Modern Hopfield Networks: How Continuous Energy Landscapes Explain Transformer Attention and Exponential Memory
When Vaswani et al. introduced the Transformer architecture in 2017, scaled dot-product self-attention was presented primarily as a pragmatic computational mechanism: an efficient, highly parallelizable alternative to recurrence and convolutions. By computing pairwise inner products between queries and keys, normalizing via softmax, and taking a weighted sum of values, attention allowed models to route information dynamically across arbitrarily distant tokens. For several years, self-attention
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