Equivariance and generalization in neural networks

The crucial role played by the underlying symmetries of high energy physics and lattice field theories calls for the implementation of such symmetries in the neural network architectures that are applied to the physical system under consideration. In these proceedings, we focus on the consequences of incorporating translational equivariance among the network properties, particularly in terms of performance and generalization. The benefits of equivariant networks are exemplified by studying a complex scalar field theory, on which various regression and classification tasks are examined. For a meaningful comparison, promising equivariant and non-equivariant architectures are identified by means of a systematic search. The results indicate that in most of the tasks our best equivariant architectures can perform and generalize significantly better than their non-equivariant counterparts, which applies not only to physical parameters beyond those represented in the training set, but also to different lattice sizes.

Is Network Structure Important for Protest Mobilization? Findings from Agent-Based Modeling

In recent decades, the focus of civic engagement research has shifted towards studying social environments’ effects on individuals’ decisions on whether to participate in a given activity or not. Online communication has been increasingly influencing the scale of social environments as well as the features of both online and offline interpersonal communications. Surely, then, individuals’ decisions concerning protest mobilization are bound to be affected by network properties. Using a series of ABM models with different network structures, we try to identify the structural factors of networks that can influence individuals who are deciding whether to join a protest. The established research in this field traditionally points to two structural factors: network topology and homophily. To our knowledge, however, the literature has not considered two above-mentioned structural factors in combination. In other words, their joint influence on protest mobilization has not been tested. To fill this research gap, we combine several network topologies with enabled/disabled homophily and examine how the combination influences protest turnout and survival. Numerical experiments show that homophily is positively associated with the survival of the protest, but negatively with its size for any network topology. Since we infer this conclusion from a theory-based computational model, we also propose how empirical testing can be conducted. Acknowledgments: This research is supported by the Russian Science Foundation under grant no. 20-18-00274, HSE University.

Evolving Network Analysis of S&P500 Components: COVID-19 Influence of Cross-Correlation Network Structure

The economy is a system of complex interactions. The COVID-19 pandemic strongly influenced economies, particularly through introduced restrictions, which formed a completely new economic environment. The present work focuses on the changes induced by the COVID-19 epidemic on the correlation network structure. The analysis is performed on a representative set of USA companies—the S&P500 components. Four different network structures are constructed (strong, weak, typically, and significantly connected networks), and the rank entropy, cycle entropy, averaged clustering coefficient, and transitivity evolution are established and discussed. Based on the mentioned structural parameters, four different stages have been distinguished during the COVID-19-induced crisis. The proposed network properties and their applicability to a crisis-distinguishing problem are discussed. Moreover, the optimal time window problem is analysed.

Identifying control ensembles for decision-making within the cortico-basal ganglia-thalamic circuit

During action selection, mammals exhibit a high degree of flexibility in adapting their decisions in response to environmental changes. Although the cortico-basal ganglia-thalamic (CBGT) network is implicated in this adaptation, it features a synaptic architecture comprising multiple feed-forward, reciprocal, and feedback pathways, complicating efforts to elucidate the roles of specific CBGT populations in the process of evidence accumulation during decision-making. In this paper we apply a strategic sampling approach, based on Latin hypercube sampling, to explore how CBGT network properties, including subpopulation firing rates and synaptic weights, map to parameters of a normative drift diffusion model (DDM) representing algorithmic aspects of information accumulation during decision-making. Through the application of canonical correlation analysis, we find that this relationship can be characterized in terms of three low-dimensional control ensembles impacting specific qualities of the emergent decision policy: responsiveness (associated with overall activity in corticothalamic and direct pathways), pliancy (associated largely with overall activity in components of the indirect pathway of the basal ganglia), and choice (associated with differences in direct and indirect pathways across action channels). These analyses provide key mechanistic predictions about the roles of specific CBGT network elements in shifting different aspects of decision policies.

BISoN: A Bayesian Framework for Inference of Social Networks

Social networks are often constructed from point estimates of edge weights. In many contexts, edge weights are inferred from observational data, and the uncertainty around point estimates can be affected by various factors. Though this has been acknowledged in previous work, methods that explicitly quantify uncertainty in edge weights have not yet been widely adopted, and remain undeveloped for common types of data. Furthermore, existing methods are unable to cope with some of the complexities often found in observational data, and do not propagate uncertainty in edge weights to subsequent analyses. We introduce a unified Bayesian framework for modelling social networks based on observational data. This framework, which we call BISoN, can accommodate many common types of observational social data, can capture confounds and model effects at the level of observations, and is fully compatible with popular methods of social network analysis. We show how the framework can be applied to common types of data and how various types of downstream analyses can be performed, including non-random association tests and regressions on network properties. Our framework opens up the opportunity to test new types of hypotheses, make full use of observational datasets, and increase the reliability of scientific inferences. We have made example R code available to enable adoption of the framework.

From Diversity to Complexity: Microbial Networks in Soils

Network analysis has been used for many years in ecological research to analyze organismal associations, for example in food webs, plant-plant or plant-animal interactions. Although network analysis is widely applied in microbial ecology, only recently has it entered the realms of soil microbial ecology, shown by a rapid rise in studies applying co-occurrence analysis to soil microbial communities. While this application offers great potential for deeper insights into the ecological structure of soil microbial ecosystems, it also brings new challenges related to the specific characteristics of soil datasets and the type of ecological questions that can be addressed. In this Perspectives Paper we assess the challenges of applying network analysis to soil microbial ecology due to the small-scale heterogeneity of the soil environment and the nature of soil microbial datasets. We review the different approaches of network construction that are commonly applied to soil microbial datasets and discuss their features and limitations. Using a test dataset of microbial communities from two depths of a forest soil, we demonstrate how different experimental designs and network constructing algorithms affect the structure of the resulting networks, and how this in turn may influence ecological conclusions. We will also reveal how assumptions of the construction method, methods of preparing the dataset, an definitions of thresholds affect the network structure. Finally, we discuss the particular questions in soil microbial ecology that can be approached by analyzing and interpreting specific network properties. Targeting these network properties in a meaningful way will allow applying this technique not in merely descriptive, but in hypothesis-driven research.

Exploring inclusiveness towards immigrants as related to basic values: A network approach

Using the 9th round of European Social Survey (ESS), we explored the relationship between Europeans’ basic values and their attitudes towards immigrants. Employing a latent class analysis (LCA), we classified the respondents based on three items capturing the extent to which participants would support allowing three groups of immigrants to enter and live in their countries: immigrants of same ethnic groups, immigrants of different ethnic groups, and immigrants from poorer countries outside Europe. Four classes of Europeans with mutually exclusive response patterns with respect to their inclusive attitudes towards immigrants were found. The classes were named Inclusive (highly inclusive), Some (selective), Few (highly selective), and Exclusive (highly exclusive). Next, using a network technique, a partial correlation network of 10 basic human values was estimated for each class of participants. The four networks were compared to each other based on three network properties namely: global connectivity, community detection, and assortativity coefficient. The global connectivity (the overall level of interconnections) between the 10 basic values was found to be mostly invariant across the four networks. However, results of the community detection analysis revealed a more complex value structure among the most inclusive class of Europeans. Further, according to the assortativity analysis, as expected, for the most inclusive Europeans, values with similar motivational backgrounds were found to be interconnected most strongly to one another. We further discussed the theoretical and practical implications of our findings.

Changes in Brain Structure, Function, and Network Properties in Patients With First-Episode Schizophrenia Treated With Antipsychotics

Purpose: Comprehensive and longitudinal brain analysis is of great significance for understanding the pathological changes of antipsychotic drug treatment in patients with schizophrenia. This study aimed to investigate the changes of structure, function, and network properties in patients with first-episode schizophrenia (FES) after antipsychotic therapy and their relationship with clinical symptoms.Materials and Methods: A total of 30 patients diagnosed with FES and 30 healthy subjects matched for sex and age were enrolled in our study. Patients at baseline were labeled as antipsychotic-naive first-episode schizophrenia (AN-FES), and patients after antipsychotic treatment were labeled as antipsychotic treatment first-episode schizophrenia (AT-FES). The severity of illness was measured by using the PANSS and CGI score. Structural and functional MRI data were also performed. Differences in GMV, ALFF, and ReHo between the FES group and healthy control group were tested using a voxel-wise two-sample t-test, and the comparison of AN-FES group and AT-FES group was evaluated by paired-sample t-test.Results: After the 1-year follow-up, the FES patients showed increased GMV in the right cerebellum, right inferior temporal gyrus, left middle frontal gyrus, parahippocampal gyrus, bilateral inferior parietal lobule, and reduced GMV in the left occipital lobe, gyrus rectus, right orbital frontal cortex. The patients also showed increased ALFF in the medial superior frontal gyrus and right precentral gyrus. For network properties, the patients showed reduced characteristic path length and increased global efficiency. The GMV of the right inferior parietal lobule was negatively correlated with the clinical symptoms.Conclusions: Our study showed that the antipsychotic treatment contributed to the structural alteration and functional improvement, and the GMV alteration may be associated with the improvement of clinical symptoms.