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Posted: Wed Dec 18, 2024 9:27 am
In response to this, the researchers proposed ii-bh gradient descent, with b representing the batch size. The study used G = ▽l(W';), where ' = – d(,b), where represents the last time step of the previous ii-bh (or the first ii-bh), so b gradient calculations can be performed in parallel at a time. 7. Dual form The parallelization introduced above is necessary, but not enough for the efficiency of "actual running time" (wll-lk i). However, in reality, it is impossible to calculate all b of G for a single l. Instead, b outer products are required to calculate them one by one.
Worse, for each G is dd, which indonesia mobile number whatsapp will result in greater memory usage and I/cost than large d. To solve these two problems, the researchers observed that: We don't actually need to concretize G, . . . , Gb, as long as we can compute Wb at the end of ii-bh and output kz, . . . , zb (as shown in Figure 7 above). Now, we can use the simplified -Lir case above to demonstrate these calculations, representing = [, . . . , b]: So Wb can be easily calculated using l.
To calculate Z = [z, . . . , zb], we know: The representation and matrix can be obtained: As above, the researchers call it the "dual form". 8. Theoretical equivalence As mentioned earlier, f can be a linear model or a neural network. There are also three variants of the update rule: li GD, bh GD, and ii-bh GD. As shown in the figure below, in these combinations, each will cause a different instantiation of the layer. In the study, the authors proved from theorems that in these induced instances, the layer with a linear model and bh GD is equivalent to linear attention - a well-known R layer.
Worse, for each G is dd, which indonesia mobile number whatsapp will result in greater memory usage and I/cost than large d. To solve these two problems, the researchers observed that: We don't actually need to concretize G, . . . , Gb, as long as we can compute Wb at the end of ii-bh and output kz, . . . , zb (as shown in Figure 7 above). Now, we can use the simplified -Lir case above to demonstrate these calculations, representing = [, . . . , b]: So Wb can be easily calculated using l.
To calculate Z = [z, . . . , zb], we know: The representation and matrix can be obtained: As above, the researchers call it the "dual form". 8. Theoretical equivalence As mentioned earlier, f can be a linear model or a neural network. There are also three variants of the update rule: li GD, bh GD, and ii-bh GD. As shown in the figure below, in these combinations, each will cause a different instantiation of the layer. In the study, the authors proved from theorems that in these induced instances, the layer with a linear model and bh GD is equivalent to linear attention - a well-known R layer.