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About this paper
Antonio Álvarez-López, Borjan Geshkovski, Domènec Ruiz-Balet
Álvarez-López, Geshkovski, and Ruiz-Balet rigorously incorporate the feed-forward perceptron block into the mean-field theory of Transformer dynamics, demonstrating that perceptrons generically induce discrete and localized stationary attention distributions, fundamentally altering the energy landscape and promoting structured representations.
Key insights
- Perceptrons fundamentally reshape the mean-field attention landscape, causing stationary measures to be generically atomic and localized, even in repulsive regimes that would otherwise allow for continuous distributions.
- An anti-concentration phenomenon occurs where, despite atomicity, clusters of attention mass are bounded (e.g., <0.575 in d=2), preventing complete collapse to a single Dirac mass and implying distributed yet localized information processing.
- The perceptron's influence breaks the inherent symmetry of pure self-attention, anchoring the locations of attention clusters to be largely independent of initial conditions, which can contribute to the stability of learned representations.
Summary by alphaXiv.
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