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arXiv AI Papersel mes pasado

REFLECT: Role-Aware Detection of Sentiment, Emotion, Politeness, and Formality

Detecting communicative meaning in dialogue requires modeling not only lexical content but also the participant-role structures through which sentiment, emotion, politeness, and formality (SEPF) are expressed. Existing approaches rely on contextual language representations while leaving semantic roles implicit. We introduce a role-aware transformer architecture that maps the four SEPF dimensions to theory-grounded Semantic Role Labeling (SRL) configurations, incorporating these configurations directly into the transformer's self-attention mechanism. Role-aware attention models non-directional internal states (sentiment and emotion), while directional role-aware attention captures initiator-to-recipient relations for external cues (politeness and formality). The resulting role-aware representations are fused with contextual embeddings through a learned gate that adaptively weights how much role information each input contributes, rather than appending semantic roles as an auxiliary feature vector. Across four benchmark datasets, the framework yields statistically reliable gains over strong BERT-based baselines for emotion, politeness, and formality, with gains concentrated in theoretically predicted cases such as low-frequency, complex emotions and highly polite expressions; sentiment improvements are marginal and non-significant, suggesting that sentiment is conveyed more through lexical choice than participant-role structure. Additional evaluation on real-world data demonstrates that the framework improves both predictive performance and model traceability. These results demonstrate that linguistically grounded modifications to transformer self-attention improve the detection of communicative meaning, generalize beyond benchmark datasets to real-world mental-health data, and yield traceable, role-grounded explanations that extend beyond predictive performance to interpretability.

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arXiv AI Papersel mes pasado

Not Just an Evaluation: A Case Study of Discourse Particle Sensitivity in Language Models

Discourse particles subtly shape the flow of discourse by reflecting conversational context and interlocutor attitudes, often leaving the truth-conditional meaning untouched. They are also often polyfunctional, with distinct senses which partially overlap with other particles; for example, the exclusive use of English "just" and "only" ("John only/just drinks water"). Despite the frequency of these words in natural language, they have gone largely unstudied due to the subtle nature of their effects. We investigate LLM sensitivity to "just" and "only" in natural conversations using behavioral and mechanistic analyses. First, we find that LLMs and humans similarly prefer the presence of these particles in context, and both are more sensitive to "just" compared to "only". Second, when sampling from LLMs with and without these particles, we find LLMs consistently rate generations as more likely, given their source context, demonstrating their particle sensitivity. In both experiments, instruction tuning increases sensitivity. Finally, we localize particle-sensitive units within LLMs and find the overlap between "just" and "only" is asymmetric: "only" units transfer selectively to exclusive "just", while all "just" units transfer to "only" equally well regardless of sense, suggesting LLM lexical-level particle representations are partially organized by sense. We release our code, sense-labeled dialogue stimuli, and human preference annotations at https://github.com/JiahuiKChen/Not_Just_an_Evaluation.

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arXiv AI Papersel mes pasado

OccludeBench: Can VLMs Find What's Missing?

How well can vision-language models (VLMs) reason about what is missing from an image? We study this question with OccludeBench, a manually curated benchmark for recovering fully occluded objects from the visual evidence that remains. OccludeBench distinguishes direct cases, where the hidden object must be recovered from a specific physical cue such as a shadow or reflection, from inferential cases, where it can be inferred from broader scene context. Across five VLMs, accuracy averages 42.7% on direct cases versus 62.7% on inferential cases, exhibiting a 20.0-point gap. Humans attain higher accuracies of 63.4% versus 68.5% for direct and inferential images, respectively, with no significant gap. To locate this failure, we introduce OccludeTrace, a four-stage diagnostic that isolates where the visual reasoning process breaks down. The bottleneck emerges when models must recover the relevant object from the projection within the full image: they succeed on only 50% of failed examples, compared with 91% of examples they answer correctly. Extended reasoning, tool use, and few-shot prompting yield inconsistent improvements and do not reliably eliminate the gap. In contrast, an inpaint-then-confront intervention, which prompts models to first generate a candidate hidden object and then evaluate that hypothesis against the visible physical cue, reduces the gap to a statistically non-significant difference for both models with image-generation capabilities. Together, our results establish a tractable, controlled diagnostic for isolating how VLMs reason about visual content that is missing from an image.

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arXiv AI Papersel mes pasado

Randomized Momentum Transport with Cheap Predictors

Momentum methods such as STORM and second-order momentum track the gradient by adding a transport correction to momentum, at the cost of an extra oracle call per iteration. We introduce randomized momentum transport, which evaluates the correction with probability q and otherwise uses a cheap prediction, with importance weighting that preserves the conditional mean and adds (q^{-1}-1) times the prediction loss to the variance. Under transport-bias, second-moment, and residual-control assumptions, linear minimization oracle (LMO) updates, including normalized, sign, and exact spectral (Muon) directions, retain an O(T^{-1/3}) stationarity bound for each fixed q>0 with a single-gradient initialization. For unnormalized STORM, some q<1 lowers the leading coefficient of our sufficient gradient budget if and only if the gradient-difference noise modulus exceeds the smoothness constant, by at most about 10\%. An online diagonal predictor admits a regret-to-convergence guarantee. At approximately equal oracle cost, querying a quarter of the corrections lowers the final training loss by 18 to 43\% on MNIST1D and raises the test accuracy of Hessian-vector transport on CIFAR-10 by 1.5 points.

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arXiv AI Papersel mes pasado

Optimal Algorithms for Nonsmooth Nonconvex Stochastic Optimization with Constraints

We present new algorithms for stochastic optimization problems in which the objective is neither smooth nor convex, subject to a convex constraint set. Our algorithms return a (δ,)-Goldstein stationary point, as recently defined for constrained problems by Liu et al. (2024), with improved complexities, and are the first to achieve optimal convergence rates for this task in several settings. In particular, we design projection-based and projection-free algorithms that achieve a O(δ^{-1}^{-3}) rate using stochastic gradients, which we show to be optimal, and a O(dδ^{-1}^{-3}) rate using zeroth-order queries, which is also optimal in its dependence on the dimension d and improves over prior work. Notably, our lower bound is given in terms of the Frank-Wolfe gap and holds even for smooth problems, which is of independent interest. These results show that in nonconvex stochastic optimization, the convergence rate is degraded neither by the presence of constraints nor by nonsmoothness. Our analysis is based on a reduction to online linear optimization, extending a related technique from unconstrained optimization.

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arXiv AI Papersel mes pasado

Your Discrete Graph Diffusion Model is Secretly Memorizing

Discrete graph diffusion models (GDMs) corrupt the graph structure by adding noise independently to nodes and edges under a Markovian noise model. In the unconditional setting without node features, an equivariant denoiser trained on a single graph is able to generate novel graphs and sample-level metrics such as edge overlap and WL kernel similarity find no evidence of memorization. In this work, we challenge this view and show for the first time that graph diffusion models indeed exhibit memorization. Analyzing the reverse diffusion trajectories of GDMs trained on two-block stochastic block models (SBMs), we find a strong train-data bias: the model recovers a corrupted training graph almost perfectly compared to a held-out test graph. We term this conditional memorization, as it surfaces only when the reverse trajectory is conditioned on a corrupted training graph and is not apparent during inference. It coincides with a growing generalization gap, where the training loss improves as the loss on held-out graphs degrades, and it cannot be mitigated by early stopping. The onset of memorization always precedes the emergence of community structure in the generated graphs, thus every checkpoint earlier produces structureless graphs. This behavior holds across all node sizes we test.

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arXiv AI Papersel mes pasado

UkrMeme: Multimodal Explainable Persuasion Detection in Ukrainian Memes

Memes play a central role in modern online communication, especially in contexts of political conflict where visual and textual cues combine to convey persuasive messages. We study persuasive technique detection in Ukrainian memes using vision-language models (VLMs). We introduce UkrMeme, a dataset of 200 organically produced Ukrainian wartime memes annotated for persuasion techniques, and PTM-UA, a Ukrainian translation of a subset of the Propaganda 950 benchmark that preserves original visual content while translating meme text. We evaluate VLMs in a zero-shot prompting setup across image, text, and multimodal inputs using hierarchical F1 metrics. Finally, we compare Layer-wise Relevance Propagation (LRP) and model-generated token attributions and analyze the semantic categories of evidence emphasized by each explanation method.

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arXiv AI Papersel mes pasado

ReplaySSM: Cache SSM Inputs, Not State

State-space models (SSMs) maintain a fixed-size recurrent state, but reading and writing it at every decoding step can bottleneck hybrid models. This eager state management causes large state I/O with low arithmetic intensity, leaves speculative decoding no cheap rollback, and feeds state quantization error into subsequent recurrent updates. We introduce ReplaySSM, which unrolls the recurrence to represent the state as a checkpoint and a buffer of recent SSM inputs. This separates output computation from checkpoint updates. By updating the checkpoint periodically, ReplaySSM avoids state writes on most steps and roughly halves the dominant state memory traffic. Keeping recent inputs also makes speculative rollback a buffer-pointer operation and enables output-only verification without materializing intermediate states. The same separation allows a low-precision checkpoint to serve output computation on most steps while a higher-precision checkpoint serves recurrent updates, so rounding error in the low-precision copy never enters later updates. We implement ReplaySSM in vLLM for Mamba-2 and Gated DeltaNet. At serving batch size 256, it accelerates standard decoding by 1.20--1.47over a tuned vLLM baseline across four hybrid models, and delivers about 1.8the throughput of vLLM's speculative decoding on the two 120B-class models. Separate state precisions also reduce output KL divergence and downstream accuracy losses compared with a shared low-precision checkpoint.

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arXiv AI Papersel mes pasado

Geometry-Aware Multi-Objective Optimization: Norm-Constrained Oracles with Entropic Weight Updates

Multiple-gradient descent is typically formulated in Euclidean geometry, whereas matrix-aware optimizers use directions induced by other norms. We analyze a single-loop multi-objective method combining a norm-constrained linear minimization oracle with entropic updates of task weights. For any finite-dimensional norm pair, we establish an O(T^{-1/2}) ergodic stationarity rate in the deterministic setting, deriving the required trajectory gradient bound from smoothness and lower-boundedness in the unregularized case. With stochastic gradients and a bounded-gradient assumption, one persistent blended-gradient momentum buffer yields an O(T^{-1/4}) rate whose leading term has no explicit dependence on the number of tasks. We also establish static regret for the inner weighting objective on arbitrary bounded gradient sequences and, with entropy regularization and a weight floor, iteration-wise inner-gap control after burn-in while retaining ergodic stationarity, conditional on a trajectory gradient bound. The optimal blended gradient can be nonunique in spectral and sign geometries, motivating a selection-independent inner gap. Our analysis extends the spectral construction studied by concurrent MOON to general norms. Experiments compare the method with existing multi-task optimizers and examine its oracle, weighting, and momentum choices.

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arXiv AI Papersel mes pasado

From Pixels to Privacy-Sensitive Features: An Information-Theoretic Framework for Reconstruction Bounds

What can an adversary recover from a model trained with DP-SGD? Its (,δ) guarantee does not answer this question directly. We derive a distortion bound that can be computed before training and applies even to an adversary who observes the parameter trajectory during training, knows every other training record and the population distribution from which the training records are drawn. The analyst may choose the representation in which error is measured, allowing the bound to target the aspects of reconstruction that are privacy-sensitive in a given application. Our information-theoretic framework separates two contributions: the information about a record revealed by training, measured through conditional mutual information, and the uncertainty already present in the data distribution, measured through source entropy. Rate-distortion theory combines them into a lower bound on the expected error of every reconstruction attack. For DP-SGD, the leakage bound depends only on the sampling rates and noise multipliers, while the source entropy is lower-bounded from a sample with finite-sample confidence. An orthogonal block construction keeps the resulting bound informative for high-dimensional images. We instantiate the framework in pixel space and in LPIPS feature space, obtaining, to our knowledge, the first lower bound on reconstruction distortion measured directly by LPIPS. On a range of image datasets the bounds establish non-trivial unavoidable expected reconstruction error within heuristically recommended privacy-budget ranges and beyond. Experiments compare the bounds with strong reconstruction attacks and identify the principal sources of the remaining slack.

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arXiv AI Papersel mes pasado

RESCUE: Is This Alarm Worth Acting On? Counterfactual Evaluation of VLA Runtime Monitors

Runtime failure monitors for robot policies are typically evaluated by how accurately they distinguish failed from successful executions. Yet an accurate alarm may arrive too late for recovery, while an unnecessary intervention may disrupt an execution that would otherwise succeed. We introduce RESCUE, a counterfactual framework for evaluating whether a monitor's alarms enable useful interventions. By restoring simulator and policy states at execution checkpoints, RESCUE compares alternative actions, identifies the latest checkpoint satisfying a specified recovery criterion, and evaluates whether acting on alarms reduces expected task-completion cost. We evaluate RESCUE with OpenVLA-OFT and π_{0.5} over LIBERO-Spatial and LIBERO-Plus using 128,340 counterfactual branches. Recoverability depends on the state--intervention pair rather than on robot state alone: at τ=0.5, 14 of 66 OpenVLA-OFT/LIBERO-Plus failures contain a recoverable checkpoint under continuation, compared with 34 of 66 under continuation or scripted recovery, while recovery reduces recoverability in other conditions. On the primary strong-policy conditions, favourable detection scores do not establish lower intervention cost. Under the evaluated stop-and-reset model, even an idealised detector can afford only a 2.0--3.3% false-alarm rate before unnecessary resets outweigh the savings from stopping failures early. These results show that monitor value depends jointly on the intervention available and the workload in which it is deployed.

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arXiv AI Papersel mes pasado

Retrieval-Augmented Multimodal Language Model with Heterogeneous Evidence Integration for Clinical Prognosis

Clinical prognosis requires integrating structured measurements, physiological waveforms, longitudinal history, and population context. We introduce PRISM (Population-Retrieved Inference for Structured Multimodal Prognosis), a multimodal language model that combines per-feature numerical tokenization, recency-weighted aggregation of longitudinal ECGs, and a dual-modality population memory bank. Retrieval operates in representation space: the model receives mean-pooled embeddings of similar training-cohort encounters, while no individual retrieved record enters the prompt. On the 1,443-task MDS-ED benchmark, PRISM achieves AUROCs of 86.2% for diagnosis, 93.1% for deterioration, 91.8% for ICU admission, and 92.8% for mortality. These results use a 96-hour pre-arrival window unavailable to reported baselines. With benchmark-window inputs only, PRISM reaches 0.8895 AUROC, compared with 0.8937 for UniPACT and 0.8889 for MDS-ED. A matched-input compact fusion model using the same five evidence streams and frozen encoders reaches 0.7652 AUROC, versus 0.9092 for PRISM. Replacing numerical EHR encoding with text serialization reduces AUROC by 3.66 points; removing pre-arrival history reduces it by 1.97 points; and zeroing retrieval reduces it by 0.99 points. Genuine retrieval outperforms random-neighbor retrieval by 0.97 macro-average points, although a paired task-level sign test does not establish a uniform advantage (p=0.067). On the external MC-MED cohort, supervised fine-tuning reaches 0.8611 AUROC, compared with 0.8227 for locally trained gradient boosting and 0.7841 for source-only PRISM. These results support structure-aware multimodal integration and supervised external adaptation.

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arXiv AI Papersel mes pasado

FedPCD: Priority-Constrained Federated Aggregation

Federated learning (FL) seeks to optimize a shared global model from decentralized client data. While effective for average performance, this process can produce unfair performance across clients, particularly under statistically heterogeneous data distributions. Existing fairness-aware and multi-objective FL methods address this through client re-weighting, gradient correction, or common-descent formulations, but often change the global optimization direction or treat client objectives symmetrically. We propose FedPCD, a priority-constrained federated optimization framework that separates the global optimization objective from client protection. FedPCD preserves the conventional federated aggregate as the primary objective, while allowing only the minimum correction necessary to meet client performance constraints. Across heterogeneous FL benchmarks, FedPCD consistently outperforms state-of-the-art baselines, achieving the highest global accuracy across all configurations and leading worst-10% client accuracy in nearly all. FedPCD further preserves competitive trade-offs between global accuracy and client performance variability. Beyond this trade-off, FedPCD demonstrates faster empirical convergence, reaching matching or superior performance in substantially fewer communication rounds.

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arXiv AI Papersel mes pasado

Beyond Temporal Proximity: Explanatory World Models for Credit Assignment in Reinforcement Learning

Generative Recommenders increasingly use Reinforcement Learning (RL) to optimize outcomes that may appear hundreds or thousands of interactions after a decision. Standard RL propagates reward according to temporal proximity rather than explicit relevance, attenuating the signal assigned to distant but important actions and creating a source of sample inefficiency. We introduce Explanatory World Models (EWM), an attribution framework that uses explanations to identify the earlier events that plausibly contributed to a realized outcome. We instantiate EWM with a frontier language model and use its explanations as learning signals using a conservative hierarchical operator that recursively redistributes reward while preserving the undiscounted episode return. To investigate what constitutes a useful explanation, we operationalize three complementary variants inspired by Halpern's actual causation, Lombrozo's explanatory simplicity, and Deutsch's hard-to-vary explanations. We evaluate EWM on two controlled long-horizon RL benchmarks, a public sequential-recommendation benchmark, and an industry-scale generative recommender. On Crafter and WordCraft, EWM substantially outperforms PPO and LaRe, with its largest gains when rewards are most delayed. On KuaiRand, EWM outperforms SFT and LaRe offline and A2C online. Finally, in an offline evaluation of an industry generative recommender, EWM considerably improves Recall and increases behavioral proxies. These results suggest that explanations can provide structured and reusable credit for learning from delayed outcomes.

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arXiv AI Papersel mes pasado

Humanize MLE Agents: Multi-Agent Session Alternation Beyond Single-Agent Limits

Existing LLM-based agent approaches for long-horizon machine learning engineering (MLE) often use context engineering, implemented through custom harnesses that manage tools, skills, and accumulated experience. However, we find that as single-session execution lengthens, the agent's reasoning intensity declines alongside slowing progress, summarized as long-horizon deceleration, and the benefits of these custom harnesses vanish as the underlying model improves, summarized as harness staleness. These findings suggest that their benefits may not persist across versions, which motivates a workflow-level approach in which agents build on one another's work across sessions. We model these alternating agent sessions as a context-reset semi-Markov decision process (CR-SMDP) and establish sufficient conditions for alternation to exceed single-agent reference limits, derive an explicit experiment-budget bound, and characterize when session caps preserve this advantage. Guided by this analysis, we introduce Humanize MLE Agents (HMA), which alternates two agents on a shared workspace, limits each session to at most k experiments and resets the context between sessions, without additional task-specific harness or prior knowledge supplements. Across 75 Kaggle tasks in MLE-bench, HMA reaches a state-of-the-art any-medal rate of 78.2%, exceeding the strongest open-source baseline by 8.0 points with a quarter of its time budget. Moreover, among six configurations spanning five heterogeneous agent pairs, HMA improves any-medal rate over the constituent baselines by 6.4 points on average, demonstrating cross-pair generality. A supplementary case on kernel optimization reaches 878 cycles, within 1.6% of the community leaderboard leader, demonstrating applicability beyond MLE.

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arXiv AI Papersel mes pasado

Proactive Agentic Orchestration

Agentic orchestration delegates tasks to sub-agents with independent contexts, providing a key path to extending the effective execution horizon of large language model agents. However, existing orchestration methods face two limitations: in execution, current methods fix sub-agents' goals and harnesses at creation time, limiting their adaptability to dynamic real-world environments; in optimization, sparse and delayed feedback constrains effective learning of the orchestration policy. To address these limitations, we introduce POrchestra, an on-the-fly proactive agentic orchestration framework. It allows sub-agents to proactively communicate with the orchestrator at any logical point to request harness adjustments while maintaining continuity of local execution. This mechanism not only enables sub-agents to adapt seamlessly to dynamic environments but also naturally inspires On-Policy Orchestration Distillation (OPOD) based on hindsight feedback. OPOD attributes sub-agents' proactive revision requests back to preceding orchestration decisions to derive targeted improvement signals, and leverages these signals as process supervision alongside the final reward to optimize the orchestration policy. We evaluate POrchestra on three long-horizon agent benchmarks spanning deep research, dynamic digital assistance, and software engineering. POrchestra improves task success by an average of 9.1% relative to the strongest baseline; combined with OPOD, it improves small-orchestrator success by an average of 10.0% relative to existing training baselines. POrchestra also achieves a more favorable cost-performance trade-off. Our code is publicly available at https://github.com/XueyangFeng/POrchestra.

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arXiv AI Papersel mes pasado

Branching On-Policy Distillation

On-policy distillation (OPD) provides teacher supervision on student-generated trajectories, but a single trajectory realizes only one continuation at each decision, limiting supervision coverage under a finite sampling budget. We propose BranchOPD (Branching On-Policy Distillation), which selects informative decision points using student uncertainty and teacher-student disagreement, resamples student-policy continuations from shared prefixes, and applies token-level teacher supervision to both main trajectories and branches. BranchOPD operates at token-level decisions in mathematics and within-turn decisions in agent tasks. Shared-prefix reuse reduces student-generated token costs by approximately 19% on ALFWorld and 31% on WebShop relative to seven independent trajectories. We also introduce protocol-boundary repair (PBR), which uses targeted supervision under protocol constraints to mitigate repetition and wasted generation. BranchOPD outperforms Vanilla OPD and Multi-Rollout OPD (n=7) across all evaluated benchmarks, with gains over Vanilla OPD of 18.55 percentage points in mean mathematics accuracy over 16 sampled answers (avg@16) and 13.8 points in mean ALFWorld ID/OOD success. Mechanistic analyses and selection ablations show that branching at uncertain decisions expands subsequent behavior coverage and outperforms random selection and turn-initial branching.

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arXiv AI Papersel mes pasado

A Scalable Learned Iterative Solver for Nonlinear MPC via Temporal Decomposition

Nonlinear model predictive control (NMPC) can be applied to large nonlinear systems with complex objectives while enforcing constraints, but the cost of solving the underlying optimization problems limits real-time application for systems with fast dynamics or many states. Neural networks can reduce this online cost by approximating the control law, but may violate constraints and typically require many precomputed optimizer solutions for training. The learning-based iterative solver for constrained optimization (LISCO) instead learns to predict primal-dual steps toward satisfaction of the Karush-Kuhn-Tucker (KKT) conditions through self-supervised training without precomputed solutions, but its dense, monolithic architecture grows with the prediction horizon. We remove this horizon dependence by exploiting the temporal structure of the problem in the solver architecture, which makes the network size independent of the horizon while leaving the training loss and the solver iteration unchanged. A closed-loop resampling strategy further aligns the training distribution with closed-loop operation at no additional sampling cost. On an economic NMPC benchmark of a CSTR cascade, the proposed solver scales to larger problems than monolithic LISCO and achieves median speedups of up to a factor of four over IPOPT. In closed loop, it achieves comparable control performance to IPOPT with no observed constraint violations.

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arXiv AI Papersel mes pasado

A Local Agentic AI Framework to Generate Edge Case Scenarios for Safety Assurance

Generating edge case scenarios is crucial for training, testing and safety assuring autonomous systems. This identifies hazardous failures to increase system reliability and robustness, ensures the system can still function safely on the boundaries of its operational design domain and learns the expected system behaviour for these edge cases. The rapid advancement in the generation and analysis capabilities of language models (LMs) has expanded their applicability and recent work has investigated LM scenario generation. However, many recent approaches rely on human-in-the-loop or rule-based strategies. This restricts the LM's ability to generate diverse and edge case scenarios; the long tail of the distribution. Our work uses local LMs in a laptop-based agentic AI framework for adaptive scenario generation. This is cheap, fully-controlled, ensures data privacy and security. It uses think, act, observe, update, and continue loops with lightweight JSON encoding to generate scenarios. We use the system requirements, system description and environment description as knowledge bases in contextual prompts for an LM to ensure scenario realism. A second, independent LM critiques each scenario using domain specific criteria so it can be refined. The refined scenarios are run in simulation and evaluation metrics collected. These metric scores are analysed and similar scenarios are created for edge cases (exploitation) or novel scenarios are generated to explore the scenario space. Post-hoc clustering using metric scores and thematic-type analysis of the rich-text scenario descriptions produced by the LM pinpoints functional gaps and their triggering conditions. This creates traceable evidence for the safety assurance case. Our work highlights the potential of a flexible and adaptive local agentic AI framework for automating edge case generation and producing traceable safety assurance evidence.

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arXiv AI Papersel mes pasado

Harmonic analysis and circuit approximation of Sobolev functions on quantum input spaces

We derive approximation rates for Sobolev functions defined on the complex unit sphere and complex projective space, representing quantum states, and on the special and projective unitary groups, representing quantum unitary operations. By using harmonic analysis on compact groups and compact homogeneous spaces, we characterize the corresponding Peter--Weyl decompositions and Sobolev spaces via irreducible representations and the Laplace--Beltrami operator. Combining spectral truncation with finite-depth quantum-circuit approximation, invoking the Solovay--Kitaev theorem, we establish quantitative rates that separate the spectral truncation error from the circuit approximation error.

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