Figure 1
Framework of the current study and network architecture.
The research framework consists of a simulation study and an fMRI study. First, we performed a simulation study using S-CTRNNPB, which models a biological brain based on predictive processing theory. Effects of S-CTRNNPB parameters (experimental conditions) on ASD-like performance were investigated. Second, we mapped the S-CTRNNPB parameter set to the fMRI parameter set. We then examined whether the relationship between the S-CTRNNPB parameters and ASD-related performance measures could also be found between fMRI parameters and ASD diagnosis/symptoms.
Experimental conditions for the simulation study are FCmodel and Neural excitability homogeneity. FCmodel is the proportion of synaptic connections between neurons of different hierarchical level, set at 20–100%. In the figure, solid and dashed blue (orange) arrows represent the presence and absence of synaptic connections between neurons, respectively. Synaptic connections between neurons of the same hierarchy are unified in all experiments; there is no connection between PBs and full-connection between lower-level neurons. Neural excitability homogeneity is defined by the variance of the activity threshold of the lower-level neuron. See the Methods for details on experimental conditions.
For the model architecture, the number of PBs and lower-level neurons are set to 2 and 30, respectively. Note that these neurons model the firing frequency of a population of neurons, not the activity of individual neurons in the biological brain. See the Supplementary Methods for details on parameter setting.
Abbreviations. S-CTRNNPB, stochastic continuous time recurrent neural network with parametric bias; PB, parametric bias; PE, prediction error; ASD, autism spectrum disorder; MRI, magnetic resonance imaging; FC, functional connectivity; ReHo, regional homogeneity.
Figure 2
Analytical results for the TD model.
(A) Learning curves. (B) Examples of target, prediction, lower-level neuron, PB activity sequences. (C) PB activities corresponding to all target sequences (PB space).
Abbreviation. MSE, mean squared error; PB, parametric bias.
Figure 3
Investigation of prediction error under various experimental conditions (A) Training error. (B) Test error.
Abbreviations. Highly Homo, highly homogeneous network condition; modestly Homo, modestly homogeneous network condition; hetero, heterogeneous network condition; FCmodel, functional connectivity in neural network model.
Figure 4
Investigation of emotion recognition performance under various experimental conditions.
(A)(B)(C)(D) Illustration of PB space when network excitability homogeneity and FCmodel differ. Note that FCmodel = 100% and FCmodel = 20% indicate that both higher-level FCmodel and lower-level FCmodel are 100% and 20%, respectively. Experimental conditions in (C) are identical to those in Figure 2(C), and these figures are identical. (E) Emotion recognition index. The emotion recognition index, i.e. average silhouette width, is a measure of the similarity between a test PB activity and a training PB activity of the same emotion. See Supplementary Methods for details.
Abbreviations. Highly Homo, highly homogeneous network condition; modestly Homo, modestly homogeneous network condition; hetero, heterogeneous network condition; FCmodel, functional connectivity in neural network model; PB, parametric bias.
Figure 5
Mechanisms by which underlying ASD-like performance induced by changes in neural network parameters caused ASD-like performance.
(A)(B) Example of a scatterplot of the tolerance of PB space. Positions of points in the scatterplot represents the PB activity obtained by training, as shown in Figures 3C and 3E. Colors of dots indicate the number of training target sequences that can be predicted with low error (PE < 0.01) by providing that PB activity. Both higher-level and lower-level FCmodel were set to 100%. (C) Bar chart of the average number of training target sequences that can be reproduced with small error (PE < 0.01). (D) Prediction error on sensory input-driven generation by setting unreliable (random) PBs. (E) Prediction error on top-down only generation by closed-loop generation.
Abbreviations. Highly Homo, highly homogeneous network condition; modestly Homo, modestly homogeneous network condition; hetero, heterogeneous network condition; PB, parametric bias; PE, prediction error; FCmodel, connectivity proportion.
Figure 6
Validation of neural network simulation results using fMRI data.
(A) Proportion of ASDs belonging to each subgroup. Labels in this figure (fMRI parameters) correspond to labels in Figure 3A, 3B and 3G (neural network parameters). Specifically, neural network parameters, i.e., network excitatory homogeneity and higher/lower-level FCmodel, are mapped to subgroups in fMRI datasets based on fMRI parameters, i.e., regional homogeneity and higher/lower-level FCmodel, respectively. (B) Scatterplot of test error and emotion recognition index. (C) For Figure (B), the diagnostic information of ASD of the subject corresponding to the neural network of each point is added. (In the scatterplot, a little Gaussian noise is added to each point on the X- and Y-axis for visibility.) Histograms of ASD diagnosis are added about test errors (X-axis) and emotion recognition index (Y-axis). (D) Histogram for the number of ASDs and TDs in A, B, and C groups.
Table 1
Relationship between ASD-like performance of the neural network and ADI-R scores of corresponding subjects.
| ADI-R SCALES | NUMBER | CORRELATION COEFFICIENTa WITH TEST ERROR (95% CI) | CORRELATION COEFFICIENTa WITH EMOTION RECOGNITION INDEX (95% CI) |
|---|---|---|---|
| Language/Communication | 297 | 0.014 (–0.105, 0.120) | –0.088 (–0.195, 0.017) |
| Reciprocal Social Interactions | 296 | –0.009 (–0.118, 0.092) | –0.123 (–0.233, –0.008) |
| Restricted, Repetitive, and Stereotyped Behaviors and Interests | 296 | 0.080 (–0.032, 0.206) | –0.111 (–0.225, 0.016) |
[i] a Spearman’s correlation coefficient.
Before the correlation analysis, mapping from the neural network parameter to the subject subgroup in fMRI datasets is adjusted by covariates, i.e., age, gender, FIQ, mean framewise displacement, and sites.
Abbreviations. S-CTRNNPB, stochastic continuous time recurrent neural network with parametric bias; ADI-R, Autism Diagnostic Interview-Revised; CI, confidence interval.