Kernel Memory Networks: A Unifying Framework for Memory Modeling

• URL: http://arxiv.org/abs/2208.09416v3
• Date: Tue, 23 Jul 2024 16:09:17 GMT
• Title: Kernel Memory Networks: A Unifying Framework for Memory Modeling
• Authors: Georgios Iatropoulos, Johanni Brea, Wulfram Gerstner,
• Abstract summary: We consider the problem of training a neural network to store a set of patterns with maximal noise robustness. A solution is derived by training each individual neuron to perform either kernel classification or with a minimum weight norm. We derive optimal models, termed kernel memory networks, that include, as special cases, many of the hetero- and auto-associative memory models.
• Score: 9.142894972380216
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider the problem of training a neural network to store a set of patterns with maximal noise robustness. A solution, in terms of optimal weights and state update rules, is derived by training each individual neuron to perform either kernel classification or interpolation with a minimum weight norm. By applying this method to feed-forward and recurrent networks, we derive optimal models, termed kernel memory networks, that include, as special cases, many of the hetero- and auto-associative memory models that have been proposed over the past years, such as modern Hopfield networks and Kanerva's sparse distributed memory. We modify Kanerva's model and demonstrate a simple way to design a kernel memory network that can store an exponential number of continuous-valued patterns with a finite basin of attraction. The framework of kernel memory networks offers a simple and intuitive way to understand the storage capacity of previous memory models, and allows for new biological interpretations in terms of dendritic non-linearities and synaptic cross-talk.

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