Year: 2024
Type: preprint
Abstract: We present a nonparametric interpretation for deep learning compatible modern Hopfield models and utilize this new perspective to debut efficient variants. Our key contribution stems from interpreting the memory storage and retrieval processes in modern Hopfield models as a nonparametric regression problem subject to a set of query-memory pairs. Interestingly, our framework not only recovers the known results from the original dense modern Hopfield model but also fills the void in the literature regarding efficient modern Hopfield models, by introducing \textit{sparse-structured} modern Hopfield models with sub-quadratic complexity. We establish that this sparse model inherits the appealing theoretical properties of its dense analogue -- connection with transformer attention, fixed point convergence and exponential memory capacity. Additionally, we showcase the versatility of our framework by constructing a family of modern Hopfield models as extensions, including linear, random masked, top-$K$ and positive random feature modern Hopfield models. Empirically, we validate our framework in both synthetic and realistic settings for memory retrieval and learning tasks.
Source: arXiv (Cornell University)
Authors: Hu, Jerry Yao-Chieh, Chen, Bo-Yu, Wu, Dennis, Ruan, Feng, Liu, Han
Institutions: National Taiwan University, Northwestern University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Award: G4813509527
OpenAlex ID: W4394591690