Daily Papers

Generating realistic interior furniture layouts that strictly adhere to architectural constraints (e.g., walls, doors, and windows) remains a fundamental challenge in automated spatial design. Existing approaches, primarily based on one-shot generation using diffusion models or Large Language Models (LLMs), lack explicit mechanisms for intermediate geometric constraint verification, often resulting in structural collisions and functionally infeasible arrangements under complex room constraints. To address these challenges, we propose Agentic Designer, a progressive, multi-agent framework that formulates structure-aware interior layout generation as an iterative and constraint-verified decision process. By decomposing layout synthesis into modular stages of proposal, verification, and adjustment, the framework coordinates three specialized agents, a Generator, an Evaluator, and a Refiner, through a Progressive Consensus Mechanism. This mechanism enforces stepwise geometric validation and correction before each placement is committed, thereby preventing error accumulation. To facilitate this structure-aware paradigm and standardize evaluation, we establish InStruct, a comprehensive benchmark that integrates a dataset comprising over 18,000 high-quality, parametrically annotated samples with a novel suite of structure-centric metrics. Extensive quantitative evaluations, qualitative analyses, and user studies show that Agentic Designer significantly outperforms state-of-the-art methods, demonstrating substantial improvements in strict structural adherence and functional design coherence.

Large Language Models (LLMs) are increasingly integrated into software engineering workflows, yet current benchmarks provide only coarse performance summaries that obscure the diverse capabilities and limitations of these models. This paper investigates whether LLMs' code-comprehension performance aligns with traditional human-centric software metrics or instead reflects distinct, non-human regularities. We introduce a diagnostic framework that reframes code understanding as a binary input-output consistency task, enabling the evaluation of classification and generative models. Using a large-scale dataset, we correlate model performance with traditional, human-centric complexity metrics, such as lexical size, control-flow complexity, and abstract syntax tree structure. Our analyses reveal minimal correlation between human-defined metrics and LLM success (AUROC 0.63), while shadow models achieve substantially higher predictive performance (AUROC 0.86), capturing complex, partially predictable patterns beyond traditional software measures. These findings suggest that LLM comprehension reflects model-specific regularities only partially accessible through either human-designed or learned features, emphasizing the need for benchmark methodologies that move beyond aggregate accuracy and toward instance-level diagnostics, while acknowledging fundamental limits in predicting correct outcomes.

Despite the rapid advancements in Vision-Language Models (VLMs), a critical gap remains in their ability to handle structured, controllable diagrammatic tasks essential for professional workflows. Existing methods predominantly rely on pixel-based synthesis, which operates in probabilistic pixel spaces and is inherently limited in editability and fidelity. Instead, we propose a new Diagram-as-Code paradigm with symbolic logic that leverages mxGraph Extensible Markup Language (XML) for precise diagram generation and editing. We present VCG-Bench, a unified benchmark for visual-centric mxGraph tasks. VCG-Bench comprises: (1) a taxonomized dataset of 1,449 diverse diagrams spanning 6 domains and 15 sub-domains, (2) a paradigm definition that integrates Generation (Vision-to-Code) and Editability (Code-to-Code), (3) a Tailored Evaluation Protocol employing multi-dimensional metrics such as mxGraph Execution Success Rate, Style Consistency Score (SCS), etc. Experimental results highlight the challenges faced by current State-of-the-Art (SOTA) VLMs in structured fidelity and instruction compliance, reflecting their vision and reasoning capabilities.

The detection of ligand binding sites for proteins is a fundamental step in Structure-Based Drug Design. Despite notable advances in recent years, existing methods, datasets, and evaluation metrics are confronted with several key challenges: (1) current datasets and methods are centered on individual protein-ligand complexes and neglect that diverse binding sites may exist across multiple complexes of the same protein, introducing significant statistical bias; (2) ligand binding site detection is typically modeled as a discontinuous workflow, employing binary segmentation and subsequent clustering algorithms; (3) traditional evaluation metrics do not adequately reflect the actual performance of different binding site prediction methods. To address these issues, we first introduce UniSite-DS, the first UniProt (Unique Protein)-centric ligand binding site dataset, which contains 4.81 times more multi-site data and 2.08 times more overall data compared to the previously most widely used datasets. We then propose UniSite, the first end-to-end ligand binding site detection framework supervised by set prediction loss with bijective matching. In addition, we introduce Average Precision based on Intersection over Union (IoU) as a more accurate evaluation metric for ligand binding site prediction. Extensive experiments on UniSite-DS and several representative benchmark datasets demonstrate that IoU-based Average Precision provides a more accurate reflection of prediction quality, and that UniSite outperforms current state-of-the-art methods in ligand binding site detection. The dataset and codes will be made publicly available at https://github.com/quanlin-wu/unisite.

We introduce the first metric for evaluating disentanglement at individual hierarchy levels of a structured latent representation. Applied to object-centric generative models, this offers a systematic, unified approach to evaluating (i) object separation between latent slots (ii) disentanglement of object properties inside individual slots (iii) disentanglement of intrinsic and extrinsic object properties. We theoretically show that for structured representations, our framework gives stronger guarantees of selecting a good model than previous disentanglement metrics. Experimentally, we demonstrate that viewing object compositionality as a disentanglement problem addresses several issues with prior visual metrics of object separation. As a core technical component, we present the first representation probing algorithm handling slot permutation invariance.

Industrial-scale recommender systems rely on a cascade pipeline in which the retrieval stage must return a high-recall candidate set from billions of items under tight latency. Existing solutions ei- ther (i) suffer from limited expressiveness in capturing fine-grained user-item interactions, as seen in decoupled dual-tower architectures that rely on separate encoders, or generative models that lack precise target-aware matching capabilities, or (ii) build structured indices (tree, graph, quantization) whose item-centric topologies struggle to incorporate dynamic user preferences and incur prohibitive construction and maintenance costs. We present GRank, a novel structured-index-free retrieval paradigm that seamlessly unifies target-aware learning with user-centric retrieval. Our key innovations include: (1) A target-aware Generator trained to perform personalized candidate generation via GPU-accelerated MIPS, eliminating semantic drift and maintenance costs of structured indexing; (2) A lightweight but powerful Ranker that performs fine-grained, candidate-specific inference on small subsets; (3) An end-to-end multi-task learning framework that ensures semantic consistency between generation and ranking objectives. Extensive experiments on two public benchmarks and a billion-item production corpus demonstrate that GRank improves Recall@500 by over 30% and 1.7times the P99 QPS of state-of-the-art tree- and graph-based retrievers. GRank has been fully deployed in production in our recommendation platform since Q2 2025, serving 400 million active users with 99.95% service availability. Online A/B tests confirm significant improvements in core engagement metrics, with Total App Usage Time increasing by 0.160% in the main app and 0.165% in the Lite version.

Cross-modal metric learning is a prominent research topic that bridges the semantic heterogeneity between vision and language. Existing methods frequently utilize simple cosine or complex distance metrics to transform the pairwise features into a similarity score, which suffers from an inadequate or inefficient capability for distance measurements. Consequently, we propose a Generalized Structural Sparse Function to dynamically capture thorough and powerful relationships across modalities for pair-wise similarity learning while remaining concise but efficient. Specifically, the distance metric delicately encapsulates two formats of diagonal and block-diagonal terms, automatically distinguishing and highlighting the cross-channel relevancy and dependency inside a structured and organized topology. Hence, it thereby empowers itself to adapt to the optimal matching patterns between the paired features and reaches a sweet spot between model complexity and capability. Extensive experiments on cross-modal and two extra uni-modal retrieval tasks (image-text retrieval, person re-identification, fine-grained image retrieval) have validated its superiority and flexibility over various popular retrieval frameworks. More importantly, we further discover that it can be seamlessly incorporated into multiple application scenarios, and demonstrates promising prospects from Attention Mechanism to Knowledge Distillation in a plug-and-play manner. Our code is publicly available at: https://github.com/Paranioar/GSSF.

We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for this problem. We construct a novel semi-metric on the set of vertices, which we call the correlation metric, that indicates to our clustering algorithms whether pairs of nodes should be in the same cluster. The paper demonstrates empirically that, compared to prior work, our algorithms sacrifice little in the objective quality to obtain significantly better run-time. Moreover, our algorithms scale to larger networks that are effectively intractable for known algorithms.

Evaluation metrics are central to binary target segmentation because they determine how progress is measured, compared, and interpreted. In this paper, target denotes the task-defined positive region to be segmented rather than a generic foreground object. It may be salient, camouflaged, transparent, glass-like, mirror-like, shadow-like, lesion-like, or defined by other application-specific semantics. We treat existing metrics as compositions of modular design choices rather than isolated formulas. The proposed framework decomposes each metric into five stages covering prediction representation, target extraction, target matching, score computation, and metric reporting. We use this framework to analyze representative metrics and show how newer metrics address specific limits in earlier protocols. The stage choices keep each metric's assumptions visible. We then discuss the design space opened by the framework and its implications for task-aware evaluation protocols. Reference code is available at https://github.com/lartpang/PySODMetrics.

Graph measures that express closeness or distance between nodes can be employed for graph nodes clustering using metric clustering algorithms. There are numerous measures applicable to this task, and which one performs better is an open question. We study the performance of 25 graph measures on generated graphs with different parameters. While usually measure comparisons are limited to general measure ranking on a particular dataset, we aim to explore the performance of various measures depending on graph features. Using an LFR graph generator, we create a dataset of 11780 graphs covering the whole LFR parameter space. For each graph, we assess the quality of clustering with k-means algorithm for each considered measure. Based on this, we determine the best measure for each area of the parameter space. We find that the parameter space consists of distinct zones where one particular measure is the best. We analyze the geometry of the resulting zones and describe it with simple criteria. Given particular graph parameters, this allows us to recommend a particular measure to use for clustering.

Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding quality without labels remains an open challenge. In this work, we propose Persistence, a topology-aware metric based on persistent homology that quantifies the geometric structure and topological richness of embedding spaces in a fully unsupervised manner. Unlike metrics that assume linear separability or rely on covariance structure, Persistence captures global and multi-scale organization. Empirical results across diverse domains show that Persistence consistently achieves top-tier correlations with downstream performance, outperforming existing unsupervised metrics and enabling reliable model and hyperparameter selection.

Attributed Graph Clustering (AGC) is a fundamental unsupervised task that integrates structural topology and node attributes to uncover latent patterns in graph-structured data. Despite its significance in industrial applications such as fraud detection and user segmentation, a significant chasm persists between academic research and real-world deployment. Current evaluation protocols suffer from the small-scale, high-homophily citation datasets, non-scalable full-batch training paradigms, and a reliance on supervised metrics that fail to reflect performance in label-scarce environments. To bridge these gaps, we present PyAGC, a comprehensive, production-ready benchmark and library designed to stress-test AGC methods across diverse scales and structural properties. We unify existing methodologies into a modular Encode-Cluster-Optimize framework and, for the first time, provide memory-efficient, mini-batch implementations for a wide array of state-of-the-art AGC algorithms. Our benchmark curates 12 diverse datasets, ranging from 2.7K to 111M nodes, specifically incorporating industrial graphs with complex tabular features and low homophily. Furthermore, we advocate for a holistic evaluation protocol that mandates unsupervised structural metrics and efficiency profiling alongside traditional supervised metrics. Battle-tested in high-stakes industrial workflows at Ant Group, this benchmark offers the community a robust, reproducible, and scalable platform to advance AGC research towards realistic deployment. The code and resources are publicly available via GitHub (https://github.com/Cloudy1225/PyAGC), PyPI (https://pypi.org/project/pyagc), and Documentation (https://pyagc.readthedocs.io).

Deep metric learning, which learns discriminative features to process image clustering and retrieval tasks, has attracted extensive attention in recent years. A number of deep metric learning methods, which ensure that similar examples are mapped close to each other and dissimilar examples are mapped farther apart, have been proposed to construct effective structures for loss functions and have shown promising results. In this paper, different from the approaches on learning the loss structures, we propose a robust SNR distance metric based on Signal-to-Noise Ratio (SNR) for measuring the similarity of image pairs for deep metric learning. By exploring the properties of our SNR distance metric from the view of geometry space and statistical theory, we analyze the properties of our metric and show that it can preserve the semantic similarity between image pairs, which well justify its suitability for deep metric learning. Compared with Euclidean distance metric, our SNR distance metric can further jointly reduce the intra-class distances and enlarge the inter-class distances for learned features. Leveraging our SNR distance metric, we propose Deep SNR-based Metric Learning (DSML) to generate discriminative feature embeddings. By extensive experiments on three widely adopted benchmarks, including CARS196, CUB200-2011 and CIFAR10, our DSML has shown its superiority over other state-of-the-art methods. Additionally, we extend our SNR distance metric to deep hashing learning, and conduct experiments on two benchmarks, including CIFAR10 and NUS-WIDE, to demonstrate the effectiveness and generality of our SNR distance metric.

Symmetric Positive Definite (SPD) matrices are ubiquitous in data analysis under the form of covariance matrices or correlation matrices. Several O(n)-invariant Riemannian metrics were defined on the SPD cone, in particular the kernel metrics introduced by Hiai and Petz. The class of kernel metrics interpolates between many classical O(n)-invariant metrics and it satisfies key results of stability and completeness. However, it does not contain all the classical O(n)-invariant metrics. Therefore in this work, we investigate super-classes of kernel metrics and we study which key results remain true. We also introduce an additional key result called cometric-stability, a crucial property to implement geodesics with a Hamiltonian formulation. Our method to build intermediate embedded classes between O(n)-invariant metrics and kernel metrics is to give a characterization of the whole class of O(n)-invariant metrics on SPD matrices and to specify requirements on metrics one by one until we reach kernel metrics. As a secondary contribution, we synthesize the literature on the main O(n)-invariant metrics, we provide the complete formula of the sectional curvature of the affine-invariant metric and the formula of the geodesic parallel transport between commuting matrices for the Bures-Wasserstein metric.

Dimensionality reduction is a fundamental task that aims to simplify complex data by reducing its feature dimensionality while preserving essential patterns, with core applications in data analysis and visualisation. To preserve the underlying data structure, multi-dimensional scaling (MDS) methods focus on preserving pairwise dissimilarities, such as distances. They optimise the embedding to have pairwise distances as close as possible to the data dissimilarities. However, the current standard is limited to embedding data in Riemannian manifolds. Motivated by the lack of asymmetry in the Riemannian metric of the embedding space, this paper extends the MDS problem to a natural asymmetric generalisation of Riemannian manifolds called Finsler manifolds. Inspired by Euclidean space, we define a canonical Finsler space for embedding asymmetric data. Due to its simplicity with respect to geodesics, data representation in this space is both intuitive and simple to analyse. We demonstrate that our generalisation benefits from the same theoretical convergence guarantees. We reveal the effectiveness of our Finsler embedding across various types of non-symmetric data, highlighting its value in applications such as data visualisation, dimensionality reduction, directed graph embedding, and link prediction.

Generative models for materials, especially inorganic crystals, hold potential to transform the theoretical prediction of novel compounds and structures. Advancement in this field depends critically on robust benchmarks and minimal, information-rich datasets that enable meaningful model evaluation. This paper critically examines common datasets and reported metrics for a crystal structure prediction taskx2014generating the most likely structures given the chemical composition of a material. We focus on three key issues: First, materials datasets should contain unique crystal structures; for example, we show that the widely-utilized carbon-24 dataset only contains approx40% unique structures. Second, materials datasets should not be split randomly if polymorphs of many different compositions are numerous, which we find to be the case for the perov-5 dataset. Third, benchmarks can mislead if used uncritically, e.g., reporting a match rate metric without considering the structural variety exhibited by identical building blocks. To address these oft-overlooked issues, we introduce several fixes. We provide revised versions of the carbon-24 dataset: one with duplicates removed, one deduplicated and split by number of atoms N, and two containing only identical structures but with different unit cells. We also propose a new split for the perov-5 dataset which ensures polymorphs are grouped within each split subset, setting a more sensible standard for benchmarking model performance. Finally, we present METRe and cRMSE, new model evaluation metrics that can correct existing issues with the match rate metric.

We present a new approach for the approximate K-nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW, HNSW). The proposed solution is fully graph-based, without any need for additional search structures, which are typically used at the coarse search stage of the most proximity graph techniques. Hierarchical NSW incrementally builds a multi-layer structure consisting from hierarchical set of proximity graphs (layers) for nested subsets of the stored elements. The maximum layer in which an element is present is selected randomly with an exponentially decaying probability distribution. This allows producing graphs similar to the previously studied Navigable Small World (NSW) structures while additionally having the links separated by their characteristic distance scales. Starting search from the upper layer together with utilizing the scale separation boosts the performance compared to NSW and allows a logarithmic complexity scaling. Additional employment of a heuristic for selecting proximity graph neighbors significantly increases performance at high recall and in case of highly clustered data. Performance evaluation has demonstrated that the proposed general metric space search index is able to strongly outperform previous opensource state-of-the-art vector-only approaches. Similarity of the algorithm to the skip list structure allows straightforward balanced distributed implementation.

Given a set of dissimilarity measurements amongst data points, determining what metric representation is most "consistent" with the input measurements or the metric that best captures the relevant geometric features of the data is a key step in many machine learning algorithms. Existing methods are restricted to specific kinds of metrics or small problem sizes because of the large number of metric constraints in such problems. In this paper, we provide an active set algorithm, Project and Forget, that uses Bregman projections, to solve metric constrained problems with many (possibly exponentially) inequality constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithm converges to the global optimal solution and that the L_2 distance of the current iterate to the optimal solution decays asymptotically at an exponential rate. We demonstrate that using our method we can solve large problem instances of three types of metric constrained problems: general weight correlation clustering, metric nearness, and metric learning; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

Dimensionality reduction is crucial both for visualization and preprocessing high dimensional data for machine learning. We introduce a novel method based on a hierarchy built on 1-nearest neighbor graphs in the original space which is used to preserve the grouping properties of the data distribution on multiple levels. The core of the proposal is an optimization-free projection that is competitive with the latest versions of t-SNE and UMAP in performance and visualization quality while being an order of magnitude faster in run-time. Furthermore, its interpretable mechanics, the ability to project new data, and the natural separation of data clusters in visualizations make it a general purpose unsupervised dimension reduction technique. In the paper, we argue about the soundness of the proposed method and evaluate it on a diverse collection of datasets with sizes varying from 1K to 11M samples and dimensions from 28 to 16K. We perform comparisons with other state-of-the-art methods on multiple metrics and target dimensions highlighting its efficiency and performance. Code is available at https://github.com/koulakis/h-nne

To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Frechet mean. In this work, we equip a set of graphs with the pseudometric defined by the norm between the eigenvalues of their respective adjacency matrix. Unlike the edit distance, this pseudometric reveals structural changes at multiple scales, and is well adapted to studying various statistical problems for graph-valued data. We describe an algorithm to compute an approximation to the sample Frechet mean of a set of undirected unweighted graphs with a fixed size using this pseudometric.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

Scientific surveys require not only summarizing large bodies of literature, but also organizing them into clear and coherent conceptual structures. Existing automatic survey generation methods typically focus on linear text generation and struggle to explicitly model hierarchical relations among research topics and structured methodological comparisons, resulting in gaps in structural organization compared to expert-written surveys. We propose MVSS, a multi-view structured survey generation framework that jointly generates and aligns citation-grounded hierarchical trees, structured comparison tables, and survey text. MVSS follows a structure-first paradigm: it first constructs a conceptual tree of the research domain, then generates comparison tables constrained by the tree, and finally uses both as structural constraints for text generation. This enables complementary multi-view representations across structure, comparison, and narrative. We introduce an evaluation framework assessing structural quality, comparative completeness, and citation fidelity. Experiments on 76 computer science topics show MVSS outperforms existing methods in organization and evidence grounding, achieving performance comparable to expert surveys.

Evaluating tabular generators remains a challenging problem, as the unique causal structural prior of heterogeneous tabular data does not lend itself to intuitive human inspection. Recent work has introduced structural fidelity as a tabular-specific evaluation dimension to assess whether synthetic data complies with the causal structures of real data. However, existing benchmarks often neglect the interplay between structural fidelity and conventional evaluation dimensions, thus failing to provide a holistic understanding of model performance. Moreover, they are typically limited to toy datasets, as quantifying existing structural fidelity metrics requires access to ground-truth causal structures, which are rarely available for real-world datasets. In this paper, we propose a novel evaluation framework that jointly considers structural fidelity and conventional evaluation dimensions. We introduce a new evaluation metric, global utility, which enables the assessment of structural fidelity even in the absence of ground-truth causal structures. In addition, we present TabStruct, a comprehensive evaluation benchmark offering large-scale quantitative analysis on 13 tabular generators from nine distinct categories, across 29 datasets. Our results demonstrate that global utility provides a task-independent, domain-agnostic lens for tabular generator performance. We release the TabStruct benchmark suite, including all datasets, evaluation pipelines, and raw results. Code is available at https://github.com/SilenceX12138/TabStruct.

Generative models trained on internet-scale data are capable of generating novel and realistic texts, images, and videos. A natural next question is whether these models can advance science, for example by generating novel stable materials. Traditionally, models with explicit structures (e.g., graphs) have been used in modeling structural relationships in scientific data (e.g., atoms and bonds in crystals), but generating structures can be difficult to scale to large and complex systems. Another challenge in generating materials is the mismatch between standard generative modeling metrics and downstream applications. For instance, common metrics such as the reconstruction error do not correlate well with the downstream goal of discovering stable materials. In this work, we tackle the scalability challenge by developing a unified crystal representation that can represent any crystal structure (UniMat), followed by training a diffusion probabilistic model on these UniMat representations. Our empirical results suggest that despite the lack of explicit structure modeling, UniMat can generate high fidelity crystal structures from larger and more complex chemical systems, outperforming previous graph-based approaches under various generative modeling metrics. To better connect the generation quality of materials to downstream applications, such as discovering novel stable materials, we propose additional metrics for evaluating generative models of materials, including per-composition formation energy and stability with respect to convex hulls through decomposition energy from Density Function Theory (DFT). Lastly, we show that conditional generation with UniMat can scale to previously established crystal datasets with up to millions of crystals structures, outperforming random structure search (the current leading method for structure discovery) in discovering new stable materials.

Identifying the intent of a citation in scientific papers (e.g., background information, use of methods, comparing results) is critical for machine reading of individual publications and automated analysis of the scientific literature. We propose structural scaffolds, a multitask model to incorporate structural information of scientific papers into citations for effective classification of citation intents. Our model achieves a new state-of-the-art on an existing ACL anthology dataset (ACL-ARC) with a 13.3% absolute increase in F1 score, without relying on external linguistic resources or hand-engineered features as done in existing methods. In addition, we introduce a new dataset of citation intents (SciCite) which is more than five times larger and covers multiple scientific domains compared with existing datasets. Our code and data are available at: https://github.com/allenai/scicite.

As large language models become increasingly capable at various writing tasks, their weakness at generating unique and creative content becomes a major liability. Although LLMs have the ability to generate text covering diverse topics, there is an overall sense of repetitiveness across texts that we aim to formalize and quantify via a similarity metric. The familiarity between documents arises from the persistence of underlying discourse structures. However, existing similarity metrics dependent on lexical overlap and syntactic patterns largely capture content overlap, thus making them unsuitable for detecting structural similarities. We introduce an abstraction based on linguistic theories in Questions Under Discussion (QUD) and question semantics to help quantify differences in discourse progression. We then use this framework to build QUDsim, a similarity metric that can detect discursive parallels between documents. Using QUDsim, we find that LLMs often reuse discourse structures (more so than humans) across samples, even when content differs. Furthermore, LLMs are not only repetitive and structurally uniform, but are also divergent from human authors in the types of structures they use.

Time series clustering promises to uncover hidden structural patterns in data with applications across healthcare, finance, industrial systems, and other critical domains. However, without validated ground truth information, researchers cannot objectively assess clustering quality or determine whether poor results stem from absent structures in the data, algorithmic limitations, or inappropriate validation methods, raising the question whether clustering is "more art than science" (Guyon et al., 2009). To address these challenges, we introduce CSTS (Correlation Structures in Time Series), a synthetic benchmark for evaluating the discovery of correlation structures in multivariate time series data. CSTS provides a clean benchmark that enables researchers to isolate and identify specific causes of clustering failures by differentiating between correlation structure deterioration and limitations of clustering algorithms and validation methods. Our contributions are: (1) a comprehensive benchmark for correlation structure discovery with distinct correlation structures, systematically varied data conditions, established performance thresholds, and recommended evaluation protocols; (2) empirical validation of correlation structure preservation showing moderate distortion from downsampling and minimal effects from distribution shifts and sparsification; and (3) an extensible data generation framework enabling structure-first clustering evaluation. A case study demonstrates CSTS's practical utility by identifying an algorithm's previously undocumented sensitivity to non-normal distributions, illustrating how the benchmark enables precise diagnosis of methodological limitations. CSTS advances rigorous evaluation standards for correlation-based time series clustering.

Metric space magnitude, an active field of research in algebraic topology, is a scalar quantity that summarizes the effective number of distinct points that live in a general metric space. The {\em weighting vector} is a closely-related concept that captures, in a nontrivial way, much of the underlying geometry of the original metric space. Recent work has demonstrated that when the metric space is Euclidean, the weighting vector serves as an effective tool for boundary detection. We recast this result and show the weighting vector may be viewed as a solution to a kernelized SVM. As one consequence, we apply this new insight to the task of outlier detection, and we demonstrate performance that is competitive or exceeds performance of state-of-the-art techniques on benchmark data sets. Under mild assumptions, we show the weighting vector, which has computational cost of matrix inversion, can be efficiently approximated in linear time. We show how nearest neighbor methods can approximate solutions to the minimization problems defined by SVMs.

Graph foundation models represent a transformative paradigm for learning transferable representations across diverse graph domains. Recent methods leverage large language models to unify graph and text modalities into a shared representation space using contrastive learning. However, systematic evaluations reveal significant performance degradation at structural boundaries where distinct topological patterns converge, with accuracy losses exceeding 20 percentage points. This issue arises from a key limitation: current methods assume all graph structures can be encoded within a single Euclidean space. In reality, tree structures require hyperbolic geometry to preserve hierarchical branching, while cyclic patterns depend on spherical geometry for closure properties. At structural boundaries, nodes experience conflicting geometric constraints that uniform encoding spaces cannot resolve. This raises a crucial challenge: Can alignment frameworks be designed to respect the intrinsic geometric diversity of graph structures? We introduce GraphShaper, a geometry-aware framework that enhances graph encoding through multi-geometric specialization. Our approach employs expert networks tailored to different geometric spaces, dynamically computing fusion weights to adaptively integrate geometric properties based on local structural characteristics. This adaptive fusion preserves structural integrity before alignment with text embeddings. Extensive experiments demonstrate that GraphShaper achieves 9.47\% accuracy improvements on citation networks and 7.63\% on social networks in zero-shot settings.

"What cannot be measured cannot be improved" while likely never uttered by Lord Kelvin, summarizes effectively the driving force behind this work. This paper presents a detailed discussion of automated metrics for evaluating structured 3D reconstructions. Pitfalls of each metric are discussed, and an analysis through the lens of expert 3D modelers' preferences is presented. A set of systematic "unit tests" are proposed to empirically verify desirable properties, and context aware recommendations regarding which metric to use depending on application are provided. Finally, a learned metric distilled from human expert judgments is proposed and analyzed. The source code is available at https://github.com/s23dr/wireframe-metrics-iccv2025

Large language model (LLM)-based systems are becoming increasingly popular for solving tasks by constructing executable workflows that interleave LLM calls, information retrieval, tool use, code execution, memory updates, and verification. This survey reviews recent methods for designing and optimizing such workflows, which we treat as agentic computation graphs (ACGs). We organize the literature based on when workflow structure is determined, where structure refers to which components or agents are present, how they depend on each other, and how information flows between them. This lens distinguishes static methods, which fix a reusable workflow scaffold before deployment, from dynamic methods, which select, generate, or revise the workflow for a particular run before or during execution. We further organize prior work along three dimensions: when structure is determined, what part of the workflow is optimized, and which evaluation signals guide optimization (e.g., task metrics, verifier signals, preferences, or trace-derived feedback). We also distinguish reusable workflow templates, run-specific realized graphs, and execution traces, separating reusable design choices from the structures actually deployed in a given run and from realized runtime behavior. Finally, we outline a structure-aware evaluation perspective that complements downstream task metrics with graph-level properties, execution cost, robustness, and structural variation across inputs. Our goal is to provide a clear vocabulary, a unified framework for positioning new methods, a more comparable view of existing body of literature, and a more reproducible evaluation standard for future work in workflow optimizations for LLM agents.

Graph Neural Networks (GNNs) have demonstrated superior performance on various graph learning tasks, including recommendation, where they leverage user-item collaborative filtering signals in graphs. However, theoretical formulations of their capability are scarce, despite their empirical effectiveness in state-of-the-art recommender models. Recently, research has explored the expressiveness of GNNs in general, demonstrating that message passing GNNs are at most as powerful as the Weisfeiler-Lehman test, and that GNNs combined with random node initialization are universal. Nevertheless, the concept of "expressiveness" for GNNs remains vaguely defined. Most existing works adopt the graph isomorphism test as the metric of expressiveness, but this graph-level task may not effectively assess a model's ability in recommendation, where the objective is to distinguish nodes of different closeness. In this paper, we provide a comprehensive theoretical analysis of the expressiveness of GNNs in recommendation, considering three levels of expressiveness metrics: graph isomorphism (graph-level), node automorphism (node-level), and topological closeness (link-level). We propose the topological closeness metric to evaluate GNNs' ability to capture the structural distance between nodes, which aligns closely with the objective of recommendation. To validate the effectiveness of this new metric in evaluating recommendation performance, we introduce a learning-less GNN algorithm that is optimal on the new metric and can be optimal on the node-level metric with suitable modification. We conduct extensive experiments comparing the proposed algorithm against various types of state-of-the-art GNN models to explore the explainability of the new metric in the recommendation task. For reproducibility, implementation codes are available at https://github.com/HKUDS/GTE.

The effectiveness of recommendation systems is pivotal to user engagement and satisfaction in online platforms. As these recommendation systems increasingly influence user choices, their evaluation transcends mere technical performance and becomes central to business success. This paper addresses the multifaceted nature of recommendations system evaluation by introducing a comprehensive suite of metrics, each tailored to capture a distinct aspect of system performance. We discuss * Similarity Metrics: to quantify the precision of content-based filtering mechanisms and assess the accuracy of collaborative filtering techniques. * Candidate Generation Metrics: to evaluate how effectively the system identifies a broad yet relevant range of items. * Predictive Metrics: to assess the accuracy of forecasted user preferences. * Ranking Metrics: to evaluate the effectiveness of the order in which recommendations are presented. * Business Metrics: to align the performance of the recommendation system with economic objectives. Our approach emphasizes the contextual application of these metrics and their interdependencies. In this paper, we identify the strengths and limitations of current evaluation practices and highlight the nuanced trade-offs that emerge when optimizing recommendation systems across different metrics. The paper concludes by proposing a framework for selecting and interpreting these metrics to not only improve system performance but also to advance business goals. This work is to aid researchers and practitioners in critically assessing recommendation systems and fosters the development of more nuanced, effective, and economically viable personalization strategies. Our code is available at GitHub - https://github.com/aryan-jadon/Evaluation-Metrics-for-Recommendation-Systems.

Entity resolution (record linkage, microclustering) systems are notoriously difficult to evaluate. Looking for a needle in a haystack, traditional evaluation methods use sophisticated, application-specific sampling schemes to find matching pairs of records among an immense number of non-matches. We propose an alternative that facilitates the creation of representative, reusable benchmark data sets without necessitating complex sampling schemes. These benchmark data sets can then be used for model training and a variety of evaluation tasks. Specifically, we propose an entity-centric data labeling methodology that integrates with a unified framework for monitoring summary statistics, estimating key performance metrics such as cluster and pairwise precision and recall, and analyzing root causes for errors. We validate the framework in an application to inventor name disambiguation and through simulation studies. Software: https://github.com/OlivierBinette/er-evaluation/

This work presents a systematic investigation into the latent knowledge encoded within Network Foundation Models (NFMs) that focuses on hidden representations analysis rather than pure downstream task performance. Different from existing efforts, we analyze the models through a three-part evaluation: Embedding Geometry Analysis to assess representation space utilization, Metric Alignment Assessment to measure correspondence with domain-expert features, and Causal Sensitivity Testing to evaluate robustness to protocol perturbations. Using five diverse network datasets spanning controlled and real-world environments, we evaluate four state-of-the-art NFMs, revealing that they all exhibit significant anisotropy, inconsistent feature sensitivity patterns, an inability to separate the high-level context, payload dependency, and other properties. Our work identifies numerous limitations across all models and demonstrates that addressing them can significantly improve model performance (by up to +0.35 F_1 score without architectural changes).

Concept-based explanation methods, such as concept bottleneck models (CBMs), aim to improve the interpretability of machine learning models by linking their decisions to human-understandable concepts, under the critical assumption that such concepts can be accurately attributed to the network's feature space. However, this foundational assumption has not been rigorously validated, mainly because the field lacks standardised metrics and benchmarks to assess the existence and spatial alignment of such concepts. To address this, we propose three metrics: the concept global importance metric, the concept existence metric, and the concept location metric, including a technique for visualising concept activations, i.e., concept activation mapping. We benchmark post-hoc CBMs to illustrate their capabilities and challenges. Through qualitative and quantitative experiments, we demonstrate that, in many cases, even the most important concepts determined by post-hoc CBMs are not present in input images; moreover, when they are present, their saliency maps fail to align with the expected regions by either activating across an entire object or misidentifying relevant concept-specific regions. We analyse the root causes of these limitations, such as the natural correlation of concepts. Our findings underscore the need for more careful application of concept-based explanation techniques especially in settings where spatial interpretability is critical.

Approximate nearest neighbor (ANN) graph indices such as HNSW and Vamana construct their edge topology in full-precision or high-fidelity quantized metric spaces, relegating binary quantization (BQ) to a post-hoc distance estimator during search. This paper asks a different question: Can binary quantization define the graph topology itself -- and if so, under what conditions? We study this question through QuIVer (Quantized Index for Vector Retrieval), a training-free ANN graph index that performs Vamana edge selection, diversity pruning, and beam-search navigation entirely within a 2-bit Sign-Magnitude BQ metric space, accessing float32 vectors only for final reranking. Systematic evaluation on twelve million-scale datasets reveals a sharp applicability boundary: BQ-native topology is highly effective on cosine-native contrastive-learning embeddings (>=88% Recall@10 at ef=64 across five datasets, 384--3072 dimensions), moderately effective on multimodal CLIP data (71--78%), and empirically unsuitable for Euclidean-native or structureless distributions (<15%). Our results suggest an empirical "impossible triangle" between aggressive compression, high throughput, and universal data compatibility. The central contribution is not merely the system, but the boundary it reveals: falsifiable criteria for when industrial vector search systems can safely trade metric fidelity for compact BQ-native navigation. On compatible workloads, the system benefits are substantial: QuIVer's BQ-native hot path (<1.3 GB for 1M vectors) yields 2.5--5.5x higher multi-threaded throughput than DiskANN Rust and HNSW variants at matched recall, with 4.7x less hot memory and no codebook or rotation training (unlike PQ/OPQ/RaBitQ).

A key puzzle in search, ads, and recommendation is that the ranking model can only utilize a small portion of the vastly available user interaction data. As a result, increasing data volume, model size, or computation FLOPs will quickly suffer from diminishing returns. We examined this problem and found that one of the root causes may lie in the so-called ``item-centric'' formulation, which has an unbounded vocabulary and thus uncontrolled model complexity. To mitigate quality saturation, we introduce an alternative formulation named ``user-centric ranking'', which is based on a transposed view of the dyadic user-item interaction data. We show that this formulation has a promising scaling property, enabling us to train better-converged models on substantially larger data sets.

We propose the Signal Dice Similarity Coefficient (SDSC), a structure-aware metric function for time series self-supervised representation learning. Most Self-Supervised Learning (SSL) methods for signals commonly adopt distance-based objectives such as mean squared error (MSE), which are sensitive to amplitude, invariant to waveform polarity, and unbounded in scale. These properties hinder semantic alignment and reduce interpretability. SDSC addresses this by quantifying structural agreement between temporal signals based on the intersection of signed amplitudes, derived from the Dice Similarity Coefficient (DSC).Although SDSC is defined as a structure-aware metric, it can be used as a loss by subtracting from 1 and applying a differentiable approximation of the Heaviside function for gradient-based optimization. A hybrid loss formulation is also proposed to combine SDSC with MSE, improving stability and preserving amplitude where necessary. Experiments on forecasting and classification benchmarks demonstrate that SDSC-based pre-training achieves comparable or improved performance over MSE, particularly in in-domain and low-resource scenarios. The results suggest that structural fidelity in signal representations enhances the semantic representation quality, supporting the consideration of structure-aware metrics as viable alternatives to conventional distance-based methods.

Despite the widespread application of latent factor analysis, existing methods suffer from the following weaknesses: requiring the number of factors to be known, lack of theoretical guarantees for learning the model structure, and nonidentifiability of the parameters due to rotation invariance properties of the likelihood. We address these concerns by proposing a fast correlation thresholding (CT) algorithm that simultaneously learns the number of latent factors and a rotationally identifiable model structure. Our novel approach translates this structure learning problem into the search for so-called independent maximal cliques in a thresholded correlation graph that can be easily constructed from the observed data. Our clique analysis technique scales well up to thousands of variables, while competing methods are not applicable in a reasonable amount of running time. We establish a finite-sample error bound and high-dimensional consistency for the structure learning of our method. Through a series of simulation studies and a real data example, we show that the CT algorithm is an accurate method for learning the structure of factor analysis models and is robust to violations of its assumptions.

In recent years, Graph Neural Networks (GNNs) have made significant advances in processing structured data. However, most of them primarily adopted a model-centric approach, which simplifies graphs by converting them into undirected formats and emphasizes model designs. This approach is inherently limited in real-world applications due to the unavoidable information loss in simple undirected graphs and the model optimization challenges that arise when exceeding the upper bounds of this sub-optimal data representational capacity. As a result, there has been a shift toward data-centric methods that prioritize improving graph quality and representation. Specifically, various types of graphs can be derived from naturally structured data, including heterogeneous graphs, hypergraphs, and directed graphs. Among these, directed graphs offer distinct advantages in topological systems by modeling causal relationships, and directed GNNs have been extensively studied in recent years. However, a comprehensive survey of this emerging topic is still lacking. Therefore, we aim to provide a comprehensive review of directed graph learning, with a particular focus on a data-centric perspective. Specifically, we first introduce a novel taxonomy for existing studies. Subsequently, we re-examine these methods from the data-centric perspective, with an emphasis on understanding and improving data representation. It demonstrates that a deep understanding of directed graphs and their quality plays a crucial role in model performance. Additionally, we explore the diverse applications of directed GNNs across 10+ domains, highlighting their broad applicability. Finally, we identify key opportunities and challenges within the field, offering insights that can guide future research and development in directed graph learning.

In this paper, we propose a new class of metric for table structure recognition (TSR) evaluation, called grid table similarity (GriTS). Unlike prior metrics, GriTS evaluates the correctness of a predicted table directly in its natural form as a matrix. To create a similarity measure between matrices, we generalize the two-dimensional largest common substructure (2D-LCS) problem, which is NP-hard, to the 2D most similar substructures (2D-MSS) problem and propose a polynomial-time heuristic for solving it. This algorithm produces both an upper and a lower bound on the true similarity between matrices. We show using evaluation on a large real-world dataset that in practice there is almost no difference between these bounds. We compare GriTS to other metrics and empirically validate that matrix similarity exhibits more desirable behavior than alternatives for TSR performance evaluation. Finally, GriTS unifies all three subtasks of cell topology recognition, cell location recognition, and cell content recognition within the same framework, which simplifies the evaluation and enables more meaningful comparisons across different types of TSR approaches. Code will be released at https://github.com/microsoft/table-transformer.

Automated analysis for engineering structures offers considerable potential for boosting efficiency by minimizing repetitive tasks. Although AI-driven methods are increasingly common, no systematic framework yet leverages Large Language Models (LLMs) for automatic structural analysis. To address this gap, we propose a novel framework that integrates LLMs with structural analysis software. LLMs serve as the core engine: they parse structural descriptions from text and translate them into executable Python scripts. Moreover, the framework integrates the generative capabilities of LLMs with code-based finite element (FE) tools like OpenSeesPy. It employs domain-specific prompt design and in-context learning strategies to enhance the LLM's problem-solving capabilities and generative stability, enabling fully automated structural analysis from descriptive text to model outputs. In our experiments, we introduce a well-curated small-scale benchmark dataset of 20 structural analysis word problems (SAWPs) with ground-truth solutions and evaluate the performance of different LLMs within our framework in solving these SAWPs. The role of system instructions, crafted by structural engineers, is also investigated to understand their impact on LLM-driven structural analysis. Additionally, the generative stability of our framework is examined. Through multiple validation experiments on the benchmark, our results demonstrate that the proposed framework can substantially increase the level of automation in solving SAWPs compared to traditional methods. Quantitatively, the framework, built on GPT-4o, achieved 100% accuracy, surpassing GPT-4 (85%), Gemini 1.5 Pro (80%), and Llama-3.3 (30%) on the test examples. Furthermore, integrating domain-specific instructions enhanced performance by 30% on problems with asymmetrical structural configurations.

Understanding the quality of a performance evaluation metric is crucial for ensuring that model outputs align with human preferences. However, it remains unclear how well each metric captures the diverse aspects of these preferences, as metrics often excel in one particular area but not across all dimensions. To address this, it is essential to systematically calibrate metrics to specific aspects of human preference, catering to the unique characteristics of each aspect. We introduce MetaMetrics, a calibrated meta-metric designed to evaluate generation tasks across different modalities in a supervised manner. MetaMetrics optimizes the combination of existing metrics to enhance their alignment with human preferences. Our metric demonstrates flexibility and effectiveness in both language and vision downstream tasks, showing significant benefits across various multilingual and multi-domain scenarios. MetaMetrics aligns closely with human preferences and is highly extendable and easily integrable into any application. This makes MetaMetrics a powerful tool for improving the evaluation of generation tasks, ensuring that metrics are more representative of human judgment across diverse contexts.

Addressing a structural-engineering request requires more than a single answer; it requires a chain of interdependent artifacts: interpreted requirements, a computable model, validation records, solver outputs, code-check records, and a final report. Evaluations centered on question answering or script generation rarely verify this complete evidence chain and may therefore reward fluent outputs even when the underlying engineering workflow is incomplete, internally inconsistent, or non-executable. To address this limitation, we present StructureClaw, an artifact-centered workbench in which LLM agents operate through governed engineering skills, typed tools, shared artifact state, and local analysis backends. We also introduce StructureClaw-Bench, an executable benchmark of 150 controlled scenarios spanning standard workflow execution, interactive robustness, and multimodal structural-model reconstruction. A scenario succeeds only when all required artifact- and execution-level assertions pass in a single run. Across ten agent-model configurations, each evaluated on the same 50 standard cases, the average Success Rate rises from 56.8% with the generic-skill baseline to 88.6% with the full automatic workflow. The interactive and multimodal evaluations identify two prominent remaining challenges: safe handling of invalid numerical inputs and fixture-consistent reconstruction of structural models. These findings show that artifact-centered evaluation can expose workflow-level failures that are difficult to identify from final responses alone, providing a more rigorous basis for evaluating and improving structural-engineering agents. The code and benchmark are available at https://github.com/structureclaw/structureclaw.

Metric space magnitude, an active subject of research in algebraic topology, originally arose in the context of biology, where it was used to represent the effective number of distinct species in an environment. In a more general setting, the magnitude of a metric space is a real number that aims to quantify the effective number of distinct points in the space. The contribution of each point to a metric space's global magnitude, which is encoded by the {\em weighting vector}, captures much of the underlying geometry of the original metric space. Surprisingly, when the metric space is Euclidean, the weighting vector also serves as an effective tool for boundary detection. This allows the weighting vector to serve as the foundation of novel algorithms for classic machine learning tasks such as classification, outlier detection and active learning. We demonstrate, using experiments and comparisons on classic benchmark datasets, the promise of the proposed magnitude and weighting vector-based approaches.

The performance of modern language models depends critically on pretraining data composition. Yet existing data selection methods rely on auxiliary classifiers for document scoring or mixture optimization, adding computational overhead and dependence on labeled data. We propose WebGraphMix, a lightweight data selection framework that computes structural centrality scores over the Common Crawl host-level web graph and uses them to vary the proportion of central versus peripheral documents in the pretraining mixture. We hypothesize that central hosts expose models to reusable abstractions, while peripheral hosts encode specialized, long-tail knowledge. WebGraphMix computes centrality scores efficiently at web scale, requiring no model training, labeled data, or downstream supervision. We integrate WebGraphMix into the DataComp-LM pipeline and train models at 400M and 1B parameter scales with 8B and 28B tokens respectively, evaluating on 23 tasks ranging from factual knowledge to symbolic reasoning. Our experiments show that central and peripheral web regions encode complementary capabilities. Mixture combining both at a ratio of 1:1 achieves 41.4% on average, compared to 39.8% for uniform sampling. Combining structural scores with document-level quality classifier scores further improves performance to 43.8%. These findings demonstrate that web graph topology is a meaningful axis for pretraining data curation, capturing information that is largely orthogonal to existing content-based approaches.

Recent works on structured text translation remain limited to the sentence level, as they struggle to effectively handle the complex document-level XML or HTML structures. To address this, we propose Format Reinforcement Learning (FormatRL), which employs Group Relative Policy Optimization on top of a supervised fine-tuning model to directly optimize novel structure-aware rewards: 1) TreeSim, which measures structural similarity between predicted and reference XML trees and 2) Node-chrF, which measures translation quality at the level of XML nodes. Additionally, we apply StrucAUC, a fine-grained metric distinguishing between minor errors and major structural failures. Experiments on the SAP software-documentation benchmark demonstrate improvements across six metrics and an analysis further shows how different reward functions contribute to improvements in both structural and translation quality.

As interest grows in generating long, detailed image captions, standard evaluation metrics become increasingly unreliable. N-gram-based metrics though efficient, fail to capture semantic correctness. Representational Similarity (RS) metrics, designed to address this, initially saw limited use due to high computational costs, while today, despite advances in hardware, they remain unpopular due to low correlation to human judgments. Meanwhile, metrics based on large language models (LLMs) show strong correlation with human judgments, but remain too expensive for iterative use during model development. We introduce SPECS (Specificity-Enhanced CLIPScore), a reference-free RS metric tailored to long image captioning. SPECS modifies CLIP with a new objective that emphasizes specificity: rewarding correct details and penalizing incorrect ones. We show that SPECS matches the performance of open-source LLM-based metrics in correlation to human judgments, while being far more efficient. This makes it a practical alternative for iterative checkpoint evaluation during image captioning model development.Our code can be found at https://github.com/mbzuai-nlp/SPECS.

Machine learning models -- including prominent zero-shot models -- are often trained on datasets whose labels are only a small proportion of a larger label space. Such spaces are commonly equipped with a metric that relates the labels via distances between them. We propose a simple approach to exploit this information to adapt the trained model to reliably predict new classes -- or, in the case of zero-shot prediction, to improve its performance -- without any additional training. Our technique is a drop-in replacement of the standard prediction rule, swapping argmax with the Fr\'echet mean. We provide a comprehensive theoretical analysis for this approach, studying (i) learning-theoretic results trading off label space diameter, sample complexity, and model dimension, (ii) characterizations of the full range of scenarios in which it is possible to predict any unobserved class, and (iii) an optimal active learning-like next class selection procedure to obtain optimal training classes for when it is not possible to predict the entire range of unobserved classes. Empirically, using easily-available external metrics, our proposed approach, Loki, gains up to 29.7% relative improvement over SimCLR on ImageNet and scales to hundreds of thousands of classes. When no such metric is available, Loki can use self-derived metrics from class embeddings and obtains a 10.5% improvement on pretrained zero-shot models such as CLIP.

In recent years, while natural language processing and multimodal learning have seen rapid advancements, the field of de novo protein design has also experienced significant growth. However, most current methods rely on proprietary datasets and evaluation rubrics, making fair comparisons between different approaches challenging. Moreover, these methods often employ evaluation metrics that capture only a subset of the desired properties of designed proteins, lacking a comprehensive assessment framework. To address these, we introduce PDFBench, the first comprehensive benchmark for evaluating de novo protein design from function. PDFBench supports two tasks: description-guided design and keyword-guided design. To ensure fair and multifaceted evaluation, we compile 22 metrics covering sequence plausibility, structural fidelity, and language-protein alignment, along with measures of novelty and diversity. We evaluate five state-of-the-art baselines, revealing their respective strengths and weaknesses across tasks. Finally, we analyze inter-metric correlations, exploring the relationships between four categories of metrics, and offering guidelines for metric selection. PDFBench establishes a unified framework to drive future advances in function-driven de novo protein design.

Multi-modal generative document parsing systems challenge traditional evaluation: unlike deterministic OCR or layout models, they often produce semantically correct yet structurally divergent outputs. Conventional metrics-CER, WER, IoU, or TEDS-misclassify such diversity as error, penalizing valid interpretations and obscuring system behavior. We introduce SCORE (Structural and COntent Robust Evaluation), an interpretation-agnostic framework that integrates (i) adjusted edit distance for robust content fidelity, (ii) token-level diagnostics to distinguish hallucinations from omissions, (iii) table evaluation with spatial tolerance and semantic alignment, and (iv) hierarchy-aware consistency checks. Together, these dimensions enable evaluation that embraces representational diversity while enforcing semantic rigor. Across 1,114 pages spanning a holistic benchmark and a field dataset, SCORE consistently revealed cross-dataset performance patterns missed by standard metrics. In 2-5% of pages with ambiguous table structures, traditional metrics penalized systems by 12-25% on average, leading to distorted rankings. SCORE corrected these cases, recovering equivalence between alternative but valid interpretations. Moreover, by normalizing generative outputs into a format-agnostic representation, SCORE reproduces traditional scores (e.g., table F1 up to 0.93) without requiring object-detection pipelines, demonstrating that generative parsing alone suffices for comprehensive evaluation. By exposing how interpretive diversity impacts evaluation outcomes and providing multi-dimensional, interpretable diagnostics, SCORE establishes foundational principles for semantically grounded, fair, and practical benchmarking of modern document parsing systems.

Object-centric reconstruction seeks to recover the 3D structure of a scene through composition of independent objects. While this independence can simplify modeling, it discards strong signals that could improve reconstruction, notably repetition where the same object model is seen multiple times in a scene, or across scans. We propose the Joint Reconstruction Model (JRM) to leverage repetition by framing object reconstruction as one of personalized generation: multiple observations share a common subject that should be consistent for all observations, while still adhering to the specific pose and state from each. Prior methods in this direction rely on explicit matching and rigid alignment across observations, making them sensitive to errors and difficult to extend to non-rigid transformations. In contrast, JRM is a 3D flow-matching generative model that implicitly aggregates unaligned observations in its latent space, learning to produce consistent and faithful reconstructions in a data-driven manner without explicit constraints. Evaluations on synthetic and real-world data show that JRM's implicit aggregation removes the need for explicit alignment, improves robustness to incorrect associations, and naturally handles non-rigid changes such as articulation. Overall, JRM outperforms both independent and alignment-based baselines in reconstruction quality.

Retrieving relevant documents from a corpus is typically based on the semantic similarity between the document content and query text. The inclusion of structural relationship between documents can benefit the retrieval mechanism by addressing semantic gaps. However, incorporating these relationships requires tractable mechanisms that balance structure with semantics and take advantage of the prevalent pre-train/fine-tune paradigm. We propose here a holistic approach to learning document representations by integrating intra-document content with inter-document relations. Our deep metric learning solution analyzes the complex neighborhood structure in the relationship network to efficiently sample similar/dissimilar document pairs and defines a novel quintuplet loss function that simultaneously encourages document pairs that are semantically relevant to be closer and structurally unrelated to be far apart in the representation space. Furthermore, the separation margins between the documents are varied flexibly to encode the heterogeneity in relationship strengths. The model is fully fine-tunable and natively supports query projection during inference. We demonstrate that it outperforms competing methods on multiple datasets for document retrieval tasks.

The optimal transport problem for measures supported on non-Euclidean spaces has recently gained ample interest in diverse applications involving representation learning. In this paper, we focus on circular probability measures, i.e., probability measures supported on the unit circle, and introduce a new computationally efficient metric for these measures, denoted as Linear Circular Optimal Transport (LCOT). The proposed metric comes with an explicit linear embedding that allows one to apply Machine Learning (ML) algorithms to the embedded measures and seamlessly modify the underlying metric for the ML algorithm to LCOT. We show that the proposed metric is rooted in the Circular Optimal Transport (COT) and can be considered the linearization of the COT metric with respect to a fixed reference measure. We provide a theoretical analysis of the proposed metric and derive the computational complexities for pairwise comparison of circular probability measures. Lastly, through a set of numerical experiments, we demonstrate the benefits of LCOT in learning representations of circular measures.

Software modernisation through the migration from monolithic architectures to microservices has become increasingly critical, yet identifying effective service boundaries remains a complex and unresolved challenge. Although numerous automated microservice decomposition frameworks have been proposed, their evaluation is often fragmented due to inconsistent benchmark systems, incompatible metrics, and limited reproducibility, thus hindering objective comparison. This work presents a unified comparative evaluation of state-of-the-art microservice decomposition approaches spanning static, dynamic, and hybrid techniques. Using a consistent metric computation pipeline, we assess the decomposition quality across widely used benchmark systems (JPetStore, AcmeAir, DayTrader, and Plants) using Structural Modularity (SM), Interface Number(IFN), Inter-partition Communication (ICP), Non-Extreme Distribution (NED), and related indicators. Our analysis combines results reported in prior studies with experimentally reproduced outputs from available replication packages. Findings indicate that the hierarchical clustering-based methods, particularly HDBScan, produce the most consistently balanced decompositions across benchmarks, achieving strong modularity while minimizing communication and interface overhead.

Reconstructing articulated objects with multiple movable parts is essential for understanding object structure and enabling physical interaction. However, this reconstruction task poses significant challenges due to the entanglement of geometry, appearance, and motion parameters during optimization. Existing methods rely primarily on photometric supervision, which commonly fails to disentangle these interdependent components, resulting in poor part decomposition with blurred boundaries and geometric artifacts. To address this limitation, we introduce StructureGS, a reconstruction framework for articulated objects that integrates structure-aware guidance into 3D Gaussian Splatting. Our approach leverages oriented bounding boxes of object parts to enforce two key structural properties: spatial coherence, which constrains each part's geometry to remain compact and spatially coherent within its designated region, and structural connectivity, which enforces physically plausible contact relationships between adjacent parts. These properties are realized through structure-aware losses that inject explicit structural constraints into the optimization process. Extensive experiments demonstrate that our method achieves state-of-the-art performance in articulated object reconstruction, producing high-quality results with well-defined part geometries.

Existing metrics used to evaluate table structure recognition algorithms have shortcomings with regard to capturing text and empty cells alignment. In this paper, we build on prior work and propose a new metric - TEDS based IOU similarity (TEDS (IOU)) for table structure recognition which uses bounding boxes instead of text while simultaneously being robust against the above disadvantages. We demonstrate the effectiveness of our metric against previous metrics through various examples.

Deep Metric Learning (DML) methods aim at learning an embedding space in which distances are closely related to the inherent semantic similarity of the inputs. Previous studies have shown that popular benchmark datasets often contain numerous wrong labels, and DML methods are susceptible to them. Intending to study the effect of realistic noise, we create an ontology of the classes in a dataset and use it to simulate semantically coherent labeling mistakes. To train robust DML models, we propose ProcSim, a simple framework that assigns a confidence score to each sample using the normalized distance to its class representative. The experimental results show that the proposed method achieves state-of-the-art performance on the DML benchmark datasets injected with uniform and the proposed semantically coherent noise.

The prediction of phase diagrams in the search for new phases is a complex and computationally intensive task. Density functional theory provides, in many situations, the desired accuracy, but its throughput becomes prohibitively limited as the number of species involved grows, even when used with local and semi-local functionals. Here, we explore the possibility of integrating machine-learning models in the workflow for the construction of ternary convex hull diagrams. In particular, we train a set of spectral neighbour-analysis potentials (SNAPs) over readily available binary phases and we establish whether this is good enough to predict the energies of novel ternaries. Such a strategy does not require any new calculations specific for the construction of the model, but just avails of data stored in binary-phase-diagram repositories. We find that a so-constructed SNAP is capable of accurate total-energy estimates for ternary phases close to the equilibrium geometry but, in general, is not able to perform atomic relaxation. This is because during a typical relaxation path a given phase traverses regions in the parameter space poorly represented by the training set. Different metrics are then investigated to assess how an unknown structure is well described by a given SNAP model, and we find that the standard deviation of an ensemble of SNAPs provides a fast and non-specie-specific metric.

Structure-property relationships are foundational to biology, chemistry and materials science, where function, reactivity and physical response emerge from spatial, chemical and periodic organization. Mechanistically explaining these relationships requires interpreting structural evidence through scientific principles and physical constraints, from stereochemistry and bonding to symmetry, energetics and periodic order. However, applying artificial intelligence to this process presents a joint challenge of representation and reasoning: models must preserve domain-native structural information while showing how specific evidence supports predictions under these constraints. Here we introduce SciReasoner, a multimodal scientific foundation model for native structural reasoning across proteins, small molecules and inorganic crystals. SciReasoner discretizes coordinates, topologies and periodic connectivities into a unified structure-aware vocabulary, treating structural tokens as addressable evidence units during reasoning. In homology-controlled Gene Ontology prediction, SciReasoner improves Cellular Component annotation for low-homology and orphan-like proteins, increasing F_{max} from 0.42 to 0.55. In chemistry, it raises single-step retrosynthesis accuracy from 0.63 to 0.72 while generating fragment-level disconnection and precursor-verification traces. In materials science, its representations separate elemental and compound phases and resolve high- and low-band-gap regimes. Across 86 benchmarks, SciReasoner achieves state-of-the-art performance on 67 tasks. Double-blind expert evaluation rates its reasoning traces as preferred or at least comparable to those of a frontier large language model in 98% of cases. By making structure an inspectable substrate for reasoning under scientific constraints, SciReasoner connects accurate prediction with interpretable scientific inference.

Directed acyclic graphs (DAGs) encode a lot of information about a particular distribution in their structure. However, compute required to infer these structures is typically super-exponential in the number of variables, as inference requires a sweep of a combinatorially large space of potential structures. That is, until recent advances made it possible to search this space using a differentiable metric, drastically reducing search time. While this technique -- named NOTEARS -- is widely considered a seminal work in DAG-discovery, it concedes an important property in favour of differentiability: transportability. To be transportable, the structures discovered on one dataset must apply to another dataset from the same domain. We introduce D-Struct which recovers transportability in the discovered structures through a novel architecture and loss function while remaining fully differentiable. Because D-Struct remains differentiable, our method can be easily adopted in existing differentiable architectures, as was previously done with NOTEARS. In our experiments, we empirically validate D-Struct with respect to edge accuracy and structural Hamming distance in a variety of settings.

With the emergence of data marketplaces, the demand for methods to assess the value of data has increased significantly. While numerous techniques have been proposed for this purpose, none have specifically addressed graphs as the main data modality. Graphs are widely used across various fields, ranging from chemical molecules to social networks. In this study, we break down graphs into two main components: structural and featural, and we focus on evaluating data without relying on specific task-related metrics, making it applicable in practical scenarios where validation requirements may be lacking. We introduce a novel framework called blind message passing, which aligns the seller's and buyer's graphs using a shared node permutation based on graph matching. This allows us to utilize the graph Wasserstein distance to quantify the differences in the structural distribution of graph datasets, called the structural disparities. We then consider featural aspects of buyers' and sellers' graphs for data valuation and capture their statistical similarities and differences, referred to as relevance and diversity, respectively. Our approach ensures that buyers and sellers remain unaware of each other's datasets. Our experiments on real datasets demonstrate the effectiveness of our approach in capturing the relevance, diversity, and structural disparities of seller data for buyers, particularly in graph-based data valuation scenarios.

While theoretically appealing, the application of the Wasserstein distance to large-scale machine learning problems has been hampered by its prohibitive computational cost. The sliced Wasserstein distance and its variants improve the computational efficiency through the random projection, yet they suffer from low accuracy if the number of projections is not sufficiently large, because the majority of projections result in trivially small values. In this work, we propose a new family of distance metrics, called augmented sliced Wasserstein distances (ASWDs), constructed by first mapping samples to higher-dimensional hypersurfaces parameterized by neural networks. It is derived from a key observation that (random) linear projections of samples residing on these hypersurfaces would translate to much more flexible nonlinear projections in the original sample space, so they can capture complex structures of the data distribution. We show that the hypersurfaces can be optimized by gradient ascent efficiently. We provide the condition under which the ASWD is a valid metric and show that this can be obtained by an injective neural network architecture. Numerical results demonstrate that the ASWD significantly outperforms other Wasserstein variants for both synthetic and real-world problems.

To solve deep metric learning problems and producing feature embeddings, current methodologies will commonly use a triplet model to minimise the relative distance between samples from the same class and maximise the relative distance between samples from different classes. Though successful, the training convergence of this triplet model can be compromised by the fact that the vast majority of the training samples will produce gradients with magnitudes that are close to zero. This issue has motivated the development of methods that explore the global structure of the embedding and other methods that explore hard negative/positive mining. The effectiveness of such mining methods is often associated with intractable computational requirements. In this paper, we propose a novel deep metric learning method that combines the triplet model and the global structure of the embedding space. We rely on a smart mining procedure that produces effective training samples for a low computational cost. In addition, we propose an adaptive controller that automatically adjusts the smart mining hyper-parameters and speeds up the convergence of the training process. We show empirically that our proposed method allows for fast and more accurate training of triplet ConvNets than other competing mining methods. Additionally, we show that our method achieves new state-of-the-art embedding results for CUB-200-2011 and Cars196 datasets.

Let T be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles, where the area of the rectangle corresponding to any node in T is equal to the weight of that node. The aspect ratio of the rectangles in such a rectangular partition necessarily depends on the weights and can become arbitrarily high. We introduce a new hierarchical partition scheme, called a polygonal partition, which uses convex polygons rather than just rectangles. We present two methods for constructing polygonal partitions, both having guarantees on the worst-case aspect ratio of the constructed polygons; in particular, both methods guarantee a bound on the aspect ratio that is independent of the weights of the nodes. We also consider rectangular partitions with slack, where the areas of the rectangles may differ slightly from the weights of the corresponding nodes. We show that this makes it possible to obtain partitions with constant aspect ratio. This result generalizes to hyper-rectangular partitions in R^d. We use these partitions with slack for embedding ultrametrics into d-dimensional Euclidean space: we give a rm polylog(Delta)-approximation algorithm for embedding n-point ultrametrics into R^d with minimum distortion, where Delta denotes the spread of the metric, i.e., the ratio between the largest and the smallest distance between two points. The previously best-known approximation ratio for this problem was polynomial in n. This is the first algorithm for embedding a non-trivial family of weighted-graph metrics into a space of constant dimension that achieves polylogarithmic approximation ratio.

Clustering non-Euclidean data is difficult, and one of the most used algorithms besides hierarchical clustering is the popular algorithm Partitioning Around Medoids (PAM), also simply referred to as k-medoids clustering. In Euclidean geometry the mean-as used in k-means-is a good estimator for the cluster center, but this does not exist for arbitrary dissimilarities. PAM uses the medoid instead, the object with the smallest dissimilarity to all others in the cluster. This notion of centrality can be used with any (dis-)similarity, and thus is of high relevance to many domains and applications. A key issue with PAM is its high run time cost. We propose modifications to the PAM algorithm that achieve an O(k)-fold speedup in the second ("SWAP") phase of the algorithm, but will still find the same results as the original PAM algorithm. If we relax the choice of swaps performed (while retaining comparable quality), we can further accelerate the algorithm by eagerly performing additional swaps in each iteration. With the substantially faster SWAP, we can now explore faster initialization strategies, because (i) the classic ("BUILD") initialization now becomes the bottleneck, and (ii) our swap is fast enough to compensate for worse starting conditions. We also show how the CLARA and CLARANS algorithms benefit from the proposed modifications. While we do not study the parallelization of our approach in this work, it can easily be combined with earlier approaches to use PAM and CLARA on big data (some of which use PAM as a subroutine, hence can immediately benefit from these improvements), where the performance with high k becomes increasingly important. In experiments on real data with k=100,200, we observed a 458x respectively 1191x speedup compared to the original PAM SWAP algorithm, making PAM applicable to larger data sets, and in particular to higher k.

Graph neural networks are emerging as promising methods for modeling molecular graphs, in which nodes and edges correspond to atoms and chemical bonds, respectively. Recent studies show that when 3D molecular geometries, such as bond lengths and angles, are available, molecular property prediction tasks can be made more accurate. However, computing of 3D molecular geometries requires quantum calculations that are computationally prohibitive. For example, accurate calculation of 3D geometries of a small molecule requires hours of computing time using density functional theory (DFT). Here, we propose to predict the ground-state 3D geometries from molecular graphs using machine learning methods. To make this feasible, we develop a benchmark, known as Molecule3D, that includes a dataset with precise ground-state geometries of approximately 4 million molecules derived from DFT. We also provide a set of software tools for data processing, splitting, training, and evaluation, etc. Specifically, we propose to assess the error and validity of predicted geometries using four metrics. We implement two baseline methods that either predict the pairwise distance between atoms or atom coordinates in 3D space. Experimental results show that, compared with generating 3D geometries with RDKit, our method can achieve comparable prediction accuracy but with much smaller computational costs. Our Molecule3D is available as a module of the MoleculeX software library (https://github.com/divelab/MoleculeX).

As large language models (LLMs) continue to evolve, efficient evaluation metrics are vital for assessing their ability to compress information and reduce redundancy. While traditional metrics like Matrix Entropy offer valuable insights, they are computationally intensive for large-scale models due to their \( O(n^3) \) time complexity with Singular Value Decomposition (SVD). To mitigate this issue, we introduce the Matrix Nuclear-Norm, which not only serves as a metric to quantify the data compression proficiency of LLM but also provides a convex approximation of matrix rank to capture both predictive discriminability and diversity. By employing the \( L_{1,2}-norm \) to further approximate the nuclear norm, we can effectively assess the model's information compression capabilities. This approach reduces the time complexity to \( O(n^2) \) and eliminates the need for SVD computation. Consequently, the Matrix Nuclear-Norm achieves speeds 8 to 24 times faster than Matrix Entropy for the CEREBRAS-GPT model as sizes increase from 111M to 6.7B. This performance gap becomes more pronounced with larger models, as validated in tests with other models like Pythia. Additionally, evaluations on benchmarks and model responses confirm that our proposed Matrix Nuclear-Norm is a reliable, scalable, and efficient tool for assessing LLMs' performance, striking a balance between accuracy and computational efficiency. The code is available at https://github.com/MLGroupJLU/MatrixNuclearNorm.

We introduce Image2Struct, a benchmark to evaluate vision-language models (VLMs) on extracting structure from images. Our benchmark 1) captures real-world use cases, 2) is fully automatic and does not require human judgment, and 3) is based on a renewable stream of fresh data. In Image2Struct, VLMs are prompted to generate the underlying structure (e.g., LaTeX code or HTML) from an input image (e.g., webpage screenshot). The structure is then rendered to produce an output image (e.g., rendered webpage), which is compared against the input image to produce a similarity score. This round-trip evaluation allows us to quantitatively evaluate VLMs on tasks with multiple valid structures. We create a pipeline that downloads fresh data from active online communities upon execution and evaluates the VLMs without human intervention. We introduce three domains (Webpages, LaTeX, and Musical Scores) and use five image metrics (pixel similarity, cosine similarity between the Inception vectors, learned perceptual image patch similarity, structural similarity index measure, and earth mover similarity) that allow efficient and automatic comparison between pairs of images. We evaluate Image2Struct on 14 prominent VLMs and find that scores vary widely, indicating that Image2Struct can differentiate between the performances of different VLMs. Additionally, the best score varies considerably across domains (e.g., 0.402 on sheet music vs. 0.830 on LaTeX equations), indicating that Image2Struct contains tasks of varying difficulty. For transparency, we release the full results at https://crfm.stanford.edu/helm/image2struct/v1.0.1/.

Scene graph generation has emerged as a prominent research field in computer vision, witnessing significant advancements in the recent years. However, despite these strides, precise and thorough definitions for the metrics used to evaluate scene graph generation models are lacking. In this paper, we address this gap in the literature by providing a review and precise definition of commonly used metrics in scene graph generation. Our comprehensive examination clarifies the underlying principles of these metrics and can serve as a reference or introduction to scene graph metrics. Furthermore, to facilitate the usage of these metrics, we introduce a standalone Python package called SGBench that efficiently implements all defined metrics, ensuring their accessibility to the research community. Additionally, we present a scene graph benchmarking web service, that enables researchers to compare scene graph generation methods and increase visibility of new methods in a central place. All of our code can be found at https://lorjul.github.io/sgbench/.

Structural fidelity is essential to scientific methodology diagrams. To communicate research logic, these diagrams must faithfully render components, directional relations, and textual annotations. Since a single error, such as a reversed arrow or an unreadable equation, can invalidate the entire figure, structural fidelity is inherently conjunctive: correctness on one axis cannot compensate for failure on another. Current open-source models fail to satisfy this criterion. Supervised fine-tuning (SFT) learns plausible layouts but cannot reliably ensure structural correctness, while scalar reward-based post-training obscures which structural dimension has failed. To address this, we introduce SciForma, a framework for the structure faithful generation of scientific methodology diagrams. Specifically, SciForma decomposes diagram quality into three structural axes: Component, Arrow, and Text, guided by a structural inventory. Built on this foundation, we curate SciFormaData-700K for structured training and SciFormaBench-2K for logic-verified evaluation. To close the gap left by SFT, we develop Multi-Dimensional Conjunctive Preference Optimization (M-DPO), which enforces simultaneous correctness across all axes and adaptively routes gradients to the most deficient dimension in post-training. The same structural inventory also enables iterative editing at inference time to correct residual errors. This combination allows SciForma-9B to exceed all open-source baselines and GPT-Image-1.5 on both SciFormaBench-2K and AIBench, bringing open scientific diagram generation close to proprietary-level structural fidelity. Our code and data will be available at: https://github.com/microsoft/SciForma.

Structural and Positional Encodings can significantly improve the performance of Graph Neural Networks in downstream tasks. Recent literature has begun to systematically investigate differences in the structural properties that these approaches encode, as well as performance trade-offs between them. However, the question of which structural properties yield the most effective encoding remains open. In this paper, we investigate this question from a geometric perspective. We propose a novel structural encoding based on discrete Ricci curvature (Local Curvature Profiles, short LCP) and show that it significantly outperforms existing encoding approaches. We further show that combining local structural encodings, such as LCP, with global positional encodings improves downstream performance, suggesting that they capture complementary geometric information. Finally, we compare different encoding types with (curvature-based) rewiring techniques. Rewiring has recently received a surge of interest due to its ability to improve the performance of Graph Neural Networks by mitigating over-smoothing and over-squashing effects. Our results suggest that utilizing curvature information for structural encodings delivers significantly larger performance increases than rewiring.

Object-centric architectures usually apply a differentiable module to the entire feature map to decompose it into sets of entity representations called slots. Some of these methods structurally resemble clustering algorithms, where the cluster's center in latent space serves as a slot representation. Slot Attention is an example of such a method, acting as a learnable analog of the soft k-means algorithm. Our work employs a learnable clustering method based on the Gaussian Mixture Model. Unlike other approaches, we represent slots not only as centers of clusters but also incorporate information about the distance between clusters and assigned vectors, leading to more expressive slot representations. Our experiments demonstrate that using this approach instead of Slot Attention improves performance in object-centric scenarios, achieving state-of-the-art results in the set property prediction task.

Understanding geometric properties of natural language processing models' latent spaces allows the manipulation of these properties for improved performance on downstream tasks. One such property is the amount of data spread in a model's latent space, or how fully the available latent space is being used. In this work, we define data spread and demonstrate that the commonly used measures of data spread, Average Cosine Similarity and a partition function min/max ratio I(V), do not provide reliable metrics to compare the use of latent space across models. We propose and examine eight alternative measures of data spread, all but one of which improve over these current metrics when applied to seven synthetic data distributions. Of our proposed measures, we recommend one principal component-based measure and one entropy-based measure that provide reliable, relative measures of spread and can be used to compare models of different sizes and dimensionalities.

Large language models have shown strong fluency in scientific writing, yet the evaluation of related work generation (RWG) remains limited. Existing RWG evaluations largely inherit summarization-oriented metrics, using lexical or semantic similarity to reference sections as proxies for quality. However, related work writing is fundamentally a citation-level scholarly positioning task: it requires selecting, organizing, and framing prior work to clarify how a target paper relates to, differs from, and contributes beyond existing research.As a result, models may generate coherent and semantically-relevant text while exhibiting academically critical failures, such as inappropriate citation selection or misplaced references, that conventional metrics do not capture.To this end, we introduce RWGBench, a benchmark that evaluates RWG from the perspective of citation decision-making rather than text similarity. RWGBench is constructed from a large-scale collection of 40,108 computer science papers and a retrieval corpus of 1.09 million documents, with a carefully curated test set comprising 100 papers and their corresponding published related work sections.We propose a multi-dimensional evaluation framework that assesses citation selection, contextual appropriateness, organization, and discourse structure.Experiments reveal systematic limitations in current systems that are obscured by standard evaluations, while Oracle studies further disentangle retrieval-level and generation-level bottlenecks. Human evaluation further shows that our citation-centric metrics align substantially better with expert judgment than surface-level text metrics. RWGBench offers a citation-centric testbed for developing and evaluating related work generation systems that are better aligned with scholarly writing practices.

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.

This work explores the visual explanation for deep metric learning and its applications. As an important problem for learning representation, metric learning has attracted much attention recently, while the interpretation of such model is not as well studied as classification. To this end, we propose an intuitive idea to show where contributes the most to the overall similarity of two input images by decomposing the final activation. Instead of only providing the overall activation map of each image, we propose to generate point-to-point activation intensity between two images so that the relationship between different regions is uncovered. We show that the proposed framework can be directly deployed to a large range of metric learning applications and provides valuable information for understanding the model. Furthermore, our experiments show its effectiveness on two potential applications, i.e. cross-view pattern discovery and interactive retrieval. The source code is available at https://github.com/Jeff-Zilence/Explain_Metric_Learning.

Similarity metrics such as representational similarity analysis (RSA) and centered kernel alignment (CKA) have been used to compare layer-wise representations between neural networks. However, these metrics are confounded by the population structure of data items in the input space, leading to spuriously high similarity for even completely random neural networks and inconsistent domain relations in transfer learning. We introduce a simple and generally applicable fix to adjust for the confounder with covariate adjustment regression, which retains the intuitive invariance properties of the original similarity measures. We show that deconfounding the similarity metrics increases the resolution of detecting semantically similar neural networks. Moreover, in real-world applications, deconfounding improves the consistency of representation similarities with domain similarities in transfer learning, and increases correlation with out-of-distribution accuracy.

We survey the large language model (LLM) serving area to understand the intricate dynamics between cost-efficiency and accuracy, which is magnified by the growing need for longer contextual understanding when deploying models at a massive scale. Our findings reveal that works in this space optimize along three distinct but conflicting goals: improving serving context length (C), improving serving accuracy (A), and improving serving performance (P). Drawing inspiration from the CAP theorem in databases, we propose a CAP principle for LLM serving, which suggests that any optimization can improve at most two of these three goals simultaneously. Our survey categorizes existing works within this framework. We find the definition and continuity of user-perceived measurement metrics are crucial in determining whether a goal has been met, akin to prior CAP databases in the wild. We recognize the CAP principle for LLM serving as a guiding principle, rather than a formal theorem, to inform designers of the inherent and dynamic trade-offs in serving models. As serving accuracy and performance have been extensively studied, this survey focuses on works that extend serving context length and address the resulting challenges.

Machine Translation (MT) evaluation metrics assess translation quality automatically. Recently, researchers have employed MT metrics for various new use cases, such as data filtering and translation re-ranking. However, most MT metrics return assessments as scalar scores that are difficult to interpret, posing a challenge to making informed design choices. Moreover, MT metrics' capabilities have historically been evaluated using correlation with human judgment, which, despite its efficacy, falls short of providing intuitive insights into metric performance, especially in terms of new metric use cases. To address these issues, we introduce an interpretable evaluation framework for MT metrics. Within this framework, we evaluate metrics in two scenarios that serve as proxies for the data filtering and translation re-ranking use cases. Furthermore, by measuring the performance of MT metrics using Precision, Recall, and F-score, we offer clearer insights into their capabilities than correlation with human judgments. Finally, we raise concerns regarding the reliability of manually curated data following the Direct Assessments+Scalar Quality Metrics (DA+SQM) guidelines, reporting a notably low agreement with Multidimensional Quality Metrics (MQM) annotations.

We present TIGERScore, a Trained metric that follows Instruction Guidance to perform Explainable, and Reference-free evaluation over a wide spectrum of text generation tasks. Different from other automatic evaluation methods that only provide arcane scores, TIGERScore is guided by the natural language instruction to provide error analysis to pinpoint the mistakes in the generated text. Our metric is based on LLaMA, trained on our meticulously curated instruction-tuning dataset MetricInstruct which covers 6 text generation tasks and 23 text generation datasets. The dataset consists of 48K quadruple in the form of (instruction, input, system output rightarrow error analysis). We collected the `system outputs' through diverse channels to cover different types of errors. To quantitatively assess our metric, we evaluate its correlation with human ratings on 5 held-in datasets, 2 held-out datasets and show that TIGERScore can achieve the highest overall Spearman's correlation with human ratings across these datasets and outperforms other metrics significantly. As a reference-free metric, its correlation can even surpass the best existing reference-based metrics. To further qualitatively assess the rationale generated by our metric, we conduct human evaluation on the generated explanations and found that the explanations are 70.8\% accurate. Through these experimental results, we believe TIGERScore demonstrates the possibility of building universal explainable metrics to evaluate any text generation task.

Recent advances in Text-to-3D (T23D) generative models have enabled the synthesis of diverse, high-fidelity 3D assets from textual prompts. However, existing challenges restrict the development of reliable T23D quality assessment (T23DQA). First, existing benchmarks are outdated, fragmented, and coarse-grained, making fine-grained metric training infeasible. Moreover, current objective metrics exhibit inherent design limitations, resulting in non-representative feature extraction and diminished metric robustness. To address these limitations, we introduce T23D-CompBench, a comprehensive benchmark for compositional T23D generation. We define five components with twelve sub-components for compositional prompts, which are used to generate 3,600 textured meshes from ten state-of-the-art generative models. A large-scale subjective experiment is conducted to collect 129,600 reliable human ratings across different perspectives. Based on T23D-CompBench, we further propose Rank2Score, an effective evaluator with two-stage training for T23DQA. Rank2Score enhances pairwise training via supervised contrastive regression and curriculum learning in the first stage, and subsequently refines predictions using mean opinion scores to achieve closer alignment with human judgments in the second stage. Extensive experiments and downstream applications demonstrate that Rank2Score consistently outperforms existing metrics across multiple dimensions and can additionally serve as a reward function to optimize generative models. The project is available at https://cbysjtu.github.io/Rank2Score/.

Clustering non-Euclidean data is difficult, and one of the most used algorithms besides hierarchical clustering is the popular algorithm Partitioning Around Medoids (PAM), also simply referred to as k-medoids. In Euclidean geometry the mean-as used in k-means-is a good estimator for the cluster center, but this does not hold for arbitrary dissimilarities. PAM uses the medoid instead, the object with the smallest dissimilarity to all others in the cluster. This notion of centrality can be used with any (dis-)similarity, and thus is of high relevance to many domains such as biology that require the use of Jaccard, Gower, or more complex distances. A key issue with PAM is its high run time cost. We propose modifications to the PAM algorithm to achieve an O(k)-fold speedup in the second SWAP phase of the algorithm, but will still find the same results as the original PAM algorithm. If we slightly relax the choice of swaps performed (at comparable quality), we can further accelerate the algorithm by performing up to k swaps in each iteration. With the substantially faster SWAP, we can now also explore alternative strategies for choosing the initial medoids. We also show how the CLARA and CLARANS algorithms benefit from these modifications. It can easily be combined with earlier approaches to use PAM and CLARA on big data (some of which use PAM as a subroutine, hence can immediately benefit from these improvements), where the performance with high k becomes increasingly important. In experiments on real data with k=100, we observed a 200-fold speedup compared to the original PAM SWAP algorithm, making PAM applicable to larger data sets as long as we can afford to compute a distance matrix, and in particular to higher k (at k=2, the new SWAP was only 1.5 times faster, as the speedup is expected to increase with k).

Graphs provide a natural representation of relational structure that arises across diverse domains. Despite this ubiquity, graph structure is typically learned in a modality- and task-isolated manner, where graph representations are constructed within individual task contexts and discarded thereafter. As a result, structural regularities across modalities and tasks are repeatedly reconstructed rather than accumulated at the level of intermediate graph representations. This motivates a representation-learning question: how should graph structure be organized so that it can persist and accumulate across heterogeneous modalities and tasks? We adopt a representation-centric perspective in which graph structure is treated as a structural substrate that persists across learning contexts. To instantiate this perspective, we propose G-Substrate, a graph substrate framework that organizes learning around shared graph structures. G-Substrate comprises two complementary mechanisms: a unified structural schema that ensures compatibility among graph representations across heterogeneous modalities and tasks, and an interleaved role-based training strategy that exposes the same graph structure to multiple functional roles during learning. Experiments across multiple domains, modalities, and tasks show that G-Substrate outperforms task-isolated and naive multi-task learning methods. The codebase, model, and datasets are available at https://github.com/zmli6/G-Substrate.

Accurate segmentation of tubular, network-like structures, such as vessels, neurons, or roads, is relevant to many fields of research. For such structures, the topology is their most important characteristic; particularly preserving connectedness: in the case of vascular networks, missing a connected vessel entirely alters the blood-flow dynamics. We introduce a novel similarity measure termed centerlineDice (short clDice), which is calculated on the intersection of the segmentation masks and their (morphological) skeleta. We theoretically prove that clDice guarantees topology preservation up to homotopy equivalence for binary 2D and 3D segmentation. Extending this, we propose a computationally efficient, differentiable loss function (soft-clDice) for training arbitrary neural segmentation networks. We benchmark the soft-clDice loss on five public datasets, including vessels, roads and neurons (2D and 3D). Training on soft-clDice leads to segmentation with more accurate connectivity information, higher graph similarity, and better volumetric scores.

The rapid growth in submissions to machine learning venues has strained the scientific peer-review system and intensified interest in LLM-based automated peer reviewers. However, how good these systems are actually, especially compared to human reviewers at catching scientific gaps, remains poorly understood. In this work, we introduce PRISM (Peer Review Intelligence via Structured Multi-dimensional assessment), a benchmarking framework that evaluates review quality across four dimensions: Depth of Analysis, Novelty Assessment,Flaw Identification & Major Issues Prioritization, and Multi-dimensional Constructiveness. Unlike most existing evaluations based on surface-level metrics like ROUGE and BLEU, or unconstrained LLM-as-a-judge prompting that conflates fluency with rigor, PRISM grounds each dimension in argument mining, retrieval-augmented verification, and consensus-based scoring. We apply PRISM to benchmark five leading automated reviewer systems and human reviewers on a stratified corpus of reviews from ICLR, ICML, and NeurIPS. The results reveal that LLMs can match or beat human reviewers on individual dimensions: comparable depth of analysis, stronger novelty verification, and highly accurate critique prioritization. However, no single system consistently matches the balanced performance of the human baseline across all dimensions at once. Each exhibits a distinct specialization profile with characteristic blind spots -- failure modes that aggregate metrics miss entirely. The implication is that LLM reviewers are best understood as targeted supplements to human review, effective within specific dimensions, but unreliable as standalone replacements. Our demo and key results can be found at https://khanhthanhdev.github.io/prism-page/.

Large language models (LLMs) have achieved remarkable success across various domains, driving significant technological advancements and innovations. Despite the rapid growth in model scale and capability, systematic, data-driven research on how structural configurations affect performance remains scarce. To address this gap, we present a large-scale dataset encompassing diverse open-source LLM structures and their performance across multiple benchmarks. Leveraging this dataset, we conduct a systematic, data mining-driven analysis to validate and quantify the relationship between structural configurations and performance. Our study begins with a review of the historical development of LLMs and an exploration of potential future trends. We then analyze how various structural choices impact performance across benchmarks and further corroborate our findings using mechanistic interpretability techniques. By providing data-driven insights into LLM optimization, our work aims to guide the targeted development and application of future models. We will release our dataset at https://huggingface.co/datasets/DX0369/LLM-Structure-Performance-Dataset

Although data diffusion embeddings are ubiquitous in unsupervised learning and have proven to be a viable technique for uncovering the underlying intrinsic geometry of data, diffusion embeddings are inherently limited due to their discrete nature. To this end, we propose neural FIM, a method for computing the Fisher information metric (FIM) from point cloud data - allowing for a continuous manifold model for the data. Neural FIM creates an extensible metric space from discrete point cloud data such that information from the metric can inform us of manifold characteristics such as volume and geodesics. We demonstrate Neural FIM's utility in selecting parameters for the PHATE visualization method as well as its ability to obtain information pertaining to local volume illuminating branching points and cluster centers embeddings of a toy dataset and two single-cell datasets of IPSC reprogramming and PBMCs (immune cells).

Radiology reports convey detailed clinical observations and capture diagnostic reasoning that evolves over time. However, existing evaluation methods are limited to single-report settings and rely on coarse metrics that fail to capture fine-grained clinical semantics and temporal dependencies. We introduce LUNGUAGE,a benchmark dataset for structured radiology report generation that supports both single-report evaluation and longitudinal patient-level assessment across multiple studies. It contains 1,473 annotated chest X-ray reports, each reviewed by experts, and 80 of them contain longitudinal annotations to capture disease progression and inter-study intervals, also reviewed by experts. Using this benchmark, we develop a two-stage framework that transforms generated reports into fine-grained, schema-aligned structured representations, enabling longitudinal interpretation. We also propose LUNGUAGESCORE, an interpretable metric that compares structured outputs at the entity, relation, and attribute level while modeling temporal consistency across patient timelines. These contributions establish the first benchmark dataset, structuring framework, and evaluation metric for sequential radiology reporting, with empirical results demonstrating that LUNGUAGESCORE effectively supports structured report evaluation. The code is available at: https://github.com/SuperSupermoon/Lunguage

Protein structure tokenization converts 3D structures into discrete or vectorized representations, enabling the integration of structural and sequence data. Despite many recent works on structure tokenization, the properties of the underlying discrete representations are not well understood. In this work, we first demonstrate that the successful utilization of structural tokens in a language model for structure prediction depends on using rich, pre-trained sequence embeddings to bridge the semantic gap between the sequence and structural "language". The analysis of the structural vocabulary itself then reveals significant semantic redundancy, where multiple distinct tokens correspond to nearly identical local geometries, acting as "structural synonyms". This redundancy, rather than being a flaw, can be exploited with a simple "synonym swap" strategy to generate diverse conformational ensembles by perturbing a predicted structure with its structural synonyms. This computationally lightweight method accurately recapitulates protein flexibility, performing competitively with state-of-the-art models. Our study provides fundamental insights into the nature of discrete protein structure representations and introduces a powerful, near-instantaneous method for modeling protein dynamics. Source code is available in https://github.com/IDEA-XL/TokenMD.

Vector Similarity Search (VSS) in high-dimensional spaces is rapidly emerging as core functionality in next-generation database systems for numerous data-intensive services -- from embedding lookups in large language models (LLMs), to semantic information retrieval and recommendation engines. Current benchmarks, however, evaluate VSS primarily on the recall-latency trade-off against a ground truth defined solely by distance metrics, neglecting how retrieval quality ultimately impacts downstream tasks. This disconnect can mislead both academic research and industrial practice. We present Iceberg, a holistic benchmark suite for end-to-end evaluation of VSS methods in realistic application contexts. From a task-centric view, Iceberg uncovers the Information Loss Funnel, which identifies three principal sources of end-to-end performance degradation: (1) Embedding Loss during feature extraction; (2) Metric Misuse, where distances poorly reflect task relevance; (3) Data Distribution Sensitivity, highlighting index robustness across skews and modalities. For a more comprehensive assessment, Iceberg spans eight diverse datasets across key domains such as image classification, face recognition, text retrieval, and recommendation systems. Each dataset, ranging from 1M to 100M vectors, includes rich, task-specific labels and evaluation metrics, enabling assessment of retrieval algorithms within the full application pipeline rather than in isolation. Iceberg benchmarks 13 state-of-the-art VSS methods and re-ranks them based on application-level metrics, revealing substantial deviations from traditional rankings derived purely from recall-latency evaluations. Building on these insights, we define a set of task-centric meta-features and derive an interpretable decision tree to guide practitioners in selecting and tuning VSS methods for their specific workloads.

Large language models (LLMs) have achieved remarkable success and demonstrated superior performance across various tasks, including natural language processing (NLP), weather forecasting, biological protein folding, text generation, and solving mathematical problems. However, many real-world data exhibit highly non-Euclidean latent hierarchical anatomy, such as protein networks, transportation networks, financial networks, brain networks, and linguistic structures or syntactic trees in natural languages. Effectively learning intrinsic semantic entailment and hierarchical relationships from these raw, unstructured input data using LLMs remains an underexplored area. Due to its effectiveness in modeling tree-like hierarchical structures, hyperbolic geometry -- a non-Euclidean space -- has rapidly gained popularity as an expressive latent representation space for complex data modeling across domains such as graphs, images, languages, and multi-modal data. Here, we provide a comprehensive and contextual exposition of recent advancements in LLMs that leverage hyperbolic geometry as a representation space to enhance semantic representation learning and multi-scale reasoning. Specifically, the paper presents a taxonomy of the principal techniques of Hyperbolic LLMs (HypLLMs) in terms of four main categories: (1) hyperbolic LLMs through exp/log maps; (2) hyperbolic fine-tuned models; (3) fully hyperbolic LLMs, and (4) hyperbolic state-space models. We also explore crucial potential applications and outline future research directions. A repository of key papers, models, datasets, and code implementations is available at https://github.com/sarangp2402/Hyperbolic-LLM-Models/tree/main.

This paper revisits datasets and evaluation criteria for Symbolic Regression, a task of expressing given data using mathematical equations, specifically focused on its potential for scientific discovery. Focused on a set of formulas used in the existing datasets based on Feynman Lectures on Physics, we recreate 120 datasets to discuss the performance of symbolic regression for scientific discovery (SRSD). For each of the 120 SRSD datasets, we carefully review the properties of the formula and its variables to design reasonably realistic sampling range of values so that our new SRSD datasets can be used for evaluating the potential of SRSD such as whether or not an SR method can (re)discover physical laws from such datasets. As an evaluation metric, we also propose to use normalized edit distances between a predicted equation and the ground-truth equation trees. While existing metrics are either binary or errors between the target values and an SR model's predicted values for a given input, normalized edit distances evaluate a sort of similarity between the ground-truth and predicted equation trees. We have conducted experiments on our new SRSD datasets using five state-of-the-art SR methods in SRBench and a simple baseline based on a recent Transformer architecture. The results show that we provide a more realistic performance evaluation and open up a new machine learning-based approach for scientific discovery. Our datasets and code repository are publicly available.

Visual explanations are often plausible but not structurally faithful. We introduce CAMBench-QR, a structure-aware benchmark that leverages the canonical geometry of QR codes (finder patterns, timing lines, module grid) to test whether CAM methods place saliency on requisite substructures while avoiding background. CAMBench-QR synthesizes QR/non-QR data with exact masks and controlled distortions, and reports structure-aware metrics (Finder/Timing Mass Ratios, Background Leakage, coverage AUCs, Distance-to-Structure) alongside causal occlusion, insertion/deletion faithfulness, robustness, and latency. We benchmark representative, efficient CAMs (LayerCAM, EigenGrad-CAM, XGrad-CAM) under two practical regimes of zero-shot and last-block fine-tuning. The benchmark, metrics, and training recipes provide a simple, reproducible yardstick for structure-aware evaluation of visual explanations. Hence we propose that CAMBENCH-QR can be used as a litmus test of whether visual explanations are truly structure-aware.

The field of face recognition (FR) has undergone significant advancements with the rise of deep learning. Recently, the success of unsupervised learning and graph neural networks has demonstrated the effectiveness of data structure information. Considering that the FR task can leverage large-scale training data, which intrinsically contains significant structure information, we aim to investigate how to encode such critical structure information into the latent space. As revealed from our observations, directly aligning the structure information between the input and latent spaces inevitably suffers from an overfitting problem, leading to a structure collapse phenomenon in the latent space. To address this problem, we propose TopoFR, a novel FR model that leverages a topological structure alignment strategy called PTSA and a hard sample mining strategy named SDE. Concretely, PTSA uses persistent homology to align the topological structures of the input and latent spaces, effectively preserving the structure information and improving the generalization performance of FR model. To mitigate the impact of hard samples on the latent space structure, SDE accurately identifies hard samples by automatically computing structure damage score (SDS) for each sample, and directs the model to prioritize optimizing these samples. Experimental results on popular face benchmarks demonstrate the superiority of our TopoFR over the state-of-the-art methods. Code and models are available at: https://github.com/modelscope/facechain/tree/main/face_module/TopoFR.

In language models, what a representation encodes is determined by the geometry of its representation space: distances, not activations, carry meaning. Existing tools characterize the shape of this geometry but do not ask what that shape is organized for. We introduce Subspace PGA, a metric that tests whether a layer's distance structure aligns with the readout subspace of the unembedding matrix W_U more than with random subspaces of equal size. Across seven Pythia models (70M--6.9B) and three cross-family models, intermediate geometry is significantly organized for prediction (peak z = 9--24), but the degree is scale-dependent: small models (d leq 1024) progressively lose it at late layers during training -- even as loss keeps improving -- while large models (d geq 2048) preserve it throughout. We trace this to a capacity trade-off: a few dominant directions migrate away from W_U's readout, masking rather than destroying the predictive structure beneath, and removing them restores alignment. Neither spectral metrics nor loss curves capture this distinction. Scale thus determines not only how well a model predicts, but how its representation geometry is organized to do so.

Intrinsic dimension (ID) is an important tool in modern LLM analysis, informing studies of training dynamics, scaling behavior, and dataset structure, yet its textual determinants remain underexplored. We provide the first comprehensive study grounding ID in interpretable text properties through cross-encoder analysis, linguistic features, and sparse autoencoders (SAEs). In this work, we establish three key findings. First, ID is complementary to entropy-based metrics: after controlling for length, the two are uncorrelated, with ID capturing geometric complexity orthogonal to prediction quality. Second, ID exhibits robust genre stratification: scientific prose shows low ID (~8), encyclopedic content medium ID (~9), and creative/opinion writing high ID (~10.5) across all models tested. This reveals that contemporary LLMs find scientific text "representationally simple" while fiction requires additional degrees of freedom. Third, using SAEs, we identify causal features: scientific signals (formal tone, report templates, statistics) reduce ID; humanized signals (personalization, emotion, narrative) increase it. Steering experiments confirm these effects are causal. Thus, for contemporary models, scientific writing appears comparatively "easy", whereas fiction, opinion, and affect add representational degrees of freedom. Our multi-faceted analysis provides practical guidance for the proper use of ID and the sound interpretation of ID-based results.

While learning models are typically studied for inputs in the form of a fixed dimensional feature vector, real world data is rarely found in this form. In order to meet the basic requirement of traditional learning models, structural data generally have to be converted into fix-length vectors in a handcrafted manner, which is tedious and may even incur information loss. A common form of structured data is what we term "semantic tree-structures", corresponding to data where rich semantic information is encoded in a compositional manner, such as those expressed in JavaScript Object Notation (JSON) and eXtensible Markup Language (XML). For tree-structured data, several learning models have been studied to allow for working directly on raw tree-structure data, However such learning models are limited to either a specific tree-topology or a specific tree-structured data format, e.g., synthetic parse trees. In this paper, we propose a novel framework for end-to-end learning on generic semantic tree-structured data of arbitrary topology and heterogeneous data types, such as data expressed in JSON, XML and so on. Motivated by the works in recursive and recurrent neural networks, we develop exemplar neural implementations of our framework for the JSON format. We evaluate our approach on several UCI benchmark datasets, including ablation and data-efficiency studies, and on a toy reinforcement learning task. Experimental results suggest that our framework yields comparable performance to use of standard models with dedicated feature-vectors in general, and even exceeds baseline performance in cases where compositional nature of the data is particularly important. The source code for a JSON-based implementation of our framework along with experiments can be downloaded at https://github.com/EndingCredits/json2vec.

Protein language models are a powerful tool for learning protein representations through pre-training on vast protein sequence datasets. However, traditional protein language models lack explicit structural supervision, despite its relevance to protein function. To address this issue, we introduce the integration of remote homology detection to distill structural information into protein language models without requiring explicit protein structures as input. We evaluate the impact of this structure-informed training on downstream protein function prediction tasks. Experimental results reveal consistent improvements in function annotation accuracy for EC number and GO term prediction. Performance on mutant datasets, however, varies based on the relationship between targeted properties and protein structures. This underscores the importance of considering this relationship when applying structure-aware training to protein function prediction tasks. Code and model weights are available at https://github.com/DeepGraphLearning/esm-s.

Scientific archives now contain hundreds of petabytes of data across genomics, ecology, climate, and molecular biology that could reveal undiscovered patterns if systematically analyzed at scale. Large-scale, weakly-supervised datasets in language and vision have driven the development of foundation models whose internal representations encode structure (patterns, co-occurrences and statistical regularities) beyond their training objectives. Most existing methods extract structure only for pre-specified targets; they excel at confirmation but do not support open-ended discovery of unknown patterns. We ask whether sparse autoencoders (SAEs) can enable open-ended feature discovery from foundation model representations. We evaluate this question in controlled rediscovery studies, where the learned SAE features are tested for alignment with semantic concepts on a standard segmentation benchmark and compared against strong label-free alternatives on concept-alignment metrics. Applied to ecological imagery, the same procedure surfaces fine-grained anatomical structure without access to segmentation or part labels, providing a scientific case study with ground-truth validation. While our experiments focus on vision with an ecology case study, the method is domain-agnostic and applicable to models in other sciences (e.g., proteins, genomics, weather). Our results indicate that sparse decomposition provides a practical instrument for exploring what scientific foundation models have learned, an important prerequisite for moving from confirmation to genuine discovery.

Transformer-based table retrieval systems flatten structured tables into token sequences, making retrieval sensitive to the choice of serialization even when table semantics remain unchanged. We show that semantically equivalent serializations, such as csv, tsv, html, markdown, and ddl, can produce substantially different embeddings and retrieval results across multiple benchmarks and retriever families. To address this instability, we treat serialization embedding as noisy views of a shared semantic signal and use its centroid as a canonical target representation. We show that centroid averaging suppresses format-specific variation and can recover the semantic content common to different serializations when format-induced shifts differ across tables. Empirically, centroid representations outrank individual formats in aggregate pairwise comparisons across MPNet, BGE-M3, ReasonIR, and SPLADE. We further introduce a lightweight residual bottleneck adapter on top of a frozen encoder that maps single-serialization embeddings towards centroid targets while preserving variance and enforcing covariance regularization. The adapter improves robustness for several dense retrievers, though gains are model-dependent and weaker for sparse lexical retrieval. These results identify serialization sensitivity as a major source of retrieval variance and show the promise of post hoc geometric correction for serialization-invariant table retrieval. Our code, datasets, and models are available at https://github.com/KBhandari11/Centroid-Aligned-Table-Retrieval{https://github.com/KBhandari11/Centroid-Aligned-Table-Retrieval}.

Existing methods for evaluating graph generative models primarily rely on Maximum Mean Discrepancy (MMD) metrics based on graph descriptors. While these metrics can rank generative models, they do not provide an absolute measure of performance. Their values are also highly sensitive to extrinsic parameters, namely kernel and descriptor parametrization, making them incomparable across different graph descriptors. We introduce PolyGraph Discrepancy (PGD), a new evaluation framework that addresses these limitations. It approximates the Jensen-Shannon distance of graph distributions by fitting binary classifiers to distinguish between real and generated graphs, featurized by these descriptors. The data log-likelihood of these classifiers approximates a variational lower bound on the JS distance between the two distributions. Resulting metrics are constrained to the unit interval [0,1] and are comparable across different graph descriptors. We further derive a theoretically grounded summary metric that combines these individual metrics to provide a maximally tight lower bound on the distance for the given descriptors. Thorough experiments demonstrate that PGD provides a more robust and insightful evaluation compared to MMD metrics. The PolyGraph framework for benchmarking graph generative models is made publicly available at https://github.com/BorgwardtLab/polygraph-benchmark.

Model dimension (d_{model}) is a fundamental hyperparameter in transformer language models, yet its role in setting the geometric limits of feature representation remains under-explored. Grounded in the Linear Representation and Superposition Hypotheses - which propose that models encode features as near-orthogonal directions in latent space - we develop a framework for estimating how many such directions a model can support. We first establish the embedding matrix as a measurable proxy for near-orthogonality constraints across the latent space: the boundary between meaningful token relationships and incidental similarity in the pairwise cosine similarity distribution gives a concrete estimate of the model's accepted deviation varepsilon from perfect orthogonality. Applying this metric across dozens of open-source models reveals two classes: models with high varepsilon whose embeddings lack near-orthogonal structure, and models with low varepsilon that maintain it. We then show that the standard Johnson-Lindenstrauss lemma greatly underestimates the packing efficiency of trained representations, and derive an adjusted capacity formula in which the number of near-orthogonal directions depends on the ratio of vectors to dimensions (k/d) rather than the raw count - a single modification that cuts prediction error by two orders of magnitude with no extra parameters. Combining these results, we define representational capacity as an upper bound on the number of distinguishable directions available for features and embeddings in a model's latent space. Capacity is exponentially sensitive to varepsilon, and larger models favor tighter orthogonality constraints over maximizing raw capacity - a pattern compatible with several explanations (a stability-capacity trade-off, a ceiling on usable concepts, or confounds with model scale) that we leave to future work.

Structure reasoning is a fundamental capability of large language models (LLMs), enabling them to reason about structured commonsense and answer multi-hop questions. However, existing benchmarks for structure reasoning mainly focus on horizontal and coordinate structures (e.g. graphs), overlooking the hierarchical relationships within them. Hierarchical structure reasoning is crucial for human cognition, particularly in memory organization and problem-solving. It also plays a key role in various real-world tasks, such as information extraction and decision-making. To address this gap, we propose HiBench, the first framework spanning from initial structure generation to final proficiency assessment, designed to benchmark the hierarchical reasoning capabilities of LLMs systematically. HiBench encompasses six representative scenarios, covering both fundamental and practical aspects, and consists of 30 tasks with varying hierarchical complexity, totaling 39,519 queries. To evaluate LLMs comprehensively, we develop five capability dimensions that depict different facets of hierarchical structure understanding. Through extensive evaluation of 20 LLMs from 10 model families, we reveal key insights into their capabilities and limitations: 1) existing LLMs show proficiency in basic hierarchical reasoning tasks; 2) they still struggle with more complex structures and implicit hierarchical representations, especially in structural modification and textual reasoning. Based on these findings, we create a small yet well-designed instruction dataset, which enhances LLMs' performance on HiBench by an average of 88.84\% (Llama-3.1-8B) and 31.38\% (Qwen2.5-7B) across all tasks. The HiBench dataset and toolkit are available here, https://github.com/jzzzzh/HiBench, to encourage evaluation.

Scientific knowledge is growing rapidly, making it challenging to track progress and high-level conceptual links across broad disciplines. While existing tools like citation networks and search engines make it easy to access a few related papers, they fundamentally lack the flexible abstraction needed to represent the density of activity in various scientific subfields. We motivate SCIENCE HIERARCHOGRAPHY, the goal of organizing scientific literature into a high-quality hierarchical structure that allows for the categorization of scientific work across varying levels of abstraction, from very broad fields to very specific studies. Such a representation can provide insights into which fields are well-explored and which are under-explored. To achieve the goals of SCIENCE HIERARCHOGRAPHY, we develop a range of algorithms. Our primary approach combines fast embedding-based clustering with LLM-based prompting to balance the computational efficiency of embedding methods with the semantic precision offered by LLM prompting. We demonstrate that this approach offers the best trade-off between quality and speed compared to methods that heavily rely on LLM prompting, such as iterative tree construction with LLMs. To better reflect the interdisciplinary and multifaceted nature of research papers, our hierarchy captures multiple dimensions of categorization beyond simple topic labels. We evaluate the utility of our framework by assessing how effectively an LLM-based agent can locate target papers using the hierarchy. Results show that this structured approach enhances interpretability, supports trend discovery, and offers an alternative pathway for exploring scientific literature beyond traditional search methods. Code, data and demo: https://github.com/JHU-CLSP/science-hierarchography{https://github.com/JHU-CLSP/science-hierarchography}

The structure learning problem consists of fitting data generated by a Directed Acyclic Graph (DAG) to correctly reconstruct its arcs. In this context, differentiable approaches constrain or regularize the optimization problem using a continuous relaxation of the acyclicity property. The computational cost of evaluating graph acyclicity is cubic on the number of nodes and significantly affects scalability. In this paper we introduce COSMO, a constraint-free continuous optimization scheme for acyclic structure learning. At the core of our method, we define a differentiable approximation of an orientation matrix parameterized by a single priority vector. Differently from previous work, our parameterization fits a smooth orientation matrix and the resulting acyclic adjacency matrix without evaluating acyclicity at any step. Despite the absence of explicit constraints, we prove that COSMO always converges to an acyclic solution. In addition to being asymptotically faster, our empirical analysis highlights how COSMO performance on graph reconstruction compares favorably with competing structure learning methods.

Document Layout analysis (DLA), is the process by which a page is parsed into meaningful elements, often using machine learning models. Typically, the quality of a model is judged using general object detection metrics such as IoU, F1 or mAP. However, these metrics are designed for images that are 2D projections of 3D space, not for the natively 2D imagery of printed media. This discrepancy can result in misleading or uninformative interpretation of model performance by the metrics. To encourage more robust, comparable, and nuanced DLA, we introduce: The Structural Semantic Unit (SSU) a relational labelling approach that shifts the focus from the physical to the semantic structure of the content; and the Coverage, Overlap, Trespass, and Excess (COTe) score, a decomposable metric for measuring page parsing quality. We demonstrate the value of these methods through case studies and by evaluating 5 common DLA models on 3 DLA datasets. We show that the COTe score is more informative than traditional metrics and reveals distinct failure modes across models, such as breaching semantic boundaries or repeatedly parsing the same region. In addition, the COTe score reduces the interpretation-performance gap by up to 76% relative to the F1. Notably, we find that the COTe's granularity robustness largely holds even without explicit SSU labelling, lowering the barriers to entry for using the system. Finally, we release an SSU labelled dataset and a Python library for applying COTe in DLA projects.

Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric A as L^TL, the problem can be cast as looking for a linear map between two sets of points in different spaces, meanwhile maintaining some data structures. The ordinal relation of the labels can be maintained via classical multidimensional scaling, a popular tool for dimension reduction in statistics. A least squares fitting term is then introduced to the cost function, which can also maintain the local data structure. The resulting model is an unconstrained problem, and can better fit the data structure. Extensive numerical results demonstrate the improvement of the new approach over the linear distance metric learning model both in speed and ranking performance.

Recent advances have discussed cell complexes as ideal learning representations. However, there is a lack of available machine learning methods suitable for learning on CW complexes. In this paper, we derive an explicit expression for the Wasserstein distance between cell complex signal distributions in terms of a Hodge-Laplacian matrix. This leads to a structurally meaningful measure to compare CW complexes and define the optimal transportation map. In order to simultaneously include both feature and structure information, we extend the Fused Gromov-Wasserstein distance to CW complexes. Finally, we introduce novel kernels over the space of probability measures on CW complexes based on the dual formulation of optimal transport.

Widely adopted evaluation metrics for sparse-view CT reconstruction--such as Structural Similarity Index Measure and Peak Signal-to-Noise Ratio--prioritize pixel-wise fidelity but often fail to capture the completeness of critical anatomical structures, particularly small or thin regions that are easily missed. To address this limitation, we propose a suite of novel anatomy-aware evaluation metrics designed to assess structural completeness across anatomical structures, including large organs, small organs, intestines, and vessels. Building on these metrics, we introduce CARE, a Completeness-Aware Reconstruction Enhancement framework that incorporates structural penalties during training to encourage anatomical preservation of significant structures. CARE is model-agnostic and can be seamlessly integrated into analytical, implicit, and generative methods. When applied to these methods, CARE substantially improves structural completeness in CT reconstructions, achieving up to +32% improvement for large organs, +22% for small organs, +40% for intestines, and +36% for vessels.

Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work, we generate a big dataset of structure-property relationships for strut-based lattices. The dataset is made available to the community which can fuel the development of methods anchored in physical principles for the fitting of fourth-order tensors. In addition, we present a higher-order GNN model trained on this dataset. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate its benefits in terms of predictive performance and reduced training requirements. Finally, we demonstrate an example application of the model to an architected material design task. The methods which we developed are applicable to fourth-order tensors beyond elasticity such as piezo-optical tensor etc.

Spatial understanding of the physical world from 2D visual inputs hinges on two complementary forms of geometric knowledge: holistic 3D structural perception and fine-grained metric scale estimation. Existing multimodal large language models (MLLMs) typically address only one facet, ingesting either depth maps or point clouds as additional model inputs, which incurs substantial computational overhead and inherits the generalization limitations of upstream prediction models. We propose GAMSI, a dual-pathway Geometry-Aware MLLM for Spatial Intelligence that takes only RGB images as input while internalizing both forms of geometric prior within a unified autoregressive backbone. Specifically, we introduce Metric-Structure Decoupled Queries (MSDQ) which employ two groups of learnable queries to respectively extract dense metric signals and sparse structural cues from the shared visual context, with a task-decoupled attention mask further preventing the two pathways from contaminating each other. Building on this, an Expert-Guided Visual Grounding (EVG) module projects the aggregated cues back to frame-level visual features and aligns them with vision foundation models, which serve purely as training-time supervision, rather than as model inputs. We further build a multi-task spatial instruction-tuning dataset (MTS) comprising 152{,}776 samples spanning 13 task types and three visual modalities, consolidated from six public datasets. Trained with a two-stage curriculum, GAMSI achieves state-of-the-art performance on seven spatial intelligence benchmarks.

We propose Equiangular Basis Vectors (EBVs) for classification tasks. In deep neural networks, models usually end with a k-way fully connected layer with softmax to handle different classification tasks. The learning objective of these methods can be summarized as mapping the learned feature representations to the samples' label space. While in metric learning approaches, the main objective is to learn a transformation function that maps training data points from the original space to a new space where similar points are closer while dissimilar points become farther apart. Different from previous methods, our EBVs generate normalized vector embeddings as "predefined classifiers" which are required to not only be with the equal status between each other, but also be as orthogonal as possible. By minimizing the spherical distance of the embedding of an input between its categorical EBV in training, the predictions can be obtained by identifying the categorical EBV with the smallest distance during inference. Various experiments on the ImageNet-1K dataset and other downstream tasks demonstrate that our method outperforms the general fully connected classifier while it does not introduce huge additional computation compared with classical metric learning methods. Our EBVs won the first place in the 2022 DIGIX Global AI Challenge, and our code is open-source and available at https://github.com/NJUST-VIPGroup/Equiangular-Basis-Vectors.

Precision and Recall are two prominent metrics of generative performance, which were proposed to separately measure the fidelity and diversity of generative models. Given their central role in comparing and improving generative models, understanding their limitations are crucially important. To that end, in this work, we identify a critical flaw in the common approximation of these metrics using k-nearest-neighbors, namely, that the very interpretations of fidelity and diversity that are assigned to Precision and Recall can fail in high dimensions, resulting in very misleading conclusions. Specifically, we empirically and theoretically show that as the number of dimensions grows, two model distributions with supports at equal point-wise distance from the support of the real distribution, can have vastly different Precision and Recall regardless of their respective distributions, hence an emergent asymmetry in high dimensions. Based on our theoretical insights, we then provide simple yet effective modifications to these metrics to construct symmetric metrics regardless of the number of dimensions. Finally, we provide experiments on real-world datasets to illustrate that the identified flaw is not merely a pathological case, and that our proposed metrics are effective in alleviating its impact.

Last-mile logistics (LML) is characterized by high fragmentation, yet existing research treats this as an exogenous constraint rather than a quantifiable and optimizable system property. This paper introduces a framework for measuring LML complexity using structural entropy, derived from Boltzmann's statistical mechanics. Unlike traditional KPIs such as distance or cost, structural entropy quantifies the cardinality of the configuration space, providing a diagnostic of inherent system disorder. We establish a formal duality with Shannon entropy, linking absolute complexity burden to distributional balance. We apply our entropy framework to 6,112 Amazon last-mile routes across five U.S. cities. Current operations exhibit persistently high normalized entropy, indicating near-maximal fragmentation. A stable non-linear scaling relationship between entropy and route distance validates the metric as a predictive indicator of operational difficulty. To evaluate spatial consolidation, we develop a system-wide entropy measure accounting for all movements by both carriers and customers. We establish a theoretical conservation principle: under idealized conditions, spatial consolidation merely redistributes entropy from carrier to customer. Both idealizing conditions are violated in practice, thereby increasing total system entropy. Our system-wide measure reveals that spatial consolidation reduces carrier entropy by up to 40% under aggressive adoption but increases total system entropy by activating customer collection trips, though trip chaining can diminish this effect. Temporal consolidation, by contrast, genuinely reduces entropy by decreasing delivery events without creating new movements. By formalizing fragmentation as a measurable structural property, this research provides a new lens for network design, consolidation policy, and evaluation last-mile system performance.

Large language models (LLMs) have recently shown strong potential in modeling relational structures. However, existing approaches remain fundamentally graph-centric: they focus on processing pairwise graph structures into tokens that LLMs can understand. In contrast, many real-world relational patterns do not naturally conform to the pairwise-edge assumption, and are better modeled as high-order associations in hypergraphs. For hypergraph structures, existing methods often fail to preserve the native semantics that multiple objects are jointly connected by the same high-order relation, limiting their ability to exploit complex structures. To address this limitation, we put forth the "Hypergraph as Language" perspective and propose Hyper-Align, a hypergraph-native alignment framework for large language models. Hyper-Align compiles the query-object-centered hypergraph context into hypergraph tokens directly consumable by a base LLM. Specifically, we introduce Hypergraph Incidence Detail Template with Overview (HIDT-O), which serializes high-order association structures into a fixed-shape hybrid template combining local incidence details and overview-level summaries. We then design a Hypergraph Incidence Projector (HIP), which maps native high-order incidence structures into the LLM token space through explicit semantic-structural decoupling and bidirectional message passing between vertices and hyperedges. We further define a concrete Hypergraph-as-Language input protocol, which jointly feeds hypergraph tokens and textual prompts into a frozen base LLM, supporting both vertex-level and hyperedge-level tasks under a unified question-answering paradigm. To systematically evaluate different methods in hypergraph structural modeling, we introduce HyperAlign-Bench. Extensive experiments show that Hyper-Align significantly outperforms existing methods across in-domain and zero-shot evaluations.

Clustering aims to group unlabelled samples based on their similarities. It has become a significant tool for the analysis of high-dimensional data. However, most of the clustering methods merely generate pseudo labels and thus are unable to simultaneously present the similarities between different clusters and outliers. This paper proposes a new framework called High-dimensional Clustering onto Hamiltonian Cycle (HCHC) to solve the above problems. First, HCHC combines global structure with local structure in one objective function for deep clustering, improving the labels as relative probabilities, to mine the similarities between different clusters while keeping the local structure in each cluster. Then, the anchors of different clusters are sorted on the optimal Hamiltonian cycle generated by the cluster similarities and mapped on the circumference of a circle. Finally, a sample with a higher probability of a cluster will be mapped closer to the corresponding anchor. In this way, our framework allows us to appreciate three aspects visually and simultaneously - clusters (formed by samples with high probabilities), cluster similarities (represented as circular distances), and outliers (recognized as dots far away from all clusters). The experiments illustrate the superiority of HCHC.

Uniformity plays a crucial role in the assessment of learned representations, contributing to a deeper comprehension of self-supervised learning. The seminal work by Wang2020UnderstandingCR introduced a uniformity metric that quantitatively measures the collapse degree of learned representations. Directly optimizing this metric together with alignment proves to be effective in preventing constant collapse. However, we present both theoretical and empirical evidence revealing that this metric lacks sensitivity to dimensional collapse, highlighting its limitations. To address this limitation and design a more effective uniformity metric, this paper identifies five fundamental properties, some of which the existing uniformity metric fails to meet. We subsequently introduce a novel uniformity metric that satisfies all of these desiderata and exhibits sensitivity to dimensional collapse. When applied as an auxiliary loss in various established self-supervised methods, our proposed uniformity metric consistently enhances their performance in downstream tasks.Our code was released at https://github.com/sunset-clouds/WassersteinUniformityMetric.

Representational similarity analysis and related methods compare the internal geometries of neural networks, but they measure only alignment between spaces, leaving a blind spot -- whether a representation's structure is reliably recoverable, not merely similar. We introduce geometric stability, a distinct axis, and Shesha, a metric that quantifies it from a single representation by correlating dissimilarity matrices built from complementary random halves of the feature dimensions. Unlike CKA and Procrustes distance, Shesha is provably non-invariant to orthogonal rotations of the feature basis. This is by design: the basis is privileged for learned models, since probes, patching, and steering act on coordinates, and a rotation-invariant metric cannot see whether the targeted structure survives them. A double dissociation isolates the mechanism -- removing the top principal component collapses CKA while Shesha holds, whereas rotating a representation into its eigenbasis, which preserves the spectrum and CKA exactly, collapses Shesha. Across 2,463 encoder configurations in seven domains, the metrics are redundant under geometry-preserving transforms and anti-correlate under compression (ρ=-0.47). Across 170 vision models spanning 6 clean and 38 corruption-shifted datasets, DINOv2 ranks first or second in transferability on three of six clean datasets yet bottom-quartile in stability on five, an isolated dissociation rather than a trade-off.