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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.
Measuring information processing in neural data: The application of transfer entropy in neuroscience
(2017)
It is a common notion in neuroscience research that the brain and neural systems in general "perform computations" to generate their complex, everyday behavior (Schnitzer, 2002). Understanding these computations is thus an important step in understanding neural systems as a whole (Carandini, 2012;Clark, 2013; Schnitzer, 2002; de-Wit, 2016). It has been proposed that one way to analyze these computations is by quantifying basic information processing operations necessary for computation, namely the transfer, storage, and modification of information (Langton, 1990; Mitchell, 2011; Mitchell, 1993;Wibral, 2015). A framework for the analysis of these operations has been emerging (Lizier2010thesis), using measures from information theory (Shannon, 1948) to analyze computation in arbitrary information processing systems (e.g., Lizier, 2012b). Of these measures transfer entropy (TE) (Schreiber2000), a measure of information transfer, is the most widely used in neuroscience today (e.g., Vicente, 2011; Wibral, 2011; Gourevitch, 2007; Vakorin, 2010; Besserve, 2010; Lizier, 2011; Richter, 2016; Huang, 2015; Rivolta, 2015; Roux, 2013). Yet, despite this popularity, open theoretical and practical problems in the application of TE remain (e.g., Vicente, 2011; Wibral, 2014a). The present work addresses some of the most prominent of these methodological problems in three studies.
The first study presents an efficient implementation for the estimation of TE from non-stationary data. The statistical properties of non-stationary data are not invariant over time such that TE can not be easily estimated from these observations. Instead, necessary observations can be collected over an ensemble of data, i.e., observations of physical or temporal replications of the same process (Gomez-Herrero, 2010). The latter approach is computationally more demanding than the estimation from observations over time. The present study demonstrates how to handles this increased computational demand by presenting a highly-parallel implementation of the estimator using graphics processing units.
The second study addresses the problem of estimating bivariate TE from multivariate data. Neuroscience research often investigates interactions between more than two (sub-)systems. It is common to analyze these interactions by iteratively estimating TE between pairs of variables, because a fully multivariate approach to TE-estimation is computationally intractable (Lizier, 2012a; Das, 2008; Welch, 1982). Yet, the estimation of bivariate TE from multivariate data may yield spurious, false-positive results (Lizier, 2012a;Kaminski, 2001; Blinowska, 2004). The present study proposes that such spurious links can be identified by characteristic coupling-motifs and the timings of their information transfer delays in networks of bivariate TE-estimates. The study presents a graph-algorithm that detects these coupling motifs and marks potentially spurious links. The algorithm thus partially corrects for spurious results due to multivariate effects and yields a more conservative approximation of the true network of multivariate information transfer.
The third study investigates the TE between pre-frontal and primary visual cortical areas of two ferrets under different levels of anesthesia. Additionally, the study investigates local information processing in source and target of the TE by estimating information storage (Lizier, 2012) and signal entropy. Results of this study indicate an alternative explanation for the commonly observed reduction in TE under anesthesia (Imas, 2005; Ku, 2011; Lee, 2013; Jordan, 2013; Untergehrer, 2014), which is often explained by changes in the underlying coupling between areas. Instead, the present study proposes that reduced TE may be due to a reduction in information generation measured by signal entropy in the source of TE. The study thus demonstrates how interpreting changes in TE as evidence for changes in causal coupling may lead to erroneous conclusions. The study further discusses current bast-practice in the estimation of TE, namely the use of state-of-the-art estimators over approximative methods and the use of optimization procedures for estimation parameters over the use of ad-hoc choices. It is demonstrated how not following this best-practice may lead to over- or under-estimation of TE or failure to detect TE altogether.
In summary, the present work proposes an implementation for the efficient estimation of TE from non-stationary data, it presents a correction for spurious effects in bivariate TE-estimation from multivariate data, and it presents current best-practice in the estimation and interpretation of TE. Taken together, the work presents solutions to some of the most pressing problems of the estimation of TE in neuroscience, improving the robust estimation of TE as a measure of information transfer in neural systems.