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Mechanistic interpretability aims to understand neural networks by identifying which learned features mediate specific behaviors. Attribution graphs reveal these feature pathways, but interpreting them requires extensive manual analysis --…
We propose the use of non-parametric, graph-based tests to assess the distributional balance of covariates in observational studies with multi-valued treatments. Our tests utilize graph structures ranging from Hamiltonian paths that connect…
We introduce graph motif parameters, a class of graph parameters that depend only on the frequencies of constant-size induced subgraphs. Classical works by Lov\'asz show that many interesting quantities have this form, including, for fixed…
We consider the task of topology discovery of sparse random graphs using end-to-end random measurements (e.g., delay) between a subset of nodes, referred to as the participants. The rest of the nodes are hidden, and do not provide any…
Graphs play a crucial role in data mining and machine learning, representing real-world objects and interactions. As graph datasets grow, managing large, decentralized subgraphs becomes essential, particularly within federated learning…
It is well-known since the seventies of last century that Depth First Search (DFS) can be used to compute strongly connected components [RE. Tarjan. SIAM Journal on Computing, 1972] and Breadth First Search (BFS) can be used to compute…
The fastest deterministic algorithms for connected components take logarithmic time and perform superlinear work on a Parallel Random Access Machine (PRAM). These algorithms maintain a spanning forest by merging and compressing trees, which…
We study the problem of testing conductance in the setting of distributed computing and give a two-sided tester that takes $\mathcal{O}(\log(n) / (\epsilon \Phi^2))$ rounds to decide if a graph has conductance at least $\Phi$ or is…
Deep graph clustering (DGC), which aims to unsupervisedly separate the nodes in an attribute graph into different clusters, has seen substantial potential in various industrial scenarios like community detection and recommendation. However,…
Memory is an important cognitive function for humans. How a brain with such a small power can complete such a complex memory function, the working mechanism behind this is undoubtedly fascinating. Engram theory views memory as the…
Graphs provide a natural way to represent data by encoding information about objects and the relationships between them. With the ever-increasing amount of data collected and generated, locating specific patterns of relationships between…
Let G = (V,E) be an n-vertex graph and M_d a d-vertex graph, for some constant d. Is M_d a subgraph of G? We consider this problem in a model where all n processes are connected to all other processes, and each message contains up to O(log…
Given two colorings of a graph, we consider the following problem: can we recolor the graph from one coloring to the other through a series of elementary changes, such that the graph is properly colored after each step? We introduce the…
Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…
Chordal graphs are important in the structural and algorithmic graph theory. A digraph analogue of chordal graphs was introduced by Haskin and Rose in 1973 but has not been a subject of active studies until recently when a characterization…
Undirected co-graphs are those graphs which can be generated from the single vertex graph by disjoint union and join operations. Co-graphs are exactly the P_4-free graphs (where P_4 denotes the path on 4 vertices). Co-graphs itself and…
Quantum networks are important for quantum communication, enabling tasks such as quantum teleportation, quantum key distribution, quantum sensing, and quantum error correction, often utilizing graph states, a specific class of multipartite…
A fundamental challenge in the empirical sciences involves uncovering causal structure through observation and experimentation. Causal discovery entails linking the conditional independence (CI) invariances in observational data to their…
Evaluating graphs learned by causal discovery algorithms is difficult: The number of edges that differ between two graphs does not reflect how the graphs differ with respect to the identifying formulas they suggest for causal effects. We…
Local certification consists in assigning labels to the nodes of a network to certify that some given property is satisfied, in such a way that the labels can be checked locally. In the last few years, certification of graph classes…