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arXiv

WorldMark: A Plug-and-Play World Knowledge Interface for Cross-Host Language Model Watermarking

Song Xiao, Yuqi Yuan, Yanshuo Zhang, Kejun Zhang

Watermarking traces the provenance of text produced by large language models by embedding statistically detectable signals during decoding. Existing schemes fall into logits-based, sampling-based, entropy-aware, and adaptive-strength families, yet all of them place watermark signals according to local token statistics. In the open-ended text-generation settings evaluated in this work, local statistics may provide insufficient guidance for placing robust watermark signals. We introduce WorldMark, a plug-and-play interface that uses World Knowledge Memory (WKM) to organize semantic and episodic knowledge in a memory graph, converts the retrieved knowledge into a token-level knowledge saliency score, and adjusts the strength of a host watermark through Asymmetric Knowledge Modulation (AKM). WorldMark requires no backbone retraining and introduces no additional detector-side model or parameter. On the primary C4 evaluation, the complete WorldMark interface improves clean and attacked detection across three adaptive-strength host variants while slightly reducing perplexity. Additional pilot experiments on C4 and OpenGen show that direct memory conditioning transfers across multiple watermark families but can be unstable without saliency-aware modulation. WorldMark requires no additional detector-side model or parameter and introduces negligible overhead under the primary protocol.

arXiv

Stochasticity Is Not the Hard Part: Reduction and Complexity in Instructional Sequencing over Prerequisite DAGs

Zonglin Han, Yichen Chen, Jiawen Jiang, Tongan Shi, Kristian A. Stevens

When a student must learn concepts connected by prerequisite dependencies, when does the order of instruction matter, and what does it cost to find the best one? We study instructional sequencing as a stochastic shortest-path problem in which attempting a concept succeeds with a state-dependent probability and failure leaves the learner state unchanged. We first prove that this stochasticity can be eliminated exactly: the problem collapses to a deterministic shortest-path problem on the lattice of prerequisite order ideals, preserving optimal values and actions. The collapse removes stochastic complexity but not combinatorial complexity: optimal sequencing remains NP-hard -- via reduction from feedback arc set in tournaments -- even with no prerequisite edges, unit costs, uniform binary nonnegative transfer, and success probabilities at least $1/2$. Hardness is not uniform: when realizable transfer preferences remain jointly acyclic with the prerequisites, any topological order of the residual joint graph is optimal, and fixed prerequisite width yields polynomial-time exact dynamic programming. A computable diagnostic, $mΔ$, bounds the value of sequencing before optimization. On 70,893 interactions from an introductory CS course, the diagnostic certifies a doubly easy regime -- little value to optimize and little space to search -- while constructed transfer instances realize the challenging regime, where myopic sequencing suffers large regret yet exact A* with a consistent heuristic expands only linearly many states on that family.

arXiv

The ethics of artificial intelligence in the life sciences: Universality, cultural diversity and an architecture of care

Jean-Pierre Changeux, Gustavo Deco, Morten L. Kringelbach

The life sciences and health research have started to benefit from artificial intelligence, which raises ethical concerns that are real but, we argue, not special. Any science should be governed by values that rest on how the human brain is built and socialised rather than anything distinct to artificial intelligence. Importantly, the human brain has a different, much less costly computational architecture than these machines. This is achieved through the orchestration of a global neuronal workspace, and through reward best described not as a quantity to be maximised but as a continuous cycle of wanting, liking and satiety. As such, this creates the deep tension running through the ethics of the human person, between the universality of ethical judgement and the diversity of morals. The brain networks of the global workspace and emotion are universally shared, but the diversity of content is shaped by epigenetic appropriation of the particulars of the physical, social and cultural world, which makes every person unique. Still, if we were to build machines on these principles rather than the present unaffordable reward maximisers, the question of their governance would change from restraint to upbringing. We set out the institutions such a future would require, together with the questions that remain open.

arXiv

Negotiating Risk Boundaries in AI for Policing Through Mixed-Stakeholder Deliberation

Mackenzie Jorgensen, Jo Reilly, Alex Sutherland, Miri Zilka

AI tools are being increasingly adopted in policing in the UK and worldwide. Racial bias is a known and well-documented risk, yet representatives of affected communities are rarely included in decisions about AI adoption. We present results from a mixed-stakeholder deliberation workshop bringing together 30 community representatives, police officers, and academics to assess the risks of 13 AI use cases in policing, with an explicit focus on racial bias. We found that participants were broadly open to AI adoption, rejecting only three use cases outright, most notably recidivism risk assessment, where objections targeted the premise rather than the implementation. Our analysis reveals that foregrounding racial equity did not narrow the deliberation. Instead, discussions gravitated toward a fundamental set of questions: does this tool actually work, will it deliver genuine benefit, and will that benefit extend to everyone? This integrated reasoning, reminiscent of the curb-cut effect in inclusive design, highlights the benefit of incorporating the racial bias lens into the risk-benefit analysis of AI use cases from the outset.

arXiv

Evaluating and Improving Pedagogical Fit in LLM-Based AI Tutors with the Pedagogical Suitability Index

Benjamin Barlog, Hudson Craig, Zedong Peng

Large language models (LLMs) are increasingly used as AI tutors, but a correct answer is not always a pedagogically appropriate one. In classroom learning, effective help depends not only on correctness, but also on whether a response matches the learner's current foundation, the course sequence, and the timing of concept introduction. Existing evaluations focus mainly on answer quality, leaving this instructional fit under-measured. We present the Pedagogical Suitability Index (PSI), a composite metric of six theory-informed sub-scores that evaluates how well LLM-generated tutoring responses align with learner readiness and curricular progression, and we further use PSI as a structured feedback signal for response improvement. We evaluate four LLM tutors (ChatGPT, Gemini, Gemma4, and Qwen3) across 240 scenario-based evaluations using paired standard and defective prompts, then apply a PSI-guided regeneration protocol to 62 weak-performing cases. Baseline differences across the four tested models were modest overall (PSI range: 0.557 to 0.638), and open-weight and closed models did not exhibit a clear separation in pedagogical fit. Under the tested prompt perturbations, overall PSI remained largely stable (Delta = -0.002), though sub-score trade-offs emerged. More importantly, PSI-guided feedback substantially improved weak-performing cases: 51 of 62 cases improved (82.3%). Focused manual evaluation of the 62 PSI-selected weak cases provides initial evidence that the identified weaknesses are instructionally meaningful and that many PSI-guided regenerations correspond to human-judged improvement. These results suggest that learner- and curriculum-aware alignment may matter more for effective tutoring than model category alone, and that such alignment is both measurable and improvable.

arXiv

Adaptive Arena-based Contestable Argumentative Network-of-Experts for Open-Ended Care Plan Coordination

Truong Thanh Hung Nguyen, Hoang-Loc Cao, Phuc Ho, Phuc Truong Loc Nguyen, René Richard, Hung Cao

Care plan coordination demands synthesizing heterogeneous clinical, functional, and psychosocial information across multiple professional disciplines, where monolithic LLM pipelines cannot perform in a transparent or safe manner. We present CANOE (Contestable Argumentative Network-of-Experts), a multi-agent neuro-symbolic framework that addresses these limitations through five modules: complexity assessment, adaptive team recruitment, role-based argumentative computation via an Arena-based Quantitative Bipolar Argumentation Framework (A-QBAF), human-in-the-loop contestation, and care-plan synthesis. Role-specialized agents generate supporting and attacking arguments for candidate interventions; conflicts are resolved through arena-based clash resolution before acceptability scores propagate across the argumentation graph. Care planners may accept, reject, edit, or add arguments, and the framework will deterministically recompute the final plan. Evaluation on Discharge Me! and MedicalRAG using ROUGE-L, AlignScore, MEDCON F1, FKGL, and LLM-as-a-judge shows that medically fine-tuned models achieve the strongest clinical correctness and safety, while CANOE's argumentative structure provides faithful explanation and human contestability.

arXiv

C$^3$PO: Evaluating Cross-Modal Composition and Counterfactual Performance in Omnimodal Models

Swapnanil Mukherjee, Agyeya Negi, Tanuja Ganu, Ponnurangam Kumaraguru

Current Multimodal Large Language Models (MLLMs) can process diverse sensory inputs, yet their reasoning remains heavily biased toward a dominant modality, resulting in brittle cross-modal reasoning. We introduce C$^3$PO, a benchmark of 3,404 samples spanning video, audio, image, and text, evaluating two abilities: information composition (fusing dispersed evidence) and counterfactual conflict (resolving deliberate contradictions). C$^3$PO's paired IC/CC structure and four-tier design enable targeted diagnosis of when and why cross-modal reasoning fails. Built through a fully automatic pipeline using 25 logically grounded templates, C$^3$PO reveals that while humans achieve 88.64% accuracy, the best model (Gemini-3.1-Pro) reaches only 73.17%, with open-source models collapsing under conflict. Through attention probes, we find 86-95% of failures stem from modality dominance: models commit to one modality while ignoring contradictory evidence, concentrating 87-95% of attention on text. Mid-layer attention entropy predicts correctness-sustained exploration succeeds, premature collapse fails. The 56-point accuracy gap between equally complex templates reveals that performance depends on modalities' structural roles in conflict resolution, not combinations. These findings show multimodal perception does not guarantee robust reasoning; architectures must enable sustained cross-modal attention to avoid premature

arXiv

Hierarchical Data Selection via Manifold Coverage and Sparse Feature Coverage in LLM Post-training

Peng Sun, Yi Yang, Antong Zhang, Chunxiao Li, Yanbo Wang, Dianbo Liu, Xin Chen, Kai Yu, Lu Chen, Tianfan Fu

As supervised fine-tuning data continues to scale, selecting high-value subsets from large candidate pools is crucial for reducing training cost and improving model performance. Existing methods often measure diversity directly in the original embedding space, where geometric metrics entangle dominant semantic directions, fine-grained supervision differences, and local noise. We address this limitation by formulating data selection as a coarse-to-fine hierarchical coverage problem and propose MASS. MASS learns low-dimensional principal manifold coordinates with a dense autoencoder for coarse semantic grouping, and then performs quality-aware sparse feature coverage within each group using a TopK sparse autoencoder. Experiments on Vision Flan and LLaVA-CoT show that MASS consistently outperforms strong data selection baselines across multiple budgets, and in several settings matches or surpasses full data training with only a small subset of data.

arXiv

Counterfactual Analysis via Large Language Models

Zonghao Yang

Counterfactual analysis aims to predict potential outcomes under hypothetical scenarios, offering valuable insights for decision-making. This paper investigates the application of large language models (LLMs), specifically the GPT-3.5 model, for counterfactual analysis. We focus on the online lending context, where the counterfactual return on investment (ROI) is crucial for evaluating different interest rate schemes. We begin by assessing the predictive performance of GPT and comparing it with advanced machine learning algorithms. The results show that prompt engineering can significantly enhance GPT's predictions, with the R-squared increasing from 1.97% to 2.84%, closely approaching the 3.48% achieved by gradient-boosted regression. Subsequently, we utilize GPT to generate counterfactual ROIs under a set of alternative interest rates. GPT exhibits logical coherence and causal reasoning in its responses. The findings underscore the potential of LLMs as effective tools for counterfactual analysis in online lending, suggesting broader applications for LLMs in various predictive and decision-making contexts.

arXiv

CASCADE: An Agentic Regulatory Network Framework for Patient-Data-Validated Downstream Perturbation Prediction

Jose A. Bird

CASCADE is an agentic framework that predicts downstream transcriptional effects of gene perturbation from precomputed ARACNe regulatory networks, exposed via MCP. Prior work validates such tools by checking whether predicted genes are known cancer genes (membership); we instead test whether the predicted direction of change matches reality, using focal-gene copy-number amplification as a dosage-based proxy for the inverse of knockdown against real TCGA patient tumor data. For MYC, CASCADE's predicted knockdown targets show strong concordance with real amplified-vs-non-amplified tumor expression across three cancer types (BRCA: 90.0%, COAD: 72.0%, STAD: 85.7%; all p<0.0013), well above permutation baselines, surviving a PAM50 subtype control and replicating in an independent cohort (METABRIC, 87.2%). Compared against curated MSigDB gene-set baselines via Fisher's exact test, CASCADE's accuracy is not shown to exceed existing public knowledge of MYC- or E2F-driven biology, though its gene-specific direction-calling clearly outperforms a naive uniform guess. Extending to fifteen additional genes, validation proves gene-specific rather than universal: proliferation-machinery regulators mostly replicate, while lineage-identity transcription factors and one cyclin-D paralog (CCND2) consistently fail, a pattern we discuss as a hedged, post-hoc hypothesis. We separately benchmark whether an LLM-based agent correctly grounds natural-language requests into CASCADE's real MCP tool calls. Across 35 queries, a documented local model reaches 71.4% exact match (85.7% for a larger model); schema and gene-alias failures are resolved by scale or server-side correction, but both models confidently default to the wrong perturbation type on ambiguous queries, a failure a targeted fix could not resolve because its trigger condition never occurs.

arXiv

Multi-Agent Reinforcement Learning for Online Traffic Scheduling in Time-Sensitive Application

Marcos Carvalho, Fatih Temiz, Shavbo Salehi, Melike Erol-Kantarci, Daniel F. Macedo

Time-sensitive networking (TSN) is increasingly integrated into mobile edge computing (MEC) to support applications with stringent latency requirements, such as extended reality (XR). However, existing TSN scheduling solutions predominantly rely on static optimization techniques or centralized learning models that are based on fixed traffic patterns, limiting their effectiveness in dynamic environments. In practice, MEC environments often host multiple co-located XR traffic flows whose characteristics evolve over time, creating complex inter-queue dependencies that current schedulers fail to capture. Addressing these challenges requires adaptive, decentralized scheduling mechanisms capable of coordinating multiple TSN queues under varying traffic conditions. To this end, this paper proposes a multi-agent reinforcement learning (MARL) framework for TSN scheduling, where each TSN queue is modeled as an autonomous agent. The Heterogeneous-Agent Proximal Policy Optimization (HAPPO) algorithm is employed to explicitly model inter-agent dependencies and jointly optimize service delivery across queues. The simulation results demonstrate that the proposed approach reduces average frame waiting times by up to 26.8% and worst-case delays by approximately 16.8%, highlighting its effectiveness in dynamic XR-driven MEC scenarios.

arXiv

Multi-Agent Transformer for Queue-Level XR Traffic Scheduling in TSN Networks

Marcos Carvalho, Fatih Temiz, Shavbo Salehi, Melike Erol-Kantarci, Daniel F. Macedo

Time-Sensitive Networking (TSN) and Mobile Edge Computing (MEC) hold strong potential for enabling ultra-reliable low-latency communication for time-sensitive applications, such as eXtended Reality (XR). However, the widespread adoption of XR introduces significant challenges due to co-located services in MEC environments, leading to contention for shared network resources. Moreover, XR traffic types have distinct characteristics and criticality in terms of timing requirements, further increasing the complexity and dynamics of such environments. Although reinforcement learning has shown promise for TSN scheduling optimization in dynamic network scenarios, existing approaches rely on centralized or high-level multi-agent designs and are typically tailored to periodic and predictable industrial traffic, limiting their applicability to XR workloads. As a result, these approaches suffer from (i) limited ability to capture inter-queue dependencies due to coarse-grained control, and (ii) poor adaptability to highly dynamic and heterogeneous XR traffic. To address these gaps, we propose a multi-agent reinforcement learning approach for queue-level XR traffic scheduling. We adopt the multi-agent transformer (MAT) to model inter-queue dependencies via attention over agents' observations and actions, enabling implicit coordination across heterogeneous co-located XR applications. Our simulation results show that the proposed method outperforms baselines, achieving up to 71.42% latency reduction and up to 83.2% reduction in failure rate, while consistently achieving high reliability across all queues.

arXiv

Hierarchical Server Architecture for Agentic Science

Vanessa Sochat, Daniel Milroy

Agentic science is transforming the landscape of computational work, extending to scientific pipelines and workload managers. The workloads require specialized hardware within and across institutions. If assessing workload needs against environments is required for scheduling, automated discovery of resources is an essential step. In this paper, we present a hierarchical, dynamic architecture and software to discover resources across diverse cloud, edge, and HPC systems. The design enables concurrent, asynchronous negotiation, selection, and dispatch of requests for work using secretary agents. The agents probe and discover 51 real and simulated providers across 7 categories. We perform 19,973 negotiation and 6,952 selection simulations to assess reliability of decisions, demonstrating high (87.71\%) negotiation accuracy and selection costs comparable to more traditional strategies. Designed for extensibility and currently supporting the Genesis Mission, this architecture exemplifies the importance of careful coordination between agents, discovery tools, and infrastructure for agentic science.

arXiv

OrchestraBench: Evaluating Multi-Agent Orchestration Failure Modes, Recovery, and Decomposition Quality

Yidian Chen, Yingzi Gu, Natan Vidra, Spurthi Setty, Sharon Zheng

Multi-agent orchestration frameworks are moving from demos to production, yet benchmarks typically report task accuracy without diagnosing why a pipeline failed, where a cascade began, or which routing decision caused the breakdown. OrchestraBench evaluates failure, recovery, and decomposition through a controlled, seed-reproducible failure-injection harness over templated enterprise workflows. It introduces cascade radius and per-failure-mode recovery as primary metrics and compares routing policies with bootstrap confidence intervals and paired tests. On a 26-case gold-labelled diagnostic, a keyword/flag router scored 0% on adversarial cases with misleading or missing surface flags, whereas an intent-reasoning model router scored 100%, matching the oracle. Controlled mechanism probes with a real Claude agent over a verifiable arithmetic dependency chain revealed three failure-handling tiers across five MAST modes: tool faults recovered fully (1.0), ambiguous delegation recovered partially (0.30), and three latent or semantic modes never recovered (0.0). This ordering persisted when the computation was reframed as a loan-approval workflow and across Sonnet, Opus, and Haiku, although absolute rates shifted with context. Blind retry reproduced latent faults and increased time to detection, indicating that detection and attribution are necessary for containment. Cascade radius increased with pipeline depth (mean 0.9 to 4.7 across depths 3-7). A trusted-state repair ablation showed that apparent containment gains primarily came from the trusted-state signal rather than autonomous detection. These results are controlled-chain mechanism probes, not domain-workload claims.

arXiv

IMMENSE: Inductive Multi-perspective User Classification in Social Networks

Francesco Benedetti, Antonio Pellicani, Gianvito Pio, Michelangelo Ceci

Online social networks increasingly expose people to users who propagate discriminatory, hateful, and violent content. Young users, in particular, are vulnerable to exposure to such content, which can have harmful psychological and social repercussions. Given the massive scale of today's social networks, in terms of both published content and number of users, there is an urgent need for effective systems to aid Law Enforcement Agencies (LEAs) in identifying and addressing users that disseminate malicious content. In this work we introduce IMMENSE, a machine learning-based method for detecting malicious social network users. Our approach adopts a hybrid classification strategy that integrates three perspectives: the semantics of the users' published content, their social relationships and their spatial information. Such contextual perspectives potentially enhance classification performance beyond text-only analysis. Importantly, IMMENSE employs an inductive learning approach, enabling it to classify previously unseen users or entire new networks without the need for costly and time-consuming model retraining procedures. Experiments carried out on a real-world Twitter/X dataset showed the superiority of IMMENSE against five state of the art competitors, confirming the benefits of its hybrid approach for effective deployment in social network monitoring systems.

arXiv

Posture and Sustainment Optimization Under Adversarial Uncertainty

Amelie Norris, Alyssa Lee, Natan Vidra, Spurthi Setty

Pre-commitment posture, the assignment of military assets to theater locations before conflict scenarios resolve, is a critical and formally unsolved problem in joint operational planning. Current practice relies on greedy heuristics that maximize value and ignore geographic coverage and are structurally vulnerable to adversaries that target high-strategic value locations. This paper presents a scenario-weighted adversarially robust posture optimization engine for the Posture and sustainability allocation (PSA) problem, modeled as a finite-horizon Markov Decision Process over assets, theater locations, and time steps. We introduce the Composite Expected Value (CEV) optimizer, which places assets by maximizing scenario-weighted expected posture efficiency over a distribution of threat scenarios, and the RobustCEV extension, which iterates against a Bayesian adversary that updates its targeting distribution in response to observed placement. Across three experiments in an Indo-Pacific basing environment with 20 assets and 5 theater locations, we demonstrate that: (1) the greedy baseline incurs a permanent 25.1% posture efficiency penalty due to geographic under-coverage and a 57.3% scenario-weighted readiness collapse under value-correlated adversarial threat; (2) the CEV optimizer recovers up to 19.8% efficiency over greedy when the threat distribution carries a geographic signal, with a curated set of 5 to 20 scenarios sufficient to capture the majority of this gain; and (3) the RobustCEV extension recovers up to 158% efficiency relative to a naive optimizer when an adaptive adversary employs a deceptive threat prior. All findings are validated using paired t-tests with Bonferroni correction and two-level variance decomposition, confirming that the performance gaps reported are structural properties of placement strategies rather than sampling artifacts.

arXiv

MiGHT-EHR: A Multi-task Graph Transformer for Heterogeneous Temporal Electronic Health Records

Anirudh Rayas, Yuan Wang, Pavan Turaga

Learning from Electronic Health Records (EHRs) has gained significant attention due to its potential to improve clinical prediction. However, effective learning remains challenging because EHRs encode heterogeneous, temporally ordered clinical interactions. In particular, EHRs contain: (i) heterogeneous clinical entities, including patients, visits, diagnoses, prescriptions, and procedures, together with their heterogeneous interactions, (ii) longitudinal patient trajectories across hospital visits and (iii) shared statistical dependencies across related clinical prediction tasks. Existing EHR learning methods capture only a subset of these properties. To bridge this gap, we propose Multi-task Graph transformer for Heterogeneous Temporal EHRs (MiGHT-EHR), which jointly models all three within a unified representation learning method. MiGHT-EHR constructs a heterogeneous graph from EHRs in which nodes represent clinical entities and edges connect statistically associated entities identified via normalized point-wise mutual information. Across MIMIC-III and MIMIC-IV datasets, MiGHT-EHR outperforms state-of-the-art methods on average across four tasks: drug recommendation, prediction of length-of-stay, mortality, and readmission, with particularly strong improvements in mortality and readmission prediction. Furthermore, a post-hoc analysis of the learned representations reveals that patient neighborhoods are organized by clinical outcomes, salient medical concepts are recoverable as linear directions in the representation space, and task probabilities are well calibrated. Collectively, these findings demonstrate that MiGHT-EHR representations support diverse prediction tasks while preserving clinically interpretable structure.

arXiv

Search2Skill: Skill Distillation Beyond Knowledge Boundaries Via Rubric-Based Reinforcement Learning

Muyang Ye, Tian Lan, Feihu Jiang, Yongshi Ye, Wuyunsiqin, Bin Zhu, Qianghuai Jia, Zhao Xu, Weihua Luo, Ye Wang, Jinyang Zhang, Longyue Wang, Lingfeng Bao

Reusable skills, which encapsulate the procedural knowledge required to solve real-world professional tasks, offer LLM-based agents a path toward self-evolution in expert domains. Existing self-evolving skill methods construct skills internally from the model's parametric knowledge or trajectories, and are therefore bounded by what the model already knows. However, the domain conventions and standard procedures underlying professional skills often lie beyond this boundary and are hard to elicit from the agent alone. To address this issue, we therefore propose a novel framework, Search2Skill, that automatically identifies the agent's capability gaps, searches external sources to address them, and distills the retrieved evidence into structured, reusable skills. Specifically, Search2Skill is optimized by a rubric-based reinforcement learning scheme that jointly improves when to search, how to search, and how to generate skills. Experiments on eight expert-level domains from three benchmarks show that Search2Skill consistently outperforms both search-augmented and trajectory-based skill-learning baselines under both streaming and held-out evaluation protocols. Further analyses show that the gains arise from skill abstraction rather than raw retrieved evidence, and that the acquired skills transfer across model scales.

arXiv

Fixed and Adaptive Topological DeepONets: Functional Measurements on Hausdorff Locally Convex Spaces

Khemraj Shukla, George Em Karniadakis

Deep Operator Networks (DeepONets; arXiv:1910.03193) typically encode an input function through point values on a fixed discretization. Building on the Topological DeepONet framework of Ismailov (arXiv:2603.11972), we replace point samples by continuous linear functionals drawn from the continuous dual of a Hausdorff locally convex space $({V},\{p_α\}_{α\in A})$, whose topology is generated by a point-separating family of seminorms rather than a single norm, and develop fixed and adaptive functional measurement systems. Measurements are combined with the coefficient-space Two-Step procedure of Lee and Shin (arXiv:2309.01020), while a training-only decoder and regularization stabilize the adaptive coordinates. We derive a discrete error decomposition separating measurement, output-basis, and neural-approximation errors, together with a Barron-rate refinement. The framework is evaluated on the antiderivative operator, a non-normable locally convex input space, heterogeneous Darcy flow, a controlled operator, and fixed-time and time-evolving Navier-Stokes vorticity operators. In the heterogeneous Darcy problem, the functional models retain nearly resolution-independent errors of 5.5-5.6% on unseen grids, while in the controlled problem adaptive measurements reduce the mean error below 1.2%. For the fixed-time Navier-Stokes problem, the Adaptive Topological DeepONet is the most accurate DeepONet-based model, attaining a mean relative $L^2$ error of 1.685% +/- 0.017% using 128 functional coordinates. A comparably sized Fourier neural operator (FNO; arXiv:2010.08895) achieves the lower error 0.832% +/- 0.172%, but requires the full 64x64 input field, twice the training time, and 10.7x greater peak GPU memory. The formulation provides compact, interpretable, and discretization-portable coordinates in the continuous dual $V'$, including for non-normable input spaces.

arXiv

Adversarial Causal Intervention Falsification

Mojtaba Eslami

Generative models can reproduce an observational distribution while encoding an incorrect causal structure. We study a sequential game in which a structural causal generator proposes observational and interventional distributions, while an adversarial experimentalist selects interventions intended to maximally falsify the generator. The discriminator is therefore not merely a real-versus-synthetic classifier: it is indexed by an intervention and tests whether the generator reproduces the corresponding post-intervention law. We introduce Adversarial Causal Intervention Falsification (ACIF), formulate oracle and implementable versions of the game, and distinguish three objects that are often conflated: observational fit, interventional equivalence over an admissible query class, and point identification of a structural causal model. For finite model and intervention classes, we prove: (i) an exact reduction of the adversarial objective to a worst-intervention integral probability metric; (ii) identification up to interventional equivalence, with point identification under a separating intervention family; (iii) existence of mixed-strategy equilibria; (iv) finite-sample uniform convergence and margin-based model-selection guarantees; and (v) a logarithmic elimination guarantee for a disagreement-driven sequential design under a balanced-separation condition. We also give a complete linear-Gaussian example in which two observationally indistinguishable causal directions are separated by a single well-chosen intervention. The framework clarifies what an adversarial causal discriminator can and cannot certify, and provides a principled bridge between causal generative modeling, active causal discovery, and experimental design.

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