Numerical Analysis
Papers
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Friday 11 September
In this work, we recast two widely used acceleration methods for fixed-point iterations, Anderson acceleration (AA) and the nonlinear generalized minimal residual method (NGMRES), as two-grid methods. By explicitly deriving the error propagation matrices for AA and NGMRES on linear problems, we show that both methods, together with several of their existing variants, can be reformulated as two-grid methods with a single pre- or postsmoothing step and a coarse-grid correction given by a projection with respect to a suitable inner product. This reformulation not only unifies AA, NGMRES, and their variants within a single algorithmic framework, but also enables the design of new variants by independently adjusting the components of the two-grid method, such as the coarse space and the smoothing steps. In particular, we propose a new variant that enlarges the coarse space by incorporating the most recently updated residual, an improvement that is naturally revealed by the two-grid formulation but is hidden in the standard formulations of the AA and NGMRES algorithms. Numerical experiments on both an SPD Poisson problem and a family of non-SPD convection-diffusion problems show that this new variant often outperforms both AA and NGMRES, as well as their variants.
Software Engineering
Beyond Establishing the Four-Day Workweek: Understanding Adaptation and Long-Term Survival in an Agile Software Organization
Context: Existing research on the four-day workweek (4DWW) has primarily examined its introduction and short-term effects, with limited understanding of its long-term survival or its interaction with agile software development. Objective: We study how a reduced-hour 4DWW is introduced, adapted, institutionalized, and sustained under changing organizational and external conditions in an agile software organization. Method: We conducted a longitudinal single-case study of a software organization operating a 32-hour, four-day week. The study draws on 15 semi-structured interviews in 2022 and 2026, analyzed using qualitative content analysis. Results: The 4DWW is better understood as an evolving arrangement than a one-off intervention. After the introduction, teams redesigned coordination, communication, meetings, agile practices, and iterations to adapt to reduced working time. Once institutionalized, the 4DWW faced ownership change, economic downturn, and market and AI pressures. Rather than reverting to five-day workweek, employees absorbed these pressures through voluntary protective adaptations, while anticipating that a rollback would harm job satisfaction, organizational commitment, and employer image. Contribution: We contribute longitudinal evidence on sustaining 4DWW in agile software development and propose two conceptual artifacts: a lifecycle model of the 4DWW and a 4DWW survival matrix, explaining how external pressures and management rationale rollback risk.
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Robotics
Language-Guided Terrain-Adaptive Neural MPC for Autonomous Traversal of Articulated Tracked Robots
In urban search and rescue, articulated tracked robots (ATRs) must traverse structured but contact-rich environments such as stairwells and cluttered building interiors. Reliable autonomy remains challenging because robot-terrain interaction (RTI) is hybrid and discontinuous, and effective flipper-track coordination is difficult to model analytically. We present ASTRIL-MPC, a language-guided neural kinematics model predictive control (MPC) framework for autonomous traversal. A learned kinematics model predicts short-horizon task-state increments from a height sequence and recent trajectories; NMPC plans with multi-objective costs and strict feasibility constraints; and a large language model (LLM) proposes bounded updates to selected weights and bounds through a safety-checked interface with range clipping, rate limiting, and consistency checks. The compiled predictor enables a full control cycle within 100 ms. Across three traversal tasks and a multi-height generalization setting, ASTRIL-MPC improves an aggregate traversal-quality score by up to 71% over a non-adaptive NMPC and by 67% over a PPO baseline, while eliminating measurable collision impacts during descent. These results indicate that combining terrain-conditioned neural kinematics, optimization-based planning, and language-guided adaptation yields data-efficient and robust autonomy for articulated tracked robots. Real-robot trials over four indoor obstacles further demonstrate transfer to contact-rich physical traversal.
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Artificial Intelligence
Embodied-BenchForge: A Closed-Loop Agentic Workflow for Embodied Benchmark Construction
Agentic systems offer a promising way to automate embodied benchmark construction, but existing approaches typically cover isolated stages or remain specialized to predefined environments and task families. More importantly, multi-step construction produces dependent intermediate artifacts that are often passed downstream without artifact-specific verification, allowing local defects to propagate into the final benchmark. We present Embodied-BenchForge, an agentic framework that transforms user-specified evaluation intents into complete embodied benchmark artifacts. It formulates construction as Closed-Loop Benchmark Synthesis, integrating forward artifact synthesis with backward verification and repair. Skill-Orchestrated Artifact Synthesis composes typed and reusable skills into executable workflows, while an artifact dependency graph records intermediate outputs and their dependencies. Requirement-Guided Verification and Repair applies artifact-specific contracts throughout construction and uses provenance to trigger local re-execution or upstream rollback when verification fails. Embodied-BenchForge constructs six benchmarks covering diverse embodied scenarios in the Offline EQA Track, together with one interactive benchmark containing 220 executable tasks in the Interactive Embodied Track. Evaluations of representative MLLMs and embodied agents show that the benchmarks distinguish model capabilities in both observation-based understanding and closed-loop execution. Quality assessment and ablations validate benchmark quality and the effectiveness of verification and repair, while repair and skill-reuse analyses demonstrate efficient localized recovery and cross-benchmark reusability.
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Artificial Intelligence · Cross-listed from eess.AS
MP-Bench: Evaluating Voice Agents as a Multiparty Conversation Participant
Conversational voice agents have advanced significantly, offering increasingly natural human-machine interactions through both cascaded and end-to-end architectures. However, while recent benchmarks extensively evaluate dyadic interactions and passive audio comprehension, they largely overlook a prevalent real-world scenario: multi-party conversations. Evaluating agents in these settings is fundamentally more challenging than in dyadic interactions due to the exponentially greater conversational complexity. For voice agents to integrate seamlessly into human group dynamics, they must not only generate contextually appropriate responses but also demonstrate a nuanced understanding of open turn-taking. To address this gap, we introduce Multiparty Bench (MP-Bench), the first benchmark specifically designed to objectively evaluate conversational speech systems as active participants within multi-party contexts. MP-Bench assesses agent behavior along two primary dimensions: turn-taking awareness and response appropriateness. Additionally, we incorporate comprehension-based question-answering tasks as a complementary evaluation. By benchmarking 12 voice agents, we find that real-time voice agents stay at or below 22% on multiparty comprehension and remain near chance on multiparty turn-taking, exposing an open challenge for real-time voice agents under multiparty scenario.
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Artificial Intelligence
Autonomous Research for Open-Ended Problems: A Case Study on Telecom Ticket Retrieval
Recent breakthroughs in LLM-based systems and their abilities in problem solving and coding have allowed progress in the AI for Science paradigm, potentially replacing human roles in machine learning (ML) research. However, while several frameworks of fully autonomous end-to-end ML research have been proposed, successful implementations of them are often limited to problems with narrow search spaces, like language modeling or biomedical ML benchmarks. In this paper, we explore how autonomous research can be adapted to solve open-ended, industry-grade ML problems, by considering a case study: telecom ticket retrieval, an open-ended task with degrees of freedom in representation, architecture, and training data generation. We discover that autonomous research for open-ended problems with commercial and open-source agents shows both promise and limitations: while autonomous research can excel in narrow hyperparameter optimization, it lacks human-like intuition and creativity and requires operational overhead. Even with minimal human supervision, autonomous research can reach $90\%$ of state-of-the-art performance (0.34 vs. 0.38 Recall@1) in a much shorter time period (10 weeks vs. 10 months of human work) at a modest cost (up to \$200 per Cursor campaign). Our empirical evidence recommends that human researchers and autonomous research frameworks work together for best results in ML research.
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Machine Learning
MAxBench: A Multinomial Concept Recovery Benchmark
Fine-grained control of language model behaviors (e.g., steering) is among the more actionable outcomes of interpretability research. For binary concepts such as refusal, a single direction in activation space often suffices for steering. However, many concepts are not binary: Animals and Countries contain many subcategories, each with multiple instances. For these concepts, the search space over possible representation geometries is far larger than for binary concepts; it is thus not clear what geometries are most appropriate, nor what methods are most effective at recovering them. In this work, we introduce MAxBench, a geometry-agnostic evaluation framework for multinomial concept representations based on sampling from the recovered concept representation. We use MAxBench to compare 10 localization methods (covering 5 geometry types) across 6 concepts and 4 models. Using this framework, we find that (i) affine subspaces steer more reliably and have greater recall than rank-one or linear subspaces; (ii) much of this advantage is due to better non-zero offsets rather than the choice of bases; (iii) manifold steering is competitive with the best methods when applicable; and (iv) no method consistently outperforms prompting, in alignment with prior findings on binary concepts. These findings underscore the importance of expanding the scope of interpretability research and meta-evaluation to concepts with more varied structure.
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Software Engineering
Involving before Evolving: A Vision for Trustworthy Enterprise Digital Twin Engineering
Enterprise Digital Twins (EDTs) promise data-driven decision support at organizational scale, but realizing them requires navigating siloed departments, tacit knowledge, and high-stakes decisions with long-horizon consequences. Existing approaches involve domain experts during model development but focus less on early organizational buy-in in EDTs. We present a vision for trustworthy EDT engineering grounded in an `involving before evolving' paradigm: rapidly involving stakeholders through a working prototype before evolving toward federation and full interoperability. Our three-stage approach combines foundation models for rapid prototyping, an ontological backbone for federated interoperability, and observability tooling for stakeholder trust. We ground our vision in an ongoing collaboration with Michelin, a multinational manufacturer, where an initial prototype has helped support stakeholder buy-in.
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Computational Engineering
NFT-Based Reward Mechanisms: Sybil Farming, Vesting, and Stochastic Verification
We study NFT-based reward mechanisms in which a user can create multiple identities and submit fraudulent claims that mature a reward subject to vesting. We assume that the issuer stochastically verifies claims during the vesting period and that identities can be linked into clusters so that the detection of one identity submitting a fraudulent claim causes the whole cluster to be forfeited through a penalty. A farmer's payoff is then non-linear in the number of identities: rewards increase linearly, while the probability of avoiding detection decreases geometrically. We characterise the optimal farming scale in the continuous relaxation of the problem. This allows us to derive a sufficient condition for deterrence and then consider the issuer's choice of reward vesting and claim verification. Vesting reduces the probability that a fraudulent claim is paid but also affects genuine participants, while verification is costly for the issuer. We characterise the sufficient deterrence frontier for the issuer in terms of auditing cost, vesting schedule, and penalty value. When small amounts of audit capacity can be added at negligible marginal cost, vesting alone is not optimal. We also distinguish the role of penalties from that of cluster-level auditing. Finally, we discuss the implications for NFT reward programmes on high-throughput ledgers, such as Hedera.
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Artificial Intelligence
Anchoring Clinical Events in Time: UID-Preserving Multimodal Reconstruction and Source-Grounded Adjudication
Clinical timelines support treatment-window analysis and leakage-free modeling, but discharge summaries often obscure chronology and structured EHR tables describe only part of the patient course. We present a UID-preserving framework that links each narrative event occurrence to its source span and retains that identity through text-only estimation, structured-evidence retrieval, timestamped source-row grounding, and joint revision. We also present GAVEL, an LLM judge that compares two UID-aligned timelines against the narrative and structured record, to augment prior matching and temporal assessments. Across six open-weight models and 40 mixed-critical-care summaries, the GLM 5.2 multimodal revision, as compared to its text-only variant, improved temporal agreement without reducing event recovery and performed competitively with clinician annotations, while other model revisions showed smaller gains and lower overall performance. Ablations showed that UIDs primarily preserve event retention, whereas source-row linkage supports temporal placement. Blinded human review upheld most GAVEL findings, and controlled adjudication favored multimodal over text-only GLM 5.2 but did not for DeepSeek V3.2. In developing the UID and judge pipeline, we are able to demonstrate 43% increased event recovery, a framework competitive with clinician annotations, and a system with occurrence-level provenance for both reconstruction and evaluation.
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Machine Learning
CanvasAnneal: Curriculum Reinforcement Learning for Diffusion Language Models
Diffusion Language Models (DLMs) offer promising parallel generation capabilities but lag behind autoregressive models in complex reasoning and tool-use tasks. While Reinforcement Learning (RL) has recently been applied to enhance DLMs, standard RL approaches suffer from an exploration bottleneck. To address this, we inject reasoning priors from a stronger teacher model to guide RL exploration. In this paper, we introduce CanvasAnneal, a curriculum-guided diffusion RL framework. During the initial RL phase, we warm-start exploration by injecting teacher-generated reasoning traces into the initial diffusion canvas. As training progresses, we gradually remove this guidance and require the model to generate more of the reasoning trajectory independently. Across mathematical reasoning and tool-use benchmarks, CanvasAnneal improves over standard diffu-GRPO on MATH500, Countdown, and Tau2 and substantially accelerates reward improvement on several tasks, while gains are task-dependent. Our results suggest that structured training-time guidance can alleviate exploration bottlenecks in diffusion RL and speed up convergence on harder tasks.
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Computation and Language
Expert-Space Exploration in MoE Reinforcement Learning
Reinforcement learning (RL) has become central to post-training of large language models. Recent advances in RL for Mixture-of-Experts (MoE) models have primarily focused on improving optimization stability and training efficiency, while treating the expert selection as a fixed component. Since routing determines the sparse computation paths that induce output distributions, expert selection offers an additional source of rollout diversity. Through empirical analysis, we find that perturbing expert routing effectively alters model output and increases rollout diversity, which is similar to increasing the decoding temperature. However, direct perturbation can activate unsuitable experts and substantially degrade rollout quality. Motivated by these observations, we introduce Expert-Space Exploration Reinforcement Learning (ESRL), an architecture-aware framework that explicitly explores the expert-routing space of MoE models. ESRL preserves high-confidence experts as anchors, and restricts stochastic routing to a plausible candidate pool, thereby retaining reliable computation paths. The perturbation strength is further adapted according to router entropy to avoid over-perturbation. To mitigate the routing mismatch introduced by perturbation, ESRL records the expert paths used during rollout and replays them during policy optimization. Experiments demonstrate that ESRL achieves the best performance across MoE backbones with top-K, top-1, and shared-expert routing, as well as across mathematics, science, and code tasks without additional sampling or computational cost. Specifically, ESRL on Qwen3-30B-A3B achieves the best among all compared methods, improving average Pass@1 and Pass@8 over GRPO by 3.2 and 4.5 percentage points, respectively. Further analyses of expert utilization and training dynamics provide insights into how exploiting MoE-specific routing structure benefits RL training.
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Machine Learning
Benign Loss Landscapes Can Coexist with Worst-Case Hardness
Deep neural networks are expressive enough to contain worst-case targets that can be evaluated in polynomial time but cannot be learned in polynomial time by gradient descent. For practical tasks they nonetheless learn well, raising the question of what non-generic structure of real-world targets enables this. Existing surrogate models cannot pose this question because they either lack hard-to-learn targets entirely (deep linear networks) or cannot evaluate such targets efficiently (kernel methods, infinite-width limits). We study tree tensor networks (TTNs), a model class that generalizes deep linear networks and Tucker decompositions. We show they embed arbitrary read-once Boolean formulas, and thus contain polynomial-size targets that cannot be learned by gradient descent in polynomial time under the same mechanism as neural networks. Despite this, we prove that their loss landscapes are conditionally benign for every realizable target: every local minimum that is minimum-norm is global. Thus, surprisingly, bad local minima are not what distinguishes between typical and worst-case problems in TTNs. Instead, learning difficulty in TTNs can arise from high-order degenerate saddle points, which we show are caused by rank-deficiency. This is explored through a case study of the parity function, illustrating the potential for TTNs to relate landscape geometry to computational hardness.
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Robotics
Dynin-Robotics: Omnimodal Unified Diffusion Vision-Language-Action Model
Visual goal and dynamics prediction can provide language-conditioned robot policies with both a target outcome and a representation of action-dependent scene changes. We bring these predictions into action generation and selection through a shared trajectory model. Dynin-Robotics implements this formulation on Dynin-Omni, an omnimodal masked-diffusion backbone, representing language, visual observations, goals, and actions as discrete tokens. By varying conditioning and target spans, the same model learns action prediction, action-conditioned next-observation prediction, terminal goal-state prediction, and trajectory-to-instruction reconstruction. These interfaces support test-time scaling through goal prediction, action-candidate evaluation, and joint refinement of action and future-state predictions. We continually pretrain the model on approximately 1.33 million trajectories from 48 Open X-Embodiment datasets and adapt it separately to downstream domains. On two VLABench tasks, robot pretraining improves adaptation within a fixed Stage-2 step budget, and the full objective mixture improves shifted-instruction success over Policy-only post-training under the same coupled decoder. Combining goal guidance with joint action-next-state denoising further improves shifted-instruction success over action-only decoding; the benefit depends on how the predictions are composed. Dynin-Robotics achieves competitive performance on LIBERO and zero-shot LIBERO-Plus, together with a 78.4% average success rate across four manipulation conditions on a Franka Research 3 robot. An optimized block-parallel implementation accelerates model-side action decoding by up to 29.2x relative to the base implementation under the reported profiling setup. These results support shared trajectory modeling as a common interface for learning complementary robot objectives and composing their predictions during control.
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Machine Learning
A Unified and Constrained View of Regularization-Based Robust Reinforcement Learning
Regularization-based methods have become a standard approach for training Deep Reinforcement Learning policies against adversarial input perturbations. In this paper, we unify these methods by deriving new upper bounds on the performance gap between the nominal and worst-case policies. Each upper bound is expressed as an existing regularization objective plus a KL-divergence penalty between the nominal and worst-case policies, which further explains why adding a KL penalty improves robustness in practice. Building on these bounds, we formulate robust training as a constrained optimization problem, showing that existing methods correspond to the special case of a fixed Lagrange multiplier. We instead update the multiplier jointly with the policy to automatically tune the regularization weight. Finally, we conduct extensive adversarial evaluations across several continuous control tasks to validate our theoretical analysis.
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Machine Learning
MCRL2: Multi-resource Cross-attention-based Representation Learning-augmented Reinforcement Learning for Cloud Microservice Scheduling
Efficient microservice scheduling is crucial for maintaining load balance across nodes in data centers and ensuring high quality of service. However, achieving this in practice remains challenging due to dynamic resource imbalance under fluctuating workloads, nonlinear coupling across multiple resource dimensions, and the heterogeneity of microservice resource demands. While reinforcement learning-based approaches have shown promise, they struggle to capture the complex interdependencies among heterogeneous resources and neglect the importance of learning informative system representations. To address these limitations, we propose MCRL2, a novel reinforcement learning approach augmented with multi-resource cross-attention-based representation learning for microservice scheduling. Specifically, we first propose MCRL, a novel representation learning approach that captures structured and informative interactions among nodes, resources, and microservices via a multi-resource cross-attention mechanism. Then, MCRL2 augments reinforcement learning through MCRL-enhanced actor-critic architecture combined with a maximum entropy objective, improving system state expressiveness and leading to more stable and effective scheduling decisions. Extensive experiments on real production cluster traces demonstrate that MCRL2 significantly outperforms existing baselines in load balancing, scheduling success rate and average completion time across diverse workload patterns.
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Artificial Intelligence
Diffusion Models and Concept Formation
Humans organize knowledge into a taxonomy of concepts with nested levels of abstraction and a basic level at which people recognize and name objects with the least cognitive effort. Cobweb is a classic cognitive account of this ability, an incremental learner that builds a probabilistic concept hierarchy by maximizing category utility. We argue that diffusion models, although designed for image synthesis, implicitly perform the same computation. The noisy marginals of a diffusion model are Gaussian smoothings of the data distribution, and the modes of these marginals form a hierarchy that corresponds to a Cobweb tree of probabilistic prototypes in four respects. Both are hierarchical density models, both are hierarchical-Bayesian models with Gaussian prototypes, both treat categorization as score-following that reduces uncertainty, and in both a basic level emerges. We locate this basic level for a diffusion model at an intermediate noise level, where recent analyses show that the reverse process commits to the class identity of a sample. The two models differ mainly in how they represent and learn the taxonomy. Cobweb learns a discrete tree incrementally, whereas a diffusion model encodes a continuous, interpolable hierarchy in a single learned score field fit to the data distribution. We test the correspondence on MNIST and Fashion-MNIST by recovering the diffusion hierarchy through mode-finding and comparing the basic levels of the two models. This reframes diffusion as a cognitive model of concept formation and offers Cobweb a continuous, scalable instantiation.
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Computation and Language
Kraken: LLM-based Speech-to-Speech Translation via Low-bitrate VQ and Dual-path Source Conditioning
Speech-to-speech translation (S2ST) has advanced significantly with speech LLMs, offering the potential for joint optimization and preserving non-linguistic information. However, these models struggle with predicting high-bitrate speech tokens in LLMs, and face the challenge of relying on S2ST training data with ideally aligned speaker identity and prosody. We propose using low-bitrate tokens based on single-layer vector quantization, trained to reconstruct self-supervised learning (SSL) features. We also employ a separate token-to-waveform decoder named Autowave-X, which is also conditioned on the source speech to improve non-linguistic transfer, thereby relaxing the training data constraints. With the integration of these techniques, we propose an S2ST model named Kraken, which augments a pre-trained LLM with speech feature inputs and the low-bitrate token outputs, followed by Autowave-X vocoder. We built the model upon Qwen3-8B and trained it using 150k hours of multilingual and multitask speech data. We demonstrated that our model exhibited better translation quality than SeamlessM4T-Large v2 and Qwen2.5-Omni, along with improved speaker and prosody transfer capabilities.
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Machine Learning
Robust Policy Optimization via Adversarial Importance Sampling
Significant progress has been made in safeguarding Deep Reinforcement Learning (DRL) policies against input perturbations. Developing robust DRL involves three main stages: algorithm design, implementation, and evaluation. In this work, we identify and address a key limitation at each stage. First, we introduce Adversarial Importance Sampling (Advis), a method that estimates and optimizes worst-case returns directly from trajectories already collected during standard training. Advis satisfies three desirable criteria that prior work does not jointly achieve: it requires no additional environment interactions, no auxiliary networks, and captures long-term robustness. Second, we introduce advrl, a modular PyTorch library that provides clean, single-file implementations of existing robustness methods and adversarial attacks, enabling rapid prototyping and reproducible evaluations. Third, we revisit evaluation under learned adversaries and show that optimal adversarial hyperparameters do not transfer across agents, which can lead to an overestimation of robustness when using a limited set of attacker configurations. Accordingly, we evaluate policies against a large and diverse set of attackers, using 6 to 14 times more configurations than prior work. Finally, experiments on continuous control environments show that Advis achieves stronger worst-case performance and greater training efficiency than existing baselines.
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Computer Vision
Unified CT and MRI Pancreas Segmentation for Label-Efficient Cross-Modality Subregion Transfer
Robust medical image segmentation across imaging modalities is challenging because of large differences in appearance and intensity distributions. Models trained on a single modality often show substantial performance drops when applied to unseen domains. In this work, we develop a unified 3D pancreas segmentation framework that applies domain-adversarial learning to 4,604 heterogeneous CT and MRI scans to learn anatomical representations. A shared nnU-Net encoder-decoder is trained for whole-pancreas segmentation, with a latent domain discriminator encouraging CT-MRI feature alignment. The learned encoder is subsequently transferred to pancreatic head-body-tail segmentation using limited MRI-only subregion annotations. An average Dice score of 87.31% on the in-distribution test set and Dice scores ranging from 84.20% to 88.09% across external OOD datasets were achieved in whole pancreas segmentation. Dice scores of 80.53% on MRI and 83.05% on CT were achieved for downstream subregion segmentation, without using CT subregion annotations. These results demonstrate that a unified anatomical representation can support both cross-modality pancreas segmentation and label-efficient downstream transfer.
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Machine Learning
DynSHAP: Towards Explainable Dynamic Survival Analysis
Deep learning models for dynamic survival analysis (DSA) achieve strong predictive performance by incorporating longitudinal patient data, but their black box nature limits clinical trust and adoption. Existing explainability methods cannot handle longitudinal, irregular inputs and functional survival outputs simultaneously, which limits their usability in DSA. We propose DynSHAP, a SHAP framework suited specifically for dynamic survival analysis. It extends common marginal SHAP estimators to this setting by treating time–feature pairs as players in the Shapley game. We further introduce Temporal DynSHAP, which learns linear dependencies in features over time and uses conditional sampling to address them in explanations. When applied to synthetic data with known ground-truth attributions, Temporal DynSHAP recovers temporally dependent features more accurately than marginal estimators for a given state-of-the-art model. Applied to two real-world clinical datasets and two DSA architectures, DynSHAP produces attributions faithful to model learning, allowing medical experts to see which patient information drove the prediction and when.
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Machine Learning
Quantile-based Loss Filtering for Outlier-Robust Stochastic Gradient Descent
We study loss-based filtering for finite-sum optimization with a subset of corrupted component functions whose gradients may be highly unreliable. Motivated by minimum-loss-based SGD (min-$k$-loss) and quantile-based methods for corrupted linear systems, we propose and analyze a general loss-filtering framework – Quantile-\(k\)-Loss SGD (Q\(k\)L-SGD) – that samples \(k\) component losses at each iteration and updates using an index chosen uniformly from the lower empirical \(q\)-quantile. We prove linear convergence of this family of methods under standard convexity assumptions, requiring the sample size to scale with the number of corruptions and a subset strong-convexity threshold. For the cases when large enough sampling is impossible or undesirable, we give a complementary small-sample probabilistic analysis that covers any sample size $k$ and the convergence behavior depends on the probability of selecting an outlier and on the curvature of the selected good step. Experiments on polynomial regression, regularized logistic regression, and regularized hinge loss show that intermediate quantiles often outperform both standard SGD and min-\(k\)-loss SGD. In particular, min-\(k\) often stalls by repeatedly selecting nearly solved components, while intermediate quantiles retain robustness and produce more informative updates.
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Machine Learning
Transfer Learning for Evolving Domains
Transfer learning explores how to leverage knowledge from various tasks or domains (sources) to enhance predictive performance in related tasks or domains (targets). Typically, transfer learning research is segmented into several isolated sub-areas (such as domain generalisation, domain adaptation, or multi-domain learning), each making distinct assumptions about target data availability, namely how much data and how many labels are available at training time. However, in many real-world applications, data availability is not fixed but evolves over time, as instances and labels are progressively collected from a new domain. Each of the classical settings then describes only a snapshot of a trajectory that a deployed system must traverse in full. We formalise this trajectory as a transfer learning problem in its own right, Transfer Learning for Evolving Domains (TrED), specified by a data availability process fixed by the environment, a learning protocol that the method is free to choose, and an evaluation criterion that scores the whole trajectory of models rather than a single one. Within this formalism, the classical settings are recovered as regimes that a learner may pass through, rather than as separate problems that TrED concatenates. We then examine the transfer learning literature to identify mechanisms that are promising building blocks for a solution, and find that most methods are tailored to a single regime and that even the strongest existing candidates do not yet optimise the whole trajectory. We argue that TrED is a well-posed and unsolved problem, and an important direction for future research.
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Game Theory
Mitigating Emergent Collusion in LLM Pricing Agents
Recent work shows that LLM-based pricing agents can produce supracompetitive outcomes in repeated oligopoly environments without being explicitly instructed to collude. We reproduce the qualitative prompt-sensitivity effect of Fish et al. using DeepSeek-V3.1: the P1 prompt produces significantly higher prices and profits than P2, although our outcomes are less monopoly-like than the original GPT-4 results. We then evaluate three regulatory interventions: a prompt-only warning, a Harrington-inspired expected-damages payoff regulator, and an active random entrant. The prompt-only regulator reduces but does not eliminate above-Nash pricing. The Harrington regulator brings P1 outcomes close to the duopoly Nash benchmark and removes the statistically significant P1–P2 gap. The active entrant produces the strongest effect, pushing both prompts below the appropriate random-entrant Nash benchmark. Overall, our experiments provide preliminary evidence that interventions that alter incentives or market participation can reduce supracompetitive pricing more effectively than prompt warnings alone.
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Machine Learning
Groupoid-Based Internal State Representations for Reinforcement Learning with Local Symmetries
Symmetries play a central role in reducing the complexity of reinforcement learning problems, yet most existing approaches rely on fixed group actions or predefined state abstractions. Classical reinforcement learning algorithms typically assume a globally structured Markov decision process with uniformly applicable actions and transitions, an assumption that limits their ability to exploit modularity and local, context-dependent regularities present in many realistic environments. We propose a reinforcement learning framework using groupoids to capture local, state-dependent symmetries and support the dy- namic discovery of equivalence structures during interaction. The agent maintains orbit representatives together with transporters that map raw states to canonical forms, enabling learning and decision-making to be performed in a symmetry-reduced space while preserving local distinctions. Empirical results demonstrate that the proposed groupoid-based approach improves sample efficiency and convergence in dense and large-scale environments exhibiting strong partial symmetries, yielding substantial performance gains over standard Q-learning. These findings show that dynamically exploiting local symmetry provides a practical and mathematically principled route to scalable and generalisable reinforcement learning.
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Computational Complexity · Cross-listed from quant-ph
QMA has perfect completeness
We prove $\mathsf{QMA} = \mathsf{QMA_1}$, i.e., every quantum Merlin-Arthur proof system can be made perfectly complete. Our construction uses only Hadamard, Toffoli, and $X$ gates, yielding a universal gate set for $\mathsf{QMA_1}$. As a consequence, quantum $3$-SAT is $\mathsf{QMA}$-complete. The construction relativizes to classical oracles, so known classical-oracle separations of $\mathsf{QMA}$ from $\mathsf{QCMA}$ extend to $\mathsf{QMA_1}$.
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Machine Learning
Attention Quantization for Tabular Foundation Models
With the recent rise and adoption of tabular foundation models, optimizing their inference performance becomes an emerging field for efficiency research. While the models are architecturally similar to transformer-based large language models (LLMs), the size and serving patterns differ significantly. We show that the focus should be on the attention calculation and less on weight or KV cache quantization, which are more popular in LLMs. We develop a quantization strategy for queries, keys, and values to FP8 and use explicit FP8 matrix multiplication instructions to speed up the attention calculation. We find that it is crucial to align the quantization error in the test rows with the quantization error in the training rows, as otherwise the accuracy drops drastically. Our Triton kernel achieves a speedup up to 1.7x over regular 16-bit kernels, and we show that on TabPFN-v3 and TabICLv2 there is no relevant accuracy loss across TabArena and BeyondArena.
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Computer Vision
Label-Guided Knowledge Distillation for 3D-CNNs in Action Recognition
As a key model compression technique, knowledge distillation aims to transfer knowledge from a high-capacity teacher model to a lightweight student model for enhancing the latter's performance. In this work, we reviewed the feature knowledge distillation for 3D-CNNs and observed that most feature distillation methods in video analysis are simple adaptations of those used in image analysis, often neglecting the differences of video features in the temporal dimension. To address this issue, we proposed Label-Guided Knowledge Distillation (LGKD) to guide the distillation of student model features using ground truth labels. Our method entails two components: sample-wise distillation and class-wise distillation, enabling the student model to learn feature representation of the teacher model at two levels. Sample-wise distillation utilizes label information and the teacher's probability distribution to guide the learning of features that significantly impact temporal accuracy while mitigating noise. Meanwhile, class-wise feature distillation employs a prototype network to further capture the relational knowledge among samples within the same category, enhancing the student's ability to learn higher-dimensional semantic information and improving model generalization. To demonstrate the effectiveness and superiority of our method, we conducted comprehensive experiments on two benchmark action recognition datasets, UCF101 and HMDB51, achieving competitive results.
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Robotics
Global Path Planner with Multi-Model Switching
This work enhances global path planning via a pure-pursuit controller with multi-model kinematic switching that sustains plan fidelity across diverse terrains. The system includes a traversability graph for terrain analysis, a Heading-Aware A* algorithm for generating feasible paths, and a multi-model Pure Pursuit controller for dynamic tracking. A core innovation is adaptive kinematic modeling, enabling real-time switching between kinematic models based on terrain features and robot states. This adaptability optimizes path efficiency and energy use in challenging scenarios. We validate the approach in simulation on different platforms, namely the Artaban quadruped and the X3 quadrotor drone, showcasing improved performance, robustness, and adaptability over standard baselines.
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Computer Vision
TileNet: Tile-Based CNN-SVM Architecture for Autonomous Unmanned Aerial Systems Inspection of Flat Roofs
Flat roofs are among the most influential components of the building envelope, governing both structural performance and thermal efficiency, and thereby contributing directly to household energy consumption, carbon emissions, and long-term environmental sustainability. Timely detection of roof defects is essential for reducing heating and cooling losses, preventing moisture-driven degradation such as mold growth, and supporting national climate-change mitigation goals. This paper presents a real-time, Unmanned Aerial System (UAS)-based deep learning framework that autonomously detects defects using live imagery captured during dual-altitude aerial passes. The multi-resolution flight strategy is designed to aid the identification of both small, fine-scale defects and larger structural issues, enabling more comprehensive assessments. To meet the strict computational and power constraints of embedded UAS hardware, the proposed framework integrates a tile-based architecture with a lightweight Convolution Neural Network-Support Vector Machine (CNN-SVM) classifier designed for low-latency onboard inference. The final model-comprising five convolutional layers and four dense layers, the last a linear SVM head, achieved a mean test accuracy of $94.4\%$ ($95\%$ confidence interval $\pm0.4\%$ over three seeds) on a photo-level split ($43,383$ training, $3,869$ validation, and $2,540$ test tiled and augmented images), outperforming GoogLeNet ($89.2\%$) and AlexNet ($79.8\%$). Experimental evaluations using real UAS imagery collected by onsite visits with DJI Matrice 350 RTK drone demonstrate that the system supports rapid, repeatable, and safe roof inspections while reducing human risk, lowering operational costs, and enabling more sustainable building maintenance.