arXiv:2607.05411v1 Announce Type: new Abstract: Higher education institutions are increasingly expected to ensure that both students and staff develop Generative AI (GenAI) literacies. In response, they are introducing professional development programs and embedding GenAI skills within student curricula. However, current educational frameworks typically assume a linear progression of GenAI literacy, implying that foundational technical understanding must precede creative application. This paper challenges such an assumption through a psychometric analysis of a taxonomy-based self-assessment instrument (n = 158). We applied Rasch measurement theory and Guttman ordering to map the latent perceived order of difficulty of GenAI skills across students, academics, and professional staff. Results reveal a fundamental divergence in perceived competence profiles: while academics follow a more traditional linear path, students exhibit an "inverted" profile, frequently mastering high-level creation tasks before acquiring foundational conceptual understanding. Furthermore, the correlation of skill difficulty between students and academics was weak (r = 0.188). We argue that this "skill bypass" creates a fragile sense of fluency, where high self-efficacy in prompting masks low literacy in AI mechanics. These findings challenge the "one-size-fits-all" curricula and provide the empirical basis for diagnostic-driven, modular interventions that foster genuine human-AI synergy.
Science Journals
arXiv:2607.05416v1 Announce Type: new Abstract: We present a new method for structural sequence analysis grounded in Algorithmic Information Theory (AIT). At its core is the Ladderpath approach, which extracts nested and hierarchical relationships among repeated substructures in linguistic sequences -- an instantiation of AIT's principle of describing data through minimal generative programs. These structures are then used to define three distance measures: a normalized compression distance (NCD), and two alternative distances derived directly from the Ladderpath representation. Integrated with a $k$-nearest neighbor classifier, these distances achieve strong and consistent performance across in-distribution, out-of-distribution (OOD), and few-shot text classification tasks. In particular, all three methods outperform both gzip-based NCD and BERT under OOD and low-resource settings. These results demonstrate that the structured representations captured by Ladderpath preserve intrinsic properties of sequences and provide a lightweight, interpretable, and training-free alternative for text modeling. This work highlights the potential of AIT-based approaches for structural and domain-agnostic sequence understanding.
arXiv:2607.06077v1 Announce Type: new Abstract: Photonic time crystals (PTCs) host momentum bandgaps, or k gaps, that enable parametric amplification and lasing of seeded fields. In nonlinear PTCs, Kerr saturation dynamically suppresses the exponential growth, reshaping k-gap amplification into an active, spatially homogeneous k gap soliton train. Here, we show that a localized perturbation on this unstable background then nucleates a transient spatiotemporal excitation: the breathing k gap event. Unlike Peregrine breathers emerging from modulational instability on a planewave background, this event extracts energy from competing host k gap solitons and remains sustained by their interaction. We identify this process as an instability on instability mechanism intrinsic to nonlinear k gap dynamics. The event is robust against noise and disorder, and can be deterministically reshaped into collective breathing patterns by periodic and phase engineered seeding. These results establish k gap engineering as a route to generating and controlling extreme spatiotemporal waves in photonic time varying media.
arXiv:2605.22775v2 Announce Type: replace Abstract: Real-time cognitive load assessment from eye-tracking signals could enable adaptive human-centered AI in safety-critical applications such as driver vigilance monitoring or automated flight deck assistance, yet two challenges persist: handling frequent data missingness from blinks and tracking failures, and efficiently modeling long-range temporal dependencies. We propose MambaGaze (Bi-Mamba), a framework that addresses these challenges through (1)~XMD encoding, which augments raw features with observation masks and time-deltas to explicitly model data uncertainty, and (2)~bidirectional Mamba-2, which captures temporal dependencies with linear computational complexity. Experiments on CLARE and CL-Drive datasets under leave-one-subject-out evaluation show that MambaGaze achieves 77.1\% accuracy and 59.2\% macro-F1 on CLARE, and 69.4\% accuracy and 51.5\% macro-F1 on CL-Drive, attaining the highest average LOSO macro-F1 (55.3\%) across all ten compared models. Input-stream ablation indicates that log-scaled time-deltas are the strongest single channel in our setting, and combining all three XMD streams provides consistent gains of 5--20\,pp macro-F1. Edge deployment benchmarks on three NVIDIA Jetson Orin platforms show real-time inference at 27--36\,FPS with power consumption below 6.6\,W, supporting feasibility for embedded cognitive load monitoring.
arXiv:2605.23128v2 Announce Type: replace Abstract: Currently, Vision-Language-Action (VLA) models have become the most adopted paradigm for robotic manipulation for its great potential for task generalization. While most generative flow-matching action decoders for VLA control are often deployed with fixed sampling horizons, limiting state-dependent compute and temporal reuse across control cycles. We present $\pi_0$-EqM, which replaces the flow-matching expert in $\pi_0$ with an Equilibrium Matching (EqM) decoder while leaving the upstream VLA stack unchanged. Under a matched 300-step budget, $\pi_0$-EqM improves RoboTwin average success from 40.4% to 50.2% across 19 tasks and remains competitive on LIBERO, with its clearest gain on LIBERO-10 (87.0%). Two threshold scans reveal a task-dependent non-monotonic relation between residual and success, which we term the stationarity--executability gap. The results suggest that inference depth in iterative VLA control is part of policy design and introduce an energy-based VLA perspective that may inform future work on composable action generation across tasks and embodiments.
arXiv:2605.23826v2 Announce Type: replace Abstract: Keyframe selection is a direct way to provide verifiable visual evidence for long-video question answering (QA). Queries differ in what they require, and finding the right frames depends on knowing what to look for. Existing keyframe selectors either score every frame against a single query, or decompose the query into a fixed schema evaluated by a single visual tool. We propose ToolMerge, a keyframe retrieval method based on decomposition and merging: an Large Language Model (LLM) based planner decomposes the query into tool calls and specifies how their per-tool rankings are merged using boolean operators. To evaluate retrieval directly, we construct Molmo-2 Moments (M2M), a benchmark in which every question is anchored to a specific time interval by construction. Across QA, question retrieval, and caption retrieval, ToolMerge is competitive with prior keyframe selectors, most notably on caption retrieval, outperforming other methods by 5%. Code and data can be found at https://github.com/michalsr/ToolMerge .
arXiv:2605.24709v2 Announce Type: replace Abstract: Streaming reinforcement learning has emerged as an online learning paradigm that conforms to the restrictions of natural learning agents that process data incrementally, i.e. with a batch size of 1 and no replay buffer. While streaming RL has recently been shown to scale with deep function approximation with full observability, partially observable settings have remained out of reach. Truncated backpropagation through time collapses to a one-step gradient horizon under the streaming setting, and exact real-time recurrent learning is prohibitively expensive. We close this gap using recurrent trace units, a diagonal recurrent architecture that enables exact RTRL with linear time and memory complexity in the parameter count, and show that they integrate cleanly into existing streaming algorithms across both discrete and continuous control. On a MemoryChain diagnostic with chain lengths from 2 to 128, our method sustains performance where streaming TBPTT(1) baselines using feedforward, GRU, and RTU networks collapse. On five POPGym tasks and on partially observable MuJoCo continuous control, the streaming approach is competitive with batched PPO on POPGym and recovers a substantial fraction of batched performance on masked MuJoCo, despite using no replay buffer or batched updates.
arXiv:2607.06087v1 Announce Type: new Abstract: This paper presents an approach and application of optimization of spatial packaging of interconnected systems with physical interactions (SPI2) in three-dimensional component placement problems. To enable its application for an automotive use case, SPI2 must support both initial design generation, including component alignment, and robust system-level coordination, requiring improved solution reliability and tractable computational cost. To address these requirements, the proposed methodology improves convergence rate and solution quality by enhancing numerical robustness in gradient-based optimization while reducing computational load. Existing SPI2 approaches are extended through the addition of alignment capabilities, enabling the representation of port-to-port alignments between components. Furthermore, the applicability of SPI2 is expanded by treating component placement locations as design variables, allowing for penalty-based coordination to ensure design feasibility and enabling integration within system-level optimization. The approach is validated using a multi-objective optimization framework based on Nondominated Sorting Genetic Algorithm II (NSGA-II), applied to a combined powertrain optimization and battery chassis integration problem. This demonstrates the effectiveness of the SPI2 in a system-level design context. The results show a twofold application of SPI2 in an automotive use case: first, as a tool for initial design generation, and second, as part of a system-level design coordinator that outperforms a discretized exhaustive search while requiring lower computational cost.
arXiv:2607.05436v1 Announce Type: new Abstract: The rapid scaling of over-parameterized machine learning architectures, particularly LLMs, raises a profound crisis: do these systems exhibit genuine intelligence, or are they merely sophisticated statistical pattern matchers? Classical flat Euclidean statistics cannot differentiate continuous interpolation from the autonomous discovery of novel causal laws. To resolve this, we introduce Statistically Meaningful Geometry (SMG), a framework modeling over-parameterized learning systems as infinite-dimensional non-parametric Orlicz fiber bundles. We prove that under persistent out-of-distribution (OOD) stimuli governed by unmodeled causal mechanisms, continuous optimization fails. Unmodeled variance is rejected by the visible horizontal base manifold, leaking into the unobservable vertical fiber space and generating an accumulation of Active Acausal Tension. Driven by the statistical manifold's non-linear curvature, this tension inevitably strikes a conjugate focal boundary ($T_{\text{crit}} = \pi^2 / K_{\text{max}}$), triggering localized volumetric collapse and a catastrophic matrix singularity ($[G_f]^{-1} \to \infty$). We demonstrate this geometric breakdown acts as the strict non-equilibrium trigger for a Gauge Symmetry Break (GSB). The system purges hidden tension from unobservable gauge redundancies, spontaneously crystallizing a new, mathematically independent horizontal coordinate axis. This non-parametric phase transition registers as a discrete $+1.0$ integer step-jump in observable Structural G-Entropy. By decoupling parameter charts and subjecting emergent axes to a Minimal Energy Path Criterion and a Causal Invariance Filter, we distinguish genuine discovery from malignant hallucinations. Ultimately, SMG provides a parameter-free, falsifiable dashboard to mathematically certify true intelligence, transforming AI for Science into an engine of autonomous paradigm shifts.
arXiv:2511.06229v3 Announce Type: replace Abstract: This paper focuses on dynamic origin-destination matrix estimation (DODE), a crucial calibration process necessary for the effective application of microscopic traffic simulations. The fundamental challenge of the DODE problem in microscopic simulations stems from the complex temporal dynamics and inherent uncertainty of individual vehicle dynamics. This makes it highly challenging to precisely determine which vehicle traverses which link at any given moment, resulting in intricate and often ambiguous relationships between origin-destination (OD) matrices and their contributions to resultant link flows. This phenomenon constitutes the credit assignment problem, a central challenge addressed in this study. We formulate the DODE problem as a Markov Decision Process (MDP) and propose a novel framework that applies model-free deep reinforcement learning (DRL). Within our proposed framework, the agent learns an optimal policy to sequentially generate OD matrices, refining its strategy through direct interaction with the simulation environment. This approach was evaluated through a toy experiment on the Nguyen-Dupuis network and a case study utilizing an actual highway subnetwork spanning Santa Clara and San Jose. Experimental results show that the proposed method consistently improves calibration performance relative to the strongest conventional baseline, reducing link-flow MSE by 23.7% in the toy experiment and by 59.2-88.3% in the real-world case study. By reframing DODE as a sequential decision-making problem, our approach addresses the credit assignment challenge through a learned policy and provides a novel framework for calibration of microscopic traffic simulations.
arXiv:2607.06094v1 Announce Type: new Abstract: Faults on a cyber-physical system (CPS) are too rare and unrepresentative to characterise, or even to select a model on, so detection must instead model normal behaviour; the standard point-adjusted evaluation, however, rewards detectors that never do. CPS normal behaviour is the union of many imbalanced, curved, thin-fringed operating regimes rather than a single blob; we state this structure as ten assumptions (A1-A10), abbreviated Massive, Implicit, Imbalanced Multimodality (MIIM). We model the normal law with a jointly learned latent representation plus explicit Gaussian-mixture mode clustering, scored in the latent rather than by a global density or a reconstruction residual, and evaluate under a deliberately fair protocol: raw point-wise metrics with no point adjustment, a trivial-detector difficulty split, prevalence-matched F1, and train-normal-only calibration. On three real CPS datasets (WADI, HAI, SKAB), the detector wins both the combined column and the difficult correlation/dynamics-fault column on all three, reaching difficult-subset AUROC 0.831 on HAI, 0.726 on WADI, and 0.610 on SKAB. The margin is largest on the two multimodal datasets the MIIM assumptions target and slimmest on the near-unimodal one, tracking multimodality as the thesis predicts, and it holds against three deep detectors (USAD, TranAD, GDN) re-computed with the same raw metrics, all of which collapse on the difficult subset. The methodological contributions are the MIIM assumption set, the difficulty-stratified fair protocol, and a latent-only score that drops reconstruction because a flexible decoder rebuilds the hard faults faithfully.
arXiv:2607.05458v1 Announce Type: new Abstract: Large language model (LLM) agents are usually improved by changing prompts, models, or hand-written workflows, while the execution harness around the model is treated as fixed infrastructure. We argue that this harness is itself a learnable control layer. We formalize harness operation as a finite-horizon Harness MDP, where a lightweight controller selects structural execution actions while the LLM executor remains frozen. The controller is trained from offline rollouts using advantage-weighted regression with only terminal task-rubric rewards. We also separate final task quality from a post-hoc Harness Maturity Score, which measures whether the harness follows reliable execution patterns rather than only whether the final answer is correct. This separation gives a finite-buffer view of harness learning: final-quality gains require high-return support in the offline buffer, while process behavior can shift whenever it aligns with advantage-weighted actions. Across six controlled domains and two public-benchmark adapters, the learned controller consistently improves verification behavior and selectively improves final task quality, with the largest gains on adapted tau-bench retail, adapted AgentBench DB-Bench, and coding with a calibrated structural verifier. Ablations against behavior cloning and Forced CHECK show that the gains are not explained by imitation or by simply adding checks. These results identify harness control as a learnable layer for frozen LLM agents, while showing that offline support limits when better process control becomes better final answers.
arXiv:2607.05894v1 Announce Type: new Abstract: Modern software supply chains comprise hundreds of transitive dependencies, yet existing analysis tools operate at either the ecosystem level (dependency graphs) or the code level (static analysis within packages). This separation creates two failure modes. First, false-positive CVE alerts for unreachable code. Second, blind spots for structurally critical micro-dependencies. We introduce cross-level risk propagation, a framework that bridges code-level risk metrics with ecosystem-level dependency exposure through a unified risk formula. Preliminary evaluation on 50 packages across npm and PyPI reveals a class of hidden amplifiers -- micro-dependencies with fewer than 50 methods but over 50,000 dependents -- that carry outsized supply-chain risk invisible to all current Software Composition Analysis (SCA) tools. Without cross-level analysis, such packages can harbor exploitable code for years because no current tool considers both internal code structure and ecosystem position simultaneously. These results suggest that cross-level analysis opens a new design space for supply-chain security.
arXiv:2605.25451v3 Announce Type: replace Abstract: Training multimodal large language models (MLLMs) is challenged by both model and data heterogeneity. Existing systems redesign the training pipeline to address these challenges, but remain bound by a Pareto frontier between compute and memory efficiency, improving one only at the expense of the other. We present BigMac, a new training pipeline for multimodal LLMs. The core idea of BigMac is to elegantly nest the encoder and generator computation into the original LLM pipeline, forming a dependency-safe nested pipeline structure. With this design, BigMac reduces the activation memory complexity of the encoder and generator to O(1) while keeping the activation memory complexity of the LLM unchanged. At the same time, it achieves the same computational efficiency as the idealized setting with unlimited memory. As a result, BigMac breaks the Pareto frontier between computational efficiency and memory usage, enabling simultaneous optimization of both computation and memory in MLLM training. We evaluate BigMac on multiple MLLMs and training workloads. Experimental results show that BigMac achieves a 1.08$\times$-1.9$\times$ training speedup over baseline systems while maintaining stable memory usage as batch size increases.
arXiv:2605.29655v3 Announce Type: replace Abstract: Autoregressive multimodal large language models (MLLMs) enable 3D generation but struggle to scale to high-resolution shapes due to inadequate 3D tokenizations. Compact set-based representations discard deterministic spatial ordering, leading to ambiguous sequence prediction, while uniform or octree-based voxel grids preserve ordering at the cost of severe redundancy and excessively long sequences. This structural trade-off limits stable and efficient autoregressive 3D generation. We present SuperVoxelGPT, a representation-first framework that resolves this tension through adaptive and deterministically ordered supervoxel tokenization. Given a prompt, we first predict a coarse geometric saliency distribution and construct a shape-adaptive supervoxel partition using saliency-guided centroidal Voronoi tessellation, allocating fine-grained cells to complex regions and larger cells to smooth regions. Conditioned on this prompt and ordered supervoxel layout, we introduce a SuperVoxelVAE and fine-tune a pretrained MLLM to autoregressively generate supervoxel tokens. Experiments using Trellis-500K data show that SuperVoxelGPT reduces token sequence length to 12.8% of uniform voxel tokenization while achieving state-of-the-art generation quality and an average 10x speedup over prior methods.
arXiv:2605.30794v2 Announce Type: replace Abstract: Multimodal Large Language Models (MLLMs) have demonstrated significant achievements in general visual question answering (VQA) tasks. However, they remain brittle on mechanical engineering drawings, where high annotation density and weak domain knowledge, compounded by unreliable spatial relation reasoning under strict projection rules and geometric constraints, make decisive cues easy to miss and frequently lead to wrong answers. To bridge this gap, we introduce the first comprehensive mechanical drawing understanding dataset, MechVQA, created through a semi-automated construction and quality-control pipeline. MechVQA contains 3.3k high-density pictures with 21K question-answer pairs, spanning 10 different fine-grained tasks across three capability levels: Recognition, Reasoning, and Judging, providing a testbed to evaluate and improve MLLM understanding on real-world mechanical drawings. On top of MechVQA, we then develop the MechVL model through a multi-stage training paradigm, building a strong domain-specialized baseline. Extensive experimental results demonstrate that MechVL outperforms the strongest closed-source baseline by 7.57 percentage points on the MechVQA total score, significantly enhancing mechanical drawing understanding ability and providing a reusable foundation for deploying MLLMs in mechanical design and inspection scenarios.
arXiv:2605.30796v5 Announce Type: replace Abstract: This paper presents a rigorous convergence analysis for the lightning plus polynomial approximation scheme, which employs rational approximations constructed with preassigned tapered, exponentially clustered poles. This pole placement strategy was originally introduced by Trefethen and his collaborators for the resolution of corner singularities. Ample numerical results indicate that this scheme achieves root-exponential convergence, and in particular attains the same optimal convergence rate as the best rational approximation to $x^\alpha$ on $[0,1]$ established by Stahl.% which is conjectured in [SIAM J. Numer. Anal., 61:2580-2600, 2023]. In this work, we establish optimal root-exponential convergence for the class of prototype functions of the form $g(z)z^\alpha$ or $g(z)z^\alpha\log z$, where $g$ is analytic on a neighborhood of the sector domain. These results confirm the validity of Conjectures 3.1 and 5.3 stated in [SIAM J. Numer. Anal., 61:2580-2600, 2023], and demonstrate that the choice $\sigma_{\mathrm{opt}} =\frac{\sqrt{2(2 - \beta)}\pi}{\sqrt{\alpha}}$ achieves the theoretically optimal convergence rate $\mathcal{O}\left(e^{-\sqrt{2(2 - \beta)N\alpha}\pi}\right)$. Notably, for the specific case of $\beta = 0$, the scheme recovers Stahl's optimal convergence rate for $x^\alpha$. Furthermore, working within the decomposition framework for corner domains proposed by Gopal and Trefethen, this paper provides a rigorous proof of optimal root-exponential convergence for lightning plus polynomial approximation problems on corner domains, and explicitly derives the optimal pole clustering parameter.
arXiv:2607.05565v1 Announce Type: new Abstract: Conventional non-invasive photothermal imaging techniques are fundamentally constrained by the diffusive nature of heat transport, which causes severe energy dissipation during subsurface reconstruction. Although modulation-based approaches partially mitigate this limitation by encoding depth information into phase delay and amplitude attenuation, they remain inherently restricted by repeated temporal excitation, long acquisition times, and stitching artifacts in large-area inspection. In this work, we propose a structured illumination scanning thermography (SISTER) framework that replaces conventional temporal modulation with continuous spatial scanning under static structured illumination. The key theoretical insight is that heat diffusion is governed by a Markov semigroup, while sample motion transforms static spatial illumination into an equivalent temporal excitation through a Galilean coordinate transformation. This formulation enables dynamic-to-static reconstruction without repeated temporal modulation and provides a unified interpretation of spatial scanning and conventional signal modulation. A scanning system is integrated to implement the proposed framework together with a dynamic-to-static reconstruction algorithm for continuous subsurface defect inspection. Both numerical simulations and experimental results demonstrate that the proposed method significantly improves spatial continuity, signal-to-noise ratio, and detection capability while effectively eliminating stitching artifacts and reducing acquisition complexity. The proposed SISTER framework establishes a unified theoretical foundation for scanning photothermal imaging and provides a practical paradigm for high-efficiency, large-scale industrial non-destructive testing.
arXiv:2607.05577v1 Announce Type: new Abstract: Long-form fiction writers need memory that answers multi-hop questions about evolving story state: who knows a secret and when they learned it, whether an event preceded the narration that revealed it, whether a setup paid off, and how a relationship shifted. General-purpose retrieval and agent-memory systems represent entities and facts but not the narratological structure these questions turn on, so they surface the wrong evidence or none at all. We introduce the Narrative World Model (NWM), a writer-memory system that pairs a narratology-grounded typed temporal-state graph with query-conditioned hybrid retrieval. To measure memory rather than the answerer, we read every system through a single held-constant Opus 4.8 reader over only that system's chapter-safe evidence, on a reproducible public corpus and a validated multi-hop benchmark, and we compare against the strongest existing temporal-knowledge-graph agent-memory framework, Graphiti/Zep (Rasmussen et al., 2025). NWM substantially and significantly outperforms this baseline on multi-hop narratological QA across both corpora, and far exceeds GraphRAG and flat retrieval. The advantage is representational rather than an artifact of extraction: it survives rebuilding the baseline with NWM's own extractor, and traces to its narratology-grounded structure and query-conditioned retrieval, not to graph size or extractor quality.
arXiv:2607.05913v1 Announce Type: new Abstract: xDECAF is an extensible tool for architecture-based data flow analysis with a focus on information security. It combines an extended data flow diagram metamodel of labeled flows and nodes, a domain-specific constraint language with different flow operations, and a browser-based editor backed by an analysis engine. In this paper, we present the xDECAF tool library and a curated catalog of over 20 example models with documented constraints and expected violations, intended as a reusable dataset for the community. The tool has already been adopted by several research lines, providing concrete evidence of its utility. The tool, dataset, and a hosted online editor are publicly available.
arXiv:2604.07607v2 Announce Type: replace Abstract: Robot learning increasingly depends on large and diverse data, yet robot data collection remains expensive and difficult to scale. Egocentric human data offer a promising alternative by capturing rich manipulation behavior across everyday environments. However, existing human datasets are often limited in scope, difficult to extend, and fragmented across institutions. We introduce EgoVerse, a collaborative platform for human data-driven robot learning that unifies data collection, processing, and access under a shared framework, enabling contributions from individual researchers, academic labs, and industry partners. The current release includes 1,362 hours (80k episodes) of human demonstrations spanning 1,965 tasks, 240 scenes, and 2,087 unique demonstrators, with standardized formats, manipulation-relevant annotations, and tooling for downstream learning. Beyond the dataset, we conduct a large-scale study of human-to-robot transfer with experiments replicated across multiple labs, tasks, and robot embodiments under shared protocols. We find that policy performance generally improves with increased human data, but that effective scaling depends on alignment between human data and robot learning objectives. Together, the dataset, platform, and study establish a foundation for reproducible progress in human data-driven robot learning. Videos and additional information can be found at https://egoverse.ai/
arXiv:2604.20394v2 Announce Type: replace Abstract: We establish nearly optimal upper and lower bounds for approximating decision tree splits in data streams. For regression with labels in the range $\{0,1,\ldots,M\}$, we give a one-pass algorithm using $\tilde{O}(M^2/\epsilon)$ space that outputs a split within additive $\epsilon$ error of the optimal split, improving upon the two-pass algorithm of Pham et al. (ISIT 2025). Furthermore, we provide a matching one-pass lower bound showing that $\Omega(M^2/\epsilon)$ space is indeed necessary. For classification, we also obtain a one-pass algorithm using $\tilde{O}(1/\epsilon)$ space for approximating the optimal Gini split, improving upon the previous $\tilde{O}(1/\epsilon^2)$-space algorithm. We complement these results with matching space lower bounds: $\Omega(1/\epsilon)$ for Gini impurity and $\Omega(1/\epsilon)$ for misclassification (which matches the upper bound obtained by sampling). Our algorithms exploit the Lipschitz property of the loss functions and use reservoir sampling along with Count--Min sketches with range queries. Our lower bounds follow from careful reductions from the INDEX problem.
arXiv:2604.20557v2 Announce Type: replace Abstract: Shared Control methods often use impedance control to track target poses in a robotic manipulator. The guidance behavior of such controllers is shaped by the used stiffness gains, which can be varying over time to achieve an adaptive guiding. When multiple target poses are tracked at the same time with varying importance, the corresponding output wrenches have to be arbitrated with weightings changing over time. In this work, we study the stabilization of both variable stiffness in impedance control as well as the arbitration of different controllers through a scaled addition of their output wrenches, reformulating both into a holistic framework. We identify passivity violations in the closed loop system and provide methods to passivate the system. The resulting approach can be used to stabilize standard impedance controllers, allowing for the development of novel and flexible shared control methods. We do not constrain the design of stiffness matrices or arbitration factors; both can be matrix-valued including off-diagonal elements and change arbitrarily over time. The proposed methods are furthermore validated in simulation as well as in real robot experiments on different systems, proving their effectiveness and showcasing different behaviors which can be utilized depending on the requirements of the shared control approach.
Spectral and combinatorial methods for efficiently computing the rank of unambiguous finite automata
arXiv:2511.09703v2 Announce Type: replace Abstract: A zero-one matrix is a matrix with entries from $\{0, 1\}$. We study monoids containing only such matrices. A finite set of zero-one matrices generating such a monoid can be seen as the matrix representation of an unambiguous finite automaton, an important generalisation of deterministic finite automata which shares many of their good properties. Let $\mathcal{A}$ be a finite set of $n \times n$ zero-one matrices generating a monoid of zero-one matrices, and $m$ be the cardinality of $\mathcal{A}$. We study the computational complexity of computing the minimum rank of a matrix in the monoid generated by $\mathcal{A}$. By using linear-algebraic techniques, we show that this problem is in $\textsf{NC}$ and can be solved in $\mathcal{O}(mn^4)$ time and $\mathcal{O}(n^2)$ space. We also provide a combinatorial algorithm finding a matrix of minimum rank in $\mathcal{O}(mn^4)$ time and $\mathcal{O}(n^3)$ space. As a byproduct, we show a very weak version of a generalisation of the \v{C}ern\'{y} conjecture: there always exists a straight line program of size $\mathcal{O}(n^2)$ describing a product resulting in a matrix of minimum rank. For the special case corresponding to total DFAs (that is, for the case where all matrices have exactly one 1 in each row), the minimum rank is the size of the smallest image of the set of all states under the action of a word. Our combinatorial algorithm finds a matrix of minimum rank in time $\mathcal{O}(n^3 + mn^2)$ in this case.
arXiv:2511.12605v2 Announce Type: replace Abstract: We present M-OWNS, a spatial marching method that combines the carrier-wave factoring of the parabolised stability equations (PSE) with a recursive one-way Navier--Stokes (OWNS-R) projection framework. A distinct numerical resolution and efficiency advantage is offered by the approach, in modelling disturbance and instability state evolution. A spectral resolution comparison analysis shows that to leading order, for any excited eigenfunction whose eigenvalue lies closer to the carrier wavenumber than to the origin, the wave-factored system resolves the mode at a coarser streamwise numerical step size relative to the unfactored system. A non-iterating variant, with the carrier wavenumber determined from the base flow, temporal frequency and spanwise wavenumber alone, achieves equivalent resolution accuracy at identical per-step cost to unfactored OWNS. For the fixed-carrier variant, M-OWNS reduces the total solve count by factors of two to eight relative to unfactored OWNS across the test cases considered, with larger reductions possible when the iterated closure condition of PSE is suitable. The method is validated across incompressible and subsonic flat-plate boundary-layers, three-dimensional crossflow disturbances, and a Mach~4.5 hypersonic boundary-layer with four forcing configurations: eigenfunction inlet forcing, wall suction/blowing, multi-mode freestream forcing and randomised inlet forcing. The wall suction/blowing case is validated against a fully elliptic linear harmonic Navier--Stokes solver. For deterministic forcing scenarios, M-OWNS captures disturbance amplitudes, acoustic radiation fields, and modal synchronisation sequences at coarser streamwise resolution than unfactored OWNS. Under broadband randomised forcing, M-OWNS resolves mixed-mode disturbance development at half the numerical cost relative to standard OWNS.