SOS DP - Space Optimization

You don't need to store all $dp[\text{mask}][i]$ values. Process bits from $0$ to $n-1$. When computing layer $i$, you only need layer $i-1$. Better: update in-place.

Start with $dp[\text{mask}] = f[\text{mask}]$. For each bit $i$ from $0$ to $n-1$, update: if bit $i$ is set in mask, add $dp[\text{mask} \oplus 2^i]$ to $dp[\text{mask}]$. The order matters: process masks with bit $i$ set after masks without it, or iterate masks in increasing order. This keeps $dp[\text{mask} \oplus 2^i]$ at its layer $i-1$ value when you read it.