The study uses = ▽(';) where ' = – (,) where represents the last time step of the previous - (or the first - ) so that gradients can be calculated in parallel at a time. . Dual form The parallelization described above is necessary but not sufficient for "actual running time" (-k) efficiency. However, in reality, it is impossible to calculate all of them for a single one. Instead, we need to calculate them one by one with the outer product. Worse, for each one, this will produce a larger memory usage and cost than the large one.
Theoretical equivalence As mentioned above, can lithuania dialing code be either a linear model or a neural network. There are three variants of the update rule: , , and - . As shown in the figure below, each of these combinations leads to a different instantiation of the layer. In the study, the authors prove from theorems that the layer with linear models and in these induced instances is equivalent to linear attention - a well-known layer. The figure summarizes the general definition of the layer in the broader context of all sequence modeling layers. .
Two variants In the study, the authors propose two variants of the layer - and - which differ only in the instantiation of . For - where is squared. For - there are two layers similar to . Specifically, the hidden dimension is the input dimension and then the activation. For better stability during , layer normalization () and residual connections are always included. That is, where can be or. Experiments The researchers evaluated and by comparing with two baselines and (modern). The dataset continues after the paper The researchers performed standard experiments with k and k context lengths on is a popular document dataset for training open source.
The main architectures and use different and architectures of are always used unless otherwise stated. . Short context: In k contexts, and have comparable performance lines with most of the lines overlapping. performs slightly worse at larger budgets. Although has better complexity than at each model size, the additional cost of offsets this advantage. In k contexts, and perform significantly better. Even the with architecture performs slightly better than . In addition, the researchers observed a very clear phenomenon: as the context length becomes longer, the advantage of over becomes larger. .