Projective field

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Sidney R. Lehky (2012), Scholarpedia, 7(10):10114. doi:10.4249/scholarpedia.10114 revision #137419 [link to/cite this article]
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Curator: Sidney R. Lehky

Projective field is a term used in neuroscience to describe connectivity of a neuron with other neurons. Each neuron has a set of neurons to which it projects its output. That output set is called the projective field of the neuron. The neuron also has a set of neurons from which it receives its inputs. That input set is called the receptive field of the neuron. In typical usage, the projective field and the receptive field are assumed to occupy different levels within a hierarchical anatomical organization, so that they each represent distinct neural populations. Note that projective field refers to a population of neurons, and not to a region of perceptual or motor space. Similarly, receptive field within this framework may refer to a population of neurons and not a region of perceptual space, distinct from common usage in experimental neuroscience.

Figure 1: Schematic network showing receptive and projective fields of a neuron.



Projective field as used in neuroscience is unrelated to the same term used by physicists in quantum projective field theory.


“Projective field” was first used by Lehky and Sejnowski (1988) in a neural network model of visual processing that extracted shape from shading (see also Lehky and Sejnowski, 1990). The model consisted of a three-layer network, trained by the backpropagation learning algorithm to extract surface curvatures of 3D objects based on shading information. Each unit in the middle layer (hidden unit) had its receptive field in the input layer, and its projective field in the output layer.


The results of Lehky and Sejnowski (1988) made clear that the function of a neuron could not be deduced solely from its receptive field. It was also necessary to examine the neuron’s projective field, the pattern of connections made by the output of the neuron. In that model of shape from shading, neurons developed receptive fields that resembled those of some cells in visual striate cortex. Although neurons with such receptive fields have commonly been interpreted as “bar detectors” or “edge detectors”, in the context of this network the neurons were in fact acting as part of a system for extracting surface curvature. This functional role of the neurons in extracting surface curvature was not obvious from examining of their receptive fields (inputs); it also required consideration of the pattern of outputs. In general, the projective field of a neuron may represent a motor output as well as a sensory output (Lockery et al., 1990).

Lehky et al. (2005) used the projective field concept to criticize models of visual receptive fields based on information theoretic criteria of efficient coding (sparse coding), arguing that what constitutes optimality of a neuron’s receptive field should also take into consideration the functionality of the neuron as influenced by its projective field connections.

It is possible for a given neuron to project to different distinct populations of neurons, forming multiple projective fields. In that case, the same neuron with the same receptive field may participate in different functionalities dependent on the context provided by those different projective fields, none of which might be deduced from the neuron’s receptive field.

Although the projective field has been presented as a single-neuron property, in some cases it cases it may be more useful to think of it at a more global level, in terms of the projection from one population of functionally related neurons to another population that constitutes the global projective field. Gross (2002) provides an example where “projective field” is used in a global sense.

Various papers on the neural basis of consciousness have highlighted the importance of projective fields when assessing the functions of neurons (for example, Chalmers, 1995; Crick and Koch, 2003).

Sejnowski (2006) provides a general discussion on the topic of projective fields emphasizing connections with experimental neuroscience, in particular considering approaches to determining projective fields such as examining the effects of neural stimulation.


  1. Chalmers DJ (1995) The puzzle of consciousness. Sci Am 273, 80-86.
  2. Crick F, Koch C (2003) A framework for consciousness. Nat Neurosci 6, 119-126.
  3. Gross CG (2002) Genealogy of the "grandmother cell". Neuroscientist 8, 512-518.
  4. Lehky SR, Sejnowski TJ (1988) Network model of shape-from-shading: neural function arises from both receptive and projective fields. Nature 333, 452-454.
  5. Lehky SR, Sejnowski TJ (1990) Neural network model of visual cortex for determining surface curvature from images of shaded surfaces. Proc R Soc Lond B Biol Sci 240, 251-278.
  6. Lehky SR, Sejnowski TJ, Desimone R (2005) Selectivity and sparseness in the responses of striate complex cells. Vision Res 45, 57-73.
  7. Lockery SR, Fang Y, Sejnowski TJ (1990) A dynamic neural network model of sensorimotor transformations in the leech. Neural Comput 2, 274-282.
  8. Sejnowski TJ (2006) What are the projective fields of cortical neurons? In: 23 Problems in Systems Neuroscience (van Hemmen JL, Sejnowski TJ, eds). New York: Oxford University Press.

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See also

Connectome, Receptive Field, Error Back-Propagation, Neural Networks

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