A search for pairs of light neutral pseudoscalar bosons (
A
) resulting from the decay of a Higgs boson is performed. The search is conducted using LHC proton-proton collision data at
s
=
13
TeV
, collected with the CMS detector in 2016–2018 and corresponding to an integrated luminosity of
138
fb
−
1
. The
A
boson decays into a highly collimated electron-positron pair. A novel multivariate algorithm using tracks and calorimeter information is developed to identify these distinctive signatures, and events are selected with two such merged electron-positron pairs. No significant excess above the standard model background predictions is observed. Upper limits on the branching fraction for
H
→
A
A
→
4
e
are set at 95% confidence level, for masses between 10 and 100 MeV and proper decay lengths below
100
μ
m
, reaching branching fraction sensitivities as low as
10
−
5
. This is the first search for Higgs boson decays to four electrons via light pseudoscalars at the LHC. It significantly improves the experimental sensitivity to axionlike particles with masses below 100 MeV .
