arXiv subjects

Claus C. Hilgetag

Publications and source records attributed to Claus C. Hilgetag.

13 recordsLinked to original sources

arXiv2025

Who Does What in Deep Learning? Multidimensional Game-Theoretic Attribution of Function of Neural Units

Neural networks now generate text, images, and speech with billions of parameters, producing a need to know how each neural unit contributes to these high-dimensional outputs. Existing explainable-AI methods, such as SHAP, attribute importance to inputs, but cannot quantify the contributions of neural units across thousands of output pixels, tokens, or logits. Here we close that gap with Multiperturbation Shapley-value Analysis (MSA), a model-agnostic game-theoretic framework. By systematically lesioning combinations of units, MSA yields Shapley Modes, unit-wise contribution maps that share the exact dimensionality of the model's output. We apply MSA across scales, from multi-layer perceptrons to the 56-billion-parameter Mixtral-8x7B and Generative Adversarial Networks (GAN). The approach demonstrates how regularisation concentrates computation in a few hubs, exposes language-specific experts inside the LLM, and reveals an inverted pixel-generation hierarchy in GANs. Together, these results showcase MSA as a powerful approach for interpreting, editing, and compressing deep neural networks.

cs.LG↗

arXiv2022

Causal Influences Decouple From Their Underlying Network Structure In Echo State Networks

Echo State Networks (ESN) are versatile recurrent neural network models in which the hidden layer remains unaltered during training. Interactions among nodes of this static backbone produce diverse representations of the given stimuli that are harnessed by a read-out mechanism to perform computations needed for solving a given task. ESNs are accessible models of neuronal circuits, since they are relatively inexpensive to train. Therefore, ESNs have become attractive for neuroscientists studying the relationship between neural structure, function, and behavior. For instance, it is not yet clear how distinctive connectivity patterns of brain networks support effective interactions among their nodes and how these patterns of interactions give rise to computation. To address this question, we employed an ESN with a biologically inspired structure and used a systematic multi-site lesioning framework to quantify the causal contribution of each node to the network's output, thus providing a causal link between network structure and behavior. We then focused on the structure-function relationship and decomposed the causal influence of each node on all other nodes, using the same lesioning framework. We found that nodes in a properly engineered ESN interact largely irrespective of the network's underlying structure. However, in a network with the same topology and a non-optimal parameter set, the underlying connectivity patterns determine the node interactions. Our results suggest that causal structure-function relations in ESNs can be decomposed into two components, direct and indirect interactions. The former are based on influences relying on structural connections. The latter describe the effective communication between any two nodes through other intermediate nodes. These widely distributed indirect interactions may crucially contribute to the efficient performance of ESNs.

cs.LG↗

arXiv2021

Brain Modelling as a Service: The Virtual Brain on EBRAINS

The Virtual Brain (TVB) is now available as open-source cloud ecosystem on EBRAINS, a shared digital research platform for brain science. It offers services for constructing, simulating and analysing brain network models (BNMs) including the TVB network simulator; magnetic resonance imaging (MRI) processing pipelines to extract structural and functional connectomes; multiscale co-simulation of spiking and large-scale networks; a domain specific language for automatic high-performance code generation from user-specified models; simulation-ready BNMs of patients and healthy volunteers; Bayesian inference of epilepsy spread; data and code for mouse brain simulation; and extensive educational material. TVB cloud services facilitate reproducible online collaboration and discovery of data assets, models, and software embedded in scalable and secure workflows, a precondition for research on large cohort data sets, better generalizability and clinical translation.

cs.CE↗

arXiv2016

A predictive structural model of the primate connectome

Anatomical connectivity imposes strong constraints on brain function, but there is no general agreement about principles that govern its organization. Based on extensive quantitative data we tested the power of three models to predict connections of the primate cerebral cortex: architectonic similarity (structural model), spatial proximity (distance model) and thickness similarity (thickness model). Architectonic similarity showed the strongest and most consistent influence on connection features. This parameter was strongly associated with the presence or absence of inter-areal connections and when integrated with spatial distance, the model allowed predicting the existence of projections with very high accuracy. Moreover, architectonic similarity was strongly related to the laminar pattern of projections origins, and the absolute number of cortical connections of an area. By contrast, cortical thickness similarity and distance were not systematically related to connection features. These findings suggest that cortical architecture provides a general organizing principle for connections in the primate brain.

q-bio.NC↗

arXiv2014

Perspective: network-guided pattern formation of neural dynamics

The understanding of neural activity patterns is fundamentally linked to an understanding of how the brain's network architecture shapes dynamical processes. Established approaches rely mostly on deviations of a given network from certain classes of random graphs. Hypotheses about the supposed role of prominent topological features (for instance, the roles of modularity, network motifs, or hierarchical network organization) are derived from these deviations. An alternative strategy could be to study deviations of network architectures from regular graphs (rings, lattices) and consider the implications of such deviations for self-organized dynamic patterns on the network. Following this strategy, we draw on the theory of spatiotemporal pattern formation and propose a novel perspective for analyzing dynamics on networks, by evaluating how the self-organized dynamics are confined by network architecture to a small set of permissible collective states. In particular, we discuss the role of prominent topological features of brain connectivity, such as hubs, modules and hierarchy, in shaping activity patterns. We illustrate the notion of network-guided pattern formation with numerical simulations and outline how it can facilitate the understanding of neural dynamics.

q-bio.NC↗

arXiv2010

Beyond the average: Detecting global singular nodes from local features in complex networks

Deviations from the average can provide valuable insights about the organization of natural systems. The present article extends this important principle to the systematic identification and analysis of singular motifs in complex networks. Six measurements quantifying different and complementary features of the connectivity around each node of a network were calculated, and multivariate statistical methods applied to identify singular nodes. The potential of the presented concepts and methodology was illustrated with respect to different types of complex real-world networks, namely the US air transportation network, the protein-protein interactions of the yeast Saccharomyces cerevisiae and the Roget thesaurus networks. The obtained singular motifs possessed unique functional roles in the networks. Three classic theoretical network models were also investigated, with the Barabási-Albert model resulting in singular motifs corresponding to hubs, confirming the potential of the approach. Interestingly, the number of different types of singular node motifs as well as the number of their instances were found to be considerably higher in the real-world networks than in any of the benchmark networks.

physics.soc-ph↗

arXiv2010

Optimal hierarchical modular topologies for producing limited sustained activation of neural networks

An essential requirement for the representation of functional patterns in complex neural networks, such as the mammalian cerebral cortex, is the existence of stable regimes of network activation, typically arising from a limited parameter range. In this range of limited sustained activity (LSA), the activity of neural populations in the network persists between the extremes of either quickly dying out or activating the whole network. Hierarchical modular networks were previously found to show a wider parameter range for LSA than random or small-world networks not possessing hierarchical organization or multiple modules. Here we explored how variation in the number of hierarchical levels and modules per level influenced network dynamics and occurrence of LSA. We tested hierarchical configurations of different network sizes, approximating the large-scale networks linking cortical columns in one hemisphere of the rat, cat, or macaque monkey brain. Scaling of the network size affected the number of hierarchical levels and modules in the optimal networks, also depending on whether global edge density or the numbers of connections per node were kept constant. For constant edge density, only few network configurations, possessing an intermediate number of levels and a large number of modules, led to a large range of LSA independent of brain size. For a constant number of node connections, there was a trend for optimal configurations in larger-size networks to possess a larger number of hierarchical levels or more modules. These results may help to explain the trend to greater network complexity apparent in larger brains and may indicate that this complexity is required for maintaining stable levels of neural activation.

q-bio.NC↗

arXiv2009

A simple rule for axon outgrowth and synaptic competition generates realistic connection lengths and filling fractions

Neural connectivity at the cellular and mesoscopic level appears very specific and is presumed to arise from highly specific developmental mechanisms. However, there are general shared features of connectivity in systems as different as the networks formed by individual neurons in Caenorhabditis elegans or in rat visual cortex and the mesoscopic circuitry of cortical areas in the mouse, macaque, and human brain. In all these systems, connection length distributions have very similar shapes, with an initial large peak and a long flat tail representing the admixture of long-distance connections to mostly short-distance connections. Furthermore, not all potentially possible synapses are formed, and only a fraction of axons (called filling fraction) establish synapses with spatially neighboring neurons. We explored what aspects of these connectivity patterns can be explained simply by random axonal outgrowth. We found that random axonal growth away from the soma can already reproduce the known distance distribution of connections. We also observed that experimentally observed filling fractions can be generated by competition for available space at the target neurons--a model markedly different from previous explanations. These findings may serve as a baseline model for the development of connectivity that can be further refined by more specific mechanisms.

q-bio.NC↗

arXiv2009

A proposal for a coordinated effort for the determination of brainwide neuroanatomical connectivity in model organisms at a mesoscopic scale

In this era of complete genomes, our knowledge of neuroanatomical circuitry remains surprisingly sparse. Such knowledge is however critical both for basic and clinical research into brain function. Here we advocate for a concerted effort to fill this gap, through systematic, experimental mapping of neural circuits at a mesoscopic scale of resolution suitable for comprehensive, brain-wide coverage, using injections of tracers or viral vectors. We detail the scientific and medical rationale and briefly review existing knowledge and experimental techniques. We define a set of desiderata, including brain-wide coverage; validated and extensible experimental techniques suitable for standardization and automation; centralized, open access data repository; compatibility with existing resources, and tractability with current informatics technology. We discuss a hypothetical but tractable plan for mouse, additional efforts for the macaque, and technique development for human. We estimate that the mouse connectivity project could be completed within five years with a comparatively modest budget.

q-bio.NC↗

arXiv2008

Criticality of spreading dynamics in hierarchical cluster networks without inhibition

An essential requirement for the representation of functional patterns in complex neural networks, such as the mammalian cerebral cortex, is the existence of stable network activations within a limited critical range. In this range, the activity of neural populations in the network persists between the extremes of quickly dying out, or activating the whole network. The nerve fiber network of the mammalian cerebral cortex possesses a modular organization extending across several levels of organization. Using a basic spreading model without inhibition, we investigated how functional activations of nodes propagate through such a hierarchically clustered network. The simulations demonstrated that persistent and scalable activation could be produced in clustered networks, but not in random networks of the same size. Moreover, the parameter range yielding critical activations was substantially larger in hierarchical cluster networks than in small-world networks of the same size. These findings indicate that a hierarchical cluster architecture may provide the structural basis for the stable and diverse functional patterns observed in cortical networks.

q-bio.NC↗

arXiv2006

Nonoptimal Component Placement, but Short Processing Paths, due to Long-Distance Projections in Neural Systems

It has been suggested that neural systems across several scales of organization show optimal component placement, in which any spatial rearrangement of the components would lead to an increase of total wiring. Using extensive connectivity datasets for diverse neural networks combined with spatial coordinates for network nodes, we applied an optimization algorithm to the network layouts, in order to search for wire-saving component rearrangements. We found that optimized component rearrangements could substantially reduce total wiring length in all tested neural networks. Specifically, total wiring among 95 primate (Macaque) cortical areas could be decreased by 32%, and wiring of neuronal networks in the nematode Caenorhabditis elegans could be reduced by 48% on the global level, and by 49% for neurons within frontal ganglia. Wiring length reductions were possible due to the existence of long-distance projections in neural networks. We explored the role of these projections by comparing the original networks with minimally rewired networks of the same size, which possessed only the shortest possible connections. In the minimally rewired networks, the number of processing steps along the shortest paths between components was significantly increased compared to the original networks. Additional benchmark comparisons also indicated that neural networks are more similar to network layouts that minimize the length of processing paths, rather than wiring length. These findings suggest that neural systems are not exclusively optimized for minimal global wiring, but for a variety of factors including the minimization of processing steps.

q-bio.NC↗

arXiv2004

Edge vulnerability in neural and metabolic networks

Biological networks, such as cellular metabolic pathways or networks of corticocortical connections in the brain, are intricately organized, yet remarkably robust toward structural damage. Whereas many studies have investigated specific aspects of robustness, such as molecular mechanisms of repair, this article focuses more generally on how local structural features in networks may give rise to their global stability. In many networks the failure of single connections may be more likely than the extinction of entire nodes, yet no analysis of edge importance (edge vulnerability) has been provided so far for biological networks. We tested several measures for identifying vulnerable edges and compared their prediction performance in biological and artificial networks. Among the tested measures, edge frequency in all shortest paths of a network yielded a particularly high correlation with vulnerability, and identified inter-cluster connections in biological but not in random and scale-free benchmark networks. We discuss different local and global network patterns and the edge vulnerability resulting from them.

q-bio.NC↗

arXiv2003

Spatial Growth of Real-world Networks

Many real-world networks have properties of small-world networks, with clustered local neighborhoods and low average-shortest path (ASP). They may also show a scale-free degree distribution, which can be generated by growth and preferential attachment to highly connected nodes, or hubs. However, many real-world networks consist of multiple, inter-connected clusters not normally seen in systems grown by preferential attachment, and there also exist real-world networks with a scale-free degree distribution that do not contain highly connected hubs. We describe spatial growth mechanisms, not using preferential attachment, that address both aspects.

cond-mat.stat-mech↗