Figure 3. (a) Vectors a = (M, 1, 2) and b = (M, −2, 1), drawn at the same length because cosine only cares about direction. The dashed arrows a′ and b′ are the same vectors with the massive dimension removed. They lie in the grey plane and are at a right angle (cosine 0). As M grows, both a and b lean toward the massive axis, and their cosine goes to 1, even though a′ and b′ do not change. (b) The same thing happens in real models: in Gemma-3-4B and 12B, one dimension pushes the cosine up to about 0.96. In Gemma-3-1B the massive dimension is large in some languages but small in others, so it pushes the cosine down instead.