@article {5360,
	title = {Skip Connections Increase the Capacity of Associative Memories in Variable Binding Mechanisms},
	number = {142},
	year = {2023},
	month = {06/2023},
	abstract = {<p>The flexibility of intelligent behavior is fundamentally attributed to the ability to separate and assign structural information from content in sensory inputs. Variable binding is the atomic computation that underlies this ability. In this work, we investigate the implementation of variable binding via pointers of assemblies of neurons, which are sets of excitatory neurons that fire together. The Assembly Calculus is a framework that describes a set of operations to create and modify assemblies of neurons. We focus on the project (which creates assemblies) and reciprocal-project (which performs vari- able binding) operations and study the capacity of networks in terms of the number of assemblies that can be reliably created and retrieved. We find that assembly calculus networks implemented through Hebbian plasticity resemble associative memories in their structure and behavior. However, for net- works with N neurons per brain area, the capacity of variable binding networks (0.01N) is an order of magnitude lower than the capacity of assembly creation networks (0.22N). To alleviate this drop in capacity, we propose a skip connection between the input and variable assembly, which boosts the capacity to a similar order of magnitude (0.1N ) as the Project operation, while maintain its biological plausibility.</p>
},
	author = {Yi Xie and Yichen Li and Akshay Rangamani}
}
@article {5137,
	title = {Understanding the Role of Recurrent Connections in Assembly Calculus},
	year = {2022},
	month = {07/2022},
	abstract = {<p>In this note, we explore the role of recurrent connections in Assembly Calculus through a number of experiments\&nbsp;conducted on models with and without recurrent connections. We observe that assemblies can be formed even in the absence of\&nbsp;recurrent connections, but also find that models with recurrent connections are more robust to noisy inputs. We also investigate\&nbsp;the spectral structure of the synaptic weights and find intriguing similarities between models of neural assemblies and\&nbsp;associative memories.</p>
},
	author = {Akshay Rangamani and Yi Xie}
}
