Shallow neural networks trained to detect collisions recover features of visual loom-selective neurons
- Department of Molecular, Cellular and Developmental Biology, Yale University, United States
- Department of Statistics and Data Science, Yale University, United States
- Wu Tsai Institute, Yale University, United States
- Interdepartmental Neuroscience Program, Yale University, United States
- Department of Physics, Yale University, United States
- Department of Neuroscience, Yale University, United States
Figures
Figure 1
Sketches of the anatomy of LPLC2 neurons (Klapoetke et al., 2017).
(A) An LPLC2 neuron has dendrites in lobula and the four layers of the lobula plate (LP): LP1, LP2, LP3, and LP4. (B) Schematic of the four branches of the LPLC2 dendrites in the four layers of the …
Figure 2
Four types of synthetic stimuli (Materials and methods).
(A) Orange lines represent trajectories of the stimuli. The black dots represent the starting points of the trajectories. For hit, miss, and retreat cases, multiple trajectories are shown. For …
Figure 3 with 1 supplement
Snapshots of optical flows and flow fields calculated by a Hassenstein Reichardt correlator (HRC) model (Figure 3—figure supplement 1, Materials and methods) for the four types of stimuli (Figure 2).
First row: 3d rendering of the spherical objects and the LPLC2 receptive field (represented by a cone) at a specific time in the trajectory. The orange arrows indicate the motion direction of each …
Figure 3—figure supplement 1
Tuning curve of HRC motion estimator and distributions of the estimated flow fields.
(A) Diagram of a simple HRC motion estimator (Materials and methods), where indicates temporal delay, the two crosses indicate multiplication, and the minus sign indicates subtraction. (B) Tuning …
Figure 4 with 1 supplement
Schematic of the models (Materials and methods).
(A) Single LRF model unit. There are four linear spatial filters, labeled LP4, LP3, LP2, and LP1, which correspond to the four LP layers (Figure 1). Each filter has real-valued elements, and if the …
Figure 4—figure supplement 1
Coordinate system for model and stimuli.
The coordinate system used in stimulus generation and modeling (Materials and methods). The frame of reference is fixed on the fly head. The frame of references are associated with each local …
Figure 5 with 3 supplements
Three distinct types of solutions appear from training a single unit on the binary classification task (LRF model).
(A) Clustering of the trained filters/weights shown as a dendrogram (Materials and methods). Different colors indicate different clusters, which are preserved for the rest of the paper: outward, …
Figure 5—figure supplement 1
More examples of the trained filters for the three types of solutions.
Trained filters: outward solution (magenta), inward solution (green), and zero solution (black). For each solution type, the trained filters from different initializations are almost identical to …
Figure 5—figure supplement 2
As in the main figure but for the RI model.
As in the main figure but for the RI model. (A) Three types of solutions appear. (B) The trajectories of loss functions. (C) For each type of solution, there are two filters: one excitatory (red) …
Figure 5—figure supplement 3
Examples of the trained outward and inward filters without imposed symmetries.
Trained solutions for models without imposing the 90-degree rotational and mirror symmetries. (A) Trained filters for the LRF model. First two rows: outward and inward filters trained with the …
Figure 6 with 3 supplements
The outward and inward solutions also arise for models with multiple units (LRF models).
(A) Left column: angular distribution of the units, where red dots are centers of the receptive fields, the grey circles are the boundaries of the receptive fields, and the black star indicates the …
Figure 6—figure supplement 1
Performance of the different solutions (LRF models).
Same as in Figure 5D but for LRF models with multiple units. The magenta and green lines/points almost completely overlap with each other in the last row.
Figure 6—figure supplement 2
More examples of the outward and inward filters (LRF models).
Outward and inward solutions for the LRF models with different numbers of units. For both outward and inward solutions, five examples are shown for each model. It can be seen that for outward …
Figure 6—figure supplement 3
Examples of the outward and inward filters for RI models.
Outward and inward solutions for RI models. For both outward and inward solutions, 10 examples are shown for each model. In many outward solutions, structures on the right side of the inhibitory …
Figure 7 with 1 supplement
LRF units with outward and inward filters show distinct patterns of responses.
(A) Trajectories of hit stimuli originating at different angles from the receptive field center, denoted by . Symbols are the same as in Figure 2 except that the upward red arrow represents the …
Figure 7—figure supplement 1
As in the main figure but for the RI units.
(A-E) As in the main figure but for the RI units.
Figure 8 with 3 supplements
Population coding of stimuli (LRF models).
(A) Top row: snapshots of the unit responses of outward solutions (magenta dots) and inward solutions (green dots) for a hit stimulus. The size of the dots represents the strength of the response. …
Figure 8—figure supplement 1
Geometry of responses as in Figure 8A, but for miss and retreat stimuli (LRF models).
Figure 8—figure supplement 2
Sample individual unit response curves (LRF models with ).
(A) Sample response curves of the active units in the outward solution with for different types of stimuli (from left to right: hit, miss, retreat, and rotation) (B) As in (A), but for an inward …
Figure 8—figure supplement 3
As in the main figure but for the RI models.
(A-D) As in the main figure but for the RI models.
Figure 9 with 3 supplements
Large populations of units improve performance (LRF models) (Materials and methods).
(A) Both ROC and PR AUC scores increase as the number of units increases. Colored lines and dots: average scores; shading: one standard deviation of the scores over the trained models. Magenta: …
Figure 9—figure supplement 1
As in the main figure but for RI models.
(A, B) As in the main figure but for RI models.
Figure 9—figure supplement 2
The ratio of the number of the two types of solutions.
The black line and dots show the ratio of the numbers of the two types of solutions in the set of randomly initialized, trained models. The gray shading is one standard deviation, assuming that the …
Figure 9—figure supplement 3
As in the main figure but for LRF models trained using stimuli that include self-rotation during hits, misses, and retreats.
(A, B) As in the main figure but for LRF models trained using stimuli that include self-rotation during hits, misses, and retreats. (C) Example filters for outward and inward solutions for the noted …
Figure 10 with 4 supplements
Units of models trained on binary classification tasks exhibit similar responses to LPLC2 neuron experimental measurements (outward solution of the LRF model with 256 units).
(A) The trained filter. (B–H) Comparisons of the responses of the unit with the trained filter in (A) and LPLC2 neurons to a variety of stimuli (Materials and methods). Black lines: data (Klapoetke …
Figure 10—figure supplement 1
As in the main figure but for an inward solution of the LRF model obtained from the same training procedure.
(A-L) As in the main figure but for an inward solution of the LRF model obtained from the same training procedure, the filter of which is shown in (A).
Figure 10—figure supplement 2
As in the main figure but for an outward solution of the RI model with 256 units.
(A-L) As in the main figure but for an outward solution of the RI model with 256 units, the trained filters of which are shown in (A).
Figure 10—figure supplement 3
As in the main figure but for a second outward solution of the RI model with 256 units.
(A-L) As in the main figure but for a second outward solution of the RI model with 256 units, the trained filters of which are shown in (A). The response curves in (B–H) are produced by setting the …
Figure 10—figure supplement 4
As in the main figure but for a third outward solution of the RI model with 256 units.
(A-L) As in the main figure but for a third outward solution of the RI model with 256 units, the trained filters of which are shown in (A). The response curves in (B–H) are produced by setting the …
Videos
Video 1
Movie for a hit stimulus (single unit).
Video 2
Movie for a miss stimulus (single unit).
The same arrangement as Video 1.
Video 3
Movie for a retreat stimulus (single unit).
The same arrangement as Video 1.
Video 4
Movie for a rotation stimulus (single unit).
The same arrangement as Video 1.
Video 5
Movie of unit responses for a hit stimulus (outward solution of the LRF model with 32 units).
Video 6
Movie of unit responses for a hit stimulus (inward solution of the LRF model with 32 units).
The same arrangement as Video 5 but for an inward model.
Video 7
Movie of unit responses for a miss stimulus (outward solution of the LRF model with 32 units).
The same arrangement as Video 5.
Video 8
Movie of unit responses for a miss stimulus (inward solution of the LRF model with 32 units).
The same arrangement as Video 6.
Video 9
Movie of unit responses for a retreat stimulus (outward solution of the LRF model with 32 units).
The same arrangement as Video 5.
Video 10
Movie of unit responses for a retreat stimulus (inward solution of the LRF model with 32 units).
The same arrangement as Video 6.
Video 11
Movie of unit responses for a rotation stimulus (outward solution of the LRF model with 32 units).
The same arrangement as Video 5.
Video 12
Movie of unit responses for a rotation stimulus (inward solution of the LRF model with 32 units).
The same arrangement as Video 6.
