LIMBO: Cortical Attractors

marilyn & maggie

Modular models. The aim is to understand how the organization of memory representations is determined by the underlying plasticity and network connectivity. Early work had considered the simplest modular network model of semantic memory, rejecting it because of inadequate storage capacity [1,2]. A more sophisticated version incorporates the key ingredients, sparsity in module activation and correlations between activation and connectivity, that allow to relieve the capacity limitations [6]. 


Metric content. To further probe representational structures and as an off-shot of information analyses, the metric and ultrametric structure of discrete perceptual and memory sets has been quantified with novel measures, first applied to responses of face cells in the primate temporal cortex [3] and of spatial view cells of hippocampal and parahippocampal cortices [5]. In an effort to reach towards studies of human performance, we have shown how to extract such measures from a neuropsychological test administered to patients with different types of memory disorders [4, 18,19]; while we are studying the effect of the underlying connectivity structures on the neuronal and behavioural response measures using the above formal network models.

Feedforward self-organization. Analytical techniques and simulations have also been applied to formal but realistic models of self-organizing competitive networks, aiming at a quantitative understanding of the functional properties of this simple type of neuronal organization [7]. The effects of learning of the spike count distribution of single cells to large sets of stimuli have been predicted using one such model [8].
What and where: lamination. Within the general research goal of attempting to understand the main evolutionary traits [9] leading from the reptilian to the mammalian cerebral cortex, a crucial question has been what drove the emergence of a laminated neocortex. Consider the conflict between relaying positional and identity information by a model cortical patch [10]. Positional ("where?") information is the one expressed by the location of activated neurons on the 2D cortical sheet; identity ("what?") information is expressed instead in the detailed activation pattern, at a fixed focus on the sheet. Simulating a simplified model patch, including three layers with initially uniform properties, it was found that the differentiation of a granular layer with distinct connectivity and firing properties leads to a small but reliable quantitative advantage in relaying an optimal mixture of both kinds of information. Further, a differentiation between supra- and infragranular layers is shown to optimally match their extrinsic connectivity, thus accounting for another advantage which isocortical lamination may have brought to mammals [11,12]. If you would like to run the simulations yourself, please ask for the code. Having evolved lamination in their topographic sensory cortical systems, mammals went about multiplying cortical areas within each system; a model of the advantages this brought to the analysis of complex stimuli has been studied using face processing as an example [13].


What and where: capacity and stability. A novel analytical approach has been recently developed (YR) to study attractor-mediated retrieval of memory patterns localized on a cortical patch. Such activity states are still distributed non-uniformly over many units, but the denser short-range connectivity allows, beyond a critical line, for the activity to be concentrated on a restricted patch rather than spread out across the entire network [14]. It has been shown analytically and with computer simulations that the storage capacity for such localized retrieval states is only slightly reduced with respect to that for non-localized retrieval, with the number of states still proportional to the number of independently modifiable synapses per pyramidal cell [15]. While analytical neural network studies of attractor dynamics provide crucial quantitative insight into its power and limitations, simulations allow approaching closer to real cortical networks. Simulations of Integrate & Fire units in a model network similar to the one considered above with non-dynamical units led to divergent results [16], stimulating an analysis of the effects of saturation (YR, AA). Moreover, localized attractor states are found to be unstable to positional drift, and their theoretical continuity is broken by spatial collapse anto a few randomly distributed favoured positions - unless a stabilizing signal is provided, e.g. acting on local neuronal gain [20]. 
Ambiguity and attractors. Visual processing of facial expressions offers a suitable physiological model with which to test predictions arising from mathematical models, also because of the evidence of parallel processing along a distinct sub-cortical pathway. This was the aim of a Human Frontier Science Programme
collaboration with the labs of Ray Dolan at UCL and of Bharathi Jagadeesh at U Washington in Seattle. Morphing paradigms allow exploring the neural bases for categorical perception, a possible manifestation of attractor dynamics at the network level ([17], see above picture). We have investigated psychophysically the effects of recent memory traces, as laid down in adaptation and priming paradigms, on the analysis of ambiguous facial expressions (NvR, [21]). fMRI and MEG experiments have partially localized these effects in cortical space [22] and at surprisingly late times [23]. Neurophysiological recordings provide clues as to the underlying network mechanisms, which can be interpreted within the attractor dynamics framework at the local network level (AA, [24]).


  1. D O'Kane & AT, Network 3:379-384 (1992)
  2. D O'Kane & AT, Journal of Physics A 25:5055-5069 (1992)
  3. AT, Biosystems 40:189-196 (1997)
  4. Papik, C Piccini, F Borgo & AT, Soc Neurosci abs 23:734.2 (1997)
  5. AT, P Georges-Francois, SP, RG Robertson & ET Rolls, in Neural Circuits and Networks, NATO ASI series (Springer) Vol F 167: 239-247 (1998)
  6. CFM & AT, Biosystems 48: 47-55 (1998)
  7. CFM, SP, GS, ET & AT, Soc Neurosci abs 23:197.1 (1997)
  8. GS & AT, Neural Comp 12:1773-1787 (2000)
  9. YR & AT, BBS commentary to Principles of Brain Evolution, by GF Striedter, BBS 29: 23 (2006)
  10. HM & AT, IBRO World Congress Neurosci abs V:123 (1999)
  11. AT, Soc Neurosci abstract 26:739.2 (2000)
  12. AT, J Comput Neurosci 14:271-282 (2003)
  13. AM & AT, Brain Res Bull 60: 387-393 (2003)
  14. YR & AT, JSTAT P07010 (2004)
  15. YR & AT, Phys Rev E 73:061904 (2006)
  16. AA, E Bienenstock & AT, preprint (2004)
  17. P RotshteinRNA Henson, AT, J Driver & RJ Dolan, Nature Neurosci 8:107-113 (2005)
  18. E Ciaramelli, Papik & AT, J Physiol Paris 100: 142-153 (2006)
  19. Papik, E Ciaramelli, C Piccini & AT, Eur J Neurosci 26:2702-12 (2007)
  20. YR & AT, PLoS Comput Biol 4(3): e1000012 (2008) 
  21. NvR, AJ & AT, the Open Behavioral Science Journal, 2:36-52 (2008)
  22. N Furl, NvR, AT & R Dolan, NeuroImage, 37:300–310 (2007)
  23. N Furl, NvR, AT, K Friston & R Dolan, PNAS USA, 104:13485-9 (2007)
  24. AAA, Y Liu, AT & B Jagadeesh, Cerebral Cortex, 18:in press (2008)

Last updated 06/07/08. Back to LIMBO, CNS, SISSA.