Residual addition happens before layernorm. This lesson shows one exact vector add, coordinate by coordinate, and then stops before the named layernorm boundary.

highlighted = computed this step

Start with two vectors

The residual path keeps the input vector h=(2,3) and adds the sublayer output s=(1,-1). Both vectors are displayed before the add, so the residual sum has a visible source.

h=(2,3),s=(1,1)h=(2,3),\quad s=(1,-1)
One Residual AdditionResidual addition is exact before the next named layernorm boundary.One Residual AdditionResidual addition is exact before the next named layernorm boundary.transformer block wiringwiring is exact; named components carry no numeric outputinput hexactdisplayed vector+ positional encodingnamed (sin/cos)attentionnamed (softmax)residual addexactvector additionlayernormnamed (√)MLP-ReLUexactrational ReLU wiringresidual addexactvector additionlayernormnamed (√)outputexactone exact residual additiondisplayed vectors are exact integers; sum is recomputedh=(2,3)+s=(1,-1)=r=(3,2)component checkcoord 12 + 13coord 23 + -12

Add coordinate by coordinate

The first coordinate is 2 + 1 = 3. The second coordinate is 3 + -1 = 2. So the exact residual vector is r=(3,2).

(2+1,  3+1)=(3,2)(2 + 1,\;3 + -1)=(3,2)
One Residual AdditionResidual addition is exact before the next named layernorm boundary.One Residual AdditionResidual addition is exact before the next named layernorm boundary.transformer block wiringwiring is exact; named components carry no numeric outputinput hexactdisplayed vector+ positional encodingnamed (sin/cos)attentionnamed (softmax)residual addexactvector additionlayernormnamed (√)MLP-ReLUexactrational ReLU wiringresidual addexactvector additionlayernormnamed (√)outputexactone exact residual additiondisplayed vectors are exact integers; sum is recomputedh=(2,3)+s=(1,-1)=r=(3,2)component checkcoord 12 + 13coord 23 + -12

Layernorm comes next

The residual result is (3,2). The next block node is layernorm, which is a named boundary here. This lesson stops at the exact residual add and does not compute a layernorm output.

r=(3,2),layernorm is named nextr=(3,2),\quad \text{layernorm is named next}
One Residual AdditionResidual addition is exact before the next named layernorm boundary.One Residual AdditionResidual addition is exact before the next named layernorm boundary.transformer block wiringwiring is exact; named components carry no numeric outputinput hexactdisplayed vector+ positional encodingnamed (sin/cos)attentionnamed (softmax)residual addexactvector additionlayernormnamed (√)MLP-ReLUexactrational ReLU wiringresidual addexactvector additionlayernormnamed (√)outputexactone exact residual additiondisplayed vectors are exact integers; sum is recomputedh=(2,3)+s=(1,-1)=r=(3,2)component checkcoord 12 + 13coord 23 + -12