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Neurobiological systems rely on hierarchical and modular architectures to carry out intricate computations using minimal resources. A prerequisite for such systems to operate adequately is the capability to reliably and efficiently transfer information across multiple modules. Here, we study the features enabling a robust transfer of stimulus representations in modular networks of spiking neurons, tuned to operate in a balanced regime. To capitalize on the complex, transient dynamics that such networks exhibit during active processing, we apply reservoir computing principles and probe the systems' computational efficacy with specific tasks. Focusing on the comparison of random feed-forward connectivity and biologically inspired topographic maps, we find that, in a sequential set-up, structured projections between the modules are strictly necessary for information to propagate accurately to deeper modules. Such mappings not only improve computational performance and efficiency, they also reduce response variability, increase robustness against interference effects, and boost memory capacity. We further investigate how information from two separate input streams is integrated and demonstrate that it is more advantageous to perform non-linear computations on the input locally, within a given module, and subsequently transfer the result downstream, rather than transferring intermediate information and performing the computation downstream. Depending on how information is integrated early on in the system, the networks achieve similar task-performance using different strategies, indicating that the dimensionality of the neural responses does not necessarily correlate with nonlinear integration, as predicted by previous studies. These findings highlight a key role of topographic maps in supporting fast, robust, and accurate neural communication over longer distances. Given the prevalence of such structural feature, particularly in the sensory systems, elucidating their functional purpose remains an important challenge toward which this work provides relevant, new insights. At the same time, these results shed new light on important requirements for designing functional hierarchical spiking networks.
Recurrent cortical networks provide reservoirs of states that are thought to play a crucial role for sequential information processing in the brain. However, classical reservoir computing requires manual adjustments of global network parameters, particularly of the spectral radius of the recurrent synaptic weight matrix. It is hence not clear if the spectral radius is accessible to biological neural networks. Using random matrix theory, we show that the spectral radius is related to local properties of the neuronal dynamics whenever the overall dynamical state is only weakly correlated. This result allows us to introduce two local homeostatic synaptic scaling mechanisms, termed flow control and variance control, that implicitly drive the spectral radius toward the desired value. For both mechanisms the spectral radius is autonomously adapted while the network receives and processes inputs under working conditions. We demonstrate the effectiveness of the two adaptation mechanisms under different external input protocols. Moreover, we evaluated the network performance after adaptation by training the network to perform a time-delayed XOR operation on binary sequences. As our main result, we found that flow control reliably regulates the spectral radius for different types of input statistics. Precise tuning is however negatively affected when interneural correlations are substantial. Furthermore, we found a consistent task performance over a wide range of input strengths/variances. Variance control did however not yield the desired spectral radii with the same precision, being less consistent across different input strengths. Given the effectiveness and remarkably simple mathematical form of flow control, we conclude that self-consistent local control of the spectral radius via an implicit adaptation scheme is an interesting and biological plausible alternative to conventional methods using set point homeostatic feedback controls of neural firing.
Understanding the dynamics of recurrent neural networks is crucial for explaining how the brain processes information. In the neocortex, a range of different plasticity mechanisms are shaping recurrent networks into effective information processing circuits that learn appropriate representations for time-varying sensory stimuli. However, it has been difficult to mimic these abilities in artificial neural network models. Here we introduce SORN, a self-organizing recurrent network. It combines three distinct forms of local plasticity to learn spatio-temporal patterns in its input while maintaining its dynamics in a healthy regime suitable for learning. The SORN learns to encode information in the form of trajectories through its high-dimensional state space reminiscent of recent biological findings on cortical coding. All three forms of plasticity are shown to be essential for the network's success. Keywords: synaptic plasticity, intrinsic plasticity, recurrent neural networks, reservoir computing, time series prediction