Hi, thank you for your great work!
I have a question regarding the Latent Trajectory Projection (LTP) mechanism described in Section 4.2.1 and illustrated in Figure S1 of the appendix. According to the paper, LTP projects each sub-prompt target latent onto the full target latent by normalizing the target latent and computing the inner product between them. Based on my understanding of vector projection, if we project the orange vector in Figure S1 onto the black one, the projected point should lie on the line passing through the origin and the black dot.
However, in Figure S1, the projected sub-target latents appear to be positioned between the original sub-target latents and the full target latent, rather than on the line through the target.
Could you please help me understand:
- Is Figure S1 a schematic representation rather than a geometrically accurate visualization, or my understanding of LTP is incorrect?
- Does the projection involve additional operations beyond standard vector projection (e.g., interpolation or rescaling)?
- Is there a specific reason why the projected latents appear positioned between the sub-targets and the full target in the visualization?
Thanks in advance.
Hi, thank you for your great work!
I have a question regarding the Latent Trajectory Projection (LTP) mechanism described in Section 4.2.1 and illustrated in Figure S1 of the appendix. According to the paper, LTP projects each sub-prompt target latent onto the full target latent by normalizing the target latent and computing the inner product between them. Based on my understanding of vector projection, if we project the orange vector in Figure S1 onto the black one, the projected point should lie on the line passing through the origin and the black dot.
However, in Figure S1, the projected sub-target latents appear to be positioned between the original sub-target latents and the full target latent, rather than on the line through the target.
Could you please help me understand:
Thanks in advance.