English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In deep learning theory, the covariance matrix of the representations servesas a proxy to examine the network's trainability. Motivated by the success ofTransformers, we study the covariance matrix of a modified Softmax-basedattention model with skip connections in the proportional limit ofinfinite-depth-and-width. We show that at initialization the limitingdistribution can be described by a stochastic differential equation (SDE)indexed by the depth-to-width ratio. To achieve a well-defined stochasticlimit, the Transformer's attention mechanism is modified by centering theSoftmax output at identity, and scaling the Softmax logits by a width-dependenttemperature parameter. We examine the stability of the network through thecorresponding SDE, showing how the scale of both the drift and diffusion can beelegantly controlled with the aid of residual connections. The existence of astable SDE implies that the covariance structure is well-behaved, even for verylarge depth and width, thus preventing the notorious issues of rank degeneracyin deep attention models. Finally, we show, through simulations, that the SDEprovides a surprisingly good description of the corresponding finite-sizemodel. We coin the name shaped Transformer for these architecturalmodifications.

The Shaped Transformer: Attention Models in the Infinite Depth-and-Width Limit