Disentangling Target Lines from Interlopers and Continuum with Neural Networks: A SPHEREx Intensity Mapping Case Study

Line-intensity mapping (LIM) traces the large-scale distribution of matter by measuring fluctuations in aggregate line emission from unresolved galaxies and the intergalactic medium, providing a powerful probe of both astrophysics and cosmology. However, interpreting LIM data is limited by our ability to disentangle the signal of a target spectral line from continuum emission and interloper lines, which are emissions from other redshifts that fall within the observed frequency band. Astrophysical modeling uncertainties further complicate matters, leaving the relative amplitudes of the map components poorly understood. In this paper, we present a neural-network (NN) approach to separate the three map components at the level of the angular power spectrum, explicitly accounting for uncertainties in their relative amplitudes. As test cases, we generate SPHEREx-like maps with variable interloper line luminosities across multiple frequency channels, with and without pixel-wise scatter and continuum contributions. We find that cross-channel correlations are essential for robust NN performance when scatter is present. The NN exhibits a hierarchy in residual errors: brighter components yield smaller residuals, and the dimmest the highest. Without continuum emission, the network recovers the target power spectrum to within $2.5\%$, while partially correcting the interloper spectra. With continuum included, the NN accurately reconstructs the power spectra of the continuum and target line, within $2\%$ and $6\%$, respectively, but fails to recover those of the interlopers. Reducing pixel-level scatter further improves performance, lowering residual errors to $1\%$ (continuum) and $3\%$ (target line).