Axiomatic scalable neurocontroller analysis via the Shapley value

Downstream network transformations dissociate neural activity from causal functional contributions

Neuroscientists rely on distributed spatio-temporal patterns of neural activity to understand how neural units contribute to cognitive functions and behavior. However, the extent to which neural activity reliably indicates a unit's causal contribution to the behavior is not well understood. To address this issue, we provide a systematic multi-site perturbation framework that captures time-varying causal contributions of elements to a collectively produced outcome. Applying our framework to intuitive toy examples and artificial neural networks revealed that recorded activity patterns of neural elements may not be generally informative of their causal contribution due to activity transformations within a network. Overall, our findings emphasize the limitations of inferring causal mechanisms from neural activities and offer a rigorous lesioning framework for elucidating causal neural contributions.

When Neural Activity Fails to Reveal Causal Contributions

Neuroscientists rely on distributed spatio-temporal patterns of neural activity to understand how neural units contribute to cognitive functions and behavior. However, the extent to which neural activity reliably indicates a unit's causal contribution to the behavior is not well understood. To address this issue, we provide a systematic multi-site perturbation framework that captures time-varying causal contributions of elements to a collectively produced outcome. Applying our framework to intuitive toy examples and artificial neuronal networks revealed that recorded activity patterns of neural elements may not be generally informative of their causal contribution due to activity transformations within a network. Overall, our findings emphasize the limitations of inferring causal mechanisms from neural activities and offer a rigorous lesioning framework for elucidating causal neural contributions.

Use of multi-perturbation Shapley analysis in lesion studies of functional networks: The case of upper limb paresis

Understanding the impact of variation in lesion topography on the expression of functional impairments following stroke is important, as it may pave the way to modeling structure-function relations in statistical terms while pointing to constraints for adaptive remapping and functional recovery. Multi-perturbation Shapley-value analysis (MSA) is a relatively novel game-theoretical approach for multivariate lesion-symptom mapping. In this methodological paper, we provide a comprehensive explanation of MSA. We use synthetic data to assess the method's accuracy and perform parameter optimization. We then demonstrate its application using a cohort of 107 first-event subacute stroke patients, assessed for upper limb (UL) motor impairment (Fugl-Meyer Assessment scale). Under the conditions tested, MSA could correctly detect simulated ground-truth lesion-symptom relationships with a sensitivity of 75% and specificity of ~90%. For real behavioral data, MSA disclosed a strong hemispheric effect in the relative contribution of specific regions-of-interest (ROIs): poststroke UL motor function was mostly contributed by damage to ROIs associated with movement planning (supplementary motor cortex and superior frontal gyrus) following left-hemispheric damage (LHD) and by ROIs associated with movement execution (primary motor and somatosensory cortices and the ventral brainstem) following right-hemispheric damage (RHD). Residual UL motor ability following LHD was found to depend on a wider array of brain structures compared to the residual motor ability of RHD patients. The results demonstrate that MSA can provide a unique insight into the relative importance of different hubs in neural networks, which is difficult to obtain using standard univariate methods.

Systematic perturbation of an artificial neural network: A step towards quantifying causal contributions in the brain

Lesion inference analysis is a fundamental approach for characterizing the causal contributions of neural elements to brain function. This approach has gained new prominence through the arrival of modern perturbation techniques with unprecedented levels of spatiotemporal precision. While inferences drawn from brain perturbations are conceptually powerful, they face methodological difficulties. Particularly, they are challenged to disentangle the true causal contributions of the involved elements, since often functions arise from coalitions of distributed, interacting elements, and localized perturbations have unknown global consequences. To elucidate these limitations, we systematically and exhaustively lesioned a small artificial neural network (ANN) playing a classic arcade game. We determined the functional contributions of all nodes and links, contrasting results from sequential single-element perturbations with simultaneous perturbations of multiple elements. We found that lesioning individual elements, one at a time, produced biased results. By contrast, multi-site lesion analysis captured crucial details that were missed by single-site lesions. We conclude that even small and seemingly simple ANNs show surprising complexity that needs to be addressed by multi-lesioning for a coherent causal characterization.

The motto “No causation without manipulation” is canonical to scientific endeavors. In particular, neuroscience seeks to identify which brain elements are causally involved in cognition and behavior, by perturbing them. However, due to multi-dimensional interactions among the elements, this goal has remained challenging. Here, we used an Artificial Neural Network as a ground-truth model to compare the inferential capacities of two principal approaches, lesioning a system one element at a time versus sampling from the set of all possible combinations of lesions. We show that lesioning one element at a time provides misleading results. Hence, we argue for employing exhaustive perturbation regimes. We further advocate using simulation experiments and ground-truth models to verify the assumptions and limitations of current approaches for brain mapping by perturbation.

A Mutation Threshold for Cooperative Takeover

One of the leading theories for the origin of life includes the hypothesis according to which life would have evolved as cooperative networks of molecules. Explaining cooperation—and particularly, its emergence in favoring the evolution of life-bearing molecules—is thus a key element in describing the transition from nonlife to life. Using agent-based modeling of the iterated prisoner’s dilemma, we investigate the emergence of cooperative behavior in a stochastic and spatially extended setting and characterize the effects of inheritance and variability. We demonstrate that there is a mutation threshold above which cooperation is—counterintuitively—selected, which drives a dramatic and robust cooperative takeover of the whole system sustained consistently up to the error catastrophe, in a manner reminiscent of typical phase transition phenomena in statistical physics. Moreover, our results also imply that one of the simplest conditional cooperative strategies, “Tit-for-Tat”, plays a key role in the emergence of cooperative behavior required for the origin of life.

Game-theoretical mapping of fundamental brain functions based on lesion deficits in acute stroke

Lesion analysis is a fundamental and classical approach for inferring the causal contributions of brain regions to brain function. However, many studies have been limited by the shortcomings of methodology or clinical data. Aiming to overcome these limitations, we here use an objective multivariate approach based on game theory, Multi-perturbation Shapley value Analysis, in conjunction with data from a large cohort of 394 acute stroke patients, to derive causal contributions of brain regions to four principal functional components of the widely used National Institutes of Health Stroke Score measure. The analysis was based on a high-resolution parcellation of the brain into 294 grey and white matter regions. Through initial lesion symptom mapping for identifying all potential candidate regions and repeated iterations of the game-theoretical approach to remove non-significant contributions, the analysis derived the smallest sets of regions contributing to each of the four principal functional components as well as functional interactions among the regions. Specifically, the factor 'language and consciousness' was related to contributions of cortical regions in the left hemisphere, including the prefrontal gyrus, the middle frontal gyrus, the ventromedial putamen and the inferior frontal gyrus. Right and left motor functions were associated with contributions of the left and right dorsolateral putamen and the posterior limb of the internal capsule, correspondingly. Moreover, the superior corona radiata and the paracentral lobe of the right hemisphere as well as the right caudal area 23 of the cingulate gyrus were mainly related to left motor function, while the prefrontal gyrus, the external capsule and the sagittal stratum fasciculi of the left hemisphere contributed to right motor function. Our approach demonstrates a practically feasible strategy for applying an objective lesion inference method to a high-resolution map of the human brain and distilling a small, characteristic set of grey and white matter structures contributing to fundamental brain functions. In addition, we present novel findings of synergistic interactions between brain regions that provide insight into the functional organization of brain networks.

Game theoretical mapping of white matter contributions to visuospatial attention in stroke patients with hemineglect

White matter bundles linking gray matter nodes are key anatomical players to fully characterize associations between brain systems and cognitive functions. Here we used a multivariate lesion inference approach grounded in coalitional game theory (multiperturbation Shapley value analysis, MSA) to infer causal contributions of white matter bundles to visuospatial orienting of attention. Our work is based on the characterization of the lesion patterns of 25 right hemisphere stroke patients and the causal analysis of their impact on three neuropsychological tasks: line bisection, letter cancellation, and bells cancellation. We report that, out of the 11 white matter bundles included in our MSA coalitions, the optic radiations, the inferior fronto-occipital fasciculus and the anterior cingulum were the only tracts to display task-invariant contributions (positive, positive, and negative, respectively) to the tasks. We also report task-dependent influences for the branches of the superior longitudinal fasciculus and the posterior cingulum. By extending prior findings to white matter tracts linking key gray matter nodes, we further characterize from a network perspective the anatomical basis of visual and attentional orienting processes. The knowledge about interactions patterns mediated by white matter tracts linking cortical nodes of attention orienting networks, consolidated by further studies, may help develop and customize brain stimulation approaches for the rehabilitation of visuospatial neglect.

Perturbation-driven paradoxical facilitation of visuo-spatial function: Revisiting the 'Sprague effect'

The 'Sprague Effect' described in the seminal paper of James Sprague (Science 153:1544-1547, 1966a) is an unexpected paradoxical effect in which a second brain lesion reversed functional deficits induced by an earlier lesion. It was observed initially in the cat where severe and permanent contralateral visually guided attentional deficits generated by the ablation of large areas of the visual cortex were reversed by the subsequent removal of the superior colliculus (SC) opposite to the cortical lesion or by the splitting of the collicular commissure. Physiologically, this effect has been explained in several ways-most notably by the reduction of the functional inhibition of the ipsilateral SC by the contralateral SC, and the restoration of normal interactions between cortical and midbrain structures after ablation. In the present review, we aim at reappraising the 'Sprague Effect' by critically analyzing studies that have been conducted in the feline and human brain. Moreover, we assess applications of the 'Sprague Effect' in the rehabilitation of visually guided attentional impairments by using non-invasive therapeutic approaches such as transcranial magnetic stimulation (TMS) and transcranial direct-current stimulation (tDCS). We also review theoretical models of the effect that emphasize the inhibition and balancing between the two hemispheres and show implications for lesion inference approaches. Last, we critically review whether the resulting inter-hemispheric rivalry theories lead toward an efficient rehabilitation of stroke in humans. We conclude by emphasizing key challenges in the field of 'Sprague Effect' applications in order to design better therapies for brain-damaged patients.

Technical considerations of a game-theoretical approach for lesion symptom mapping

Background

Various strategies have been used for inferring brain functions from stroke lesions. We explored a new mathematical approach based on game theory, the so-called multi-perturbation Shapley value analysis (MSA), to assess causal function localizations and interactions from multiple perturbation data. We applied MSA to a dataset composed of lesion patterns of 148 acute stroke patients and their National Institutes of Health Stroke Scale (NIHSS) scores, to systematically investigate the influence of different parameter settings on the outcomes of the approach. Specifically, we investigated aspects of MSA methodology including the choice of the predictor algorithm (typology and kernel functions), training dataset (original versus binary), as well as the influence of lesion thresholds. We assessed the suitability of MSA for processing real clinical lesion data and established the central parameters for this analysis.

Results

We derived general recommendations for the analysis of clinical datasets by MSA and showed that, for the studied dataset, the best approach was to use a linear-kernel support vector machine predictor, trained with a binary training dataset, where the binarization was implemented through a median threshold of lesion size for each region. We demonstrated that the results obtained with different MSA variants lead to almost identical results as the basic MSA.

Conclusions

MSA is a feasible approach for the multivariate lesion analysis of clinical stroke data. Informed choices need to be made to set parameters that may affect the analysis outcome.

Mapping causal functional contributions derived from the clinical assessment of brain damage after stroke

Lesion analysis reveals causal contributions of brain regions to mental functions, aiding the understanding of normal brain function as well as rehabilitation of brain-damaged patients. We applied a novel lesion inference technique based on game theory, Multi-perturbation Shapley value Analysis (MSA), to a large clinical lesion dataset. We used MSA to analyze the lesion patterns of 148 acute stroke patients together with their neurological deficits, as assessed by the National Institutes of Health Stroke Scale (NIHSS). The results revealed regional functional contributions to essential behavioral and cognitive functions as reflected in the NIHSS, particularly by subcortical structures. There were also side specific differences of functional contributions between the right and left hemispheric brain regions which may reflect the dominance of the left hemispheric syndrome aphasia in the NIHSS. Comparison of MSA to established lesion inference methods demonstrated the feasibility of the approach for analyzing clinical data and indicated its capability for objectively inferring functional contributions from multiple injured, potentially interacting sites, at the cost of having to predict the outcome of unknown lesion configurations. The analysis of regional functional contributions to neurological symptoms measured by the NIHSS contributes to the interpretation of this widely used standardized stroke scale in clinical practice as well as clinical trials and provides a first approximation of a 'map of stroke'.

Causal functional contributions and interactions in the attention network of the brain: an objective multi-perturbation analysis

Spatial attention is a prime example for the distributed network functions of the brain. Lesion studies in animal models have been used to investigate intact attentional mechanisms as well as perspectives for rehabilitation in the injured brain. Here, we systematically analyzed behavioral data from cooling deactivation and permanent lesion experiments in the cat, where unilateral deactivation of the posterior parietal cortex (in the vicinity of the posterior middle suprasylvian cortex, pMS) or the superior colliculus (SC) cause a severe neglect in the contralateral hemifield. Counterintuitively, additional deactivation of structures in the opposite hemisphere reverses the deficit. Using such lesion data, we employed a game-theoretical approach, multi-perturbation Shapley value analysis (MSA), for inferring functional contributions and network interactions of bilateral pMS and SC from behavioral performance in visual attention studies. The approach provides an objective theoretical strategy for lesion inferences and allows a unique quantitative characterization of regional functional contributions and interactions on the basis of multi-perturbations. The quantitative analysis demonstrated that right posterior parietal cortex and superior colliculus made the strongest positive contributions to left-field orienting, while left brain regions had negative contributions, implying that their perturbation may reverse the effects of contralateral lesions or improve normal function. An analysis of functional modulations and interactions among the regions revealed redundant interactions (implying functional overlap) between regions within each hemisphere, and synergistic interactions between bilateral regions. To assess the reliability of the MSA method in the face of variable and incomplete input data, we performed a sensitivity analysis, investigating how much the contribution values of the four regions depended on the performance of specific configurations and on the prediction of unknown performances. The results suggest that the MSA approach is sensitive to categorical, but insensitive to gradual changes in the input data. Finally, we created a basic network model that was based on the known anatomical interactions among cortical-tectal regions and reproduced the experimentally observed behavior in visual orienting. We discuss the structural organization of the network model relative to the causal modulations identified by MSA, to aid a mechanistic understanding of the attention network of the brain.

Evolutionary game theory: molecules as players

In many situations macromolecules, such as proteins, DNA and RNA, can be considered as players in the sense of game theory. In this review we discuss the usefulness of game theory in describing macromolecular processes.

Multiperturbation analysis of distributed neural networks: the case of spatial neglect

This study assesses the feasibility of using a multiperturbation analysis (MPA) approach for lesion-symptom mapping. We analyze the relative contribution of damage in different brain regions to the expression of spatial neglect, as revealed in line-bisection performance. The data set comprised of normalized lesion information and bisection test results from 23 first-event right-hemisphere stroke patients. Obtaining quantitative measures of task relevance for different regions of interest (ROIs), the following ROIs were found to be the most contributing: the supramarginal and angular gyri of the inferior parietal lobule, the superior parietal lobule, the anterior part of the temporo-parietal junction connecting the superior temporal and supramarginal gyri, and the thalamus. MPA is likely to play an important role in elucidating the anatomical substrate of complex functions.

Evolving self-assembly in autonomous homogeneous robots: experiments with two physical robots

This research work illustrates an approach to the design of controllers for self-assembling robots in which the self-assembly is initiated and regulated by perceptual cues that are brought forth by the physical robots through their dynamical interactions. More specifically, we present a homogeneous control system that can achieve assembly between two modules (two fully autonomous robots) of a mobile self-reconfigurable system without a priori introduced behavioral or morphological heterogeneities. The controllers are dynamic neural networks evolved in simulation that directly control all the actuators of the two robots. The neurocontrollers cause the dynamic specialization of the robots by allocating roles between them based solely on their interaction. We show that the best evolved controller proves to be successful when tested on a real hardware platform, the swarm-bot. The performance achieved is similar to the one achieved by existing modular or behavior-based approaches, also due to the effect of an emergent recovery mechanism that was neither explicitly rewarded by the fitness function, nor observed during the evolutionary simulation. Our results suggest that direct access to the orientations or intentions of the other agents is not a necessary condition for robot coordination: Our robots coordinate without direct or explicit communication, contrary to what is assumed by most research works in collective robotics. This work also contributes to strengthening the evidence that evolutionary robotics is a design methodology that can tackle real-world tasks demanding fine sensory-motor coordination.

Use of game-theoretical methods in biochemistry and biophysics

Evolutionary game theory can be considered as an extension of the theory of evolutionary optimisation in that two or more organisms (or more generally, units of replication) tend to optimise their properties in an interdependent way. Thus, the outcome of the strategy adopted by one species (e.g., as a result of mutation and selection) depends on the strategy adopted by the other species. In this review, the use of evolutionary game theory for analysing biochemical and biophysical systems is discussed. The presentation is illustrated by a number of instructive examples such as the competition between microorganisms using different metabolic pathways for adenosine triphosphate production, the secretion of extracellular enzymes, the growth of trees and photosynthesis. These examples show that, due to conflicts of interest, the global optimum (in the sense of being the best solution for the whole system) is not always obtained. For example, some yeast species use metabolic pathways that waste nutrients, and in a dense tree canopy, trees grow taller than would be optimal for biomass productivity. From the viewpoint of game theory, the examples considered can be described by the Prisoner's Dilemma, snowdrift game, Tragedy of the Commons and rock-scissors-paper game.

Can single knockouts accurately single out gene functions?

Background

When analyzing complex biological systems, a major objective is localization of function – assessing how much each element contributes to the execution of specific tasks. To establish causal relationships, knockout and perturbation studies are commonly executed. The vast majority of studies perturb a single element at a time, yet one may hypothesize that in non-trivial biological systems single-perturbations will fail to reveal the functional organization of the system, owing to interactions and redundancies.

Results

We address this fundamental gap between theory and practice by quantifying how misleading the picture arising from classical single-perturbation analysis is, compared with the full multiple-perturbations picture. To this end we use a combination of a novel approach for quantitative, rigorous multiple-knockouts analysis based on the Shapley value from game theory, with an established in-silico model of Saccharomyces cerevisiae metabolism. We find that single-perturbations analysis misses at least 33% of the genes that contribute significantly to the growth potential of this organism, though the essential genes it does find are responsible for most of the growth potential. But when assigning gene contributions for individual metabolic functions, the picture arising from single-perturbations is severely lacking and a multiple-perturbations approach turns out to be essential.

Conclusion

The multiple-perturbations investigation yields a significantly richer and more biologically plausible functional annotation of the genes comprising the metabolic network of the yeast.

Feature Selection via Coalitional Game Theory

We present and study the contribution-selection algorithm (CSA), a novel algorithm for feature selection. The algorithm is based on the multiperturbation shapley analysis (MSA), a framework that relies on game theory to estimate usefulness. The algorithm iteratively estimates the usefulness of features and selects them accordingly, using either forward selection or backward elimination. It can optimize various performance measures over unseen data such as accuracy, balanced error rate, and area under receiver-operator-characteristic curve. Empirical comparison with several other existing feature selection methods shows that the backward elimination variant of CSA leads to the most accurate classification results on an array of data sets.