Reducing a cortical network to a Potts model yields storage capacity estimates

Naim, Michelangelo; Boboeva, Vezha; Kang, Chol Jun; Treves, Alessandro

doi:10.1088/1742-5468/aab683

Cited by 28 publications

(46 citation statements)

References 55 publications

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“…3(b). We refer to [31] for a detailed analysis of the approximate thermodynamic and dynamic equivalence of the full multimodular model and the Potts network. We do not dwell on the correspondence here, but use it to discuss correlations in the Potts framework.…”

Section: Connectivitymentioning

confidence: 99%

“…The initial studies of the capacity of the Potts network [34,31] featured patterns that were uncorrelated. Uncorrelated patterns are generated by assigning Potts states to different units in different patterns independently.…”

Section: Generating Correlated Representationsmentioning

confidence: 99%

“…In [31], we have discussed the application of the self-consistent signal to noise analysis (SCSNA) to the Potts network with uncorrelated patterns. In the following section we extend this analysis to the case of correlated patterns encoded by a Potts network with diluted random connectivity (Eq.…”

Section: Self-consistent Signal To Noise Analysismentioning

confidence: 99%

“…The averaging in Eqs. (47)-(49) can be performed analytically and we refer to [34] and [31] for their expressions. The storage capacity α c is defined as the maximal α that solves the set of equations Eqs.…”

Section: Self-consistent Signal To Noise Analysismentioning

confidence: 99%

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The capacity for correlated semantic memories in the cortex

Boboeva

Brasselet

Treves

2018

Preprint

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We analyze an autoassociative network of Potts units, coupled via tensor connections, as an effective model of extended cortical networks with distinct short and long-range synaptic connections. To study semantic memory, organized in terms of the relations between the attributes of real-world knowledge, we formulate a generative model of item representation with correlations. The model ascribes such correlations to the influence of underlying "factors": items with more shared factors have more correlated representations. Moreover, if many factors are balanced, correlations are overall low; whereas if a few factors dominate (increasing a dominance parameter ζ), they become strong. Our model allows for correlations that are neither trivial (random) nor merely hierarchical (an ultrametric tree). The network can retrieve one from up to p c CS 2 /a weakly correlated items, of order 10,000,000 with human cortical parameters. When its storage capacity is exceeded, however, retrieval fails completely only for low ζ; above a critical dominance value ζ c , a phase transition leads to a regime where the network still extracts considerable information about the cued item, even if not recovering its detailed representation: possibly a model of semantic memory resilience in remember/know paradigms.

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Section: Connectivitymentioning

confidence: 99%

Section: Generating Correlated Representationsmentioning

confidence: 99%

Section: Self-consistent Signal To Noise Analysismentioning

confidence: 99%

Section: Self-consistent Signal To Noise Analysismentioning

confidence: 99%

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The capacity for correlated semantic memories in the cortex

Boboeva

Brasselet

Treves

2018

Preprint

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“…The Potts network, aimed at describing the cortex, or a large part of it, is comprised of N such units, constituting the A-system, Figure 3 b. We refer to [ 31 ] for a detailed analysis of the approximate thermodynamic and dynamic equivalence of the full multi-modular model and the Potts network. We do not dwell on the correspondence here, but use it to discuss correlations in the Potts framework.…”

Section: Introductionmentioning

confidence: 99%

The Capacity for Correlated Semantic Memories in the Cortex

Boboeva

Brasselet

Treves

2018

Entropy

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A statistical analysis of semantic memory should reflect the complex, multifactorial structure of the relations among its items. Still, a dominant paradigm in the study of semantic memory has been the idea that the mental representation of concepts is structured along a simple branching tree spanned by superordinate and subordinate categories. We propose a generative model of item representation with correlations that overcomes the limitations of a tree structure. The items are generated through "factors" that represent semantic features or real-world attributes. The correlation between items has its source in the extent to which items share such factors and the strength of such factors: if many factors are balanced, correlations are overall low; whereas if a few factors dominate, they become strong. Our model allows for correlations that are neither trivial nor hierarchical, but may reproduce the general spectrum of correlations present in a dataset of nouns. We find that such correlations reduce the storage capacity of a Potts network to a limited extent, so that the number of concepts that can be stored and retrieved in a large, human-scale cortical network may still be of order 10 7 , as originally estimated without correlations. When this storage capacity is exceeded, however, retrieval fails completely only for balanced factors; above a critical degree of imbalance, a phase transition leads to a regime where the network still extracts considerable information about the cued item, even if not recovering its detailed representation: partial categorization seems to emerge spontaneously as a consequence of the dominance of particular factors, rather than being imposed ad hoc. We argue this to be a relevant model of semantic memory resilience in Tulving's remember/know paradigms.

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Computational constraints on the associative recall of spatial scenes

et al. 2023

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We consider a model of associative storage and retrieval of compositional memories in an extended cortical network. Our model network is comprised of Potts units, which represent patches of cortex, interacting through long-range connections. The critical assumption is that a memory, for example of a spatial view, is composed of a limited number of items, each of which has a pre-established representation: storing a new memory only involves acquiring the connections, if novel, among the participating items. The model is shown to have a much lower storage capacity than when it stores simple unitary representations. It is also shown that an input from the hippocampus facilitates associative retrieval. When it is absent, it is advantageous to cue rare rather than frequent items. The implications of these results for emerging trends in empirical research are discussed.

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Reducing a cortical network to a Potts model yields storage capacity estimates

Cited by 28 publications

References 55 publications

The capacity for correlated semantic memories in the cortex

The capacity for correlated semantic memories in the cortex

The Capacity for Correlated Semantic Memories in the Cortex

Computational constraints on the associative recall of spatial scenes

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