Does growing neurons during training improve convolutional EEG decoders?

Three backbones grown from a narrow start

Convolutional EEG decoders are normally trained at a fixed width, meaning the number of filters in each layer, and that width is usually chosen by the authors on one dataset and reused elsewhere. This study asks a narrower question: if a decoder starts narrow and adds neurons during training, does it end up better than the published reference width on the same subjects?

The authors grew three convolutional backbones on twelve motor-imagery datasets from MOABB, under three protocols: within-session (5-fold cross-validation inside a session), cross-session (leave-one-session-out) and cross-subject (leave-one-subject-out). Each backbone contributed two models, a reference at its published width and a growing counterpart starting narrow, for 34,596 fits in total. All models shared a 200-epoch budget, the AdamW optimiser, a learning rate of 6.25×10⁻⁴, batch size 64, no early stopping and three seeds per fold.

Scores follow MOABB conventions: ROC-AUC for the six two-class datasets and accuracy for the six others, both in percent, so model differences are reported in points. The datasets range from two to four classes and from four to 109 subjects.

Growth picks neurons from a residual spectrum

A growable layer is a pair of consecutive convolutions with at most a normalisation between them, so kernels can be added to the output of the first and the input of the second without touching other layers. Every five epochs the layer gets a growth opportunity, and the procedure decides where to grow, which neurons to add, how to initialise them and how many to keep.

The target is the change in the layer's output that would most reduce the loss at first order. Its projection onto the tangent space is the best reachable move; the leftover residual is what the paper calls the expressivity bottleneck. Fitting new neurons to that residual becomes a low-rank approximation, and a singular value decomposition returns candidate neurons ordered by first-order contribution.

The key adaptation for EEG is the selection threshold. The original method used an absolute threshold, which on EEG fell either above a backbone's whole spectrum or below all of it. Here candidates are kept only if their singular value is at least 10% of the largest one, so the same relative criterion applies across backbones. A width cap stops each layer at its target width, so a growing backbone never ends wider than its reference model.

A line search over scaling factors {0, 0.1, 0.5, 1.0} then sets how strongly the selected block is added, scored on the last fifth of the epoch's training batches. If the search returns zero, the update is deleted and the network is unchanged, which the paper calls a skipped neuron addition.

ShallowFBCSPNet gains 2.9 points with fewer parameters

The growing ShallowFBCSPNet is the clearest positive result. Within-session it scores 2.9 points above its reference model, with a 95% bootstrap interval over subjects of [+2.3, +3.5], and it is ahead on all twelve datasets. Cross-session the gain is 2.8 points [+1.9, +3.7], and cross-subject it shrinks to 0.9 points [+0.4, +1.3].

The gain does not come from extra capacity. The growing Shallow reaches +2.8 points with about 6×10⁴ parameters, against −0.1 points at 1.05×10⁵ for the reference model, which is 0.57x the parameters. The network stays small because growth stops before the target width: only 29% of Shallow folds reach width 40, and the median fold is scored at width 26.

How far it grows tracks the amount of training data. The share of Shallow fits reaching width 40 rises from none on Shin2017A, with 16 training trials per fold, to 94% on BNCI2014-001, with 230 trials (Spearman ρ = 0.77 across the twelve datasets). Cross-subject, where the training set pools all other subjects, it reaches 78%. The cost is training time: 22 seconds per fold for the growing Shallow against 14 seconds for the reference model, at the same 200-epoch budget.

SCCNet barely moves and the deep surrogate falls behind

SCCNet shows a much smaller contrast. Its growing version changes by at most 1.2 points: +0.4 within-session and −0.2 cross-subject, both with intervals crossing zero and both below the minimum detectable effect at 80% power, so the authors draw no conclusion from those two cells. Only the cross-session result, +1.2 points [+0.4, +2.1], is treated as informative. SCCNet reaches its full width of 22 on 78% of folds, so it largely reproduces the reference width and the small contrast follows.

The deep backbone is a different case and cannot be read as a clean test of growth. The growth implementation did not support the pooling operations inside the selected deeper blocks of Deep4Net, so the authors substituted a two-stage VGG-style surrogate they call Deep, pooling only at the end of a stage. That makes the comparison exploratory and not architecture-matched.

With that caveat, the growing Deep is behind on every dataset in all three protocols: −4.0 points within-session, −3.6 cross-session and −7.3 cross-subject. Because architecture and capacity differ from Deep4Net, the deficit cannot be attributed to growth alone.

A 2.9-point gain is small next to seed variance

The paper is explicit about effect size. The median standard deviation across seeds is 4.4 points, so the largest gain of 2.9 points is 0.7 times the spread of a single configuration. It appears only when averaged over 324 subjects. The authors also note that a nine-subject dataset cannot separate two architectures, and that effects of a few points are usual on this data.

Seven of the nine pooled cells survive Holm correction, and four of those favour the growing backbone while three favour the reference model. The two excluded cells are both SCCNet.

The paper also reports a separate alignment condition. Running Euclidean alignment as a second complete condition lowers all six models by 2.4 to 5.1 points within-session and raises them by 1 to 2 points only cross-subject. The authors note that taking alignment as the default would have favoured the growing backbones cross-subject and hidden a loss on every model within-session, so the main results are reported as raw scores without alignment.

Skipped neuron additions separate the backbones

What distinguishes the backbone that gains from the ones that do not is the skipped neuron addition rate, defined as the share of growth opportunities where the line search returns zero. It orders the three backbones the same way the accuracy results do: the growing Shallow skips 74.9% of its opportunities, the growing SCCNet 3.5% and the growing Deep 0.7%. Over the 542,187 opportunities of the campaign, Deep adds almost every update it is offered.

The same ordering appears one step earlier, in selection. Of the neurons proposed at a growth opportunity, Shallow keeps a median of 15% and SCCNet 85%, while Deep keeps all of them. The candidate spectra explain why: they span 3.1 to 4.0 decades for Shallow and 0.9 to 3.3 for SCCNet, but only 0.3 to 1.4 for Deep. On a spectrum that flat, no threshold separates the candidates and every proposal goes in.

The authors are careful about mechanism. A single growth step changes little: its predicted first-order gain is a median of 10⁻³·⁶ of the gain of one ordinary epoch for Shallow, and 10⁻¹·⁰ for Deep, and the held-out loss one epoch before and after a step is centred on zero for all three backbones. Any effect must therefore come through the training trajectory that growth induces, not through the individual step.

One simpler explanation is tested and rejected. If a width chosen on a large corpus were simply too large for one session, the growing backbone should gain most where training sets are smallest. Binned by training-set size, it has no advantage in the smallest bins and is behind in every bin cross-subject.

The skip rate is a training-signal diagnostic

The paper's own interpretation is that growth helps when its selection criterion can rank the candidate neurons. Where the candidate spectrum spans several decades, the first-order estimate can order the neurons and reject most of them, so the network stays small and improves. Where the spectrum is flat, every update is accepted, the network grows to its cap and gains nothing.

The practical consequence the authors draw is that the skipped neuron addition rate, reported alongside the final width, needs no test data and could indicate where a decoder can be grown small from scratch. That is a diagnostic computed from the training signal of a single run, not a guarantee of accuracy.

The scope is bounded by what was actually run: twelve motor-imagery datasets, three protocols, and three backbones, one of which was a non-architecture-matched surrogate. The Shallow result is the one that survives as a comparison between a growing model and its own reference width on the same subjects, and it is a result about a smaller network scoring slightly higher, not about a large accuracy jump.

Sources used in this answer