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Artificial Intelligence in Health Federated learning health stack against pandemics

Figure 2. Architectural structure of the proposed hierarchical federated learning

The training process begins with the central server (S) aggregation. As HE supports only addition and
broadcasting the initialized model parameters W to all multiplication, we use homomorphic addition to find the
0
local servers, ensuring uniformity across local models for aggregate sum and then multiply the aggregate sum by the
their cluster-level distributions. After receiving the reciprocal of the number of clients in each cluster. This can
initialized model parameters, each C trains its local model be represented as:
ij
on a batch of data b , sampled from its dataset D , and 1
ij
r
ij
generates local model gradients G for round r. This is [[ ]]G r i jp [[G ij r ]] (III)
ij

r
represented as: p
G ← train Wb( 0 , r ij ) (I) where, |p| represents the cluster size. Following this,
ij
r
i
where r represents the current round index, and R is the each local server L transmits aggregated encrypted model
parameters [[ ]]G
i
from their respective clusters to the
r
total number of training rounds. The symbol “←” denotes central server S. The central server further performs global
the assignment operator, indicating that the result of the aggregation on received model parameters. This can be
operation on the right-hand side is assigned to the variable represented as:
on the left-hand side. The proposed framework uses HE
19
1
operations to ensure the security of the model gradients [[ ]]G [[ ]]G i (IV)
during client–server communications and employs a r n in r
hierarchical structure to enhance scalability. The depth of
the hierarchy can be increased to ensure the required where |n| represents the number of participating local
scaling. During the transmission of model gradients, a clients. The central server S then sends the aggregated
key-generating authority generates a public–private/secret model parameters back to the local servers, which are
ij
key pair ( pk sk, r ) for each client C at the beginning of responsible for disseminating these parameters to the
ij
r
ij
each round r. Once the keys are received, each client clients in their respective clusters. Before proceeding to the
encrypts its local gradients G using HE. This is next round of training, each client C decrypts the received
ij
ij
r
represented as: aggregated encrypted model parameters using the private
ij
key sk for that round. This decryption process can be
r
[[G ij r ]] ← encrypt (pk G r ij ) (II) represented as:
ij
,
r
After encryption, every client C transmits the G ← decrypt sk( ij ,[[ G ]]) (V)
ij
encrypted gradients [[G r ij ]] (here [[]] represents encrypted r r r
values) to its corresponding local server L. Upon receiving Each client C then proceeds to train its local model on
ij
i
the encrypted model updates from all clients within the another batch of data b ij r+1 , which may either be static or
cluster, the local server L performs homomorphic dynamically collected. This training is performed on the
i
Volume 2 Issue 4 (2025) 79 doi: 10.36922/AIH025080013