Estimating the clique number in a graph is central to various applications, e.g., community detection, graph retrieval, etc. Existing estimators often rely on non-differentiable combinatorial components. Here, we propose a full differentiable estimator for clique number estimation, which can be trained from distant supervision of clique numbers, rather than demonstrating actual cliques. Our key insight is a formulation of the maximum clique problem (MCP) as a maximization of the size of fully dense square submatrix, within a suitably row-column-permuted adjacency matrix. We design a differentiable mechanism to search for permutations that lead to the discovery of such dense blocks. However, the optimal permutation is not unique, which leads to the learning of spurious permutations. To tackle this problem, we view the MCP problem as a sequence of subgraph matching tasks, each detecting progressively larger cliques in a nested manner. This allows effective navigation through suitable node permutations. These steps result in MxNet, an end-to-end differentiable model, which learns to predict clique number without explicit clique demonstrations, with the added benefit of interpretability. Experiments on eight datasets show the superior accuracy of our approach.

Multimodal Large Language Models (LLMs) hold promise for biomedical reasoning, but current benchmarks fail to capture the complexity of real-world clinical workflows. Existing evaluations primarily assess unimodal, decontextualized question-answering, overlooking multi-agent decision-making environments such as Molecular Tumor Boards (MTBs). MTBs bring together diverse experts in oncology, where diagnostic and prognostic tasks require integrating heterogeneous data and evolving insights over time. Current benchmarks lack this longitudinal and multimodal complexity. We introduce MTBBench, an agentic benchmark simulating MTB-style decision-making through clinically challenging, multimodal, and longitudinal oncology questions. Ground truth annotations are validated by clinicians via a co-developed app, ensuring clinical relevance. We benchmark multiple open and closed-source LLMs and show that, even at scale, they lack reliability—frequently hallucinating, struggling with reasoning from time-resolved data, and failing to reconcile conflicting evidence or different modalities. To address these limitations, MTBBench goes beyond benchmarking by providing an agentic framework with foundation model-based tools that enhance multi-modal and longitudinal reasoning, leading to task-level performance gains of up to 9.0% and 11.2%, respectively. Overall, MTBBench offers a challenging and realistic testbed for advancing multimodal LLM reasoning, reliability, and tool-use with a focus on MTB environments in precision oncology.

Graph Edit Distance (GED) measures the (dis-)similarity between two given graphs in terms of the minimum-cost edit sequence, which transforms one graph to the other. GED is related to other notions of graph similarity, such as graph and subgraph isomorphism, maximum common subgraph, etc. However, the computation of exact GED is NP-Hard, which has recently motivated the design of neural models for GED estimation. However, they do not explicitly account for edit operations with different costs. In response, we propose $\texttt{GraphEdX}$, a neural GED estimator that can work with general costs specified for the four edit operations, viz., edge deletion, edge addition, node deletion, and node addition. We first present GED as a quadratic assignment problem (QAP) that incorporates these four costs. Then, we represent each graph as a set of node and edge embeddings and use them to design a family of neural set divergence surrogates. We replace the QAP terms corresponding to each operation with their surrogates. Computing such neural set divergence requires aligning nodes and edges of the two graphs. We learn these alignments using a Gumbel-Sinkhorn permutation generator, additionally ensuring that the node and edge alignments are consistent with each other. Moreover, these alignments are cognizant of both the presence and absence of edges between node pairs. Through extensive experiments on several datasets, along with a variety of edit cost settings, we show that $\texttt{GraphEdX}$ consistently outperforms state-of-the-art methods and heuristics in terms of prediction error. The code is available at https://github.com/structlearning/GraphEdX.

Existing subset selection methods for efficient learning predominantly employ discrete combinatorial and model-specific approaches, which lack generalizability--- for each new model, the algorithm has to be executed from the beginning. Therefore, for an unseen architecture, one cannot use the subset chosen for a different model. In this work, we propose $\texttt{SubSelNet}$, a non-adaptive subset selection framework, which tackles these problems. Here, we first introduce an attention-based neural gadget that leverages the graph structure of architectures and acts as a surrogate to trained deep neural networks for quick model prediction. Then, we use these predictions to build subset samplers. This naturally provides us two variants of $\texttt{SubSelNet}$. The first variant is transductive (called Transductive-$\texttt{SubSelNet}$), which computes the subset separately for each model by solving a small optimization problem. Such an optimization is still super fast, thanks to the replacement of explicit model training by the model approximator. The second variant is inductive (called Inductive-$\texttt{SubSelNet}$), which computes the subset using a trained subset selector, without any optimization. Our experiments show that our model outperforms several methods across several real datasets.