#kernel-design

Power-Law Kernel Initialization: Theory-Guided Init Gives 0.039 BPB Free at 10M Scale

Does initializing a diagonal SSM's output projection to match the theoretical power-law MI decay structure (beta~1.15) improve convergence speed or final BPB over uniform initialization?

• Condition 3 (concentrated rates + PL C_proj) achieves val BPB 0.9739 vs baseline 1.0127, a 0.039 BPB improvement with ze…
• Convergence is consistently faster: at step 2000, Condition 3 val BPB is 1.1029 vs baseline 1.1741 (0.071 gap). At step …