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On Bubbles and Drifts: Continuous attractor networks in brain models Thomas Trappenberg Dalhousie University, Canada.

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Presentation on theme: "On Bubbles and Drifts: Continuous attractor networks in brain models Thomas Trappenberg Dalhousie University, Canada."— Presentation transcript:

1 On Bubbles and Drifts: Continuous attractor networks in brain models Thomas Trappenberg Dalhousie University, Canada

2 Once upon a time... (my CANN shortlist) Wilson & Cowan (1973) Grossberg (1973) Amari (1977) … Sampolinsky & Hansel (1996) Zhang (1997) … Stringer et al (2002)

3 It’s just a `Hopfield’ net … Recurrent architecture Synaptic weights

4 In mathematical terms … Updating network states (network dynamics) Gain function Weight kernel

5 Weights describe the effective interaction profile in Superior Colliculus TT, Dorris, Klein & Munoz, J. Cog. Neuro. 13 (2001)

6 Network can form bubbles of persistent activity (in Oxford English: activity packets) End states

7 Space is represented with activity packets in the hippocampal system From Samsonovich & McNaughton Path integration and cognitive mapping in a continuous attractor neural J. Neurosci. 17 (1997)

8 There are phase transitions in the weight- parameter space

9 CANNs work with spiking neurons Xiao-Jing Wang, Trends in Neurosci. 24 (2001)

10 Shutting-off works also in rate model Time Node

11 Various gain functions are used End states

12 CANNs can be trained with Hebb Hebb: Training pattern:

13 Normalization is important to have convergent method Random initial states Weight normalization w(x,50) Training time x xy w(x,y)

14 Gradient-decent learning is also possible (Kechen Zhang) Gradient decent with regularization = Hebb + weight decay

15 CANNs have a continuum of point attractors Point attractors and basin of attraction Line of point attractors Can be mixed: Rolls, Stringer, Trappenberg A unified model of spatial and episodic memory Proceedings B of the Royal Society 269: (2002)

16 Neuroscience applications of CANNs Persistent activity (memory) and winner-takes-all (competition) Working memory ( e.g. Compte, Wang, Brunel etc ) Place and head direction cells ( e.g. Zhang, Redish, Touretzky, Samsonovitch, McNaughton, Skaggs, Stringer et al. ) Attention ( e.g. Olshausen, Salinas & Abbot, etc ) Population decoding ( e.g. Wu et al, Pouget, Zhang, Deneve, etc ) Oculomotor programming ( e.g. Kopecz & Schoener, Trappenberg ) etc

17 Superior colliculus intergrates exogenous and endogenous inputs

18 Superior Colliculus is a CANN TT, Dorris, Klein & Munoz, J. Cog. Neuro. 13 (2001)

19 CANN with adaptive input strength explains express saccades

20 CANN are great for population decoding (fast pattern matching implementation)

21 CANN (integrators) are stiff

22 … and drift and jump TT, ICONIP'98

23 Modified CANN solves path-integration

24 CANNs can learn dynamic motor primitives Stringer, Rolls, TT, de Araujo, Neural Networks 16 (2003).

25 Drift is caused by asymmetries NMDA stabilization

26 CANN can support multiple packets Stringer, Rolls & TT, Neural Networks 17 (2004)

27 How many activity packets can be stable? T.T., Neural Information Processing-Letters and Reviews, Vol. 1 (2003)

28 Stabilization can be too strong TT & Standage, CNS’04

29 CANN can discover dimensionality

30 : activity of node i : firing rate : synaptic efficacy matrix : global inhibition : visual input : time constant : scaling factor : #connections per node : slope : threshold Continuous dynamic (leaky integrator): The model equations: NMDA-style stabilization: Hebbian learning:


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