Attractor-network models of mouse-cortex recurrence
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1CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference The plasticity rules surveyed in{ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across{ref}sec-paired-recording,{ref}sec-connectomic-micons,{ref}sec-celltype-motifs,{ref}sec-persistent-activityand{ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall... -
2CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference The plasticity rules surveyed in{ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across{ref}sec-paired-recording,{ref}sec-connectomic-micons,{ref}sec-celltype-motifs,{ref}sec-persistent-activityand{ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall... -
3CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference The plasticity rules surveyed in{ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across{ref}sec-paired-recording,{ref}sec-connectomic-micons,{ref}sec-celltype-motifs,{ref}sec-persistent-activityand{ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall... -
4CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference The plasticity rules surveyed in{ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across{ref}sec-paired-recording,{ref}sec-connectomic-micons,{ref}sec-celltype-motifs,{ref}sec-persistent-activityand{ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall... -
5CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference The plasticity rules surveyed in{ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across{ref}sec-paired-recording,{ref}sec-connectomic-micons,{ref}sec-celltype-motifs,{ref}sec-persistent-activityand{ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall... -
6CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference The plasticity rules surveyed in{ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across{ref}sec-paired-recording,{ref}sec-connectomic-micons,{ref}sec-celltype-motifs,{ref}sec-persistent-activityand{ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall... -
7CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference The plasticity rules surveyed in{ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across{ref}sec-paired-recording,{ref}sec-connectomic-micons,{ref}sec-celltype-motifs,{ref}sec-persistent-activityand{ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall... -
8CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference The plasticity rules surveyed in{ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across{ref}sec-paired-recording,{ref}sec-connectomic-micons,{ref}sec-celltype-motifs,{ref}sec-persistent-activityand{ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall... -
9CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference The plasticity rules surveyed in{ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across{ref}sec-paired-recording,{ref}sec-connectomic-micons,{ref}sec-celltype-motifs,{ref}sec-persistent-activityand{ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall... -
10CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference The plasticity rules surveyed in{ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across{ref}sec-paired-recording,{ref}sec-connectomic-micons,{ref}sec-celltype-motifs,{ref}sec-persistent-activityand{ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall... -
2CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference0 The plasticity rules surveyed in{ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across{ref}sec-paired-recording,{ref}sec-connectomic-micons,{ref}sec-celltype-motifs,{ref}sec-persistent-activityand{ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall... -
2CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference1 The plasticity rules surveyed in{ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across{ref}sec-paired-recording,{ref}sec-connectomic-micons,{ref}sec-celltype-motifs,{ref}sec-persistent-activityand{ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall... -
2CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference2 The plasticity rules surveyed in{ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across{ref}sec-paired-recording,{ref}sec-connectomic-micons,{ref}sec-celltype-motifs,{ref}sec-persistent-activityand{ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall... -
2CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference3 The plasticity rules surveyed in{ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across{ref}sec-paired-recording,{ref}sec-connectomic-micons,{ref}sec-celltype-motifs,{ref}sec-persistent-activityand{ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall... -
2CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference4 The plasticity rules surveyed in{ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across{ref}sec-paired-recording,{ref}sec-connectomic-micons,{ref}sec-celltype-motifs,{ref}sec-persistent-activityand{ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall... -
2CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference5 The Hopfield model and its graded-response extension show analytically that a symmetric recurrent matrix with N binary or sigmoid units, trained by an outer-product (Hebbian) rule, supports up to \alpha N \approx 0.14 N stored patterns as content-addressable fixed points 2CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference6. The mean-field analysis of 2CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference7 carries this capacity argument into balanced E/I networks and concludes th... -
2CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference8 The Hopfield model and its graded-response extension show analytically that a symmetric recurrent matrix with N binary or sigmoid units, trained by an outer-product (Hebbian) rule, supports up to \alpha N \approx 0.14 N stored patterns as content-addressable fixed points 2CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference9. The mean-field analysis of 3CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference0 carries this capacity argument into balanced E/I networks and concludes th... -
3CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference1 The Hopfield model and its graded-response extension show analytically that a symmetric recurrent matrix with N binary or sigmoid units, trained by an outer-product (Hebbian) rule, supports up to \alpha N \approx 0.14 N stored patterns as content-addressable fixed points 3CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference2. The mean-field analysis of 3CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference3 carries this capacity argument into balanced E/I networks and concludes th... -
3CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference4 The Hopfield model and its graded-response extension show analytically that a symmetric recurrent matrix with N binary or sigmoid units, trained by an outer-product (Hebbian) rule, supports up to \alpha N \approx 0.14 N stored patterns as content-addressable fixed points 3CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference5. The mean-field analysis of 3CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference6 carries this capacity argument into balanced E/I networks and concludes th... -
3CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference7 The Hopfield model and its graded-response extension show analytically that a symmetric recurrent matrix with N binary or sigmoid units, trained by an outer-product (Hebbian) rule, supports up to \alpha N \approx 0.14 N stored patterns as content-addressable fixed points 3CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference8. The mean-field analysis of 3CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference9 carries this capacity argument into balanced E/I networks and concludes th... -
4CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference0 The Hopfield model and its graded-response extension show analytically that a symmetric recurrent matrix with N binary or sigmoid units, trained by an outer-product (Hebbian) rule, supports up to \alpha N \approx 0.14 N stored patterns as content-addressable fixed points 4CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference1. The mean-field analysis of 4CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference2 carries this capacity argument into balanced E/I networks and concludes th... -
4CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference3 The Hopfield model and its graded-response extension show analytically that a symmetric recurrent matrix with N binary or sigmoid units, trained by an outer-product (Hebbian) rule, supports up to \alpha N \approx 0.14 N stored patterns as content-addressable fixed points 4CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference4. The mean-field analysis of 4CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference5 carries this capacity argument into balanced E/I networks and concludes th... -
4CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference6 The Hopfield model and its graded-response extension show analytically that a symmetric recurrent matrix with N binary or sigmoid units, trained by an outer-product (Hebbian) rule, supports up to \alpha N \approx 0.14 N stored patterns as content-addressable fixed points 4CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference7. The mean-field analysis of 4CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference8 carries this capacity argument into balanced E/I networks and concludes th... -
4CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference9 The Hopfield model and its graded-response extension show analytically that a symmetric recurrent matrix with N binary or sigmoid units, trained by an outer-product (Hebbian) rule, supports up to \alpha N \approx 0.14 N stored patterns as content-addressable fixed points 5CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference0. The mean-field analysis of 5CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference1 carries this capacity argument into balanced E/I networks and concludes th... -
5CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference2 Continuous attractors are a separate theoretical genus from Hopfield’s discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of 5CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference3 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19... -
5CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference4 Continuous attractors are a separate theoretical genus from Hopfield’s discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of 5CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference5 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19... -
5CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference6 Continuous attractors are a separate theoretical genus from Hopfield’s discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of 5CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference7 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19... -
5CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference8 Continuous attractors are a separate theoretical genus from Hopfield’s discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of 5CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference9 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19... -
6CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference0 Continuous attractors are a separate theoretical genus from Hopfield’s discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of 6CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference1 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19... -
6CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference2 Continuous attractors are a separate theoretical genus from Hopfield’s discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of 6CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference3 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19... -
6CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference4 Continuous attractors are a separate theoretical genus from Hopfield’s discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of 6CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference5 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19... -
6CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference6 Continuous attractors are a separate theoretical genus from Hopfield’s discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of 6CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference7 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19... -
6CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference8 Continuous attractors are a separate theoretical genus from Hopfield’s discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of 6CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference9 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19... -
7CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference0 Continuous attractors are a separate theoretical genus from Hopfield’s discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of 7CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference1 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19... -
7CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference2 Continuous attractors are a separate theoretical genus from Hopfield’s discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of 7CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference3 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19... -
7CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference4 Continuous attractors are a separate theoretical genus from Hopfield’s discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of 7CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference5 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19... -
7CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference6 Continuous attractors are a separate theoretical genus from Hopfield’s discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of 7CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference7 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19... -
7CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference8 Continuous attractors are a separate theoretical genus from Hopfield’s discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of 7CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference9 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19... -
8CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference0 Continuous attractors are a separate theoretical genus from Hopfield’s discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of 8CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference1 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19... -
8CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference2 Continuous attractors are a separate theoretical genus from Hopfield’s discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of 8CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference3 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19... -
8CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference4 Attractor fraction of recurrent E→E connectivity. Two independent estimates of what fraction of recurrent excitatory connectivity participates in attractor-network structure: a rat CA3a anatomy-based recurrent connection probability of c\approx0.2 interpreted within the Hopfield/autoassociative framework 8CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference5, and RNN-fitted bump-attractor connectivity fractions of \approx20\% in macaque FEF and $... -
8CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference6 Attractor fraction of recurrent E→E connectivity. Two independent estimates of what fraction of recurrent excitatory connectivity participates in attractor-network structure: a rat CA3a anatomy-based recurrent connection probability of c\approx0.2 interpreted within the Hopfield/autoassociative framework 8CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference7, and RNN-fitted bump-attractor connectivity fractions of \approx20\% in macaque FEF and $... -
8CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference8 Attractor fraction of recurrent E→E connectivity. Two independent estimates of what fraction of recurrent excitatory connectivity participates in attractor-network structure: a rat CA3a anatomy-based recurrent connection probability of c\approx0.2 interpreted within the Hopfield/autoassociative framework 8CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference9, and RNN-fitted bump-attractor connectivity fractions of \approx20\% in macaque FEF and $... -
9CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference0 9CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference1 showed analytically that the symmetry exploited in the canonical bump generates an entire family of continuous attractor networks, including one- and two-dimensional manifolds and ring topologies, all from variations on the same like-to-like recurrence. This widens the empirical target: the mouse cortex does not need to be a Compte–Wang bump to qualify as a continuous attractor, only to instantiate o... -
9CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference2 Line attractors require continuous degeneracy along a one-dimensional manifold of fixed points, sustained by precisely tuned positive feedback or by mechanisms that act as if the feedback were so tuned. 9CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference3 proposed this geometry for the brainstem oculomotor neural integrator, and the optogenetic perturbations of 9CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference4 in the zebrafish oculomotor integrator confirmed an attractor state organised... -
9CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference5 Line attractors require continuous degeneracy along a one-dimensional manifold of fixed points, sustained by precisely tuned positive feedback or by mechanisms that act as if the feedback were so tuned. 9CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference6 proposed this geometry for the brainstem oculomotor neural integrator, and the optogenetic perturbations of 9CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference7 in the zebrafish oculomotor integrator confirmed an attractor state organised... -
9CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference8 Line attractors require continuous degeneracy along a one-dimensional manifold of fixed points, sustained by precisely tuned positive feedback or by mechanisms that act as if the feedback were so tuned. 9CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference9 proposed this geometry for the brainstem oculomotor neural integrator, and the optogenetic perturbations of 10CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference0 in the zebrafish oculomotor integrator confirmed an attractor state organised... -
10CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference1 Line attractors require continuous degeneracy along a one-dimensional manifold of fixed points, sustained by precisely tuned positive feedback or by mechanisms that act as if the feedback were so tuned. 10CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference2 proposed this geometry for the brainstem oculomotor neural integrator, and the optogenetic perturbations of 10CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference3 in the zebrafish oculomotor integrator confirmed an attractor state organised... -
10CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference4 Line attractors require continuous degeneracy along a one-dimensional manifold of fixed points, sustained by precisely tuned positive feedback or by mechanisms that act as if the feedback were so tuned. 10CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference5 proposed this geometry for the brainstem oculomotor neural integrator, and the optogenetic perturbations of 10CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference6 in the zebrafish oculomotor integrator confirmed an attractor state organised... -
10CitationThe plasticity rules surveyed in {ref}
sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference7 Line attractors require continuous degeneracy along a one-dimensional manifold of fixed points, sustained by precisely tuned positive feedback or by mechanisms that act as if the feedback were so tuned. 10CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference8 proposed this geometry for the brainstem oculomotor neural integrator, and the optogenetic perturbations of 10CitationThe plasticity rules surveyed in {ref}sec-plasticitysculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}sec-paired-recording, {ref}sec-connectomic-micons, {ref}sec-celltype-motifs, {ref}sec-persistent-activityand {ref}sec-pattern-completion, which family of attractor architectures can the matrix actuall...content/13_attractor_network_models.md:line 5Open reference9 in the zebrafish oculomotor integrator confirmed an attractor state organised... -
... 136 additional anchors in refs_json
References
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- [Hopfield1984] “The plasticity rules surveyed in {ref}`sec-plasticity` sculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}`sec-paired-recording`, {ref}`sec-connectomic-micons`, {ref}`sec-celltype-motifs`, {ref}`sec-persistent-activity` and {ref}`sec-pattern-completion`, which family of attractor architectures can the matrix actuall...”
- [Compte2000] “The plasticity rules surveyed in {ref}`sec-plasticity` sculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}`sec-paired-recording`, {ref}`sec-connectomic-micons`, {ref}`sec-celltype-motifs`, {ref}`sec-persistent-activity` and {ref}`sec-pattern-completion`, which family of attractor architectures can the matrix actuall...”
- [BenYishai1995] “The plasticity rules surveyed in {ref}`sec-plasticity` sculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}`sec-paired-recording`, {ref}`sec-connectomic-micons`, {ref}`sec-celltype-motifs`, {ref}`sec-persistent-activity` and {ref}`sec-pattern-completion`, which family of attractor architectures can the matrix actuall...”
- [Zhang1996] “The plasticity rules surveyed in {ref}`sec-plasticity` sculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}`sec-paired-recording`, {ref}`sec-connectomic-micons`, {ref}`sec-celltype-motifs`, {ref}`sec-persistent-activity` and {ref}`sec-pattern-completion`, which family of attractor architectures can the matrix actuall...”
- [Samsonovich1997] “The plasticity rules surveyed in {ref}`sec-plasticity` sculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}`sec-paired-recording`, {ref}`sec-connectomic-micons`, {ref}`sec-celltype-motifs`, {ref}`sec-persistent-activity` and {ref}`sec-pattern-completion`, which family of attractor architectures can the matrix actuall...”
- [Burak2009] “The plasticity rules surveyed in {ref}`sec-plasticity` sculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}`sec-paired-recording`, {ref}`sec-connectomic-micons`, {ref}`sec-celltype-motifs`, {ref}`sec-persistent-activity` and {ref}`sec-pattern-completion`, which family of attractor architectures can the matrix actuall...”
- [Seung1996] “The plasticity rules surveyed in {ref}`sec-plasticity` sculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}`sec-paired-recording`, {ref}`sec-connectomic-micons`, {ref}`sec-celltype-motifs`, {ref}`sec-persistent-activity` and {ref}`sec-pattern-completion`, which family of attractor architectures can the matrix actuall...”
- [SebastianSeung1998] “The plasticity rules surveyed in {ref}`sec-plasticity` sculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}`sec-paired-recording`, {ref}`sec-connectomic-micons`, {ref}`sec-celltype-motifs`, {ref}`sec-persistent-activity` and {ref}`sec-pattern-completion`, which family of attractor architectures can the matrix actuall...”
- [Wang1999] “The plasticity rules surveyed in {ref}`sec-plasticity` sculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}`sec-paired-recording`, {ref}`sec-connectomic-micons`, {ref}`sec-celltype-motifs`, {ref}`sec-persistent-activity` and {ref}`sec-pattern-completion`, which family of attractor architectures can the matrix actuall...”
- [Wang2004] “The plasticity rules surveyed in {ref}`sec-plasticity` sculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}`sec-paired-recording`, {ref}`sec-connectomic-micons`, {ref}`sec-celltype-motifs`, {ref}`sec-persistent-activity` and {ref}`sec-pattern-completion`, which family of attractor architectures can the matrix actuall...”
- [Camperi1998] “The plasticity rules surveyed in {ref}`sec-plasticity` sculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}`sec-paired-recording`, {ref}`sec-connectomic-micons`, {ref}`sec-celltype-motifs`, {ref}`sec-persistent-activity` and {ref}`sec-pattern-completion`, which family of attractor architectures can the matrix actuall...”
- [Mongillo2008] “The plasticity rules surveyed in {ref}`sec-plasticity` sculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}`sec-paired-recording`, {ref}`sec-connectomic-micons`, {ref}`sec-celltype-motifs`, {ref}`sec-persistent-activity` and {ref}`sec-pattern-completion`, which family of attractor architectures can the matrix actuall...”
- [Lim2014] “The plasticity rules surveyed in {ref}`sec-plasticity` sculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}`sec-paired-recording`, {ref}`sec-connectomic-micons`, {ref}`sec-celltype-motifs`, {ref}`sec-persistent-activity` and {ref}`sec-pattern-completion`, which family of attractor architectures can the matrix actuall...”
- [Khona2022] “The plasticity rules surveyed in {ref}`sec-plasticity` sculpt the recurrent excitatory matrix that the present section now asks the theory of: given the mouse cortical E→E architecture documented across {ref}`sec-paired-recording`, {ref}`sec-connectomic-micons`, {ref}`sec-celltype-motifs`, {ref}`sec-persistent-activity` and {ref}`sec-pattern-completion`, which family of attractor architectures can the matrix actuall...”
- [Roudi2007] “The Hopfield model and its graded-response extension show analytically that a symmetric recurrent matrix with $N$ binary or sigmoid units, trained by an outer-product (Hebbian) rule, supports up to $\alpha N \approx 0.14 N$ stored patterns as content-addressable fixed points [Hopfield1982, Hopfield1984]. The mean-field analysis of [Roudi2007] carries this capacity argument into balanced E/I networks and concludes th...”
- [Feng2024] “The Hopfield model and its graded-response extension show analytically that a symmetric recurrent matrix with $N$ binary or sigmoid units, trained by an outer-product (Hebbian) rule, supports up to $\alpha N \approx 0.14 N$ stored patterns as content-addressable fixed points [Hopfield1982, Hopfield1984]. The mean-field analysis of [Roudi2007] carries this capacity argument into balanced E/I networks and concludes th...”
- [PereiraObilinovic2023] “The Hopfield model and its graded-response extension show analytically that a symmetric recurrent matrix with $N$ binary or sigmoid units, trained by an outer-product (Hebbian) rule, supports up to $\alpha N \approx 0.14 N$ stored patterns as content-addressable fixed points [Hopfield1982, Hopfield1984]. The mean-field analysis of [Roudi2007] carries this capacity argument into balanced E/I networks and concludes th...”
- [Pereira2018] “The Hopfield model and its graded-response extension show analytically that a symmetric recurrent matrix with $N$ binary or sigmoid units, trained by an outer-product (Hebbian) rule, supports up to $\alpha N \approx 0.14 N$ stored patterns as content-addressable fixed points [Hopfield1982, Hopfield1984]. The mean-field analysis of [Roudi2007] carries this capacity argument into balanced E/I networks and concludes th...”
- [Sandberg2003] “The Hopfield model and its graded-response extension show analytically that a symmetric recurrent matrix with $N$ binary or sigmoid units, trained by an outer-product (Hebbian) rule, supports up to $\alpha N \approx 0.14 N$ stored patterns as content-addressable fixed points [Hopfield1982, Hopfield1984]. The mean-field analysis of [Roudi2007] carries this capacity argument into balanced E/I networks and concludes th...”
- [Inagaki2019] “The Hopfield model and its graded-response extension show analytically that a symmetric recurrent matrix with $N$ binary or sigmoid units, trained by an outer-product (Hebbian) rule, supports up to $\alpha N \approx 0.14 N$ stored patterns as content-addressable fixed points [Hopfield1982, Hopfield1984]. The mean-field analysis of [Roudi2007] carries this capacity argument into balanced E/I networks and concludes th...”
- [Seelig2015] “Continuous attractors are a separate theoretical genus from Hopfield's discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of [BenYishai1995] for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...”
- [TurnerEvans2020] “Continuous attractors are a separate theoretical genus from Hopfield's discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of [BenYishai1995] for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...”
- [Hulse2021] “Continuous attractors are a separate theoretical genus from Hopfield's discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of [BenYishai1995] for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...”
- [Itskov2011] “Continuous attractors are a separate theoretical genus from Hopfield's discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of [BenYishai1995] for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...”
- [Carroll2014] “Continuous attractors are a separate theoretical genus from Hopfield's discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of [BenYishai1995] for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...”
- [DeAlmeida2007] “Continuous attractors are a separate theoretical genus from Hopfield's discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of [BenYishai1995] for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...”
- [Sigalas2025] “Continuous attractors are a separate theoretical genus from Hopfield's discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of [BenYishai1995] for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...”
- [Miller2006] “Continuous attractors are a separate theoretical genus from Hopfield's discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of [BenYishai1995] for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...”
- [Qi2015] “Continuous attractors are a separate theoretical genus from Hopfield's discrete one: the demand is not for a large discrete catalogue of stored patterns but for dense like-to-like recurrence whose translation invariance produces a continuum of marginally stable activity profiles. The ring-attractor architecture of [BenYishai1995] for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...”
- [Machens2008] “[Machens2008] showed analytically that the symmetry exploited in the canonical bump generates an entire *family* of continuous attractor networks, including one- and two-dimensional manifolds and ring topologies, all from variations on the same like-to-like recurrence. This widens the empirical target: the mouse cortex does not need to be a Compte–Wang bump to qualify as a continuous attractor, only to instantiate o...”
- [Goncalves2014] “Line attractors require continuous degeneracy along a one-dimensional manifold of fixed points, sustained by precisely tuned positive feedback or by mechanisms that act *as if* the feedback were so tuned. [Seung1996] proposed this geometry for the brainstem oculomotor neural integrator, and the optogenetic perturbations of [Goncalves2014] in the zebrafish oculomotor integrator confirmed an attractor state organised...”
- [Renart2003] “Line attractors require continuous degeneracy along a one-dimensional manifold of fixed points, sustained by precisely tuned positive feedback or by mechanisms that act *as if* the feedback were so tuned. [Seung1996] proposed this geometry for the brainstem oculomotor neural integrator, and the optogenetic perturbations of [Goncalves2014] in the zebrafish oculomotor integrator confirmed an attractor state organised...”
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