Nonparametric Modern Hopfield Models
This work addresses a gap in the literature for researchers in machine learning and neuroscience by providing more efficient Hopfield models, though it is incremental as it builds on existing dense models.
The authors tackled the lack of efficient variants in modern Hopfield models by introducing a nonparametric interpretation that leads to sparse-structured models with sub-quadratic complexity, while maintaining theoretical properties like exponential memory capacity and empirical validation in synthetic and realistic tasks.
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.