Question: Does RaBitQ support symmetric distance estimation from quantized codes?

[eiclpy]

Is it possible to estimate the distance between two vectors (e.g., p and q) using only their quantized binary codes (code(p), code(q)) and the associated quantizer parameters, without needing access to the original raw vectors? If this is supported, it would be extremely helpful for many use cases that are storage-constrained.

[gaoj0017]

Yes. Basically, there is an interface to maps a raw vector to the following representation.

$$\mathbf{p} \approx \Delta_p \cdot \mathbf{p}_u + v_p\cdot \mathbb{1}_D $$ $$\mathbf{q} \approx \Delta_q \cdot \mathbf{q}_u + v_q\cdot \mathbb{1}_D $$

Then

$$\left< \mathbf{p},\mathbf{q}\right>\approx\Delta_p\cdot\Delta_q\cdot \left< \mathbf{p}_u,\mathbf{q}_u\right> + v_q\cdot \Delta_p\cdot sum(\mathbf{p}_u) + v_p\cdot \Delta_q\cdot sum(\mathbf{q}_u) + v_p\cdot v_q\cdot D$$

where $sum(\cdot)$ means the summation of all coordinates of a vector. We can also combine it with residuals and accelerate it with specialized distance kernels.

[Revendell]

good idea!