There is of course a trade off. DrDAM poorly approximates energy landscapes that are:
1️⃣Far from memories
2️⃣“Spiky” (i.e., low temperature/high beta)

We need more random features Y to reconstruct highly occluded/correlated data!

DrDAM can meaningfully approximate the memory retrievals of MrDAM! Shown are reconstructions of occluded imgs from TinyImagenet, retrieved by strictly minimizing the energies of both DrDAM and MrDAM.

MrDAM energies can be decomposed into:
1️⃣A similarity func between stored patterns & noisy input
2️⃣A rapidly growing separation func (e.g., exponential)

Together, they reveal kernels (e.g., RBF) that can be approximated via the kernel trick & random features (Rahimi&Recht, 2007)

Why say “Distributed”?🤔

In traditional Memory representations of DenseAMs (MrDAM) one row in the weight matrix stores one pattern. In our new Distributed representation (DrDAM) patterns are entangled via superposition, “distributed” across all dims of a featurized memory vector

Excited to share "Dense Associative Memory through the Lens of Random Features" accepted to #neurips2024🎉

DenseAMs need new weights for each stored pattern–hurting scalability. Kernel methods let us add memories without adding weights!

Distributed memory for DenseAMs, unlocked🔓