Convergent Temperature Representations in Artificial and Biological Neural Networks

Abstract

Discoveries in biological neural networks (BNNs) shaped artificial neural networks (ANNs) and computational parallels between ANNs and BNNs have recently been discovered. However, it is unclear to what extent discoveries in ANNs can give insight into BNN function. Here, we designed and trained an ANN to perform heat gradient navigation and found striking similarities in computation and heat representation to a known zebrafish BNN. This included shared ON- and OFF-type representations of absolute temperature and rates of change. Importantly, ANN function critically relied on zebrafish-like units. We furthermore used the accessibility of the ANN to discover a new temperature-responsive cell type in the zebrafish cerebellum. Finally, constraining the ANN by the C. elegans motor repertoire retuned sensory representations indicating that our approach generalizes. Together, these results emphasize convergence of ANNs and BNNs on stereotypical representations and that ANNs form a powerful tool to understand their biological counterparts.

Keywords: C. elegans; artificial neural network; comparative computation; computation; representation; thermosensation; zebrafish.

Figure 1:. A convolutional network for gradient navigation

A) Location of temperature modulated neurons (blue) in the zebrafish brain and sensory trigeminal ganglia. Temperature modulated neurons in a hindbrain processing area are in green. B) Structure of the convolutional network for zebrafish temperature prediction. Curves on top depict example network input of the training dataset. Conv: Convolutional layer, ReLu indicates that network uses rectifying linear units, Drop: Indicates dropout during training. C) Schematic of the network task. Given temperature and movement history in a heat gradient, the network predicts the resting temperature after different behavior selections (stay, move straight, turn left or right). D) Log of the squared error in temperature predictions on a test data set after the indicated number of training steps (dashed vertical lines demarcate training epochs). E) Evolutionary algorithm to learn p(Swim) weights (left panel) and progression of heat gradient navigation error across generations (right panel). Error-bars are bootstrap standard error across 20 evolved networks. Generation 7 in grey and last generation in blue for comparison with F) and G). F) For fully trained predictive network in generation 0 (orange), evolved generation 7 (grey) and network after completed evolution (blue) the average swim frequency by temperature in the gradient. G) Radial heat gradient occupancy of naïve (black), trained (orange) and evolved (blue) networks. Dashed vertical line at 26 °C indicates desired temperature. H-H”) Example trajectory for 30 minutes of navigation in a circular gradient for larval zebrafish (H), the predictive ANN (H’) and the reinforcement learning ANN (H”) I) Average turn angles of zebrafish or indicated networks when the last swim-bout was going towards the preferred temperature (blue bars) or away (red bars) relative to the same direction in a non-gradient condition. **: Wilcoxon test across N=25 fish, p=0.0027; ***: Wilcoxon test across N=20 networks, p=8.857×10⁻⁵; p>0.7: Wilcoxon test across N=20 networks, p=0.7938. J) Plot of turn coherence for larval zebrafish (blue), predictive ANN (grey) and reinforcement learning ANN (orange) during heat gradient navigation. For successive turns the probability of turning into the same direction as turn 0 is plotted. Dashed line indicates chance level. Shading in all panels indicates bootstrap standard error across 25 fish or 20 networks respectively. See also Figure S1.

Figure 2:. The network learns a zebrafish-like neural representation

A) Activity correlation between previously described zebrafish hindbrain heat response types and all identified response types in the predictive ANN given the same stimulus. The naming refers to the names given to the cell types in (Haesemeyer et al., 2018). Circles indicate matched types with a Pearson correlation > 0.6. B) Responses of fish-like ON cell types assigned by the correlation in A. Top panel: Network responses of adapting “Fast ON” cells (red) and non-adapting “Slow ON” cells (orange) in the network. Bottom panel shows corresponding zebrafish calcium responses for comparison. Stimulus depicted in grey on top for reference, vertical dashed lines indicate example rising and falling phase starts. C) Responses of fish-like OFF cell types assigned by the correlation in A. Top panel: Network responses of adapting “Fast OFF” cells (green) and non-adapting “Slow OFF” cells (blue) in the network. Bottom panel shows corresponding zebrafish calcium responses for comparison. D) “Integrating OFF cell” type identified in the network (purple, top panel) was used as a regressor to identify the same, previously unidentified, cell type in zebrafish data by probing the dataset for cells that have calcium responses with a correlation r>0.6 to the regressor (bottom panel, shading indicates bootstrap standard error across 146 zebrafish neurons). D’) The newly identified zebrafish cells cluster spatially, especially in a tight rostral band of the cerebellum (arrow). Top panel: Dorsal view of the brain (anterior left, left side bottom). Bottom panel: side view of the brain, anterior left, dorsal top). Scale bars: 100 μm. E) Connectivity weights between layer 1 neuron types in the temperature branch (columns) feeding into the indicated types of layer 2 neurons (rows). Fish-like types are indicated by corresponding colored bars and remaining non-fish like clusters are indicated by thinner gray bars on the right side. Error bars indicate standard deviation. Shading indicates bootstrap standard error across 20 networks in all panels. See also Figures S2 and S3.

Figure 3. White noise analysis reveals ANN processing

A) White noise analysis of behavior induced by the network depicting the average stimulus in the last second preceding a swim. Straight swim kernel orange, turn kernel blue. Inset shows zebrafish kernels for comparison with straight bout kernel in orange and turn kernel in blue. Arrowhead indicates OFF response just before swim start in zebrafish and networks. B–F) During the same white noise stimulation paradigm used in A) the behavior triggered average activity of the indicated cell types. Orange lines depict behavior triggered average activity before straight swims, blue lines before turns. B) Behavior triggered average activity of “Fast ON” units. C) Behavior triggered average activity of “Slow ON” units. D) Behavior triggered average activity of “Fast OFF” units. E) Behavior triggered average activity of “Slow OFF” units. F) Behavior triggered average activity of “Integrating OFF” units. Shading indicates bootstrap standard error across 20 networks in all panels. See also Figure S4.

Figure 4:. Ablations reveal importance of zebrafish like cell types

A) Effect of random unit ablations on gradient navigation performance as fraction within 1 °C of desired temperature. Shown is performance f or naïve, fully trained and for random ablations of the indicated fraction of units in the temperature branch for zebrafish networks. Inset depicts location for all ablations. B) Occupancy in radial heat gradient for trained zebrafish networks (black) and after ablations of the indicated cell types (colored lines). C) Quantification of gradient navigation performance as fraction within 1 °C of desired temperature for naïve and trained zebrafish networks as well as after ablations of the indicated cell types identified in larval zebrafish (colored bars) and those types not identified in fish (“Non-fish”), grey bars. Ablations are ordered according to severity of phenotype. D) Effect on gradient navigation of ablating all types identified in zebrafish (blue line) or all non-fish types (red line). Note that these are non-evolved networks to allow retraining analysis. Trained performance shown in black for reference. The number of ablated units was matched in both conditions (see Star Methods). E) Log of the squared error in temperature predictions of networks on the test data set after ablating all fish-like types in the temperature branch when either retraining weights in the temperature branch (red line) or in the mixed branch (blue line). Inset indicates retraining locations. F) Effect of re-training networks after ablating all zebrafish like neurons. Re-training was either limited to the temperature branch (red line) or the mixed branch (blue line). Solid grey line visualizes trained and dotted grey line ablated performance. G-H) Recovered fraction of individual cell types after retraining the temperature branch (red bars) or after retraining the mixed branch (blue bars). Insets depict retraining locations. G) Cell type fractions in temperature branch. H) Cell type fractions in mixed branch. Shading and error bars in all panels indicate bootstrap standard error across 20 networks.

Figure 5:. A network for C. elegans thermotaxis

A) Architecture of the C. elegans convolutional network. Note that the architecture is the same as in Figure 1d except for the predictive output which is matched to the behavioral repertoire of C. elegans. B) Schematic of the task of the C. elegans ANN: The network uses a 4s history of experienced temperature and generated behaviors to predict the resting temperature after a C. elegans behavior. C) Log squared error of temperature predictions on test data set during training. D) Occupancy in a radial heat gradient of naïve (black) and trained (orange) C. elegans networks. Dashed vertical line at 26 °C indicates desired temperature. E) Comparison of all unit responses in the temperature branch of the zebrafish and C. elegans heat gradient ANN in PCA space when presenting the same time varying stimulus used in Figure 2b to both networks. The first four principal components capture > 95% of the variance. Plots show occupational density along each PC for the zebrafish network (blue) and the C. elegans network (orange). F) Responses of two C. elegans like cell types when presenting a temperature ramp depicted in black on top. The red type shows adapting responses like the AFD neuron (compare to Clark et al., 2007; Kotera et al., 2016) while the orange type reports temperature level as suggested for the AWC/AIY neurons (compare to Kuhara et al., 2008). G) Occupancy in radial heat gradient for trained C. elegans networks (black) and after ablations of the indicated cell types (colored lines). H) Quantification of gradient navigation performance as fraction within 1 °C of desired temperature for naïve and trained C. elegans networks as well as after ablations of the indicated cell types. Ablations are ordered by severity of phenotype. I) Responses of two C. elegans cell types with strong gradient navigation phenotypes in H) to the same temperature ramp presented in F). J) For each network type the number of principal components needed to explain at least 99% of the total network unit variance when the stimulus depicted in 2B is presented to the network. Naive networks black, fully trained orange. Note, that naive reinforcement learning networks already require 2 components since these networks have fewer units overall and therefore have a noisier representation in the naive state. Shading and error bars in all panels indicate bootstrap standard error across 20 networks. See also Figure S5.