction.

The cropped coordinates match the inputs the earlier heads read on the 6 rows checked; the heads’ fitted scaling is invertible but changes the distances the match uses. Checked: CCA reconstructed on all 11,200 windows, the training-free scorers spot-checked on 6 rows, all 35 ridge fits refitted independently.

Keeping temporal CCA and adding a bounded learned correction to its score reached 86.15% on held-out frequencies (82.84%–89.35%), against 80.90% for CCA alone: +5.24 pp (+3.91 to +6.62). On the seen 32-way task it reached 73.19% against 65.46% (+7.73 pp, +6.10 to +9.46). The correction can reorder only candidates whose CCA correlations lie within 0.2 of each other. Of all held-out decisions, it turned 7.39% from wrong to right and 2.14% from right to wrong. Giving the energy head six canonical correlations from the cropped-spectrum match, which makes it the adapted head, added +17.51 pp on held-out frequencies (+15.46 to +19.70); that gain bundles several matching operations.

The candidate frequencies still supply CCA’s sine and cosine references and the numeric code of each frequency. Filter-bank CCA and supervised spatial templates were not compared. The adapted head against CCA alone was not a planned contrast and has no interval. Each trained arm is the mean of three fixed training seeds. Six prespecified contrasts on each task; 95% percentile intervals from 2,000 paired person bootstrap draws (seed 20261015), conditional on the fitted models and the three fixed training seeds; no multiplicity correction.

Wearable-102: 102 people, 12 targets from 9.25 to 14.75 Hz, 12,240 two-second windows per sensor, dry and wet headbands, recordings as stored; 105 unchanged BETA models. The documentation cannot rule out that some people also appear in BETA.

The 105 models of card 6 (7 participant folds × 5 frequency rotations × 3 seeds), trained on BETA, were run unchanged on Wearable-102. On the same windows the models averaged 65.45% on dry electrodes and 81.04% on wet, and matched CCA 65.38% and 81.65%. Paired with matched CCA, the models changed the score by +0.07 pp dry (−0.71 to +0.91) and −0.61 pp wet (−1.48 to +0.23); both intervals include zero, and no equivalence margin was set. The models’ score is CCA plus a bounded learned term, so the change from matched CCA is what the learned term adds.

Matched CCA here uses sine and cosine references up to the third harmonic, as the models’ own CCA term does, and reached 65.38% dry and 81.65% wet; the dry-versus-wet page’s CCA uses references up to the fourth harmonic on the same windows and reached 65.47% and 81.56%.

A cropped-spectrum check (Wearable-102) reached 57.78% dry and 73.01% wet; it is shown as a diagnostic only.

Limits. Wearable-102’s stored amplitude unit is undocumented and the correction reads amplitude spectra, so these are as-stored figures. Its windows start 0.14 s after stimulus onset and BETA’s at onset, and hardware, reference, people and frequency grid change at the same time, so no single factor is isolated. Both methods receive the 12 candidate frequencies. Each person’s accuracy is computed for each of the 105 models and averaged over models, then over people, with no ensemble, refit or model choice. This task on other recordings stands apart from the BETA results of cards 1 to 6.

Dry and wet are the two primary contrasts and both sensors the secondary one. 95% percentile intervals from 2,000 paired person bootstrap draws (seed 20261015), conditional on the fixed 105 source models; no multiplicity correction.

Next in the thread: one set of learned weights scores each candidate’s channel-by-channel matrices at the fundamental and two harmonics, with no per-frequency parameters: fixed learned linear readouts of cross-spectral features, with prescribed trial-dependent normalization or whitening. The design is frozen and the run is in progress; its results join this page after review.