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In the paper proposing recurrent convolutional neural networks (RCNN), "Recurrent Convolutional Neural Network for Object Recognition", it is stated that "recurrent synapses typically outnumber feed-forward and top-down (or feedback) synapses".

Up to this point, my understanding was that top-down processing and recurrent connections refer to the same thing... What is the difference between the two?

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The different types of connections can be histologically identified and separated on the basis of their connectivity in the cortex.

Recurrent synapses in the cortex can be defined as (Douglas & Martin, 1995):

[...] connections between layer 2 and 3 pyramidal cells, in which a target neuron projects back to its source neuron in a tight positive feedback loop

Feedforward and feedback neurons can be histologically defined as (Berezovskii et al., 2011):

In general, feedforward (FF) projections originate in the superficial layers of the cortex and terminate in layer 4, while feedback (FB) connections originate in the superficial and deep layers, and their axon terminals tend to avoid layer 4.

The cortical layers and their functions are schematically depicted in Fig. 1.

cortex
Fig. 1. Schematic of the cortex showing recurrent connections (rc) in layer 2/3 and feedforward and feedback connections that avoid layer 4. source: Rolls & Mills (2017)

References
- Berezovskii et al., J Comp Neurol (2011); 519(18): 3672–83
- Rolls & Mills, Neurobiol Learn Mem (2017); 145: 205–21

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