Connectome-constrained spatially embedded recurrent neural networks
Poster No:
1577
Submission Type:
Abstract Submission
Authors:
Maroš Rovný1, Danyal Akarca2, Jascha Achterberg3, Duncan Astle4
Institutions:
1University of Cambridge, Cambridge, United Kingdom, 2Imperial College London, London, United Kingdom, 3University of Oxford, Oxford, United Kingdom, 4Cambridge University, Cambridge, United Kingdom
First Author:
Co-Author(s):
Introduction:
The approach of spatially embedded recurrent neural networks by Achterberg & Akarca et al. (2023) uses a custom regularization function to embed the recurrent layer within a recurrent neural network in Euclidean space by scaling the weight matrix by a distance matrix. Further addition of the communicability matrix, which denotes local random diffusion over the network, allows the network to consider not only space but also topology.
Here, we develop the spatially embedded recurrent network framework by including the Earth Mover's Distance (EMD) between network and target communicability distributions. This allows us to embed a recurrent neural network in Euclidean brain space and topological space based on an exemplar human connectome.
Here, we develop the spatially embedded recurrent network framework by including the Earth Mover's Distance (EMD) between network and target communicability distributions. This allows us to embed a recurrent neural network in Euclidean brain space and topological space based on an exemplar human connectome.
Methods:
Task As in the original work (Achterberg & Akarca et al., 2023), we trained a recurrent artificial network to perform a simple one-step inference task with both memory and decision components, as shown in Figure 1a. Cross-entropy loss is used during training to quantify and improve the network's performance in the task, in addition to the two embedding terms.
Spatial embedding To provide the network with spatial information, we used the method proposed by Achterberg & Akarca et al. (2023):
{loss}_{spatial}\ =||W\odot D|| (1)
Where W is the weight matrix of the recurrent layer and D is the distance matrix containing the Euclidean distances between brain regions.
Topological embedding To provide the network with topological information, we used a novel approach based on the optimal transport problem:
{loss}_{topological}\ =\ \ EMD\ (\ C_{empirical}\ ,\ C_{artificial}\ ) (2)
Where EMD is the Earth Mover's Distance (Wasserstein implementation, Peyré & Cuturi, 2018) between the flattened empirical and artificial weighted communicability matrices C (Crofts & Higham, 2009).
Empirical networks For the spatial component of our embedding, we used the Brainnetome parcellation, consisting of 246 nodes covering both cortical and subcortical areas. For the topological embedding, we used a weighted diffusion-tensor imaging-based connectome of a randomly chosen subject from the Cambridge Attention, Learning, and Memory (CALM) cohort (Holmes et al., 2019).
Spatial embedding To provide the network with spatial information, we used the method proposed by Achterberg & Akarca et al. (2023):
{loss}_{spatial}\ =||W\odot D|| (1)
Where W is the weight matrix of the recurrent layer and D is the distance matrix containing the Euclidean distances between brain regions.
Topological embedding To provide the network with topological information, we used a novel approach based on the optimal transport problem:
{loss}_{topological}\ =\ \ EMD\ (\ C_{empirical}\ ,\ C_{artificial}\ ) (2)
Where EMD is the Earth Mover's Distance (Wasserstein implementation, Peyré & Cuturi, 2018) between the flattened empirical and artificial weighted communicability matrices C (Crofts & Higham, 2009).
Empirical networks For the spatial component of our embedding, we used the Brainnetome parcellation, consisting of 246 nodes covering both cortical and subcortical areas. For the topological embedding, we used a weighted diffusion-tensor imaging-based connectome of a randomly chosen subject from the Cambridge Attention, Learning, and Memory (CALM) cohort (Holmes et al., 2019).
Results:
Communicability distributions As shown in Figure 1b, the communicability distribution of a artificial network approximates the empirical network over training.
Weight matrices As seen in Figure 1c, the weight matrix of the artificial networks shows organisational similarities to the empirical one, attained not by the direct introduction of an empirical weight matrix but by the interaction of spatial constraints and topological information.
Functional decoding Figure 2 shows side-by-side comparison of functional decoding between only-task and embedded networks. Functional decoding correlates the activation of individual neurons with the memory and decision components of the task, informing about the localization of these components within the network. The two networks differ in the location and proportion of memory and decision neurons, as well as the number of mixed selective neurons.
Weight matrices As seen in Figure 1c, the weight matrix of the artificial networks shows organisational similarities to the empirical one, attained not by the direct introduction of an empirical weight matrix but by the interaction of spatial constraints and topological information.
Functional decoding Figure 2 shows side-by-side comparison of functional decoding between only-task and embedded networks. Functional decoding correlates the activation of individual neurons with the memory and decision components of the task, informing about the localization of these components within the network. The two networks differ in the location and proportion of memory and decision neurons, as well as the number of mixed selective neurons.
·Figure 1
·Figure 2
Conclusions:
By using Earth mover's distance between the network's own and brain-based communicability distributions, we were able to create networks that could solve a memory and decision-making task while at the same time shaping their connections to an end-state analogous to that of a connectome. Crucially, the networks differ not only in structure but also function, uniquely distributing the information and computation among their neurons.
The promise of our approach is exciting: it could be used to understand the importance of different topological properties of the human brain on its overall efficiency in learning and performing a task. Moreover, it could be used to compare the brains of individuals or groups with varied neural phenotypes, which could lead to insights in clinical research.
The promise of our approach is exciting: it could be used to understand the importance of different topological properties of the human brain on its overall efficiency in learning and performing a task. Moreover, it could be used to compare the brains of individuals or groups with varied neural phenotypes, which could lead to insights in clinical research.
Modeling and Analysis Methods:
Methods Development 1
Other Methods 2
Keywords:
Computational Neuroscience
Other - recurrent neural network; multi-objective optimization; spatial embedding; topological embedding; connectome
1|2Indicates the priority used for review
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2. Crofts, J. J., & Higham, D. J. (2009). A weighted communicability measure applied to complex brain networks. Journal of The Royal Society Interface, 6(33), 411–414. https://doi.org/10.1098/RSIF.2008.0484
3. Holmes, J., Bryant, A., & Gathercole, S. E. (2019). Protocol for a transdiagnostic study of children with problems of attention, learning and memory (CALM) 17 Psychology and Cognitive Sciences 1701 Psychology 17 Psychology and Cognitive Sciences 1702 Cognitive Sciences 11 Medical and Health Sciences 1117 Public Health and Health Services. BMC Pediatrics, 19(1), 1–11. https://doi.org/10.1186/S12887-018-1385-3/FIGURES/1
4. Pathak, A., Roy, D., & Banerjee, A. (2022). Whole-Brain Network Models: From Physics to Bedside. Frontiers in Computational Neuroscience, 16, 866517. https://doi.org/10.3389/FNCOM.2022.866517/BIBTEX
5. Peyré, G., & Cuturi, M. (2018). Computational Optimal Transport. Found. Trends Mach. Learn., 11(5–6), 1–257. https://doi.org/10.1561/2200000073