Algorithm 2.

Federated Adversarial Domain Alignment

	Input: 1. X = {X1, . . . , XN}, fMRI data from N institutions/sites; 2. ${\mathbf{G}}_{{\theta }_G}=\{G_{{\theta }_{G_1}},\dots ,G_{{\theta }_{G_N}}\},$ local feature generators within N sites, where ${\theta }_{G_n}$ is the generator’s parameters of site n; 3. ${\mathbf{C}}_{{\theta }_C}=\{C_{{\theta }_{C_1}},\dots ,C_{{\theta }_{C_N}}\},$ local classifiers within N sites, where ${\theta }_{C_n}$ is the classifier’s parameters of site n; 4. ${\mathbf{D}}_{{\theta }_D}=\{D_{{\theta }_{D_1}},\dots ,D_{{\theta }_{D_N}}\},$ discriminators from embedded features, where ${\theta }_{D_n}$ is the discriminator parameters that identify the data from site n; 5. Y = {Y1,...,YN}, fMRI labels (HC or ASD); 6. M(·), noise generator; 7. K, number of optimization iterations; 8. τ, global model updating pace; 9. {${\mathbf{G}}_{{\overline{\theta }}_G}$, ${\mathbf{C}}_{{\overline{\theta }}_c}$}, global model.
1:	Initialize parameters {θG, θC, θD}
2:	for k = 1 to K do
3:	t ← 0	▷ initialize pace counter
4:	for i = 1 to N do
5:	Sample mini-batch from source site ${\{(X_i^S,Y_i^S)\}}_{i=1}^N$ and target site ${\{(X_j^T)\}}_{j=1}^N$
6:	Compute gradient with cross-entropy classification loss $\mathcal{L}$ce (Eq. 2) to update ${\theta }_{G_i}^{(k)}\text{and}{\theta }_{C_i}^{(k)}$
7:	Domain Alignment:
8:	Update ${\theta }_{D_i}^{(k)},\{{\theta }_{G_i}^{(k)},{\theta }_{G_j}^{(k)}\}$ with Eq. 7 and Eq. 8 respectively to align the domain distribution
9:	end for
10:	t ← t + 1	▷ models communicate
11:	if t%τ = 0 then
12:	${\overline{\theta }}_G^{(k)}\leftarrow \frac{1}{N}{\sum }_n({\theta }_{G_i}^{(k)}+M({\theta }_{G_i}^{(k)}))$
13:	${\overline{\theta }}_C^{(k)}\leftarrow \frac{1}{N}{\sum }_n({\theta }_{C_i}^{(k)}+M({\theta }_{C_i}^{(k)}))$	▷ update global model per τ steps
14:	for n = 1 to N do
15:	${\theta }_{G_i}^{(k)}\leftarrow {\overline{\theta }}_G^{(k)}$
16:	${\theta }_{C_i}^{(k)}\leftarrow {\overline{\theta }}_C^{(k)}$	▷ deploy weights to local model
17:	end for
18:	end if
19:	end for
	Return: global model $\{{\mathbf{\text{G}}}_{{\overline{\theta }}_G},{\mathbf{\text{C}}}_{{\overline{\theta }}_c}\}$