Attractor-network models of mouse-cortex recurrence

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Attractor-network models of mouse-cortex recurrence

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  • 1Citationpaper:paper-8c0e0bbea6c4The 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...content/13_attractor_network_models.md:line 5Open reference 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...

  • 2Citationpaper:paper-609b7f4ccc1cThe 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...content/13_attractor_network_models.md:line 5Open reference 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...

  • 3Citationpaper:paper-6244370d231fThe 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...content/13_attractor_network_models.md:line 5Open reference 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...

  • 4Citationpaper:paper-ae017bc14c12The 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...content/13_attractor_network_models.md:line 5Open reference 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...

  • 5Citationpaper:paper-d1c7bc0af905The 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...content/13_attractor_network_models.md:line 5Open reference 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...

  • 6Citationpaper:paper-371804127ee1The 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...content/13_attractor_network_models.md:line 5Open reference 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...

  • 7Citationpaper:paper-722b6739a08bThe 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...content/13_attractor_network_models.md:line 5Open reference 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...

  • 8Citationpaper:paper-3d2fe19ac470The 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...content/13_attractor_network_models.md:line 5Open reference 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...

  • 9Citationpaper:paper-0ca9f77275afThe 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...content/13_attractor_network_models.md:line 5Open reference 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...

  • 10Citationpaper:paper-9fd49c797038The 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...content/13_attractor_network_models.md:line 5Open reference 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...

  • 2Citationpaper:paper-609b7f4ccc1cThe 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...content/13_attractor_network_models.md:line 5Open reference0 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...

  • 2Citationpaper:paper-609b7f4ccc1cThe 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...content/13_attractor_network_models.md:line 5Open reference1 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...

  • 2Citationpaper:paper-609b7f4ccc1cThe 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...content/13_attractor_network_models.md:line 5Open reference2 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...

  • 2Citationpaper:paper-609b7f4ccc1cThe 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...content/13_attractor_network_models.md:line 5Open reference3 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...

  • 2Citationpaper:paper-609b7f4ccc1cThe 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...content/13_attractor_network_models.md:line 5Open reference4 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...

  • 2Citationpaper:paper-609b7f4ccc1cThe 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...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 2Citationpaper:paper-609b7f4ccc1cThe 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...content/13_attractor_network_models.md:line 5Open reference6. The mean-field analysis of 2Citationpaper:paper-609b7f4ccc1cThe 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...content/13_attractor_network_models.md:line 5Open reference7 carries this capacity argument into balanced E/I networks and concludes th...

  • 2Citationpaper:paper-609b7f4ccc1cThe 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...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 2Citationpaper:paper-609b7f4ccc1cThe 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...content/13_attractor_network_models.md:line 5Open reference9. The mean-field analysis of 3Citationpaper:paper-6244370d231fThe 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...content/13_attractor_network_models.md:line 5Open reference0 carries this capacity argument into balanced E/I networks and concludes th...

  • 3Citationpaper:paper-6244370d231fThe 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...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 3Citationpaper:paper-6244370d231fThe 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...content/13_attractor_network_models.md:line 5Open reference2. The mean-field analysis of 3Citationpaper:paper-6244370d231fThe 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...content/13_attractor_network_models.md:line 5Open reference3 carries this capacity argument into balanced E/I networks and concludes th...

  • 3Citationpaper:paper-6244370d231fThe 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...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 3Citationpaper:paper-6244370d231fThe 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...content/13_attractor_network_models.md:line 5Open reference5. The mean-field analysis of 3Citationpaper:paper-6244370d231fThe 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...content/13_attractor_network_models.md:line 5Open reference6 carries this capacity argument into balanced E/I networks and concludes th...

  • 3Citationpaper:paper-6244370d231fThe 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...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 3Citationpaper:paper-6244370d231fThe 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...content/13_attractor_network_models.md:line 5Open reference8. The mean-field analysis of 3Citationpaper:paper-6244370d231fThe 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...content/13_attractor_network_models.md:line 5Open reference9 carries this capacity argument into balanced E/I networks and concludes th...

  • 4Citationpaper:paper-ae017bc14c12The 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...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 4Citationpaper:paper-ae017bc14c12The 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...content/13_attractor_network_models.md:line 5Open reference1. The mean-field analysis of 4Citationpaper:paper-ae017bc14c12The 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...content/13_attractor_network_models.md:line 5Open reference2 carries this capacity argument into balanced E/I networks and concludes th...

  • 4Citationpaper:paper-ae017bc14c12The 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...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 4Citationpaper:paper-ae017bc14c12The 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...content/13_attractor_network_models.md:line 5Open reference4. The mean-field analysis of 4Citationpaper:paper-ae017bc14c12The 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...content/13_attractor_network_models.md:line 5Open reference5 carries this capacity argument into balanced E/I networks and concludes th...

  • 4Citationpaper:paper-ae017bc14c12The 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...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 4Citationpaper:paper-ae017bc14c12The 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...content/13_attractor_network_models.md:line 5Open reference7. The mean-field analysis of 4Citationpaper:paper-ae017bc14c12The 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...content/13_attractor_network_models.md:line 5Open reference8 carries this capacity argument into balanced E/I networks and concludes th...

  • 4Citationpaper:paper-ae017bc14c12The 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...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 5Citationpaper:paper-d1c7bc0af905The 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...content/13_attractor_network_models.md:line 5Open reference0. The mean-field analysis of 5Citationpaper:paper-d1c7bc0af905The 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...content/13_attractor_network_models.md:line 5Open reference1 carries this capacity argument into balanced E/I networks and concludes th...

  • 5Citationpaper:paper-d1c7bc0af905The 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...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 5Citationpaper:paper-d1c7bc0af905The 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...content/13_attractor_network_models.md:line 5Open reference3 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...

  • 5Citationpaper:paper-d1c7bc0af905The 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...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 5Citationpaper:paper-d1c7bc0af905The 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...content/13_attractor_network_models.md:line 5Open reference5 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...

  • 5Citationpaper:paper-d1c7bc0af905The 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...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 5Citationpaper:paper-d1c7bc0af905The 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...content/13_attractor_network_models.md:line 5Open reference7 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...

  • 5Citationpaper:paper-d1c7bc0af905The 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...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 5Citationpaper:paper-d1c7bc0af905The 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...content/13_attractor_network_models.md:line 5Open reference9 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...

  • 6Citationpaper:paper-371804127ee1The 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...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 6Citationpaper:paper-371804127ee1The 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...content/13_attractor_network_models.md:line 5Open reference1 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...

  • 6Citationpaper:paper-371804127ee1The 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...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 6Citationpaper:paper-371804127ee1The 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...content/13_attractor_network_models.md:line 5Open reference3 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...

  • 6Citationpaper:paper-371804127ee1The 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...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 6Citationpaper:paper-371804127ee1The 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...content/13_attractor_network_models.md:line 5Open reference5 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...

  • 6Citationpaper:paper-371804127ee1The 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...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 6Citationpaper:paper-371804127ee1The 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...content/13_attractor_network_models.md:line 5Open reference7 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...

  • 6Citationpaper:paper-371804127ee1The 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...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 6Citationpaper:paper-371804127ee1The 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...content/13_attractor_network_models.md:line 5Open reference9 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...

  • 7Citationpaper:paper-722b6739a08bThe 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...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 7Citationpaper:paper-722b6739a08bThe 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...content/13_attractor_network_models.md:line 5Open reference1 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...

  • 7Citationpaper:paper-722b6739a08bThe 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...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 7Citationpaper:paper-722b6739a08bThe 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...content/13_attractor_network_models.md:line 5Open reference3 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...

  • 7Citationpaper:paper-722b6739a08bThe 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...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 7Citationpaper:paper-722b6739a08bThe 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...content/13_attractor_network_models.md:line 5Open reference5 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...

  • 7Citationpaper:paper-722b6739a08bThe 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...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 7Citationpaper:paper-722b6739a08bThe 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...content/13_attractor_network_models.md:line 5Open reference7 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...

  • 7Citationpaper:paper-722b6739a08bThe 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...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 7Citationpaper:paper-722b6739a08bThe 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...content/13_attractor_network_models.md:line 5Open reference9 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...

  • 8Citationpaper:paper-3d2fe19ac470The 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...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 8Citationpaper:paper-3d2fe19ac470The 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...content/13_attractor_network_models.md:line 5Open reference1 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...

  • 8Citationpaper:paper-3d2fe19ac470The 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...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 8Citationpaper:paper-3d2fe19ac470The 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...content/13_attractor_network_models.md:line 5Open reference3 for orientation-selective columns, the head-direction ring of [Zhang1996, Samsonovich19...

  • 8Citationpaper:paper-3d2fe19ac470The 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...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 8Citationpaper:paper-3d2fe19ac470The 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...content/13_attractor_network_models.md:line 5Open reference5, and RNN-fitted bump-attractor connectivity fractions of \approx20\% in macaque FEF and $...

  • 8Citationpaper:paper-3d2fe19ac470The 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...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 8Citationpaper:paper-3d2fe19ac470The 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...content/13_attractor_network_models.md:line 5Open reference7, and RNN-fitted bump-attractor connectivity fractions of \approx20\% in macaque FEF and $...

  • 8Citationpaper:paper-3d2fe19ac470The 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...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 8Citationpaper:paper-3d2fe19ac470The 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...content/13_attractor_network_models.md:line 5Open reference9, and RNN-fitted bump-attractor connectivity fractions of \approx20\% in macaque FEF and $...

  • 9Citationpaper:paper-0ca9f77275afThe 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...content/13_attractor_network_models.md:line 5Open reference0 9Citationpaper:paper-0ca9f77275afThe 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...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...

  • 9Citationpaper:paper-0ca9f77275afThe 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...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. 9Citationpaper:paper-0ca9f77275afThe 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...content/13_attractor_network_models.md:line 5Open reference3 proposed this geometry for the brainstem oculomotor neural integrator, and the optogenetic perturbations of 9Citationpaper:paper-0ca9f77275afThe 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...content/13_attractor_network_models.md:line 5Open reference4 in the zebrafish oculomotor integrator confirmed an attractor state organised...

  • 9Citationpaper:paper-0ca9f77275afThe 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...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. 9Citationpaper:paper-0ca9f77275afThe 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...content/13_attractor_network_models.md:line 5Open reference6 proposed this geometry for the brainstem oculomotor neural integrator, and the optogenetic perturbations of 9Citationpaper:paper-0ca9f77275afThe 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...content/13_attractor_network_models.md:line 5Open reference7 in the zebrafish oculomotor integrator confirmed an attractor state organised...

  • 9Citationpaper:paper-0ca9f77275afThe 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...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. 9Citationpaper:paper-0ca9f77275afThe 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...content/13_attractor_network_models.md:line 5Open reference9 proposed this geometry for the brainstem oculomotor neural integrator, and the optogenetic perturbations of 10Citationpaper:paper-9fd49c797038The 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...content/13_attractor_network_models.md:line 5Open reference0 in the zebrafish oculomotor integrator confirmed an attractor state organised...

  • 10Citationpaper:paper-9fd49c797038The 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...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. 10Citationpaper:paper-9fd49c797038The 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...content/13_attractor_network_models.md:line 5Open reference2 proposed this geometry for the brainstem oculomotor neural integrator, and the optogenetic perturbations of 10Citationpaper:paper-9fd49c797038The 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...content/13_attractor_network_models.md:line 5Open reference3 in the zebrafish oculomotor integrator confirmed an attractor state organised...

  • 10Citationpaper:paper-9fd49c797038The 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...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. 10Citationpaper:paper-9fd49c797038The 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...content/13_attractor_network_models.md:line 5Open reference5 proposed this geometry for the brainstem oculomotor neural integrator, and the optogenetic perturbations of 10Citationpaper:paper-9fd49c797038The 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...content/13_attractor_network_models.md:line 5Open reference6 in the zebrafish oculomotor integrator confirmed an attractor state organised...

  • 10Citationpaper:paper-9fd49c797038The 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...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. 10Citationpaper:paper-9fd49c797038The 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...content/13_attractor_network_models.md:line 5Open reference8 proposed this geometry for the brainstem oculomotor neural integrator, and the optogenetic perturbations of 10Citationpaper:paper-9fd49c797038The 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...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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  2. [Hopfield1984] paper:paper-609b7f4ccc1c “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...”
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  4. [BenYishai1995] paper:paper-ae017bc14c12 “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...”
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  6. [Samsonovich1997] paper:paper-371804127ee1 “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...”
  7. [Burak2009] paper:paper-722b6739a08b “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...”
  8. [Seung1996] paper:paper-3d2fe19ac470 “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...”
  9. [SebastianSeung1998] paper:paper-0ca9f77275af “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...”
  10. [Wang1999] paper:paper-9fd49c797038 “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...”
  11. [Wang2004] paper:paper-4ced38bcaa48 “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...”
  12. [Camperi1998] paper:paper-82cc68a1cfa2 “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...”
  13. [Mongillo2008] paper:paper-d8ab6604e68f “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...”
  14. [Lim2014] paper:paper-693a3131bf1c “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...”
  15. [Khona2022] paper:paper-98bec99f4818 “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...”
  16. [Roudi2007] paper:paper-d7fe1849b1b1 “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...”
  17. [Feng2024] paper:paper-e1ae0ef9d7c1 “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...”
  18. [PereiraObilinovic2023] paper:paper-f19775f67a0a “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...”
  19. [Pereira2018] paper:paper-de8241e97a69 “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...”
  20. [Sandberg2003] paper:paper-33cb9e915244 “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...”
  21. [Inagaki2019] paper:67bd565b-2a75-461d-9061-05fb0bb877c2 “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...”
  22. [Seelig2015] paper:paper-b7c259ebd4f5 “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...”
  23. [TurnerEvans2020] paper:paper-978fdd504cb1 “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...”
  24. [Hulse2021] paper:paper-ef4afa8c9177 “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...”
  25. [Itskov2011] paper:paper-cc210cf0ab9f “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...”
  26. [Carroll2014] paper:paper-c2eb477f7f17 “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...”
  27. [DeAlmeida2007] paper:paper-89ce835df6b0 “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...”
  28. [Sigalas2025] paper:paper-c491238def42 “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...”
  29. [Miller2006] paper:paper-2a584616def5 “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...”
  30. [Qi2015] paper:paper-6f65acac5807 “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...”
  31. [Machens2008] paper:paper-d67a891db8a0 “[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...”
  32. [Goncalves2014] paper:paper-afef655cdbc4 “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...”
  33. [Renart2003] paper:paper-0a3094c92786 “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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