论文库

High-granularity topic modelling extracts hundreds of niche topics from a corpus, yet this regime is rarely studied and is more commonly framed as a failure mode: "over-clustering," in which coherent themes fragment into redundant subtopics. We argue that this framing conflates genuine redundancy with topics that are semantically similar but meaningfully distinct, and that the central challenge in high-granularity modelling is separating the two. Recent post-hoc refinement methods address topic redundancy through either embedding-based similarity thresholding or LLM-guided merging. We show that neither suffices in high-granularity settings and propose embedding-gated iterative merge (EGIM), a hybrid approach that iteratively generates context-rich topic representations, uses embedding similarity to propose candidate merges across the topic space, then applies LLM judgement to accept only genuinely redundant pairs while preserving niche distinctions. Across two patent corpora and one legal corpus, LLM judgement rejects 83% of embedding-identified candidates as non-redundant. EGIM improves discriminability on merged topics by 25-55% over a prior iterative LLM baseline while better preserving the original topic distribution.

The ability of deep neural networks to learn hierarchical features is widely regarded as a key mechanism underlying their success in high-dimensional learning. Existing theory partially supports this view by establishing approximation rates based on parameter counts and sample complexity guarantees for compositional models without incurring the curse of dimensionality (CoD). To study overparameterized regimes, where the number of parameters exceeds the sample size, we develop a framework that measures complexity via the parameter norm. Within this approach, we establish approximation rates and excess risk bounds for learning sparse compositional functions whose compositional structure is represented by directed acyclic graphs (DAGs), using Frobenius norm-constrained deep neural networks. Our results have broad applicability since every function that is efficiently Turing computable admits sparse compositional representations. In particular, we cover a range of representative models, including multi-index models, binary tree structures, and general compositional architectures. The rates we derive show that deep networks can exploit the compositional structure of the target functions, effectively avoiding the CoD through hierarchical representations.

Given a graph $G$ and an integer $k$, the reconfiguration graph $\mathcal{R}_{k}(G)$ has the proper $k$-colourings of $G$ for vertices, two of which are adjacent if and only if they differ on precisely one vertex of $G$. In $2022$, Cambie, Cranston and the author proved that the diameter of $\mathcal{R}_{Δ+2}(G)$ is at most $n+2μ$, and put forth a collection of conjectures that in its strongest and most beautiful form would imply that the diameter of $\mathcal{R}_{Δ+2}(G)$ is precisely equal to $n + μ$, for every graph $G$ with $n$ vertices, matching number $μ$ and maximum degree $Δ$. Here we disprove most of those conjectures. Our constructions have reconfiguration diameter at least $n+\frac{3}{2}μ-2$. We also provide counterexamples that are $Δ$-regular, we show that every graph has reconfiguration diameter at least $n+\frac{1}{2} μ$, and we advertise an extension to hypergraphs. It is now much more mysterious how the diameter behaves, so we propose a number of open problems.

Chess board recognition is the task of mapping the image of a chess board to the information of which piece is on which square. So far this task has two established benchmarks: ChessCog is synthetic, and ChessReD comes from smartphone pictures of a single chess board setup. We introduce ChessQueries, a new method combining a ViT encoder with a DETR-style decoder, which outperforms existing methods. On the ChessReD benchmark, we improve the state of the art from 15.3% to 99.2%, and demonstrate strong capabilities on out-of-distribution datasets. Our method saturates the task on the two datasets, with an average 0.01 wrong squares per board (vs. SotA: 3.4 / 0.15 respectively). We also share a new, harder public dataset, parsed from broadcasted top-level chess tournaments. Code, model weights and the SLCC data have been released.

Large language models (LLMs) can supply autonomous systems with plans, predictions, and judgments, but these contributions are sometimes wrong. This review asks how a system can maximize an LLM's utility while managing its fallibility. Our answer is to adapt the system's reliance on the LLM as evidence about the LLM's performance accumulates. Systems built from imperfect components, such as noisy sensors and faulty software, have long worked in this way, and the classical methods they use can be applied to LLM-based systems as well. A system can change its reliance on an LLM in several ways, depending on the LLM's role and on the other components in the system. Each change needs an estimate of the LLM's reliability, and the LLM's role and the kind of contribution it makes determine what to estimate. Classical methods from decision theory, estimation, and online learning then turn these estimates into reliance decisions. These decisions can reduce how often LLM errors affect the system. However, some errors matter even when they are rare. An independently verified mechanism can prevent such errors from being executed. Without one, adapting reliance using reliability estimates can still keep their risk within a bound. Studies on adapting reliance on LLMs are emerging but limited, and the reviewed comparisons suggest that adapting reliance can improve system performance.

Layer-local self-supervised objectives remove the backward pass between layers, but almost all still compute their loss over a batch of samples and are therefore local in space but not in time. We introduce Temporal Regularized Learning (TeReL), a spatially and temporally local learning rule for self-supervised representation learning from sequential input streams. The key idea is to instantiate a VICReg-style objective with temporally adjacent positives and non-differentiated running population statistics, yielding a per-neuron online loss with bounded state. The objective is a soft form of Slow Feature Analysis, and its gradient is a Hebbian update of the feedforward weights and an anti-Hebbian update of one lateral matrix per layer. The aim of the experiments is to show that the rule works in a small network, not to compete with backpropagation. On a class-chunked MNIST stream, a two-layer fully connected network trained with batch size one outperforms random features (96.48% versus 95.09% linear-probe accuracy) and classical SFA, and a variant that relaxes both locality constraints is comparable to supervised backpropagation. Because training and inference use the same computation, the network can keep learning from unlabeled data during inference without loss of accuracy.

Federated learning (FL) is a promising framework for learning from distributed data while maintaining privacy. The development of efficient FL algorithms encounters various challenges, including heterogeneous data and systems, limited communication capacities, and constrained local computational resources. Recently developed FedADMM methods show great resilience to both data and system heterogeneity. However, they still suffer from performance deterioration if the hyperparameters are not carefully tuned. To address this issue, we propose an inexact and self-adaptive FedADMM algorithm, termed FedADMM-InSa. First, we design an inexactness criterion for the clients' local updates to eliminate the need for empirically setting the local training accuracy. This inexactness criterion can be assessed by each client independently based on its unique condition, thereby reducing the local computational cost and mitigating the undesirable straggle effect. The convergence of the resulting inexact ADMM is proved under the assumption of strongly convex loss functions. Additionally, we present a self-adaptive scheme that dynamically adjusts each client's penalty parameter, enhancing algorithm robustness by mitigating the need for empirical penalty parameter choices for each client. Extensive numerical experiments on both synthetic and real-world datasets are conducted. As validated by some numerical tests, our proposed algorithm can reduce the clients' local computational load significantly and also accelerate the learning process compared to the vanilla FedADMM. The source code is available at https://github.com/DCN-FAU-AvH/FedADMM-InSa.

Prior research has shown that providing feedback on group dynamics can improve the quality of small-group conversations. However, publicly delivered feedback that targets specific individuals may reduce social acceptability due to negative experiences such as social pressure, embarrassment, and resistance. This work investigates how public feedback can be designed to remain socially acceptable while maintaining its effectiveness in XR-based small-group conversations. Informed by social science and HCI literature, we identified three design strategies (incorporate humor, reduce social attention, and use indirectness) and proposed a set of metaphor- and agent-based 3D feedback probes. We then conducted a two-phase study: (1) an online survey with 50 participants to examine how such feedback designs are perceived under public and private delivery, and (2) follow-up interviews with 14 participants who completed the survey to better understand their interpretations and elicit additional insights. Results show that metaphor- and agent-based feedback can reduce social discomfort while maintaining effectiveness. Interview findings further highlighted the role of three strategies in making feedback easier to accept, while requiring careful balance. We also discussed design implications for creating socially acceptable 3D feedback to support inclusive small-group conversations in XR.

Artificial intelligence (AI) is changing how biological research is done. Biological foundation models trained on millions of nucleotides, protein, and single-cell measurements predict protein structures, mutation effects, and cellular responses to genetic perturbations. Agentic systems, AI assistants built on large language models, can run multistep analyses from plain-language requests and increasingly call foundation models as tools. Yet it is often unclear when these models' outputs can be trusted. We frame this as a model's knowledge boundary: the range of inputs, tasks, and conditions over which its outputs are reliable. This review explains how foundation models are built and proposes that five design elements (data, architecture, training scheme, evaluation scheme, and post-analysis) define this boundary. We examine evidence on where current models succeed or fail and present standardized descriptions of model limits so that researchers, and the agents acting for them, can use these tools reliably.

Synthesizing high-frequency eye movements requires preserving long-range temporal dependencies and subject-specific oculomotor dynamics. However, methods based on generative adversarial networks (GANs) and variational autoencoders (VAEs) can struggle to preserve these characteristics simultaneously. We introduce DiffSSMEye, a conditional denoising diffusion probabilistic model with bidirectional Structured State Space Sequence (S4) layers for generating five-second gaze-velocity sequences at 1,000 Hz. Generation is conditioned on a coarse gaze reference, user identity, and task, where identity and task embeddings are incorporated through feature-wise linear modulation. Identity-preservation, multi-resolution spectral, and integrated-drift losses complement noise prediction to constrain biometric consistency, frequency structure, and displacement error. Subject-disjoint evaluation on GazeBase across seven tasks yields mean real--synthetic embedding cosine similarities of 0.91--0.95. DiffSSMEye also achieves the lowest median spatial errors among these baselines for horizontal and random saccade tasks. These results demonstrate improved spatial accuracy and biometric feature consistency for subject-specific gaze synthesis.

In July 2026, the European Commission (EC) set out the anonymization measures Alphabet must implement to share Google Search data with competing search engines under Article 6(11) of the Digital Markets Act. As the first concrete illustration of how the EC operationalizes anonymization under the EU digital rulebook, this methodology could become a regulatory benchmark. In this paper, we show why it should not. We critically review the anonymization measures proposed by the EC, from the characterization of residual risk to the suppression thresholds and the reliance on contractual safeguards. For each of those issues, we highlight significant conceptual flaws, and, where applicable, we illustrate these flaws with empirical observations from real Google Search data provided by Alphabet and protected under the EC's measures. Importantly, we present examples of low-effort reidentification, record linkage, and confidential attribute inference achieved through straightforward and automatable attack patterns. Our findings show that the approach of the EC relies on unjustified heuristics rather than formal privacy guarantees, underestimates the risks inherent in free-text search queries, and sacrifices data utility without achieving meaningful protection. We also demonstrate that the proposed measures do not meet any of the three anonymization criteria established by the European Data Protection Board (EDPB): no record isolation, no linkage, and no inference. Practitioners and regulators are therefore cautioned against treating these measures as a sound anonymization practice.

Decision making often requires balancing exploitation of familiar options with exploration of uncertain alternatives. One strategy for exploration is random exploration, in which choices become more variable and less tied to the option that currently appears best. However, it remains unclear whether this variability reflects genuine stochasticity or instead a deterministic structure that traditional cognitive models fail to capture. We examined this question using the Horizon Task in an aggregated dataset of 1,392 participants completing over 1,270,695 trials. In this task, exploration becomes more valuable when participants have more future choices, and choice variability increases under longer horizons. We tested whether more expressive neural network models could recover deterministic structure from this additional variability. Although neural networks provided better overall fits to behavior than the traditional model, long-horizon choices remained consistently less predictable than short-horizon choices. These findings show that limited model expressiveness cannot fully account for the increased variability associated with random exploration, suggesting random exploration truly is substantially random.

Large language model (LLM) agents use external skills to reuse task procedures and experience with tools. General-purpose skills describe shared execution procedures, while specific tool choices, operating practices, and output requirements vary across users. In long-horizon tasks, subgoals, available inputs, and environmental states change as execution progresses. Agents must select currently applicable skills from an expanding skill pool and prepare candidates for subsequent steps. We propose Skill Adapter, which enables personalized modification and online routing of general-purpose skills. The system distills local adjustments from user requirements and execution feedback and stores them as Adapters linked to general-purpose skills. The routing agent selects general-purpose skills and applicable Adapters based on the current subtask, execution progress, and environmental feedback, incrementally maintaining a task-level online skill library that the main LLM reads on demand. The system preloads candidates for subsequent nodes and rechecks their applicability once actual inputs are determined. Reinforcement learning optimizes the two types of decisions using modification gains and routing outcomes, respectively. We evaluate Skill Adapter on ALFWorld, WebShop, and SkillsBench. Compared with SkillRL, it improves task success rates by an average of 11.43 percentage points and reduces mean execution time on all three benchmarks. Skill Adapter retains its performance advantage when the skill pool grows to 1,000 skills.

Federated Learning (FL) is a distributed learning paradigm that enables multiple clients to collaborate on building a machine learning model without sharing their private data. Although FL is considered privacy-preserved by design, recent data reconstruction attacks demonstrate that an attacker can recover clients' training data based on the parameters shared in FL. However, most existing methods fail to attack the most widely used horizontal Federated Averaging (FedAvg) scenario, where clients share model parameters after multiple local training steps. To tackle this issue, we propose an interpolation-based approximation method, which makes attacking FedAvg scenarios feasible by generating the intermediate model updates of the clients' local training processes. Then, we design a layer-wise weighted loss function to improve the data quality of reconstruction. We assign different weights to model updates in different layers concerning the neural network structure, with the weights tuned by Bayesian optimization. Finally, experimental results validate the superiority of our proposed approximate and weighted attack (AWA) method over the other state-of-the-art methods, as demonstrated by the substantial improvement in different evaluation metrics for image data reconstructions. The source code is available at https://github.com/DCN-FAU-AvH/FL-AWA-attack.

Nonlinear time-optimal model predictive control (TOMPC) enables highly performant control of constrained systems, but its computational cost prohibits real-time use on fast dynamical systems. Neural network imitation of the TOMPC control law can reduce online computational costs, yet existing work mostly targets quadratic cost formulations in simulation and addresses the challenges of neural controllers in isolation. This work imitates a long-horizon nonconvex TOMPC with hard terminal constraints, whose high computational cost limits training-data generation. We present (i) \emph{self-informed sampling (SIFS)}, a data-efficient expert-sampling strategy that uses a learned time-to-go to query the expert only where the policy deviates from time-optimal behavior, (ii) a complete training and control architecture that jointly addresses dataset correlation, suboptimal expert labels, covariate shift, constraint satisfaction and model mismatch, and (iii) real-world validation on a Furuta pendulum. SIFS matches standard dataset aggregation performance in roughly one-third of the training time and with less than half the training data. The resulting controller matches the region of attraction of the expert TOMPC while raising the control frequency from 1.4~Hz to 1~kHz. On hardware, the controller swings up and stabilizes the pendulum along trajectories closely matching the expert TOMPC solution.

Robot agents built on vision-language models depend on both the planner and its harness: the tools, feedback, memory, and recovery logic around it. Can improvements to a large teacher's harness be carried into a compact agent with lower inference compute cost? We present TinyAstral, a two-stage approach. We first freeze an open-weight teacher and improve its harness through recursive self-improvement (RSI): frontier LLM agents read the teacher's trajectories and propose harness edits, and each edit is accepted only if it passes a paired statistical test. We then freeze the final harness, collect teacher trajectories with reasoning and failure recovery, and distill a small student that replaces the teacher in the same harness. On RoboTwin, harness evolution raises the teacher's success from 33.4% to 63.6%; the final 4B student reaches 62.8%. Across four harness versions, distilled 4B students score close to their corresponding teachers, and later versions yield stronger students, showing that harness evolution gains carry into compact models. The harness gains also transfer to other frozen planners without retraining. On identical episodes, the final 4B student outperforms open 4B agents, the open 27B harness-RSI model SenseNova-RoboRSI, and our own teacher model placed in three competitors' harnesses. It stays close to its teacher on all three training benchmarks, and on three benchmarks never used for RSI or training it scores close to a 552B planner running the same harness. On the measured deployment episodes, it uses about one fifth of its teacher's accelerator time. Project page: https://garfield-kh.github.io/TinyAstral/

Crypto agility maturity models aim to support organizations in preparing for cryptographic transitions, such as migrating to post-quantum cryptography. Recognizing the importance of measurable maturity, NIST references several such models in its guidance. Given NIST's influence on cybersecurity practice, these models may shape organizational planning and governance mechanisms. However, their design quality has not been systematically evaluated. In this work, we assess three industry-driven maturity models against established design principles. Our analysis reveals recurring weaknesses, particularly the lack of measurable, reproducible assessment criteria and limited prescriptive guidance for improving crypto agility. At the same time, we highlight individual strengths that can assist practitioners in choosing among the models and derive concrete recommendations for strengthening future crypto agility maturity models.

Postpartum mental distress affects roughly one in five mothers in low- and lower-middle-income countries, yet recognition and support remain limited where formal mental-health care is scarce, and family relationships govern health decisions. We report a five-month interview study with 20 mothers in urban, urban slum, and rural Bangladesh who had given birth within the previous two years. Mothers encountered the concept of postpartum depression incidentally, through Facebook and YouTube recommendations rather than deliberate search or clinical guidance, and then used these platforms for private sensemaking without disclosing. Recognition, however, rarely traveled beyond the self: mothers could identify their distress while families dismissed it, leaving them with knowledge but no authority to act. Participants sought validation as a precondition for support and described recovery as relational rather than clinical or digital. We argue that postpartum technologies should engage partners, families, and community health workers rather than placing recognition solely on mothers.

Recent advances in neural density estimation have enabled amortized Bayesian inference for complex stochastic simulators. However, these methods rely on simulators accurately reflecting the true data-generating process and can degrade significantly under model misspecification. We consider the setting where multiple unlabeled observations are available and introduce robust variational neural posterior estimation (RVNP), an amortized Bayesian inference method that uses an importance-weighted autoencoder to jointly learn a misspecification-robust posterior proxy and an explicit error model that captures the simulation-to-reality gap. Our results show that RVNP can recover robust posterior inference in a data-driven and interpretable manner, outperforming previous methods on multiple metrics across misspecified benchmarks.

Coding agents have demonstrated strong capabilities in software development, yet their ability to tackle long-horizon engineering tasks governed by physical constraints remains less understood. We study this question through analog circuit layout, which demands domain knowledge, geometric reasoning, and iterative interaction with design and verification tools. We introduce \textbf{AnalogLayoutWorld}, an open-source agent benchmark with 40 expert-reviewed tasks for end-to-end layout generation from fixed transistor-level netlists. It combines an integrated design environment with independent physical and post-layout electrical verification, as well as objective layout quality metrics co-designed with analog layout experts. Across 13 model--harness configurations, 91.1\% of attempts produce GDS layouts, but only 23.0\% satisfy the benchmark's acceptance criteria. We also evaluate Novara, an internally developed agent system, which achieves the highest reported aggregate score. Our analysis links performance differences to test-time scaling under fixed budgets, suggesting that reasoning efficiency and effective use of verification feedback help sustain design quality as task complexity grows.

Federated learning is an emerging distributed paradigm that addresses the challenges posed by heterogeneous, privacy-sensitive data. It enables multiple clients to train a model collaboratively by aggregating their local updates at a server. However, conventional aggregation schemes typically use fixed weights that fail to reflect unequal and time-varying client contributions, leading to biased and unstable learning. To improve fairness and stability, we propose the Trajectory Shapley Value (TSV), a contribution metric that evaluates how each client influences the optimization trajectory of the global model using a validation-based, temporally consistent utility. Building on TSV, we design FedTSV, an adaptive aggregation method that converts per-round evaluations into dynamic client weights, allowing the server to respond to heterogeneous and adversarial participation in real time. Experiments on benchmark datasets show that FedTSV accelerates convergence, improves robustness, and yields more equitable contribution assessments, thereby providing a principled foundation for fairness-aware federated optimization. The source code is available at https://github.com/DCN-FAU-AvH/FedTSV.

Educational simulations are a well-established pedagogical technique that gives learners opportunities to apply knowledge, respond to challenges, and reflect on their performance. High-quality simulations, however, are difficult to build, requiring instructor input, scenario design, character development, scaffolding, technical implementation, and repeated revision. This paper presents Primer, an open-source, LLM-agnostic AI-supported system that helps educators create adaptive educational simulations. Educators contribute their knowledge of the subject, lesson, and students, while generative AI produces responsive variations of practice for students. Primer uses a multi-agent system centered around executing educator's instructional intent through the entire learning experience. We hope that by releasing Primer as an open-source system, including its prompts and GitHub repository, we provide a foundation for development and research on educator-in-the-loop AI authoring, multi-agent educational workflows, and simulation-based pedagogy. Further, by allowing the use of various AI models, including local and open source models, we provide the opportunity for implementation under varied governance regimes. Primer points toward a model of educational AI in which instructors can create locally grounded practice opportunities based on their own materials, goals, examples, and knowledge of students.

Vision transformers (ViTs) serve as the backbone for countless vision tasks, including dense prediction tasks, such as segmentation and depth estimation, even though the quadratic complexity of self-attention severely limits feature resolution and induces spatial artifacts. In this work, we introduce ElasticDino, a lightweight adapter which produces high-resolution feature maps, adhering to the fine details of the input image. As a key insight, we observe the consistency of artifacts across channels, and simultaneously resolve them to match the input image structure. Using a slim architecture based on spatial deformations, ElasticDino produces pixel-aligned, high-resolution feature maps efficiently. Leveraging deformations allows strictly preserving sharp semantics, and thereby avoiding the smoothness biases inherent to alternative approaches. Due to the absence of ground truth, we employ pixel-level semantic segmentation and depth estimation with linear heads to predict a set of downstream dense tasks, guiding the deformation process without leaking task-specific semantics into the model. We demonstrate superior accuracy over current methods on a range of popular dense task benchmarks, with better computational performance.

While Gaussian Splatting-based Feature Fields (GSFFs) have shown promise for visual localization, this paper highlights that photometrically optimized GSFFs are inherently not suitable for 2D-3D matching. The volumetric extent of each Gaussian induces many-to-one pixel-to-point mappings that destabilize PnP-based pose estimation, while photometric optimization gives rise to superfluous Gaussians devoid of multi-view consistency. To address these issues, we propose SplitGS-Loc, a GSFFs construction framework for localization, which disambiguates 2D-3D correspondences by exploiting Gaussian attributes. Our key design, Mixture-of-Gaussians-based splitting, decomposes each Gaussian into smaller Gaussians, replacing ambiguous many-to-one with precise one-to-one correspondences. In parallel, we exploit composition weights from GS rasterization to select Gaussians that significantly and consistently contribute across multiple views and aggregate discriminative features through strong pixel-Gaussian associations. The resulting compact yet discriminative feature fields enable stable PnP convergence, achieving competitive performance on localization benchmarks. Extensive experiments validate that SplitGS-Loc extends the utility of photometric GSFFs to accurate and efficient localization by exploiting Gaussian attributes, without per-scene training for feature fields or iterative pose refinement. The code is available at: https://github.com/misoleekr/SplitGS-Loc.

Even though many semantic segmentation methods exist that are able to perform well on many medical datasets, they are often not designed for direct use in clinical practice. The two main concerns are generalization to unseen data with a different visual appearance, e.g., images acquired using a different scanner, and efficiency in terms of computation time and required Graphics Processing Unit (GPU) memory. In this work, we employ a multi-organ segmentation model based on the SpatialConfiguration-Net (SCN), which integrates prior knowledge of the spatial configuration among the labelled organs to resolve spurious responses in the network outputs. Furthermore, we modified the architecture of the segmentation model to reduce its memory footprint as much as possible without drastically impacting the quality of the predictions. Lastly, we implemented a minimal inference script for which we optimized both execution time and required GPU memory.

Fresh-market blueberries require selective, gentle picking, which is labor-intensive and expensive. Over-the-row machine harvesters are fast but non-selective, bruising mixed-ripeness fruit and limiting yield to the processing market. Selective robotic harvesters typically target individual fruits rather than fruit clusters, which limits harvesting efficiency for small, densely clustered blueberries. This paper presents CLASP, a Cluster-Level Autonomous Selective Picking robot with a Soft Active Rolling-Band Gripper (SARB-Gripper). Two compliant bands envelop the cluster and roll against the fruit, drawing mature berries off in sequence, while closed-loop regulation of the pulling force keeps the applied load below the immature detachment threshold. A global-to-local perception pipeline pairs an eye-to-hand camera for global cluster detection and target selection with an eye-in-hand camera for local localization and cluster orientation estimation. Field measurements confirm a clear detachment-force separation between mature and immature fruit, and the SARB-Gripper reproduces a commanded pulling force to within \SI{3.7}{\percent}, enabling selective harvesting at the cluster level. In end-to-end field trials, CLASP autonomously grasped 23 of 25 presented clusters (\SI{92}{\percent}). With the component cost of approximately \$3326 per unit, CLASP offers a scalable approach to selective cluster-level harvesting for fresh-market blueberries.

We present a polynomial-time approximation scheme (PTAS) for all Boolean arity-two maximum constraint satisfaction problems (Boolean Max-2-CSP) where the constraint graph is either interval or has bounded rank-width. This class of problems includes, for example, Max-Cut, Max-DiCut, Max-2-Lin(2), and Max-2-SAT. In particular, this settles the approximability of Max-Cut on interval graphs. To achieve these results, we show the following. 1. For any $\varepsilon > 0$, there is an $n^{\mathcal O(r \varepsilon^{-2})}$-time $(1 - \varepsilon$)-approximation for Boolean Max-2-CSP on graphs of rank-width at most $r$. 2. There is a polynomial-time algorithm that, for any interval graph $G = (V, E)$ and $\varepsilon > 0$, finds a subgraph $H = (V, F)$ of $G$ such that $|F| \geq (1 - \varepsilon) |E|$ and $H$ has rank-width at most $\operatorname{poly}(\varepsilon^{-1})$. Our techniques additionally extend to all bounded-alphabet arity-two max CSPs.

We compute the asymptotic dimension of spaces of multiparameter persistence modules of bounded presentation under the interleaving distance. The $d$-parameter modules with at most $n$ generators and $m$ relations have asymptotic dimension, and Assouad-Nagata dimension, exactly $d(n+m)$, the number of coordinates of their generator and relation grades, over every field; for two parameters this is $2(n+m)$. The space has continuous moduli, already for two parameters and $n,m\ge2$: over an infinite field it contains, at every scale, infinite uniformly separated families of pairwise non-isomorphic modules with one fibered barcode, so it is not doubling even at a fixed fibered barcode; already for $m\ge1$ it is not coarsely equivalent to a proper metric space. The proof is an induction on the number of distinct grade coordinates: an interleaving small compared with the gaps between these coordinates moves each of them by at most twice its size and preserves the induced grid representation, so the continuous moduli are invisible at large scale. Each class of modules at finite distance therefore embeds coarsely into Hilbert space; for $n,m\ge2$ over an uncountable field, the classes that contain these families admit no such embedding into a separable Hilbert space. Under the two-parameter matching distance $2(n+m)$ is a lower bound, attained for one generator and for two generators with at most one relation; on a finite net of $S$ slices the asymptotic dimension is at most $2nS$.