Cognitive Capacity of Neuromorphic Hierarchical Modular Reservoirs
Poster No:
1176
Submission Type:
Abstract Submission
Authors:
Filip Milisav1, Andrea Luppi2, Laura Suárez3, Guillaume Lajoie4, Bratislav Misic1
Institutions:
1Montréal Neurological Institute, McGill University, Montréal, Canada, 2University of Oxford, Oxford, United Kingdom, 3Mila - Quebec Artifical Intelligence Institute, Montréal, Canada, 4University of Montreal, Montréal, Canada
First Author:
Co-Author(s):
Introduction:
The brain is organized in a hierarchy of nested and increasingly polyfunctional circuits. This architecture is believed to strike a balance between information segregation in specialized neuronal communities and global integration via intermodular communication (Hilgetag, 2020). Yet, how hierarchical modularity shapes network function remains unclear. Here, we constrain artificial neural networks with wiring patterns informed by the hierarchical modular topology of biological neural networks. This allows us to causally relate hierarchical network architectures to cognitive capacity across a range of dynamics.
Methods:
We take advantage of reservoir computing (Lukoševičius, 2009), an ideal paradigm for neuromorphic network design. This framework pairs a nonlinear recurrent neural network (RNN; reservoir) with a linear readout module that approximates a target signal through a linear combination of the RNN signals. Only the readout module is trained, leaving RNN connectivity patterns unchanged.
Here, we use a stochastic block model (Holland, 1983) to specify 3 hierarchical modularity levels. Starting from 8 modules at the first level, intermodular connectivity is tuned at each level, successively nesting pairs of lower-order modules into higher-order modules (Fig. 1a). We generate 100 synthetic graphs per level while maintaining consistent network density and node degree. By uniformly scaling connection weights, we explore network dynamics across spectral radii (α) spanning stable (α < 1) to chaotic (α > 1) regimes.
To evaluate cognitive capacities, we test memory and multitasking performance. For memory, the readout module is trained to reproduce a delayed version of a random input signal. Performance is assessed using the R2 regression score, averaged across 16 time-lags and all pairwise combinations of the original 8 modules as input and output nodes. For multitasking, we add a sinusoidal-to-square wave transformation task, assigning memory tasks to half the modules and non-linear transformation tasks to the other half (Fig. 1c). R2 scores are averaged across all tasks.
To investigate hierarchical modularity in empirical brain networks, we use diffusion-weighted MRI data from 327 participants of the Human Connectome Project (Van Essen, 2013). Nested community partitions are identified using Louvain modularity maximization (Blondel, 2008; Fig. 1g) and (hierarchical) modular null networks are created by applying degree-preserving rewiring on between-module edges (Fig. 1h).
Here, we use a stochastic block model (Holland, 1983) to specify 3 hierarchical modularity levels. Starting from 8 modules at the first level, intermodular connectivity is tuned at each level, successively nesting pairs of lower-order modules into higher-order modules (Fig. 1a). We generate 100 synthetic graphs per level while maintaining consistent network density and node degree. By uniformly scaling connection weights, we explore network dynamics across spectral radii (α) spanning stable (α < 1) to chaotic (α > 1) regimes.
To evaluate cognitive capacities, we test memory and multitasking performance. For memory, the readout module is trained to reproduce a delayed version of a random input signal. Performance is assessed using the R2 regression score, averaged across 16 time-lags and all pairwise combinations of the original 8 modules as input and output nodes. For multitasking, we add a sinusoidal-to-square wave transformation task, assigning memory tasks to half the modules and non-linear transformation tasks to the other half (Fig. 1c). R2 scores are averaged across all tasks.
To investigate hierarchical modularity in empirical brain networks, we use diffusion-weighted MRI data from 327 participants of the Human Connectome Project (Van Essen, 2013). Nested community partitions are identified using Louvain modularity maximization (Blondel, 2008; Fig. 1g) and (hierarchical) modular null networks are created by applying degree-preserving rewiring on between-module edges (Fig. 1h).
Results:
At criticality (α = 1), where the brain is believed to operate (Cocchi, 2017), higher-order hierarchical modular networks consistently outperform lower-order modular networks, as well as degree-preserving rewired null networks (Fig. 1b, c; insets), for both memory (Fig. 1b) and multitasking (Fig. 1c) capacity (two-tailed Wilcoxon-Mann-Whitney–WMW–tests, p < 0.05).
Further analysis of activity dynamics at criticality reveals that higher-order hierarchical modular networks exhibit longer and more diverse neural timescales (Murray, 2014; Fig. 1d), higher maximal Lyapunov exponents (Vogt, 2022; Fig. 1e) – indicating closer proximity to criticality, and increased active information storage (Boedecker, 2012; Fig. 1f; two-tailed WMW tests, p < 0.05). These properties align with a more flexible memory system.
In empirical hierarchical modularity patterns, hierarchical modular surrogates also show a higher memory capacity than strictly modular surrogates at criticality (Fig. 1h; two-tailed WMW tests, p < 10-7). These results might explain recent reports showing that reservoirs constrained with human brain connectivity patterns perform optimally near criticality (Suárez, 2021).
Further analysis of activity dynamics at criticality reveals that higher-order hierarchical modular networks exhibit longer and more diverse neural timescales (Murray, 2014; Fig. 1d), higher maximal Lyapunov exponents (Vogt, 2022; Fig. 1e) – indicating closer proximity to criticality, and increased active information storage (Boedecker, 2012; Fig. 1f; two-tailed WMW tests, p < 0.05). These properties align with a more flexible memory system.
In empirical hierarchical modularity patterns, hierarchical modular surrogates also show a higher memory capacity than strictly modular surrogates at criticality (Fig. 1h; two-tailed WMW tests, p < 10-7). These results might explain recent reports showing that reservoirs constrained with human brain connectivity patterns perform optimally near criticality (Suárez, 2021).
Conclusions:
Altogether, across multiple benchmarks, these results show that hierarchical modularity can yield computationally advantageous functional properties, providing insight into the relation between brain structure and function with potential applications for neuromorphic engineering.
Learning and Memory:
Learning and Memory Other
Modeling and Analysis Methods:
Connectivity (eg. functional, effective, structural) 1
Diffusion MRI Modeling and Analysis 2
Keywords:
Cognition
Computational Neuroscience
Machine Learning
Memory
Modeling
Other - hierarchical modularity; reservoir computing; criticality
1|2Indicates the priority used for review
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Provide references using APA citation style.
Boedecker, J. (2012). Information processing in echo state networks at the edge of chaos. Theory in Biosciences, 131, 205-213.
Cocchi, L. (2017). Criticality in the brain: A synthesis of neurobiology, models and cognition. Progress in Neurobiology, 158, 132-152.
Hilgetag, C. C. (2020). ‘Hierarchy’ in the organization of brain networks. Philosophical Transactions of the Royal Society B, 375(1796), 20190319.
Holland, P. W. (1983). Stochastic blockmodels: First steps. Social networks, 5(2), 109-137.
Lukoševičius, M. (2009). Reservoir computing approaches to recurrent neural network training. Computer Science Review, 3(3), 127-149.
Murray, J. D. (2014). A hierarchy of intrinsic timescales across primate cortex. Nature Neuroscience, 17(12), 1661-1663.
Suárez, L. E. (2021). Learning function from structure in neuromorphic networks. Nature Machine Intelligence, 3(9), 771-786.
Van Essen, D. C. (2013). The WU-Minn Human Connectome Project: An overview. Neuroimage, 80, 62-79.
Vogt, R. (2022). On Lyapunov Exponents for RNNs: Understanding information propagation using dynamical systems tools. Frontiers in Applied Mathematics and Statistics, 8, 818799.