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Nonlinear circuits for naturalistic visual motion estimation.

Fitzgerald JE, Clark DA - Elife (2015)

Bottom Line: Furthermore, a diversity of inputs to motion detecting neurons can provide access to more complex higher-order correlations.Collectively, these results illustrate how non-canonical computations improve motion estimation with naturalistic inputs.This argues that the complexity of the fly's motion computations, implemented in its elaborate circuits, represents a valuable feature of its visual motion estimator.

View Article: PubMed Central - PubMed

Affiliation: Center for Brain Science, Harvard University, Cambridge, United States.

ABSTRACT
Many animals use visual signals to estimate motion. Canonical models suppose that animals estimate motion by cross-correlating pairs of spatiotemporally separated visual signals, but recent experiments indicate that humans and flies perceive motion from higher-order correlations that signify motion in natural environments. Here we show how biologically plausible processing motifs in neural circuits could be tuned to extract this information. We emphasize how known aspects of Drosophila's visual circuitry could embody this tuning and predict fly behavior. We find that segregating motion signals into ON/OFF channels can enhance estimation accuracy by accounting for natural light/dark asymmetries. Furthermore, a diversity of inputs to motion detecting neurons can provide access to more complex higher-order correlations. Collectively, these results illustrate how non-canonical computations improve motion estimation with naturalistic inputs. This argues that the complexity of the fly's motion computations, implemented in its elaborate circuits, represents a valuable feature of its visual motion estimator.

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Accuracy of the weighted 4-quadrant model across model parameters.(A, B) We computed the correlation coefficient between the velocity and the response of the weighted 4-quadrant model for all possible sets of model parameters. Since rescaling the weight vector does not affect the correlation coefficient, we assumed that all model parameters satisfy . We color-coded each set of model parameters by its accuracy and projected the parameter space onto various subspaces. (A) We first examined the quadrant basis by projecting onto the {(− −), (− +)} (left) and {(+ −), (+ +)} (right) subspaces. (B) We next examined the correlational basis by projecting onto the {even = 2, odd} (left) and {odd*, even >2} (right) subspaces. These project into different linear combinations of the original quadrant weightings. One of the projections is the pure HRC (even = 2), while the other projections contain only odd correlations, of two different types (odd and odd*), or only even correlations of order greater than 2 (even >2). These projections show that accurate weighted 4-quadrant models always put positive weight into 2-point correlations and negative weight into odd-ordered correlations. Note that the glider responses predicted by the weighted 4-quadrant model mirror this pattern (Figure 3D).DOI:http://dx.doi.org/10.7554/eLife.09123.017
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fig8: Accuracy of the weighted 4-quadrant model across model parameters.(A, B) We computed the correlation coefficient between the velocity and the response of the weighted 4-quadrant model for all possible sets of model parameters. Since rescaling the weight vector does not affect the correlation coefficient, we assumed that all model parameters satisfy . We color-coded each set of model parameters by its accuracy and projected the parameter space onto various subspaces. (A) We first examined the quadrant basis by projecting onto the {(− −), (− +)} (left) and {(+ −), (+ +)} (right) subspaces. (B) We next examined the correlational basis by projecting onto the {even = 2, odd} (left) and {odd*, even >2} (right) subspaces. These project into different linear combinations of the original quadrant weightings. One of the projections is the pure HRC (even = 2), while the other projections contain only odd correlations, of two different types (odd and odd*), or only even correlations of order greater than 2 (even >2). These projections show that accurate weighted 4-quadrant models always put positive weight into 2-point correlations and negative weight into odd-ordered correlations. Note that the glider responses predicted by the weighted 4-quadrant model mirror this pattern (Figure 3D).DOI:http://dx.doi.org/10.7554/eLife.09123.017

Mentions: Since the weighted 4-quadrant model only has four parameters, it's possible to exhaustively study its parameter dependence. We have in mind models that are correctly scaled, in which case the mean squared error is determined by the correlation coefficient (Appendix 2). Since the value of the correlation coefficient is unchanged when all four weighting coefficients are scaled by the same positive factor, it suffices to consider weighting coefficients drawn from the 3-sphere, such that . Because the 3-sphere has a finite volume, we were able to densely sample the correlation coefficient for all parameter values (Appendix figure 3). This function has one global maximum, corresponding to the optimal weight vector discussed in the main text. Its global minimum occurs on the polar opposite side of the 3-sphere, where the weighted 4-quadrant model is most strongly anti-correlated with the velocity. More generally, correlation coefficients corresponding to model parameters on opposite poles of the 3-sphere always have the same magnitude and opposite sign. Both models explain the same amount of variance about the velocity, and they become equivalent after they're correctly scaled. Thus, we henceforth focus our discussion on the hemisphere where the correlation coefficient was positive.10.7554/eLife.09123.017Appendix figure 3.Accuracy of the weighted 4-quadrant model across model parameters.


Nonlinear circuits for naturalistic visual motion estimation.

Fitzgerald JE, Clark DA - Elife (2015)

Accuracy of the weighted 4-quadrant model across model parameters.(A, B) We computed the correlation coefficient between the velocity and the response of the weighted 4-quadrant model for all possible sets of model parameters. Since rescaling the weight vector does not affect the correlation coefficient, we assumed that all model parameters satisfy . We color-coded each set of model parameters by its accuracy and projected the parameter space onto various subspaces. (A) We first examined the quadrant basis by projecting onto the {(− −), (− +)} (left) and {(+ −), (+ +)} (right) subspaces. (B) We next examined the correlational basis by projecting onto the {even = 2, odd} (left) and {odd*, even >2} (right) subspaces. These project into different linear combinations of the original quadrant weightings. One of the projections is the pure HRC (even = 2), while the other projections contain only odd correlations, of two different types (odd and odd*), or only even correlations of order greater than 2 (even >2). These projections show that accurate weighted 4-quadrant models always put positive weight into 2-point correlations and negative weight into odd-ordered correlations. Note that the glider responses predicted by the weighted 4-quadrant model mirror this pattern (Figure 3D).DOI:http://dx.doi.org/10.7554/eLife.09123.017
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fig8: Accuracy of the weighted 4-quadrant model across model parameters.(A, B) We computed the correlation coefficient between the velocity and the response of the weighted 4-quadrant model for all possible sets of model parameters. Since rescaling the weight vector does not affect the correlation coefficient, we assumed that all model parameters satisfy . We color-coded each set of model parameters by its accuracy and projected the parameter space onto various subspaces. (A) We first examined the quadrant basis by projecting onto the {(− −), (− +)} (left) and {(+ −), (+ +)} (right) subspaces. (B) We next examined the correlational basis by projecting onto the {even = 2, odd} (left) and {odd*, even >2} (right) subspaces. These project into different linear combinations of the original quadrant weightings. One of the projections is the pure HRC (even = 2), while the other projections contain only odd correlations, of two different types (odd and odd*), or only even correlations of order greater than 2 (even >2). These projections show that accurate weighted 4-quadrant models always put positive weight into 2-point correlations and negative weight into odd-ordered correlations. Note that the glider responses predicted by the weighted 4-quadrant model mirror this pattern (Figure 3D).DOI:http://dx.doi.org/10.7554/eLife.09123.017
Mentions: Since the weighted 4-quadrant model only has four parameters, it's possible to exhaustively study its parameter dependence. We have in mind models that are correctly scaled, in which case the mean squared error is determined by the correlation coefficient (Appendix 2). Since the value of the correlation coefficient is unchanged when all four weighting coefficients are scaled by the same positive factor, it suffices to consider weighting coefficients drawn from the 3-sphere, such that . Because the 3-sphere has a finite volume, we were able to densely sample the correlation coefficient for all parameter values (Appendix figure 3). This function has one global maximum, corresponding to the optimal weight vector discussed in the main text. Its global minimum occurs on the polar opposite side of the 3-sphere, where the weighted 4-quadrant model is most strongly anti-correlated with the velocity. More generally, correlation coefficients corresponding to model parameters on opposite poles of the 3-sphere always have the same magnitude and opposite sign. Both models explain the same amount of variance about the velocity, and they become equivalent after they're correctly scaled. Thus, we henceforth focus our discussion on the hemisphere where the correlation coefficient was positive.10.7554/eLife.09123.017Appendix figure 3.Accuracy of the weighted 4-quadrant model across model parameters.

Bottom Line: Furthermore, a diversity of inputs to motion detecting neurons can provide access to more complex higher-order correlations.Collectively, these results illustrate how non-canonical computations improve motion estimation with naturalistic inputs.This argues that the complexity of the fly's motion computations, implemented in its elaborate circuits, represents a valuable feature of its visual motion estimator.

View Article: PubMed Central - PubMed

Affiliation: Center for Brain Science, Harvard University, Cambridge, United States.

ABSTRACT
Many animals use visual signals to estimate motion. Canonical models suppose that animals estimate motion by cross-correlating pairs of spatiotemporally separated visual signals, but recent experiments indicate that humans and flies perceive motion from higher-order correlations that signify motion in natural environments. Here we show how biologically plausible processing motifs in neural circuits could be tuned to extract this information. We emphasize how known aspects of Drosophila's visual circuitry could embody this tuning and predict fly behavior. We find that segregating motion signals into ON/OFF channels can enhance estimation accuracy by accounting for natural light/dark asymmetries. Furthermore, a diversity of inputs to motion detecting neurons can provide access to more complex higher-order correlations. Collectively, these results illustrate how non-canonical computations improve motion estimation with naturalistic inputs. This argues that the complexity of the fly's motion computations, implemented in its elaborate circuits, represents a valuable feature of its visual motion estimator.

Show MeSH