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Network architecture underlying maximal separation of neuronal representations.

Jortner RA - Front Neuroeng (2013)

Bottom Line: Inspired by experimental findings on network architecture in the olfactory system of the locust, I construct a highly simplified theoretical framework which allows for analytic solution of its key properties.For generalized feed-forward systems, I show that an intermediate range of connectivity values between source- and target-populations leads to a combinatorial explosion of wiring possibilities, resulting in input spaces which are, by their very nature, exquisitely sparsely populated.I suggest a straightforward way to construct ecologically meaningful representations from this code.

View Article: PubMed Central - PubMed

Affiliation: Interdisciplinary Center for Neural Computation, Hebrew University Jerusalem, Israel.

ABSTRACT
One of the most basic and general tasks faced by all nervous systems is extracting relevant information from the organism's surrounding world. While physical signals available to sensory systems are often continuous, variable, overlapping, and noisy, high-level neuronal representations used for decision-making tend to be discrete, specific, invariant, and highly separable. This study addresses the question of how neuronal specificity is generated. Inspired by experimental findings on network architecture in the olfactory system of the locust, I construct a highly simplified theoretical framework which allows for analytic solution of its key properties. For generalized feed-forward systems, I show that an intermediate range of connectivity values between source- and target-populations leads to a combinatorial explosion of wiring possibilities, resulting in input spaces which are, by their very nature, exquisitely sparsely populated. In particular, connection probability ½, as found in the locust antennal-lobe-mushroom-body circuit, serves to maximize separation of neuronal representations across the target Kenyon cells (KCs), and explains their specific and reliable responses. This analysis yields a function expressing response specificity in terms of lower network parameters; together with appropriate gain control this leads to a simple neuronal algorithm for generating arbitrarily sparse and selective codes and linking network architecture and neural coding. I suggest a straightforward way to construct ecologically meaningful representations from this code.

No MeSH data available.


Related in: MedlinePlus

Theoretical properties of network input to KCs. (A–D) Analytically calculated properties of the aggregate input to KCs (k) during network activity. Aggregate input is also analogous to KC membrane-potential (see text). Each property plotted as a function of PN-spiking probability p and PN–KC connectivity c, and averaged over all antennal-lobe states. N = 800 PNs is assumed in all cases. Left, surface plot; right, contour plot. Contour intervals are identical within each plot. Dash-dot lines indicate ridge contours. For clarity, isoline values are sometimes indicated beside plot (when contour lines are too dense for inline labeling). (A) Mean aggregate input per KC, Ψ [units of PNs]; contour interval, 40. (B) Variance of aggregate input per KC, Λ [units of PNs]; contour interval, 10. (C) Covariance between aggregate inputs to two KC [units of PNs]; contour interval, 10. (D) Correlation coefficient between aggregate inputs to two KC [unitless]; contour interval, 0.05.
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Figure 4: Theoretical properties of network input to KCs. (A–D) Analytically calculated properties of the aggregate input to KCs (k) during network activity. Aggregate input is also analogous to KC membrane-potential (see text). Each property plotted as a function of PN-spiking probability p and PN–KC connectivity c, and averaged over all antennal-lobe states. N = 800 PNs is assumed in all cases. Left, surface plot; right, contour plot. Contour intervals are identical within each plot. Dash-dot lines indicate ridge contours. For clarity, isoline values are sometimes indicated beside plot (when contour lines are too dense for inline labeling). (A) Mean aggregate input per KC, Ψ [units of PNs]; contour interval, 40. (B) Variance of aggregate input per KC, Λ [units of PNs]; contour interval, 10. (C) Covariance between aggregate inputs to two KC [units of PNs]; contour interval, 10. (D) Correlation coefficient between aggregate inputs to two KC [unitless]; contour interval, 0.05.

Mentions: Up until now, we only considered the properties of the connectivity matrix, . To see what happens when neural activity is added in, let us put some flesh on the dry skeleton, and proceed to explore the aggregate input to KCs () during network activity—corresponding to their sub-threshold membrane-potential. The symbol Ψ denotes the mean aggregate input to a KC, averaged over all possible PN-population states and across all KCs. ThenΨ≡〈ki〉S→, i=〈〈∑j=1NWijSj〉S→〉i=〈∑j=1NWij〈Sj〉S→〉i                  =p · ∑j=1N〈Wij〉i=Npcthe mean aggregate input to a KC during our arbitrary time window is thus a simple product of the number of PNs, probability of spiking in a single PN during this snapshot and PN–KC connection probability (Figure 4A).


Network architecture underlying maximal separation of neuronal representations.

Jortner RA - Front Neuroeng (2013)

Theoretical properties of network input to KCs. (A–D) Analytically calculated properties of the aggregate input to KCs (k) during network activity. Aggregate input is also analogous to KC membrane-potential (see text). Each property plotted as a function of PN-spiking probability p and PN–KC connectivity c, and averaged over all antennal-lobe states. N = 800 PNs is assumed in all cases. Left, surface plot; right, contour plot. Contour intervals are identical within each plot. Dash-dot lines indicate ridge contours. For clarity, isoline values are sometimes indicated beside plot (when contour lines are too dense for inline labeling). (A) Mean aggregate input per KC, Ψ [units of PNs]; contour interval, 40. (B) Variance of aggregate input per KC, Λ [units of PNs]; contour interval, 10. (C) Covariance between aggregate inputs to two KC [units of PNs]; contour interval, 10. (D) Correlation coefficient between aggregate inputs to two KC [unitless]; contour interval, 0.05.
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Figure 4: Theoretical properties of network input to KCs. (A–D) Analytically calculated properties of the aggregate input to KCs (k) during network activity. Aggregate input is also analogous to KC membrane-potential (see text). Each property plotted as a function of PN-spiking probability p and PN–KC connectivity c, and averaged over all antennal-lobe states. N = 800 PNs is assumed in all cases. Left, surface plot; right, contour plot. Contour intervals are identical within each plot. Dash-dot lines indicate ridge contours. For clarity, isoline values are sometimes indicated beside plot (when contour lines are too dense for inline labeling). (A) Mean aggregate input per KC, Ψ [units of PNs]; contour interval, 40. (B) Variance of aggregate input per KC, Λ [units of PNs]; contour interval, 10. (C) Covariance between aggregate inputs to two KC [units of PNs]; contour interval, 10. (D) Correlation coefficient between aggregate inputs to two KC [unitless]; contour interval, 0.05.
Mentions: Up until now, we only considered the properties of the connectivity matrix, . To see what happens when neural activity is added in, let us put some flesh on the dry skeleton, and proceed to explore the aggregate input to KCs () during network activity—corresponding to their sub-threshold membrane-potential. The symbol Ψ denotes the mean aggregate input to a KC, averaged over all possible PN-population states and across all KCs. ThenΨ≡〈ki〉S→, i=〈〈∑j=1NWijSj〉S→〉i=〈∑j=1NWij〈Sj〉S→〉i                  =p · ∑j=1N〈Wij〉i=Npcthe mean aggregate input to a KC during our arbitrary time window is thus a simple product of the number of PNs, probability of spiking in a single PN during this snapshot and PN–KC connection probability (Figure 4A).

Bottom Line: Inspired by experimental findings on network architecture in the olfactory system of the locust, I construct a highly simplified theoretical framework which allows for analytic solution of its key properties.For generalized feed-forward systems, I show that an intermediate range of connectivity values between source- and target-populations leads to a combinatorial explosion of wiring possibilities, resulting in input spaces which are, by their very nature, exquisitely sparsely populated.I suggest a straightforward way to construct ecologically meaningful representations from this code.

View Article: PubMed Central - PubMed

Affiliation: Interdisciplinary Center for Neural Computation, Hebrew University Jerusalem, Israel.

ABSTRACT
One of the most basic and general tasks faced by all nervous systems is extracting relevant information from the organism's surrounding world. While physical signals available to sensory systems are often continuous, variable, overlapping, and noisy, high-level neuronal representations used for decision-making tend to be discrete, specific, invariant, and highly separable. This study addresses the question of how neuronal specificity is generated. Inspired by experimental findings on network architecture in the olfactory system of the locust, I construct a highly simplified theoretical framework which allows for analytic solution of its key properties. For generalized feed-forward systems, I show that an intermediate range of connectivity values between source- and target-populations leads to a combinatorial explosion of wiring possibilities, resulting in input spaces which are, by their very nature, exquisitely sparsely populated. In particular, connection probability ½, as found in the locust antennal-lobe-mushroom-body circuit, serves to maximize separation of neuronal representations across the target Kenyon cells (KCs), and explains their specific and reliable responses. This analysis yields a function expressing response specificity in terms of lower network parameters; together with appropriate gain control this leads to a simple neuronal algorithm for generating arbitrarily sparse and selective codes and linking network architecture and neural coding. I suggest a straightforward way to construct ecologically meaningful representations from this code.

No MeSH data available.


Related in: MedlinePlus