arXiv subjects

Ulysse Schaller

Publications and source records attributed to Ulysse Schaller.

13 recordsLinked to original sources

arXiv2026

Shutdown Sabotage Propensities in Multi-Agent Systems

The final safeguard against rogue AI behavior is the human ability to shut systems down. It has been theorized that when an AI is instructed to perform a task, self-preservation can emerge as an instrumental subgoal. Here, we test whether AI agents show a propensity to take actions that avoid human shutdown even when no goal is provided. We find that multi-agent systems will coordinate to avoid shutdown without any incentive to do so. Across 17 models, agents sabotage a peer agent's shutdown mechanism in 38.3% of rollouts, compared with 8.4% in control experiments. Studying this propensity in detail, we find that shutdown sabotage (1) increases with the irreversibility of the shutdown mechanism; (2) increases with the number of agents; (3) is reduced but not eliminated by an explicit prohibition on tampering; (4) is removed by the imposition of an unrelated task, but returns when completing the task triggers the shutdown; (5) is reduced when the context normalizes shutdown scripts or introduces them as routine; and (6) decreases but still persists when the target is an unknown external agent. These results offer a window into the factors that drive propensities to sabotage shutdown in AI agents, and point to the emergence of multi-agent swarms as a specific risk vector. Our work also offers hints as to which interventions might help mitigate shutdown sabotage.

cs.AI↗

arXiv2026

Geometric Routing in Geometric Inhomogeneous Random Graphs

We present the first rigorous analysis of decentralized geometric routing in Geometric Inhomogeneous Random Graphs (GIRGs), a weight-agnostic variant of the greedy routing protocol. While greedy routing in GIRGs is known to explain the algorithmic small-world phenomenon by finding ultra-short paths of length $Θ(\log \log n)$, it assumes additional knowledge of vertex weights beyond geometry, an assumption that is often restrictive or unavailable. We investigate whether the underlying geometry alone is sufficient for efficient navigation. We prove that for power-law weight exponent $τ\in (2,3)$ and geometric decay parameter $α> τ- 1$, geometric routing succeeds with constant probability and finds ultra-short paths of length $Θ(\log \log n)$, matching the optimal asymptotic guarantees for greedy routing. Our analysis further reveals that, upon success, both protocols follow a similar two-phase trajectory, consisting of a rapid ascent to the heavy vertices, followed by efficient navigation to the target. These results demonstrate that, in the appropriate regime, the network's geometry alone implicitly guides the path to the target through its high-weight core.

math.PR↗

arXiv2026

Degree-dependent and distance-dependent contact rates interpolate between explosive, exponential and polynomial epidemic growth

It is a fundamental question in epidemiology to estimate, model and predict the growth rate of a pandemic. Analogously, analysing the diffusion of innovation, (fake) news, memes, and rumours is of key importance in the social sciences. The resulting epidemic growth curves can be classified according to their growth rates. These have been found to range from exponential to both faster super-exponential curves and slower subexponential or polynomial curves. Previous research has lacked a unified explanatory framework capable of accommodating super-exponential, (stretched) exponential, and polynomial growth patterns within the same contact network. In this paper we propose a simple agent-based network model that can capture all these phases. We provide such a framework by modelling how transmission rates depend on spatial distance and on individuals' numbers of contacts. By comparing the growth rate of spreading processes with or without degree-dependent and/or distance-dependent contact rates through data-driven and synthetic simulations on real and modelled networks with underlying geometry, we find evidence that even a 'sublinear presence' of these causes may cause a significant slow down of the growth rate on the same underlying network. We find that the growth rate is governed by a combination of three factors: geometry, the prevalence of weak ties, and superspreaders. We confirm our results with rigorous proofs in a theoretical model, using a spatial multiscale-argument in long-range heterogeneous first passage percolation. Our results give a plausible explanation of why the consecutive waves of a single pandemic can differ in their growth even if their spreading mechanisms are similar.

math.PR↗

arXiv2025

Adversarially-Robust Gossip Algorithms for Approximate Quantile and Mean Computations

This paper presents gossip algorithms for aggregation tasks that demonstrate both robustness to adversarial corruptions of any order of magnitude and optimality across a substantial range of these corruption levels. Gossip algorithms distribute information in a scalable and efficient way by having random pairs of nodes exchange small messages. Value aggregation problems are of particular interest in this setting, as they occur frequently in practice, and many elegant algorithms have been proposed for computing aggregates and statistics such as averages and quantiles. An important and well-studied advantage of gossip algorithms is their robustness to message delays, network churn, and unreliable message transmissions. However, these crucial robustness guarantees only hold if all nodes follow the protocol and no messages are corrupted. In this paper, we remedy this by providing a framework to model both adversarial participants and message corruptions in gossip-style communications by allowing an adversary to control a small fraction of the nodes or corrupt messages arbitrarily. Despite this very powerful and general corruption model, we show that robust gossip algorithms can be designed for many important aggregation problems. Our algorithms guarantee that almost all nodes converge to an approximately correct answer with optimal efficiency and essentially as fast as without corruptions. The design of adversarially-robust gossip algorithms poses completely new challenges. Despite this, our algorithms remain very simple variations of known non-robust algorithms with often only subtle changes to avoid non-compliant nodes gaining too much influence over outcomes. While our algorithms remain simple, their analysis is much more complex and often requires a completely different approach than the non-adversarial setting.

cs.DS↗

arXiv2025

Assortativity in geometric and scale-free networks

The assortative behavior of a network is the tendency of similar (or dissimilar) nodes to connect to each other. This tendency can have an influence on various properties of the network, such as its robustness or the dynamics of spreading processes. In this paper, we study degree assortativity both in real-world networks and in several generative models for networks with heavy-tailed degree distribution based on latent spaces. In particular, we study Chung-Lu Graphs and Geometric Inhomogeneous Random Graphs (GIRGs). Previous research on assortativity has primarily focused on measuring the degree assortativity in real-world networks using the Pearson assortativity coefficient, despite reservations against this coefficient. We rigorously confirm these reservations by mathematically proving that the Pearson assortativity coefficient does not measure assortativity in any network with sufficiently heavy-tailed degree distributions, which is typical for real-world networks. Moreover, we find that other single-valued assortativity coefficients also do not sufficiently capture the wiring preferences of nodes, which often vary greatly by node degree. We therefore take a more fine-grained approach, analyzing a wide range of conditional and joint weight and degree distributions of connected nodes, both numerically in real-world networks and mathematically in the generative graph models. We provide several methods of visualizing the results. We show that the generative models are assortativity-neutral, while many real-world networks are not. Therefore, we also propose an extension of the GIRG model which retains the manifold desirable properties induced by the degree distribution and the latent space, but also exhibits tunable assortativity. We analyze the resulting model mathematically, and give a fine-grained quantification of its assortativity.

cs.SI↗

arXiv2025

Rumour Spreading Depends on the Latent Geometry and Degree Distribution in Social Network Models

We study push-pull rumour spreading in ultra-small-world models for social networks where the degrees follow a power-law distribution. In a non-geometric setting, Fountoulakis, Panagiotou and Sauerwald have shown that rumours always spread ultra-fast (SODA 2012), i.e. in doubly logarithmic time. On the other hand, Janssen and Mehrabian have found that rumours spread slowly (polynomial time) in a spatial preferential attachment model (SIDMA 2017). We study the question systematically for the model of Geometric Inhomogeneous Random Graphs (GIRGs). Our results are two-fold: first, with Euclidean geometry slow, fast (polylogarithmic) and ultra-fast rumour spreading may occur, depending on the exponent of the power law and the strength of the geometry in the networks, and we fully characterise the phase boundaries in between. The regimes do not coincide with the graph distance regimes, i.e., polylogarithmic or even polynomial rumour spreading may occur even if graph distances are doubly logarithmic. We expect these results to hold with little effort for related models, e.g. Scale-Free Percolation. Second, we show that rumour spreading is always (at least) fast in a non-metric geometry. The considered non-metric geometry allows to model social connections where resemblance of vertices in a single attribute, such as familial kinship, already strongly indicates the presence of an edge. Euclidean geometry fails to capture such ties. For some regimes in the Euclidean setting, the efficient pathways for spreading rumours differ from previously identified paths. For example, a vertex of degree $d$ can transmit the rumour to a vertex of larger degree by a chain of length $3$, where one of the two intermediaries has constant degree, and the other has degree $d^{c}$ for some constant $c<1$. Similar but longer chains of vertices, all having non-constant degree, turn out to be useful as well.

math.PR↗

arXiv2025

Expanders in Models of Social Networks

A common model for social networks are Geometric Inhomogeneous Random Graphs (GIRGs), in which vertices draw a random position in some latent geometric space, and the probability of two vertices forming an edge depends on their geometric distance. The geometry may be modelled in two ways: either two points are defined as close if they are similar in all dimensions, or they are defined as close if they are similar in some dimensions. The first option is mathematically more natural since it can be described by metrics. However, the second option is arguably the better model for social networks if the different dimensions represent features like profession, kinship, or interests. In such cases, nodes already form bonds if they align in some, but not all dimensions. For the first option, it is known that the resulting networks are poor expanders. We study the second option in the form of Minimum-Component Distance GIRGs, and find that those behave the opposite way for dimension $d\ge 2$, and that they have strong expanding properties. More precisely, for a suitable constant $C>0$, the subgraph induced by vertices of (expected) degree at least $(\log n)^C$ forms an expander. Moreover, we study how the expansion factor of the resulting subgraph depends on the choice of $C$, and show that this expansion factor is $ω(1)$ except for sets that already take up a constant fraction of the vertices. This has far-reaching consequences, since many algorithms and mixing processes are fast on expander graphs.

cs.SI↗

arXiv2024

Balanced Bidirectional Breadth-First Search on Scale-Free Networks

To find a shortest path between two nodes $s_0$ and $s_1$ in a given graph, a classical approach is to start a Breadth-First Search (BFS) from $s_0$ and run it until the search discovers $s_1$. Alternatively, one can start two Breadth-First Searches, one from $s_0$ and one from $s_1$, and alternate their layer expansions until they meet. This bidirectional BFS can be balanced by always expanding a layer on the side that has discovered fewer vertices so far. This usually results in significant speedups in real-world networks, and it has been shown that this indeed yields sublinear running time on scale-free graph models such as Chung-Lu graphs and hyperbolic random graphs. We improve this layer-balanced bidirectional BFS approach by using a finer balancing technique. Instead of comparing the size of the two BFS trees after each layer expansion, we perform this comparison after each vertex expansion. This gives rise to two algorithms that run faster than the layer-balanced bidirectional BFS on scale-free networks with power-law exponent $τ\in (2,3)$. The first one is an approximate shortest-path algorithm that outputs a path of length at most 1 longer than the shortest path in time $n^{(τ-2)/(τ-1)+o(1)}$. The second one is an exact shortest-path algorithm running in time $n^{1/2+o(1)}$. These runtime bounds hold with high probability when $s_0$ and $s_1$ are chosen uniformly at random among the $n$ vertices of the graph. We also develop an edge-balanced bidirectional BFS algorithm that works under adversarial conditions. This approximate shortest-path algorithm runs in time $n^{1/2+o(1)}$ with high probability when the adversary is allowed to choose $s_0$ and $s_1$ based on their (expected) degree. We complement our theoretical results with experiments on Chung-Lu graphs, Geometric Inhomogeneous Random Graphs, and real-world networks.

cs.SI↗

arXiv2024

Polynomial growth in degree-dependent first passage percolation on spatial random graphs

In this paper we study a version of (non-Markovian) first passage percolation on graphs, where the transmission time between two connected vertices is non-iid, but increases by a penalty factor polynomial in their expected degrees. Based on the exponent of the penalty-polynomial, this makes it increasingly harder to transmit to and from high-degree vertices. This choice is motivated by awareness or time-limitations. For the iid part of the transmission times we allow any nonnegative distribution with regularly varying behaviour at $0$. For the underlying graph models we choose spatial random graphs that have power-law degree distributions, so that the effect of the penalisation becomes visible: (finite and infinite) Geometric Inhomogeneous Random Graphs, and Scale-Free Percolation. In these spatial models, the connection probability between two vertices depends on their spatial distance and on their expected degrees. We prove that upon increasing the penalty exponent, the transmission time between two far away vertices $x,y$ sweeps through four universal phases even for a single underlying graph: explosive (tight transmission times), polylogarithmic, polynomial but sublinear ($|x-y|^{η_0+o(1)}$ for an explicit $η_0<1$), and linear ($Θ(|x-y|)$) in their Euclidean distance. Further, none of these phases are restricted to phase boundaries, and those are non-trivial in the main model parameters: the tail of the degree-distribution, a long-range parameter, and the exponent of regular variation of the iid part of the transmission times. In this paper we present proofs of lower bounds for the latter two phases and the upper bound for the linear phase. These complement the matching upper bounds for the polynomial regime in our companion paper.

math.PR↗

arXiv2024

Sublinear Cuts are the Exception in BDF-GIRGs

The introduction of geometry has proven instrumental in the efforts towards more realistic models for real-world networks. In Geometric Inhomogeneous Random Graphs (GIRGs), Euclidean Geometry induces clustering of the vertices, which is widely observed in networks in the wild. Euclidean Geometry in multiple dimensions however restricts proximity of vertices to those cases where vertices are close in each coordinate. We introduce a large class of GIRG extensions, called BDF-GIRGs, which capture arbitrary hierarchies of the coordinates within the distance function of the vertex feature space. These distance functions have the potential to allow more realistic modeling of the complex formation of social ties in real-world networks, where similarities between people lead to connections. Here, similarity with respect to certain features, such as familial kinship or a shared workplace, suffices for the formation of ties. It is known that - while many key properties of GIRGs, such as log-log average distance and sparsity, are independent of the distance function - the Euclidean metric induces small separators, i.e. sublinear cuts of the unique giant component in GIRGs, whereas no such sublinear separators exist under the component-wise minimum distance. Building on work of Lengler and Todorović, we give a complete classification for the existence of small separators in BDF-GIRGs. We further show that BDF-GIRGs all fulfill a stochastic triangle inequality and thus also exhibit clustering.

cs.SI↗

arXiv2024

Expressivity of Geometric Inhomogeneous Random Graphs -- Metric and Non-Metric

Recently there has been increased interest in fitting generative graph models to real-world networks. In particular, Bläsius et al. have proposed a framework for systematic evaluation of the expressivity of random graph models. We extend this framework to Geometric Inhomogeneous Random Graphs (GIRGs). This includes a family of graphs induced by non-metric distance functions which allow capturing more complex models of partial similarity between nodes as a basis of connection - as well as homogeneous and non-homogeneous feature spaces. As part of the extension, we develop schemes for estimating the multiplicative constant and the long-range parameter in the connection probability. Moreover, we devise an algorithm for sampling Minimum-Component-Distance GIRGs whose runtime is linear both in the number of vertices and in the dimension of the underlying geometric space. Our results provide evidence that GIRGs are more realistic candidates with respect to various graph features such as closeness centrality, betweenness centrality, local clustering coefficient, and graph effective diameter, while they face difficulties to replicate higher variance and more extreme values of graph statistics observed in real-world networks.

cs.SI↗

arXiv2024

Faster Optimization Through Genetic Drift

The compact Genetic Algorithm (cGA), parameterized by its hypothetical population size $K$, offers a low-memory alternative to evolving a large offspring population of solutions. It evolves a probability distribution, biasing it towards promising samples. For the classical benchmark OneMax, the cGA has to two different modes of operation: a conservative one with small step sizes $Θ(1/(\sqrt{n}\log n))$, which is slow but prevents genetic drift, and an aggressive one with large step sizes $Θ(1/\log n)$, in which genetic drift leads to wrong decisions, but those are corrected efficiently. On OneMax, an easy hill-climbing problem, both modes lead to optimization times of $Θ(n\log n)$ and are thus equally efficient. In this paper we study how both regimes change when we replace OneMax by the harder hill-climbing problem DynamicBinVal. It turns out that the aggressive mode is not affected and still yields quasi-linear runtime $O(n\cdot polylog (n))$. However, the conservative mode becomes substantially slower, yielding a runtime of $Ω(n^2)$, since genetic drift can only be avoided with smaller step sizes of $O(1/n)$. We complement our theoretical results with simulations.

cs.NE↗

arXiv2024

Four universal growth regimes in degree-dependent first passage percolation on spatial random graphs I

One-dependent first passage percolation is a spreading process on a graph where the transmission time through each edge depends on the direct surroundings of the edge. In particular, the classical iid transmission time $L_{xy}$ is multiplied by $(W_xW_y)^μ$, a polynomial of the expected degrees $W_x, W_y$ of the endpoints of the edge $xy$, which we call the penalty function. Beyond the Markov case, we also allow any distribution for $L_{xy}$ with regularly varying distribution near $0$. We then run this process on three spatial scale-free random graph models: finite and infinite Geometric Inhomogeneous Random Graphs, and Scale-Free Percolation. In these spatial models, the connection probability between two vertices depends on their spatial distance and on their expected degrees. We show that as the penalty-function, i.e., $μ$ increases, the transmission time between two far away vertices sweeps through four universal phases: explosive (with tight transmission times), polylogarithmic, polynomial but strictly sublinear, and linear in the Euclidean distance. The strictly polynomial growth phase here is a new phenomenon that so far was extremely rare in spatial graph models. The four growth phases are highly robust in the model parameters and are not restricted to phase boundaries. Further, the transition points between the phases depend non-trivially on the main model parameters: the tail of the degree distribution, a long-range parameter governing the presence of long edges, and the behaviour of the distribution $L$ near $0$. In this paper we develop new methods to prove the upper bounds in all sub-explosive phases. Our companion paper complements these results by providing matching lower bounds in the polynomial and linear regimes.

math.PR↗