Neutral stability, rate propagation, and critical branching in feedforward networks

Neural Computation

Volumn 25, Issue 7, 2013, Pages 1768-1806

  Cayco Gajic, N Alex ^a   Shea Brown, Eric ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACTION POTENTIAL; ANIMAL; ARTIFICIAL NEURAL NETWORK; BIOLOGICAL MODEL; BRAIN; COMPUTER SIMULATION; HUMAN; LETTER; NERVE CELL; NERVE CELL INHIBITION; NERVE CELL NETWORK; PHYSIOLOGY; PROBABILITY; SYNAPTIC TRANSMISSION; TIME;

ACTION POTENTIALS; ANIMALS; BRAIN; COMPUTER SIMULATION; HUMANS; MARKOV CHAINS; MODELS, NEUROLOGICAL; NERVE NET; NEURAL INHIBITION; NEURAL NETWORKS (COMPUTER); NEURONS; SYNAPTIC TRANSMISSION; TIME FACTORS;

EID: 84880984918     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/NECO_a_00461     Document Type: Letter

References (41)

1. Abeles, M., Bergman, H., Margalit, E., & Vaadia, E. (1993). Spatiotemporal firing patterns in the frontal cortex of behaving monkeys. Journal of Neurophysiology, 70, 1629-1638.
2. Amari, S., Nakahara, H., Wu, S., & Sakai, Y. (2003). Synchronous firing and higherorder interactions in the neuron pool. Neural Computation, 15, 127-142.
3. Beggs, J., & Plenz, D. (2003). Neuronal avalanches in neocortical circuits. Journal of Neuroscience, 23, 11167-11177.
4. Bertschinger, N., & Natschlager, T. (2004). Real-time computation at the edge of chaos in recurrent neural networks. Neural Computation, 16, 1413-1436.
5. Braitenberg, V., & Schüz, A. (1998). Cortex: Statistics and geometry of neuronal connectivity. Berlin: Springer.
6. Diesmann, M.,Gewaltig,M.,&Aertsen, A. (1999). Stable propagation of synchronous spiking in cortical neural networks. Nature, 402, 529-533.
7. Gabernet, L., Jadhav, S. P., Feldman, D. E., Carandini, M., & Scanziani, M. (2005). Somatosensory integration controlled by dynamic thalamocortical feed-forward inhibition. Neuron, 48, 315-327.
8. Ganguli, S.,Huh,D.,&Sompolinsky, H. (2008).Memory traces in dynamical systems. Proceedings of the National Academy of Sciences USA, 105, 18970-18975.
9. Ganmor, E., Segev, R., & Schneidman, E. (2011). Sparse low-order interaction network underlies a highly correlated and learnable population code. Proceedings of the National Academy of Sciences USA, 108, 9679-9684.
10. Hahn, G., Petermann, T., Havenith, M., Yu, S., Plenz, D., Singer, W., et al. (2010). Neuronal avalanches in spontaneous activity in vivo. Journal of Neurophysiology, 104, 3312-3322.
11. Hennig, M. H., Adams, C.,Willshaw, D., & Sernagor, E. (2009). Early-stage waves in the retinal network emerge close to a critical state transition between local and global functional connectivity. Journal of Neuroscience, 29, 1077-1086.
12. Jaynes, E. T. (1957). Information theory and statistical mechanics. Physical Review, 106, 620-630.
13. Kitzbichler, M. G., Smith, M. L., Christensen, S. R., & Bullmore, E. (2009). Broadband criticality of human brain network synchronization. PLoS Computational Biology, 5(3), e1000314.
14. Kremkow, J., Perrinet, L. U., Masson, G. S., & Aertsen, A. (2010). Functional consequences of correlated excitatory and inhibitory conductances in cortical networks. Journal of Computational Neuroscience, 28, 579-594.
15. Kumar, A., Rotter, S., & Aertsen, A. (2008). Conditions for propagating synchronous spiking and asynchronous firing rates in a cortical network model. Journal of Neuroscience, 28, 5268-5280.
16. Kumar, A., Rotter, S., & Aertsen, A. (2010). Spiking activity propagation in neuronal networks: Reconciling different perspectives on neural coding. Nature Reviews Neuroscience, 11, 615-627.
17. Legenstein, R.,&Maass,W. (2007).Whatmakes a dynamical system computationally powerful? In S. Haykin, J. C. Principe, T. J. Sejnowski, & J. G. McWhirter (Eds.), New directions in statistical signal processing: From systems to brains (pp. 127-154). Cambridge, MA: MIT Press.
18. Lim, S.,&Goldman, M. (2012). Noise tolerance of attractor and feedforwardmemory models. Neural Computation, 24, 332-390.
19. Litvak, V., Sompolinsky, H., Segev, I., & Abeles, M. (2003). On the transmission of rate code in long feedforward networks with excitatory-inhibitory balance. Journal of Neuroscience, 23, 3006-3015.
20. Longtin, A. (1993). Stochastic resonance in neuron models. Journal of Statistical Physics, 70, 309-327.
21. Macke, J., Opper, M., & Bethge, M. (2011). Common input explains higher-order correlations and entropy in a simple model of neural population activity. Physical Review Letters, 106(20), 208102.
22. Martignon, L., Deco, G., Laskey, K., Diamond,M., Freiwald,W., & Vaadia, E. (2000). Neural coding: higher-order temporal patterns in the neurostatistics of cell assemblies. Neural Computation, 12, 2621-2653.
23. McCulloch, W. S., & Pitts, W. H. (1943). A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 7, 115-133.
24. McDonnell, M., & Abbott, D. (2009). What is stochastic resonance? Definitions, misconceptions, debates, and its relevance to biology. PLoS Computational Biology, 5(5), e1000348.
25. Montani, F., Ince, R. A. A., Senatore, R., Arabzadeh, E., Diamond, M. E., & Panzeri, S. (2009). The impact of high-order interactions on the rate of synchronous discharge and information transmission in somatosensory cortex. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 367(1901), 3297-3310.
26. Mora, T., & Bialek, W. (2011). Are biological systems poised at criticality?. Journal of Statisitical Physics, 144, 268-302.
27. Nowotny, T., & Huerta, R. (2003). Explaining synchrony in feed-forward networks. Biological Cybernetics, 89, 237-241.
28. Ohiorhenuan, I. E., Mechler, F., Purpura, K. P., Schmid, A. M., & Victor, J. D. (2010). Sparse coding and high-order correlations in fine-scale cortical networks. Nature, 466, 617-621.
29. Petermann, T., Thiagarajan, T. C., Lebedev, M. A., Nicolelis, M. A., Chialvo, D. R., & Plenz, D. (2009). Spontaneous cortical activity in awake monkeys composed of neuronal avalanches. Proceedings of the National Academy of the Sciences, 106(37), 15921-15926.
30. Reyes, A. (2003). Synchrony-dependent propagation of firing rate in iteratively constructed networks in vitro. Nature Neuroscience, 6, 593-599.
31. Rosenbaum, R., Trousdale, J., & Josic, K. (2010). Pooling and correlated neural activity. Frontiers in Computational Neuroscience, 4(9). doi:10.3389/fncom.2010.00009
32. Schneidman, E., Berry,M., Segev, R., & Bialek,W. (2006).Weak pairwise correlations imply strongly correlated network states in a neural population. Nature, 440, 1007-1012.
33. Shlens, J., Field, G. D., Gauthier, J. L., Grivich, M. I., Petrusca, D., Sher, A., et al. (2006). The structure of multi-neuron firing patterns in primate retina. Journal of Neuroscience, 26, 8254-8266.
34. Staude, B., Rotter, S., & Grün, S. (2010). CuBIC: Cumulant based inference of higherorder correlations inmassively parallel spike trains. Journal of Computational Neuroscience, 29, 327-350.
35. Staude, B., Grün, S., & Rotter, S. (2010). Higher-order correlations and cumulants. In S. Grün & S. Rotter (Eds.), Analysis of parallel spike trains (pp. 253-280). New York: Springer.
36. Tetzlaff, T., Geisel, T., & Diesmann, M. (2002). The ground state of cortical feedforward networks. Neurocomputing, 44-46, 673-678.
37. Toyoizumi, T. (2012). Nearly extensive sequential memory lifetime achieved by coupled nonlinear neurons. Neural Computation, 24, 2678-2699.
38. Trefethen, L. N., & Embree, N. (2005). Spectra and pseudospectra: The behavior of nonnormal matrices and operators. Princeton, NJ: Princeton University Press.
39. van Rossum, M., Turrigiano, G., & Nelson, S. (2002). Fast propagation of firing rates through layered networks of noisy neurons. Journal of Neuroscience, 22, 1956-1966.
40. Vogels, T., & Abbott, L. F. (2005). Signal propagation and logic gating in networks of integrate-and-fire neurons. Journal of Neuroscience, 25(46), 10786-10795.
41. Yu, S., Yang, H., Nakahara, H., Santos, G., Nikolic, D., & Plenz, D. (2011). Higherorder interactions characterized in cortical activity. Journal of Neuroscience, 31, 17514-17526