Can `singularity` attack units that are in their base?

Yes, Singularity can target units that are at their base.

According to the RiftJudge FAQs regarding Singularity (FAQ #513, #3724), Singularity does not contain any location restrictions (such as "at a battlefield"). Therefore, it can target units regardless of their location, including those at their base.

As noted in FAQ #3724: "If the spell does not mention a location (like Singularity), the unit remains a legal target even after moving and will be affected."