# Evaluating the structure of cognitive tasks
with transfer learning

Bruno Aristimunha1,2 Raphael Y. de Camargo2 Walter H. Lopez Pinaya3
Sylvain Chevallier1 Alexandre Gramfort1 Cédric Rommel1,4

1Université Paris-Saclay, Inria, France
2Federal University of ABC, Santo Andre, Brazil
3King’s College London, London, United Kingdom
4Valeo.ai, Paris, France

###### Abstract

Electroencephalography (EEG) decoding is a challenging task due to the limited
availability of labelled data. While transfer learning is a promising
technique to address this challenge, it assumes that transferable data domains
and task are known, which is not the case in this setting. This study
investigates the transferability of deep learning representations between
different EEG decoding tasks. We conduct extensive experiments using state-of-
the-art decoding models on two recently released EEG datasets, ERP CORE and
M3CV, containing over 140 subjects and 11 distinct cognitive tasks. We measure
the transferability of learned representations by pre-training deep neural
networks on one task and assessing their ability to decode subsequent tasks.
Our experiments demonstrate that, even with linear probing transfer,
significant improvements in decoding performance can be obtained, with gains
of up to 28% compare with the pure supervised approach. Additionally, we
discover evidence that certain decoding paradigms elicit specific and narrow
brain activities, while others benefit from pre-training on a broad range of
representations. By revealing which tasks transfer well and demonstrating the
benefits of transfer learning for EEG decoding, our findings have practical
implications for mitigating data scarcity in this setting. The transfer maps
generated also provide insights into the hierarchical relations between
cognitive tasks, hence enhancing our understanding of how these tasks are
connected from a neuroscientific standpoint.

_K_ eywords Transfer Learning $\cdot$ Deep Learning $\cdot$
Electroencephalography $\cdot$ Event-Related Potential $\cdot$ Brain-Computer
Interfaces

##  1 Introduction

While brain encoding consists in predicting brain activations given a certain
stimulus, brain decoding tackles the inverse problem: translating recorded
neural activity into its originating stimulus or behavior [1]. This stimulus
or behavior can be a visual or auditory element presented, the subject
internal mental state (e.g. sleep stage), or the cognitive or motor task being
performed during the experiment. Brain decoding has several important
applications, such as the diagnosis of neurological disorders [2, 3, 4], the
detection of seizures [5, 6], automatic processing of polysomnographic
recordings [7] and brain-computer interfaces [8, 9, 10], among others.
Electroencephalography (EEG) is a common and affordable way to record the
neural activity in this context [11]. It has the benefit of being non-
invasive, having very high time resolution compared to functional magnetic
resonance imaging (fMRI) and not requiring a complex and costly infrastructure
such as magnetoencephalography (MEG). In recent years, there has been an
increasing interest in using deep learning (DL) models for EEG decoding [12].
As an example, DL has been shown to be the gold standard when it comes to
automatic sleep stage classification [13, 14, 15] and has also demonstrated
impressive performances in brain-computer interfaces [16, 17, 18, 19].

Unfortunately, DL models are notorious for being data-hungry to extract
generalizable discriminative representations. This characteristic can be a
problem when it comes to EEG decoding since the acquisition of labelled EEG
data remains a constraint, resulting in datasets of limited size. Indeed, EEG
annotation often requires a specialist to run experiments or visually inspect
recorded signals for specific patterns. In addition, EEG signals have a very
low signal-to-noise ratio, especially when we compare to other fields of
application which were DL thrived, such as image, speech, and text. This
characteristic makes EEG decoding even more challenging for DL methods in the
context of small datasets.

A common technique in DL for dealing with scarce data scenarios is transfer
learning (TL), which consists in applying what you have learned in one context
to another [20]. In other words, it can be used to leverage a large dataset to
improve the performance in a related smaller dataset, making it a promising
technique to alleviate the lack of EEG decoding data. However, TL assumes the
knowledge of transferable data domains and tasks, which is not fully
understood when it comes to brain data. Indeed, even beyond EEG decoding,
understanding hierarchical relations between cognitive tasks remains a core
question in neuroscience.

Inspired by the Taskonomy study [21] from the computer vision field, this work
investigates the relations between cognitive tasks in an EEG decoding setting.
Specifically, we measure the transferability of representations learned by DL
models between cognitive tasks. This transferability is measured by pre-
training DL models to decode the EEG signals of subjects carrying certain
tasks and assessing how well a classifier can reuse the learned
representations to decode a subsequent task. We carry extensive experiments
with three state-of-the-art decoding models [18, 16, 17] trained and evaluated
on two recently released EEG datasets, ERP CORE [22] and M3CV [23], containing
in total over 140 subjects with 11 distinct decoding modalities. This enables
us to create transfer maps capturing the relationships between pairs of
cognitive tasks, as presented in Figure 1. From an EEG processing perspective,
our maps can be used to leverage related datasets for alleviating EEG data
scarcity with transfer learning. We show that even with a linear probing
transfer method, we are able to boost by up to $28\%$ the performance of some
tasks. From a neuroscientific standpoint, our results broaden our
understanding of the connections between cognitive tasks. We discover evidence
that some decoding paradigms elicit very specific and narrow brain activities,
since no other paradigm transfer well into them. On the other hand, the
decoding of some cognitive tasks benefits from pre-training on all other
paradigms, thus demonstrating that they rely on a broad range of
representations.

We organize the paper as follows. First, section 2 introduces the relevant
related work in transfer learning, EEG decoding and cognitive tasks structure
investigation. In section 3, we formalize transfer learning for EEG decoding.
Then, section 4 outlines our experimental setting, including a description of
the two EEG datasets and their respective decoding modalities, as well as our
training and data processing protocols. Subsequently, we present the main
results of our experiments in section 5, highlighting the significant
improvements in decoding performance achieved through transfer learning.
Finally, in section 6, we discuss the broader implications of our findings and
offer insights into the hierarchical and asymmetric relations between
cognitive tasks.

(a) ShallowNet (b) EEGNet (c) EEGInception

Figure 1:  Revealing cognitive connections through transfer learning. This
graph depicts the transferability of representations used for EEG decoding,
capturing the intricate interplay between cognitive tasks. Each node
corresponds to a distinct paradigm within the ERP CORE dataset. Arrow width
represents the average transfer performance when using the representations
learned from a source task to decode a target task. MMN is a great target task
for transfer learning, benefiting from representations learned from all source
tasks. On the contrary, LRP is mostly a source task: its representations are
useful for a wide range of other paradigms.

##  2 Related Works

###  2.1 Transfer Learning and Taskonomy

Transfer learning refers to the technique of leveraging knowledge acquired
from one source domain and task to enhance the performance in another target
domain and task [24, 25]. Domain adaptation, domain generalization and self-
supervised learning are hence considered sub-fields of TL under this broad
definition [25, 26, 27]. The most common TL approach consists in fine-tuning
on a target dataset a model that was pre-trained on a source dataset. In this
context, the main factor determining the success of TL is the relationship
between source and target domains and tasks. TL might indeed hinder learning
performance in some situations, such as when the source and target are
unrelated, which is known as negative transfer [28, 29].

Numerous studies have examined the relationship between tasks for TL purposes
[21, 30, 31, 32, 33, 34]. One of the most influential works in this area is
Taskonomy [21], which investigates these relationships in the context of
computer vision tasks. Although we take great inspiration from it, our works
differ primarily in the definition of what a "task" is. While Taskonomy tries
to uncover the relation between _visual learning tasks_ (i.e. _given an image,
what is the visual label?_), we focus in relating _cognitive tasks_ (i.e.
_given the measured brain activity, what is the subject doing?_). In this
sense, while Taskonomy works with the same input images, analyzing transfer to
different output distributions $P_{S}(Y)\to P_{T}(Y)$, our setting is more
challenging as we need to transfer between joint distributions of input EEG
signals and output decoded stimuli $P_{S}(X,Y)\to P_{T}(X,Y)$. This
distinction is made clearer in section 3.

###  2.2 Transfer learning with brain data

Most EEG decoding works involving transfer learning focus on cross-subject
evaluation within the same decoding task [35, 36, 37, 38, 39, 40, 41, 42, 43,
20, 44, 45, 46]. Given the extremely high inter-subject variability of EEG
signals, this is a crucial question in the design of real-world systems able
to generalize from one subject to another. While we study the transfer between
different tasks, previous studies consider the same fixed task in different
data domains corresponding to each subject or session. They enter in the more
specific sub-category of domain adaptation and generalization.

Most related to our work, [47, 48, 34, 49] measure the transferability between
cognitive tasks, drawing inspiration from the Taskonomy framework [21].
However, these works are all based on fMRI data and most use _encoding_ models
for very specific types of visual or language stimuli. In contrast, our work
uses EEG _decoding_ models to compare a broader range of stimuli in different
modalities. By working with decoding instead of encoding models, our results
are not only useful to understand the relation between cognitive tasks, but
also to improve the performance of automatic EEG processing systems in real-
world scenarios where data is scarce.

Similar to our work, Qu et al. [49] also uses decoding models to create a
transferability map between a large set of cognitive tasks with fMRI data. By
working with EEG data rather than fMRI, our analysis can better detect signal-
level patterns at the expense of a smaller spatial precision, making it
complementary to this previous study. Moreover, while all experiments in [49]
were conducted on a single dataset with a small fully connected network
architecture, our experimental analysis encompasses consistent results on two
very distinct datasets using three different state-of-the-art deep neural
network architectures.

###  2.3 Uncovering cognitive tasks relations with EEG

Beyond the framework of transfer learning, researchers in the EEG decoding
community have been interested in identifying the latent structure between
cognitive tasks by other means. For example, Rommel et al. [50] analyzed what
data augmentations work best for decoding different cognitive tasks. They
showed that some augmentations work well for many different tasks,
demonstrating that they share some common invariances, while others only
improve the decoding performance in some specific cases. Although some
structure arises as a by-product of this study, it focuses on task
invariances. Our work differs substantially from [50] since our analysis
directly connects one cognitive task to another based on transferred
predictive performance instead of invariances.

As another example, studies conducted by Banville et al. [51, 52] have
demonstrated that self-supervised representations can encode clinically-
relevant structures from EEG data, such as the sleep stages, pathology, age,
apnea and gender information, without any access to such labels. A similar
outcome was observed in [53, 54]. While these methods are capable of learning
representations useful for different downstream tasks, these works do not
study transfer to different domains and datasets in practice. Our work focuses
not only on discovering the structure between predefined supervised tasks but
also quantitatively assesses the transferred performances into new data
domains and tasks.

##  3 Method

Figure 2: A. Data splitting and alignment. Source and target tasks correspond
to different ERP and BCI paradigms; B. EEG decoding models as a representer
network and a classification head; C. Standard EEG decoding training and
evaluation; D. Transfer with linear probing. Only the classification head
$h_{\psi}$ is re-trained, while the representer network $r_{w_{S}}$ trained on
the source task is kept intact.

###  3.1 EEG Decoding

From a machine learning perspective, EEG decoding is defined as a
classification problem using a dataset of $N$ pairs of trial recordings and
decoding labels $\mathcal{E}=\\{(\mathbf{x}_{i},y_{i})\\}_{i=1}^{N}$. Each
trial recording $\mathbf{x}\in\mathcal{X}=\mathbb{R}^{m\times c}$ is modelled
as a matrix with $m$ rows and $c$ columns, where $m$ is the number of time-
steps and $c$ is the number of electrodes. The decoding labels
$y\in\mathcal{Y}$ correspond to the class of stimulus to predict, where
$\mathcal{Y}$ is a discrete set containing 2 or 3 classes in the decoding
scenarios studied in this paper. We assume the dataset is randomly split into
a training set $\mathcal{E}_{\text{train}}$ of size $N_{\text{train}}$ and
test set $\mathcal{E}_{\text{test}}$ of size $N_{\text{test}}$. The decoding
problem amounts to using the training set $\mathcal{E}_{\text{train}}$ to
learn a model $f_{\theta}:\mathcal{X}\to\mathcal{Y}$ with parameters $\theta$
mapping each trial $\mathbf{x}$ to the associated label $y$. This is achieved
by optimizing the model parameters to minimize an average loss function $\ell$
across the training dataset:

$\min_{\theta}\frac{1}{N_{\text{train}}}\sum_{\mathcal{E}_{\text{train}}}\ell(f_{\theta}(\mathbf{x}_{i}),y_{i})\enspace.$
(1)

In all our experiments, the loss function $\ell$ used is the balanced cross-
entropy. The generalization performance of the trained model is assessed on
the test set $\mathcal{E}_{\text{test}}$ (c.f. Figure 2 A, B, C).

###  3.2 Transfer learning

More generally, we assume that our dataset corresponds to observations of a
joint random variable $(X,Y)$ valued on a space
$\mathcal{X}\times\mathcal{Y}$, where some decision function $f$ exists such
that $Y=f(X)$. Hence, problem (1) amounts to trying to approximate the
decision function $f$ by optimizing the model $f_{\theta}$ to fit the training
data sampled from $P(X,Y)$.

Following [25], a _domain_ is defined by a feature space and inputs
distribution $\mathcal{D}=\\{\mathcal{X},P(X)\\}$. Likewise, a task consists
of an output space and a decision function $\mathcal{T}=\\{\mathcal{Y},f\\}$.
Transfer learning aims to use the knowledge extracted from a source domain
$\mathcal{D}_{S}$ and task $\mathcal{T}_{S}$ to improve the performance of a
model $f_{\theta}$ on another target domain $\mathcal{D}_{T}$ and task
$\mathcal{T}_{T}$. Both domains and tasks are materialized by source and
target datasets ${\mathcal{E}_{S}=\\{(x_{i},y_{i})\sim
P_{S}(X,Y);Y=f_{S}(X)\\}}$ and ${\mathcal{E}_{T}=\\{(x_{i},y_{i})\sim
P_{T}(X,Y);Y=f_{T}(X)\\}}$.

In our context of EEG decoding, the source and target datasets correspond to
different ERP and BCI cognitive tasks performed by the same cohort of subjects
in comparable experimental settings (c.f. section 4). Hence, while source and
target domains share the same feature space $\mathcal{X}=\mathbb{R}^{m\times
c}$, they differ in terms of marginal distributions of input trial recordings
$P_{S}(X)\neq P_{T}(X)$. Regarding learning tasks, source and target datasets
differ in terms of decision functions $f_{S}\neq f_{T}$ and output spaces
$\mathcal{Y}_{S}\neq\mathcal{Y}_{T}$. As opposed to our setting, Taskonomy
[21] works with a common source and target domains
$(\mathcal{X}_{S},P_{S}(X))=(\mathcal{X}_{T},P_{T}(X))$.

###  3.3 Transferability through linear probing

We evaluate the transferability between source and target datasets through
_linear probing_ [55, 56], as described below. We assume that $f_{\theta}$ is
a neural network made of two parts: a representer model
$r_{\omega}:\mathcal{X}\to\mathcal{R}$, with parameters $\omega$, and a
classifier head $h_{\psi}:\mathcal{R}\to\mathcal{Y}$, with parameters $\psi$

$f_{\theta}(x)=h_{\psi}\left(r_{\omega}(\mathbf{x})\right).$ (2)

The parameters $\theta$ of the model are hence the concatenation of $\omega$
and $\psi$. While the representer $r_{\omega}$ is responsible for learning
useful representations for the learning task, the classifier head $h_{\omega}$
is just the last linear layer of the network used to deliver the
classification decision. When assessing the transferability between a source
and target datasets (c.f. Figure 2):

  1. 1.

We first train the whole model $f_{\theta_{S}}=h_{\psi_{S}}\circ
r_{\omega_{S}}$ on the training split of the source dataset
$\mathcal{E}_{S,\text{train}}$ by solving equation (1) ;

  2. 2.

Then we freeze the representer parameters $\omega_{S}$ and retrain the
classifier head $h_{\psi_{T}}$ from scratch on the training split of the
target dataset $\mathcal{E}_{T,\text{train}}$:

$\psi_{T}\in\arg\min_{\psi}\frac{1}{N_{\text{train}}}\sum_{\mathcal{E}_{T,\text{train}}}\ell(h_{\psi}\left(r_{\omega_{S}}(\mathbf{x}_{i})\right),y_{i})\,;$
(3)

  3. 3.

Finally, we evaluate the network obtained $h_{\psi_{T}}\circ r_{\omega_{S}}$
on the test split of the target dataset $\mathcal{E}_{T,\text{test}}$ and use
this metric to assess the transferability between $S$ and $T$.

We evaluate the transferability through linear probing since it assesses
whether the representations learned from the source dataset allow us to
classify the target data. In contrast, fine-tuning (i.e. pushing the training
of the whole model $h$ and $r$ further with target data) would modify the
learned source representations, which would complicate the analysis [57].

##  4 Experiments

###  4.1 ERP CORE and M3CVdatasets

During EEG decoding experiments, subjects perform cognitive tasks with stimuli
that evoke specific brain signatures. When the nature of the stimuli is
similar, they can be categorized into the same paradigm. EEG decoding studies
have been interested in a very large and diverse number of paradigms, which
can be categorized as exogenous (where an external stimulus is used e.g. event
related potential) or endogenous (where stimuli are induced by a predetermined
mental task or behavior, e.g. motor imagery) [58, 8]. Only a small number of
EEG datasets contain recordings in a diverse set of paradigms with the same
subjects and configurations. Most existing datasets include a limited number
of subjects [59, 60] or a limited number of cognitive tasks [61, 62, 63].

In our study, we use two of the few EEG datasets that explore a large
diversity of paradigms with a single large cohort of subjects in comparable
experimental settings. The first dataset, ERP CORE [22], comprises $40$
subjects ($25$ females and $15$ males between $18$ and $30$ years old). It
focuses on exogenous paradigms, featuring seven isolated tasks eliciting
specific event-related potential components (ERP), namely Active Visual
Oddball (P3b), Word Pair Judgement (N400), Face Perception (N170), Passive
Auditory Oddball (MMN), Flankers (LRP and ERN) and Simple Visual Search
(N2pc).

The second dataset, M3CV [23], is a large multi-task, multi-session, multi-
subject investigation of EEG commonality and variability. It includes $106$
subjects who performed specific tasks in six different paradigms. In this
work, we only focus on trials for which the subject and task labels were
available, namely: Motor Execution (ME), Transient-State Sensory (TSS),
Resting-State (RS) and Steady-State Sensory (SSS). This reduces our dataset to
$95$ subjects ($22$ females and $73$ males between $19$ and $24$ years old)
corresponding to the enrolment and calibration subsets of the original
dataset. The different paradigms for both datasets are presented in Figure 3.
Other details about these datasets are also listed in Table 1.

Figure 3:  Illustration of experiments recorded in ERP CORE (A to F) and M3CVdatasets (G to J). Labels under the stimuli correspond to what subjects are supposed to answer during the trials. They do not necessarily correspond to decoding labels. A. In the active visual oddball task P3b, participants viewed random letters and responded to whether each stimulus was matched to the target (T) or not. One of the letters was designated as the target for each block of trials, with a probability of $0.2$. B. The word pair judgment task N400, involved participants viewing a red prime word followed by a green target word and indicating whether the target word was semantically related or unrelated to the prime word. C. During the face perception task N170, participants viewed images of faces, cars, scrambled faces, or scrambled cars and indicated whether the stimulus was an "object" (face or car) or a "texture" (scrambled face or scrambled car). D. The passive auditory oddball task MMN involved participants watching a silent video while speakers played standard and deviant tones. Deviant tones had a probability of $0.2$. E. In the flanker’s task, participants indicated the direction of the central arrowhead, which was surrounded by arrowheads pointing in the same (congruent trials) or opposite (incongruent trials) directions. This task elicited the lateralized readiness potential (LRP) and the error-related negativity (ERN). F. In the simple visual search task N2pc, either pink or blue was designated the target colour at the beginning of each trial block. Participants had to indicate whether the gap was on the top or bottom of the coloured square. G. During the Motor Execution task (ME), participants responded to a visual cue by _executing_ movements with their left hand (LH), right hand (RH), or right foot (FT). H. Transient-State Sensory (TSS) potentials were elicited by visual, auditory, and somatosensory stimuli. All three categories of stimuli were arranged in random order and lasted 50 milliseconds each. I. In the Resting-State task (RS), participants completed two runs with eyes closed (EC) and two with eyes open (EO), each lasting one minute. J. The Steady-State Sensory (SSS) task involved separate trains of visual, auditory, and somatosensory stimuli, with different stimulation frequencies and recording times for each run. Table 1: Dataset, Cognitive task, time-locking event, time window and number of classes for all the sub-datasets in ERP CORE and M3CV. Dataset | Cognitive Task ($\mathcal{E}$) | Time-Locking Event | Window size (ms) $(m)$ | # classes ($\mathcal{Y}$)
---|---|---|---|---
ERP CORE | N170 | Stimulus-locked | -200 to 800 | 2
ERP CORE | MMN | Stimulus-locked | -200 to 800 | 2
ERP CORE | N2pc | Stimulus-locked | -200 to 800 | 2
ERP CORE | N400 | Stimulus-locked | -200 to 800 | 2
ERP CORE | P3 | Stimulus-locked | -200 to 800 | 2
ERP CORE | LRP | Response-locked | -800 to 200 | 2
ERP CORE | ERN | Response-locked | -600 to 400 | 2
M3CV | ME | Stimulus-locked | 0 to 1000 | 3
M3CV | RS | Stimulus-locked | 0 to 1000 | 2
M3CV | SSS | Stimulus-locked | 0 to 1000 | 3
M3CV | TSS | Stimulus-locked | 0 to 1000 | 2

###  4.2 Defining the decoding labels

The two EEG datasets under investigation offer many options to define the
decoding labels $y$. For instance, one could consider the subject’s response
accuracy to the stimulus or whether the answer was in the appropriate time
frame. Another possible label definition involves predicting the stimulus
presented based on the recorded signal or the presence or absence of the task
component [64, 22]. We describe hereafter how we defined the decoding labels
in our experiments, starting with the ERP CORE dataset.

The _Flankers_ task aims to elicit two possible ERP components: _ERN_ and
_LRN_. ERN characterizes situations in which the subject makes an error, even
when they are not consciously aware of them [65]. It is elicited here by
asking subjects to indicate whether they saw a left or right trigger. We
assigned one label to trials where the subject’s response matched the target
stimulus, and another label when it did not. If the trigger and response were
both left or right, the trial was labelled as correct; otherwise, it was
incorrect [66, 22, 67].

The same Flankers task is used to elicit the _LRN component_ , which is
related to the side of the response hand. Unlike ERN, this component is
associated with preparing the response rather than its execution, as reported
in previous studies [66, 67]. Hence, we relied solely on the subject’s
response to determine the label for each trial in this case. Specifically, if
the subject answered with the left hand, we assigned one label; if they
responded with the right hand, we assigned a different label.

The _Word Pair Judgment_ task is used to elicit the _N400_ component. It
consists in presenting participants with a prime word, followed by a target
word and asking them to judge whether they are semantically related or not
[68]. To define the label for each trial, we use the stimulus definition.
Specifically, if the presented words were semantically related, we assigned
one label; if they were unrelated, we assigned a different label.

The _N2pc_ component is elicited through a _Simple Visual Search_ task [69].
In this task, participants had to visually identify a specific target item (in
blue or pink) among multiple distractors (in black). Notably, each item is an
outlined square with a gap on top or bottom, and subjects had to indicate the
position of the gap on the target item (c.f. Figure 3). Despite the task
assigned to the subjects, what is decoded in this experiment is the position
of the target within the screen, i.e. whether it appeared on the left or right
side, since this is what the N2pc component really captures. As usually done
for this experiment [64], we excluded trials with incorrect responses to
ensure that the subjects were paying attention to the target.

The _N170 component_ [70] was elicited by presenting stimuli in the form of
cars, faces, and deformed versions of these objects, in what is called the
_Face Perception_ task. Participants had to identify whether the presented
stimulus was intact or scrambled. To simplify the analysis, we excluded
scrambled stimuli as recommended by the original authors of ERP CORE [64], and
labelled the remaining ones according to whether they represented a car or a
face.

Concerning the _Active Visual Oddball_ task, participants were asked to watch
a sequence of random letters among A, B, C, D or E. The first letter in a
trial had the role of target, and subjects had to answer whether the following
letters matched the target or not, which should elicit the _P3b component_
[71]. To assign trial labels for this task, we considered two factors. First,
we checked whether the letter on the screen matched the target letter. Second,
we verified whether the participant provided the correct answer or not. If
both conditions were satisfied, we assigned one label to the trial. If not, we
assigned another label.

Finally, the _Passive Auditory Oddball_ task aims to elicit the _MMN
component_ [72]. In our study, the stimuli were used to define the trials
labels. Specifically, we assigned one label if the individual heard a standard
tone at 80 dB and another label if they heard a deviant tone at 70 dB.

In the M3CVdataset, the definition of labels was more straightforward. For
instance, decoding labels for the _RS_ task simply corresponded to whether the
subjects had their eyes open or closed. For the _TSS_ and _SSS_ tasks, labels
were directly defined based on the stimulus presented to the subjects, i.e.
whether it was a visual, auditory or somatosensory stimulation (3-class
classification problem). Likewise, decoding labels of the _ME_ task
corresponded to the movement being executed by the subjects, i.e. either the
right foot, the right hand or the left hand (3-class classification problem).

###  4.3 EEG pre-processing and epoching

Both datasets were pre-processed following the authors’ recommendations in all
our experiments. Namely, ERP CORE recordings were filtered between $[0.5-40]$
Hz with overlap-add FIR filtering. Electric potentials were referenced on the
average of electrodes P9 and P10 for all tasks except N170, for which we used
the average of all 33 electrodes as commonly done in the literature [22].
Stimuli events were shifted $26$ ms forward in time to account for the LCD
monitor delay in the MMN task. We downsampled the data from $1000$ Hz to $250$
Hz and used ICA [73] to correct artefacts and discard particularly bad trials.
Finally, trials were cropped into $1000$ ms windows based on the stimulus or
response depending on the task, following values reported by [22]. This
dataset was entirely pre-processed using the MNE-Python library [74].

For the M3CVdataset, we used the dataset pre-processed by the authors as
described below. Signals were band-pass filtered between $[0.01-200]$ Hz using
a 4th order Butterworth filter and notch filtered between $[49-51]$ Hz.
Potentials were referenced on the average of electrodes TP9 and TP10. Visual
inspection and ICA were used to remove artefacts, and bad channels were
replaced by the average of the three neighbouring channels. Finally, $1000$ ms
signals were cropped from each trial. More pre-processing details can be found
in [23].

###  4.4 Data splitting

The datasets were randomly split into a training, a validation, and a test set
with respective proportions of $56\%$, $24\%$ and $20\%$. Each split contains
data from different subjects since we want to assess the cross-subject
generalization of our models. Trainings and evaluations were repeated with
different splits following a 5-fold cross-validation scheme.

In the standard decoding experiments (subsection 5.1), models were trained and
evaluated using data from the same cognitive task (c.f. Figure 2 C). In the
transfer learning experiments (subsection 5.2), models were pre-trained on
training subjects of some task $A$, then fine-tuned through linear probing on
data from the same subjects performing a different task $B$ and finally
evaluated on unseen test subjects carrying out this same task $B$, as
described in subsection 3.3 and illustrated in Figure 2 D. Thanks to this data
splitting alignment across cognitive tasks, we ensure that the test subjects
remain the same after transfer, avoiding any leakage between test and training
sets.

###  4.5 Decoding models

We evaluated the transferability of learned tasks using three state-of-the-art
deep learning models: ShallowNet [18], EEGNet [16], and EEGInception [17].
ShallowNet is an efficient network inspired by the Filter Bank Common Spatial
Pattern method [75]. It contains $36k$ trainable parameters. EEGNet model has
a convolutional layer for channel-based EEG data filtering, a depth-wise
convolutional layer acting as a spatial filter across channels, a separable
convolutional layer for categorical feature extraction, and a fully connected
layer as classification head. Finally, EEGInception has $15k$ parameters and
extracts low- and high-frequency features in parallel at different scales.
These architectures delivered state-of-the-art results in several EEG decoding
tasks and datasets [76, 77, 78, 79, 80, 81]. In all our experiments, we used
the implementations of these models available in the Braindecode library [18]
with default hyperparameter values.

As baselines, we also tested Riemannian methods, which are known as the best
machine learning techniques for BCI and ERP, together with DL models. To this
end, we evaluated both Minimum Distance to Riemannian Mean (MDM) [82, 83] and
Tangent Space methods with either logistic regression or support vector
machine classifiers. We also evaluated these methods with a varied set of
covariance matrices, such as ERPCovariances [84] and Xdawn [85]. These methods
were implemented and trained using the MOABB and PyRiemann library [86, 87].

###  4.6 Training setting

All DL models were initialized with the Xavier sampling [88] and trained with
the AdamW optimiser [89] using default parameters $\beta_{1}=0.9$ and
$\beta_{2}=0.999$ and a weight decay of $5\times 10^{-4}$. The initial
learning rate was set to $10^{-4}$ for ShallowNet and EEGInception, and to
$6.25\times 10^{-4}$ for EEGNet. Trainings lasted at most 200 epochs and an
early stopping [90] procedure with a patience of 50 epochs was used. The
training of all deep learning models was carried out using Pytorch and
Braindecode libraries [91, 18] on an Nvidia DGX with 4 A100 boards.

##  5 Results and Findings

###  5.1 Decoding perfomance

We first analyse the decoding performance of studied models on ERP CORE and
M3CVdatasets in a standard decoding setting, without any transfer. Overall, DL
methods deliver superior balanced accuracies than baseline methods, as shown
in Figure 4.

Their scores also exhibit lower standard deviations than machine learning
methods, demonstrating the stability of learned representations across subject
splits. Notably, EEGNet consistently led to the best performance on ERP CORE
for all paradigms, whereas ShallowNet outperformed others on three out of four
paradigms of the M3CVdataset. Also, note that our results on ERP CORE are
consistent with those reported in [92, 93].

(a) ERP CORE dataset

(b) M3CVdataset

Figure 4:  Cross-subject balanced accuracy across paradigms. Error bars
correspond to the standard-deviation across 5-fold cross-validation. DL
methods outperform machine learning baselines on most paradigms. EEGNet is
consistently better than other architectures in ERP CORE . ShallowNet leads to
the best scores across M3CVparadigms, except for TSS.

To support this analysis, we performed a permutation signed-rank test for each
model pair within each paradigm to determine whether observed performance gaps
are significant (Figure 5). The resulting p-values were combined using
Stouffer’s method, with a weighting given by the square root of the number of
subjects, and a Bonferroni correction was applied to account for multiple
comparisons, as done in [86]. The standardized mean difference was calculated
within each dataset to determine the effect size. Examining Figure 4(b), we
observe that EEGNet slightly outperforms ShallowNet, although the difference
is not statistically significant, as highlighted in Figure 5(b).

(a) ERP CORE dataset

(b) M3CVdataset

Figure 5:  Significant pairwise standardized mean performance difference
between decoding models from Figure 4. Statistical significance was computed
using a corrected permutation test, with a cutoff p-value of $0.05$.

From a paradigms perspective, the most challenging task within the ERP CORE
dataset is the MMN paradigm, which is unique in that the subject does not have
an active response moment. Conversely, the least difficult tasks correspond to
the ERN and LRP.

Overall, the best DL architectures (EEGNet for ERP CORE and ShallowNet for
M3CV) lead to similar performances across paradigms, even in scenarios with
different numbers of classes (e.g. two classes in RS vs. three classes in ME,
SSS and TSS). This suggests that the results are robust and confirms that the
selected decoding architectures are well-suited to the different experimental
paradigms studied in this work.

###  5.2 Transfer learning performance

####  5.2.1 ERP CORE

We now analyse the transfer performance between paradigms to quantify how
transferable each cognitive task is in relation to one another. Figure 6 shows
the obtained balanced accuracy for each pair of source and target cognitive
tasks in the ERP CORE dataset. A first intriguing observation is the asymmetry
of the transfer matrices obtained, regardless of the model used, indicating
that the transferability between tasks is highly directional. We can see that
some tasks do not transfer well, leading to accuracies close to chance ($50\%$
in this dataset, as all classification problems are binary). Notably, no
source task is correctly transferring to either to LRP or N400 paradigms. This
means that these cognitive tasks rely on very specific representations that
are not elicited by the other tasks and are hence erased by models pre-trained
on other paradigms.

Figure 6:  Transfer balanced accuracy for each pair of sources and target
cognitive tasks in the ERP CORE dataset. Cell values correspond to average
performance and standard-deviation across 5-fold cross-validation. Diagonal
values correspond to standard decoding balanced accuracies, without transfer
(c.f. subsection 5.1).

Conversely, representations learned on some source tasks seem useful for
decoding others, at least to a level of accuracy comparable to a model fully
trained and evaluated in a standard fashion (diagonal values in the figures).
For example, LRP proves to be a good source task when transferring to ERN and
MMN. This suggests that LRP elicits some brain activations common to ERN and
MMN, which are learned by the decoding networks into its hidden
representations.

More strikingly, pre-training on some source tasks, such as ERN, improves
performance on some other target tasks, like N170, even _exceeding_ the
reference performance of a model fully trained on this target task. The best
example of this is the MMN task, whose performance is boosted beyond the
reference accuracy when transferring _from all possible source tasks_. With
ShallowNet, for example, we observe improvements of
$28.3\%,6.1\%,4.6\%,3.7\%,2.7\%,$ and $2.2\%$ for the LRP, N2pc, ERN, N400,
P3, and ERN source tasks, respectively. This is also observed for EEGNet and
EEGInception, although more discretely.

In order to better visualize these complex connections between tasks, we
processed the matrices from Figure 6 into transferability maps, shown in
Figure 1. Arrows’ widths are proportional to corresponding transfer
accuracies, where performances close to chance level were omitted. More
precisely, they correspond to transferability scores $s_{S,T}$ for each source
and target tasks, obtained by linearly rescaling the corresponding accuracies
$a_{S,T}$ so that $0$ corresponds to the chance level $c_{T}$ and $1$
corresponds to the reference accuracy without transfer (i.e. matrix diagonal
$a_{T,T}$):

$s_{S,T}=\frac{\max(a_{S,T}-c_{T},0)}{a_{T,T}-c_{T}}\,.$ (4)

The Scalable Force-Directed Placement (SFD) layout algorithm [94] was used to
create the graphs. This figure clearly shows that LRP is a very good source
task and that MMN is a great target task. Note that all three different
architectures lead to consistent maps overall, evidencing the stability of our
findings.

As another way to compare tasks, we also clustered them as done in [21] by
representing each task by its row vector in the transferability matrix
rescaled through (4). This led to the dendrograms depicted in Figure 7(a). By
comparing tasks through their row vectors, we are trying to see whether they
transfer in a similar fashion to other tasks. Most tasks cluster together,
with N400-N2pc and N170-ERN being the closest pairs. We also see that LRP
stands outside of the cluster, as it is a particularly good source task.

(a) ERP CORE

(b) M3CV

Figure 7:  Hierarchical clustering dendrogram, showing the resemblance between
source tasks in both datasets. Each task is represented by its row in the
transferability matrices (Figures 6 and 8) rescaled through Equation 4.
Pairwise distances were than computed using the Euclidean distance, before
clustering the tasks with the UPGMA algorithm [95].

####  5.2.2 M3CV

Moving on to M3CV, we see in Figure 8 that we also obtain very asymmetrical
transferability matrices for this dataset. The best example of this asymmetry
are the tightly related SSS and TSS tasks, which share the same class labels:
visual, auditory or somatosensory stimuli. Surprisingly, while SSS transfers
relatively well to TSS, the opposite is not true, showing that steady-state
representations have something specific which is not captured when pre-
training on transient state data.

Another striking observation is that the EEGInception matrix differs from
ShallowNet and EEGNet ones. This is probably due to the lower pre-training
performance of this model seen on Figure 4(b), evidencing that it learned
weaker representations. Interestingly, we see on both ERP CORE and M3CVresults
that transfer performances across models (Figures 6 and 8) rank consistently
with pre-training performances (Figure 4).

From a paradigms perspective, we can see that no transfer accuracies exceed
the reference diagonal values in this dataset. Nonetheless, RS appears as a
great target task, benefiting from representations learned in all source
tasks. To a smaller extent, TSS also exibits good performances for all source
tasks when using the ShallowNet architecture. We hypothesize that this is only
visible for this architecture because it is the only one capable of extracting
the information shared by all 4 paradigms, given its superior decoding
performance for this dataset (c.f. 4(b)). On the contrary, it appears that it
is very difficult to transfer onto the SSS paradigm, the extreme case being
obtained with EEGInception, for which the chance accuracy is attained for all
sources ($33\%$ in this case, since it is a 3-class classification problem).

Figure 8: Average performance of the three deep learning models for the
transfer learning setting in the M3CVDataset.

As for ERP CORE , we computed the transferability maps for M3CVin Figure 9.
This visualization allows to clearly see the consistent connections from TSS,
ME and SSS towards RS, regardless of the model employed. The same pattern is
visible for TSS with ShallowNet, which receives broad arrows from all
neighbouring tasks. We also note a persistent bidirectional connection between
TSS and ME, which is quite surprising given that they are very different
tasks.

(a) ShallowNet (b) EEGNet (c) EEGInception

Figure 9:  Transferability map of the M3CVdataset. Each node corresponds to a
distinct paradigm, while arrows width represent the average transfer
performance when using the representations learned from a source task to
decode a target task. All tasks transfer well to RS. While SSS transfers to
TSS, the opposite is not true. Surprisingly, ME and TSS transfer well to each
other in both ways.

The similarity between the best target tasks, RS and TSS, becomes even more
apparent on the clustering dendogram from Figure 7(b) Indeed, these paradigms
are grouped in their own cluster with EEGNet and appear as the closest
paradigms with ShallowNet and EEGInception. This figure also confirms that SSS
is a very particular task, as it is outside the main cluster for two out of
three dendograms.

##  6 Discussion and impact

Our analyses have yielded a reliable cognitive map through the use of transfer
learning and its successful generalization across various cognitive paradigms.
The resulting taxonomy maps, which encapsulate the knowledge of model
parameters, open up diverse possibilities for practical applications and
further research. In this discussion, we will delve into some potential
applications of cognitive mapping from the perspective of machine learning
models, emphasizing the benefits and implications they offer.

First and foremost, these cognitive maps can significantly enhance and
optimize the training of predictive models. As exemplified in this study, one
compelling approach is to leverage a task that exhibits strong transferability
as a template for decoding challenging cognitive tasks, as shown for MMN or
N170 ERPs. This aspect proves especially crucial in psychophysical
experiments, where subject numbers are limited while experimental variables
are abundant. These factors seem to be observed in other areas, such as
computer vision [96].

Additionally, the cognitive taxonomy maps can play a pivotal role in the
design of improved Human Machine Interfaces (HMIs) for Brain-Computer
Interface (BCI) applications. Our focus particularly centers around integrated
BCIs [8], which extend beyond mere control functions and delve into scenarios
involving error detection and negative potential. By incorporating insights
gained from cognitive mapping, we can significantly enhance the performance
and effectiveness of HMIs in such contexts. For example, the detection of ERN
could help to mitigate situations where the BCI system selects unwanted
commands, resulting in user frustration.

Furthermore, the clinical applications of cognitive mapping hold immense
potential, especially in aiding patients with schizophrenia who encounter
difficulties in emotion detection and facial recognition [97]. Leveraging the
insights derived from the N170 task [98], we can devise interventions that
boost performance and facilitate improved outcomes for individuals grappling
with these challenges. This is especially useful in the context of remediation
of emotion recognition, where schizophrenic patients have difficulties to
recognise faces and to extract relevant cues (like eyebrows or mouth
movements) for interpreting social interaction adequately. Objective
information indicating that the patient has recognised a face during an
interaction, instead of focusing on irrelevant details for instance, could
help therapists for rehabilitation purposes.

Moreover, our findings shed light on the functional networks underlying
related tasks. Notably, closely related tasks often engage similar functional
networks, suggesting the presence of shared evoked components [66, 67]. This
implies that activations observed in one task can enhance and refine the
performance of another task. While these tasks may exhibit distinct temporal
dynamics and spatial orientations, they ultimately serve the same overarching
purpose and engage overlapping cortical networks. Unraveling the sources
responsible for generating event-related potentials (ERPs) becomes more
feasible when considering these perspective-dependent variations in activation
patterns. This understanding illuminates the intricate interplay among
different components of the cortical network.

One compelling avenue for applying the insights gained from our study lies in
the realm of source localization, a classic inverse problem in neuroscience
[74]. Cognitive mapping can serve as a potent constraint in reconstructing
brain activity, leveraging functional regularization. Source localization
methods rely on physical and anatomical constraints to yield plausible
solutions. Information regarding share evoked components could help to define
functional constraints on estimated solution. By leveraging the connections
uncovered through cognitive mapping, we can construct robust source
localization models with enhanced accuracy and interpretability.

Finally, we can address the issue of BCI illiteracy, which refers to the
challenges faced by individuals to effectively operate BCIs [99, 100]. Our
transfer learning approach, which could be applied at the subject level, holds
promise in mitigating this challenge. BCI illiteracy is mostly observed on few
specific tasks for a given user while accuracy on other tasks are correct [8].
Based on our results, a first possible approach is to apply task transfer,
training on an effective decoding task for a user to transfer the results to
an inefficient task. A second and more exploratory approach is to investigate
user transfer, that is transfer the most effective decoding task from one
subject and apply it to another with poor decoding abilities. This area
presents an exciting and promising avenue for further exploration and
improvement.

##  7 Conclusion

Our study investigates the transferability of deep learning representations
through extensive experiments on two EEG datasets. To our knowledge, our work
is the first to construct representation transfer maps for EEG decoding. These
maps reveal a complex and asymmetric hierarchical relationship between
cognitive tasks, enhancing our understanding of brain decoding and neural
representations. Our findings also have very practical implications for
mitigating data scarcity, demonstrating performance improvements in real world
data.

One limitation of our work is that we focus on ERP and BCI datasets. Future
work could hence extend our analysis to a broader range of cognitive tasks, or
even investigate the transferabily across datasets that do not share the same
cohort of subjects. Other interesting avenues for investigation could be the
study of other types of transferability, for example by carrying out a similar
analysis in a self-supervised setting.

## Acknowledgments

We would like to thank Dr André Cravo for his valuable feedback on this
manuscript. This work was supported by the ANR BrAIN (ANR-20-CHIA-0016), ANR
AI-Cog grants (ANR-20-IADJ-0002), DATA IA (project YARN). The work of BA was
supported in part by the CAPES under Grant 001 and Data IA mobilité
internationale. The work of WHLP was supported by Wellcome Innovations under
Grant [WT213038/Z/18/Z].

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