arXiv:2607.14906v1 Announce Type: new
Abstract: Accurate and reliable environmental mapping is a fundamental requirement for multi-robot autonomy. While continuous mapping techniques like Gaussian Process Occupancy Mapping (GPOM) provide rich spatial correlation and uncertainty estimates, they lack formal, finite-sample guarantees on their predictive reliability. Conformal prediction can equip each robot's local map with a distribution-free coverage guarantee, but this local guarantee degrades in practice: temporal correlation along a robot's trajectory breaks the exchangeability on which conformal calibration relies, and each robot observes only a spatially limited, non-uniform portion of the environment. Taking these degraded per-agent guarantees as given, we develop a distributed fusion algorithm that recovers the desired coverage across the team. Robots exchange only lightweight scalar e-values with their neighbors, and a receiver fuses them using a per-neighborhood miscoverage budget and an uncertainty-attenuated fusion operator. We prove that the fused set-valued map recovers the target user-specified coverage level regardless of the communication graph topology or the underlying sensor noise distribution. However, a drawback is that wherever the fused evidence is insufficient, the map declines to commit and returns both labels (free and occupied), leaving a significant fraction of the domain unclassified rather than thresholded into a single decision. Simulated multi-agent mapping experiments demonstrate that the fused predictor reliably meets its theoretical coverage bounds, and illustrate that denser communication topologies significantly enhance map efficiency by shrinking this unclassified fraction.
Science Journals
When Machine Unlearning Meets Retrieval-Augmented Generation (RAG): Keep Secret or Forget Knowledge?
arXiv:2410.15267v3 Announce Type: replace
Abstract: The deployment of large language models (LLMs) like ChatGPT and Gemini has shown their powerful natural language generation capabilities. However, these models can inadvertently learn and retain sensitive information and harmful content during training, raising significant ethical and legal concerns. To address these issues, machine unlearning has been introduced as a potential solution. While existing unlearning methods take into account the specific characteristics of LLMs, they often suffer from high computational demands, limited applicability, or the risk of catastrophic forgetting. To address these limitations, we propose a lightweight behavioral unlearning framework based on Retrieval-Augmented Generation (RAG) technology. By modifying the external knowledge base of RAG, we simulate the effects of forgetting without directly interacting with the unlearned LLM. We approach the construction of unlearned knowledge as a constrained optimization problem, deriving two key components that underpin the effectiveness of RAG-based unlearning. This RAG-based approach is particularly effective for closed-source LLMs, where existing unlearning methods often fail. We evaluate our framework through extensive experiments on both open-source and closed-source models, including ChatGPT, Gemini, Llama-2-7b-chat, and PaLM 2. The results demonstrate that our approach meets five key unlearning criteria: effectiveness, universality, harmlessness, simplicity, and robustness. Meanwhile, this approach can extend to multimodal large language models and LLM-based agents.
arXiv:2607.14924v1 Announce Type: new
Abstract: We investigate how to support authoring narrative visualizations in motion in sports videos, drawing on automated data preparation, systematic analysis, technology probe design, and evaluation, using swimming races as a case study. Sports videos are widely broadcast and shared across social media, where content creators increasingly seek to present and explain complex events to general audiences. Visualization in motion has been explored as an efficient way to embed data into videos and to move with the data referents, providing additional information and helping audiences understand races. However, existing approaches primarily focus on embedding visualizations in videos, lacking exploration of how to support authoring narratives that coordinate views, data, and temporal progression to explain the unfolding races. To address this gap, we use swimming videos as an ideal case for exploration, as swimming is a sport with rich, dynamic data and visualizations in practice. We develop an automated pipeline that extracts structured data from videos, derive narrative constructs through observational analysis of sports broadcasts, and design a technology probe that supports authoring using data prepared by our pipeline and narrative constructs derived from our observations. We evaluate our approach with experienced content creators and/or graphic designers to examine the benefits and challenges of authoring narrative visualizations in motion. All supplemental materials are described in the Supplemental Material Pointers section and are on OSF: osf.io/bq47n/.
arXiv:2607.15099v1 Announce Type: new
Abstract: The increasing reliance on automatic code generation in mobile application development often leads to code that neglects fundamental design principles and architectural quality. In this work, we address this challenge by capturing and exploiting the inherent variability of software design patterns to systematically generate customizable and well-structured mobile applications. We propose the use of the Universal Variability Language (UVL) to explicitly model the structural and behavioral variation points of common design patterns, such as Singleton, Strategy, Observer, Adapter, and Factory Method. These models are integrated with reusable Jinja templates, enabling code generation in Swift. Our approach leverages Software Product Line (SPL) engineering principles, treating design patterns as configurable assets within a product line and supporting automated generation of custom design patterns. We also analyze the configuration space of the modeled patterns, offering insights into their variability complexity. By formalizing design pattern variability and embedding it into the generation process, our work bridges model-driven engineering with practical mobile development, promoting the production of maintainable, reusable, and architecturally sound applications.
arXiv:2607.12395v2 Announce Type: replace
Abstract: Reinforcement learning with verifiable rewards without human-annotated data, often referred to as zero RL, has emerged as a powerful paradigm for eliciting chain-of-thought reasoning. However, due to computational constraints, existing studies are largely restricted to small models, leaving the training dynamics and emergent capabilities at a large scale unexplored. To meaningfully explore this frontier, we aim to elicit high-quality reasoning behaviors from the model. However, we find that naive scaling often suffers from poor readability, token redundancy, and a lack of adaptive reasoning depth. To address these challenges, we present a stable and efficient training pipeline, incorporating algorithmic and system optimizations such as clipped importance sampling, training-inference ratio correction, and mixed-precision control. Our experiments offer three key findings that validate the "bitter lesson" of scaling: (1) scaling to 1T parameters significantly enhances sample efficiency and performance ceilings; (2) the training process progresses sequentially through an initial discovery phase followed by a sharpening phase; and (3) the model spontaneously develops advanced cognitive behaviors, including anthropomorphism, structured formatting, self-verification, parallel reasoning, and context anxiety, rendering hand-crafted heuristics redundant. Evaluated on seven mathematical benchmarks, Ring-2.5-1T-Zero achieves competitive performance. Additionally, to assess CoT quality beyond final-answer correctness, we propose a structured evaluation framework across three dimensions: comprehensibility, reproducibility, and efficiency, where our model demonstrates clear advantages in producing structured and concise reasoning traces. By sharing our observed emergent phenomena, we hope to provide the community with deeper insights into scaling behaviors, particularly at the 1-trillion scale.
arXiv:2506.05373v2 Announce Type: replace
Abstract: This research models the social media content creation and the choices that creators make as a Stackelberg game. The platform's algorithms, such as TikTok's and YouTube's, function as leaders, and they set rules to maximize users' engagement with their platforms. Then, content creators, who function as followers in this Stackelberg Game, respond to this by selecting strategies; in this instance, we are specifically focusing on collaboration or conflict, referred to in this paper as 'beefing.' They do this in order to maximize views and personal payoffs. The viewer's preferences are already placed within the algorithmic utility function, while the external sponsors will impose penalties on high-risk strategies, namely, beefing multiple times. This paper ultimately demonstrates, through the use of math, how shifts in algorithmic weights determine equilibrium creator behavior.
arXiv:2607.12771v2 Announce Type: replace
Abstract: Reaction mechanisms consist of the step-by-step sequences of elementary reactions that explain chemical transformations. Learning the mechanism logic is therefore essential for enhancing the fundamental chemical intelligence of large language models (LLMs). The stepwise deduction of reaction mechanism aligns naturally with the reasoning paradigms of reasoning LLMs. However, current chemical LLMs primarily emphasize coarse-grained name reactions for product prediction and retrosynthesis, often leading to physical inconsistencies and hallucinations. In contrast, specialized small-scale generative models for mechanism inference typically suffer from restricted generalization capacity across diverse chemical spaces. To overcome these limitations, we built a novel, large-scale reasoning dataset of reaction mechanisms. Furthermore, we established the FukuyamaBench, a difficult benchmark derived from Fukuyama's Advanced Organic Reaction Mechanism book, to rigorously evaluate model performance on hierarchical mechanism reasoning. Our fine-tuned Qwen3-30B-A3B achieves 8.3% exact pathway match on FukuyamaBench Set~A, surpassing the specialized FlowER model (5.1%), demonstrating that mechanism-aware training substantially enhances chemical reasoning in language models.
arXiv:2607.14957v1 Announce Type: new
Abstract: Online firestorms are rapid collective escalations of highly negative user-generated content and may cause substantial reputational and economic damage. Existing detectors usually work with volume signals, sentiment scores, or predefined linguistic features. Such signals are useful, but they capture contextual meaning shifts in evolving discussion threads only indirectly. This paper proposes an LLM-based detection system with two operating modes. The first mode classifies complete Reddit threads retrospectively by combining local chunk-level assessments into a thread-level judgment. The second mode processes threads sequentially and issues early warnings when a sliding window exceeds calibrated thresholds. In this mode, the language model estimates three firestorm indicators: negativity share, escalation level, and contributor count. On a balanced Reddit dataset, the global mode achieves strong classification performance, while the early warning mode reaches high recall and detects escalating threads after only a small number of comments and distinct contributors. The results indicate that LLMs can be used not only for static judgment tasks, but also as repeated estimators in context-aware monitoring of social media discourse.
arXiv:2607.15006v1 Announce Type: new
Abstract: The broad adoption of Artificial Intelligence (AI), especially Generative AI, raises pressing questions about how users interact with these systems to produce new content. In this paper, we introduce the concept of authorship calibration, defined as users awareness of their actual authorship when interacting with AI. Using the CoAuthor dataset, we empirically examine how authorship calibration varies across users and how it relates to their frequency of AI use. Our results reveal high variability: users relying heavily on AI tend to misjudge their authorship, whereas those using AI less frequently exhibit more accurate authorship calibration. These findings suggest that AI can obscure users perception of their own authorship. In learning contexts, miscalibration can affect metacognitive monitoring and learning strategies, ultimately impacting learning outcomes. Fostering authorship calibration then appears essential for promoting responsible and educationally meaningful AI integration.
arXiv:2607.15113v1 Announce Type: new
Abstract: In the online graph exploration problem, a single agent needs to visit every vertex of an initially unknown graph, which is learned over time in an online fashion, and return to its starting position. We prove that the competitive ratio of this problem is at least 4, improving on the previously best known lower bound of 10/3. A key ingredient of our proof is showing that several restrictions can be imposed on the agent's behavior without affecting the competitive ratio. As a byproduct, we also obtain that certain graph properties, such as the triangle inequality or being subcubic, can be assumed without affecting the competitive ratio.
arXiv:2607.14998v1 Announce Type: new
Abstract: This paper suggests the adoption of a novel inversion in AI ethics: instead of asking how humans should treat artificial superintelligence (ASI), it examines how future sentient ASI may morally consider and evaluate humanity. We are not only designing intelligent systems but also shaping the initial conditions under which those systems form judgments about us. The paper proposes a preliminary set of post-human moral principles that may govern sentient ASI actions. The implication is that technical design choices (some are suggested), humanity's moral behaviour, and the essence of what it means to be human, may influence humanity's long-term standing in a post-ASI world.
arXiv:2607.14967v1 Announce Type: new
Abstract: Most existing approaches to AI-Generated Text Detection (AIGTD) treat documents as static objects and base their decisions on aggregate statistics or globally compressed embeddings. However, this perspective overlooks the inherently dynamic nature of autoregressive generation, where content evolves progressively through the latent space. In this paper, we reformulate AIGTD as the problem of distinguishing between latent generation trajectories. Instead of relying on static representations, we model how textual representations evolve across the sequence. To this end, we propose Geometric Trajectory and Contrastive Learning (GTCL), a framework that segments the document into ordered local units, encodes each unit in an embedding space, and constructs a structured and sequence-level representation. GTCL then applies contrastive learning to these trajectories to learn geometric regularities associated with the autoregressive generation. Evaluations performed on three different benchmarks and several approaches show that GTCL outperforms detection baselines consistently, which implies that explicitly modeling sequential dynamics provides robust discriminative signals across models and domains. These results suggest that modeling trajectory differences could improve detection and open up a dynamic direction that has been underexplored in previous AIGTD literature.
arXiv:2607.14316v1 Announce Type: cross
Abstract: It is conjectured that every idempotent Schur multiplier can be written as a finite sum of contractive idempotents. This conjecture is equivalent to the statement that any boolean matrix $A$ with factorization norm $\lVert A\rVert_{\gamma_2}$ at most $\gamma$ can be expressed as a signed sum $$A = \sum_{i=1}^L \pm B_i,$$ where, up to permutation of rows and columns, each $B_i$ is a blow-up of an identity matrix, and $L$ depends only on $\gamma$. In this note we show that if $A$ is an $n\times n$ boolean matrix with $\lVert A\rVert_{\gamma_2} \le \gamma$, then it admits such an expression with $L = 2^{O(\gamma^9) + \log^*\! n}$, where $\log^*$ is the iterated logarithm function.
As an application, any sequence of matrices with bounded factorization norm belongs to the complexity class $\mathrm{P}^\mathrm{EQ}$ of communication problems with polylogarithmic equality-oracle complexity.
arXiv:2607.15094v1 Announce Type: new
Abstract: Multimodal models such as CLIP learn a shared embedding space for cross-modal retrieval, but continual adaptation to sequentially arriving data can disrupt the cross-modal alignment acquired from earlier phases. Conventional continual-learning methods return a single checkpoint, which commits every retrieval direction to the same stability-plasticity trade-off. We propose AlphaWiSE, a post-hoc weight-space interpolation method that composes two frozen source checkpoints. For each aligned parameter tensor identified by its checkpoint key, AlphaWiSE fits one scalar interpolation coefficient shared by all tensor entries. The coefficients are fitted on a smaller exemplar memory and used to materialize one interpolated checkpoint. The deployed model has the same architecture and parameter count as either source checkpoint, which does not require additional inference time. Extensive experiments on audio-image-text retrieval show consistent improvements over strong continual-learning baselines across multiple retrieval directions and evaluation metrics.
arXiv:2607.15004v1 Announce Type: new
Abstract: Dynamic target tracking is essential for Unmanned Aerial Vehicles (UAVs) operating in complex urban environments, where both the target and the camera viewpoint change continuously. Existing Vision-Language-Action (VLA) policies can track visible targets effectively, but their performance often degrades when buildings, vegetation, or roadside objects block the line of sight. During sustained occlusion, a policy may lose the target state, execute actions toward an incorrect region, and amplify this error through subsequent observations until re-acquisition becomes impossible. To this end, we present CosFly-VLA, a spatially aware VLA model that jointly grounds the target, estimates its visibility, and generates continuous flight actions through a structured prediction interface. To train this policy, we use a large-scale recipe over diverse data sources. Spatially Grounded Continued Pretraining (CPT) on a 500k mixed pool injects UAV-view depth, distance, and 3-D spatial reasoning. A three-stage Curriculum-based Supervised Fine-Tuning (SFT) process then specializes the tracker through multi-head warm-up followed by two-stage curriculum learning over natural and hard / long-occlusion data. Chain-of-Thought (CoT) training subsequently teaches recovery-oriented reasoning traces before structured answers. Finally, a closed-loop Reinforcement Learning (RL) stage optimizes tracking behavior with a multi-component reward covering stand-off tracking, grounding quality, collision avoidance, and task success. Relative to OpenVLA, CosFly-VLA-0.8B reduces open-loop Average Displacement Error (ADE) by 34.1% on seen-test and 35.3% on unseen-test. Closed-loop optimization improves Success Rate (SR) by 29.8% and 2.5%, respectively. These results demonstrate progress from visible-frame imitation toward spatially grounded action-closed-loop control, evaluated under a shared oracle state history.
arXiv:2607.15235v1 Announce Type: new
Abstract: Long-term environmental monitoring in wireless sensor networks (WSNs) often uses sparse sampling to extend network lifetime, but sparse sensing can miss short-lived, localized, and potentially diffusive anomalies. This paper proposes a sentinel-assisted adaptive sampling framework as a cooperative sensing-control pipeline for WSN anomaly monitoring. During normal periods, nodes perform sparse sensing driven by Kalman filter (KF) predictive uncertainty. During anomalous periods, continuously sampled sentinel nodes perform hybrid GLR-based detection with node-relative thresholds, and local detections trigger one-hop neighborhood wake-up with recovery-aware alert control.
Experiments on the Intel Berkeley Research Lab temperature dataset with abrupt random spatiotemporal anomalies show that the proposed method raises the anomaly-window sampling ratio (AWSR) from 0.439 to 0.933 in the main experiment. It also improves AWSR over Adaptive Data Acquisition with Energy Efficiency and Critical-Sensing Guarantee (AAS) and Adapted e-Sampling while reducing total cost by 15.4\% and 2.1\%, respectively. These results show that integrating KF-based sparse sampling, sentinel GLR detection, and local alert propagation improves anomaly-window visibility while maintaining a lower sampling-cost trade-off.
arXiv:2607.15238v1 Announce Type: new
Abstract: Language identification is commonly addressed using either neural architectures or statistical n-gram models. Neural approaches typically require substantial computational resources, whereas classical frequency-based methods offer efficient linear-time performance, but rely on distance metrics that are not always appropriate for compositional data.
This work models character and bigram frequency distributions as compositional vectors constrained to the simplex and mapped via the centered log-ratio (CLR) transformation bijectively onto the $(D-1)$-dimensional zero-sum subspace of $\mathbb{R}^D$, where Euclidean distances correspond to Aitchison distances. A pipeline is proposed, combining CLR-transformed unigram and bigram features with Laplace smoothing to address sparsity. The method is evaluated on six languages.
Experimental results show that the proposed approach achieves robust accuracy across different text lengths, with strong performance for longer sequences. These findings indicate that compositional representations provide a deterministic and computationally efficient alternative for language identification, particularly in settings where interpretability and low resource consumption are essential.
arXiv:2607.15016v1 Announce Type: new
Abstract: Ensuring robot safety in unknown, dynamic environments is a fundamental requirement. It involves inferring the states of an unknown and time-varying number of moving objects from noisy, incomplete measurements. We address safe control under the induced multi-object state uncertainty with a risk-aware belief control barrier function (BCBF) framework. The uncertainty is captured by a random finite set (RFS) belief, estimated by a sequential Monte Carlo probability hypothesis density (SMC-PHD) filter that represents it with a set of particles. Building directly on these particles, we construct a nonsmooth BCBF, establish forward invariance of the safe set under continuous prediction, and derive an explicit condition under which discrete updates preserve safety. Simulation and real-world underwater experiments demonstrate the effectiveness and efficiency of the proposed approach.
arXiv:2511.06237v2 Announce Type: replace
Abstract: Enabling lifelong learning in LLMs demands resolving the stability-plasticity dilemma (i.e., models must incorporate new knowledge without overwriting prior representations) while maintaining scalability under bounded parameter growth. Existing PEFT methods fail to satisfy this triad; shared-parameter approaches suffer from catastrophic interference, while task-isolated expansions preclude knowledge transfer and scale linearly. We propose Mixtures of SubExperts (MoSEs), a modular and sparse framework that factorizes model capacity into reusable, compositional primitives. MoSEs augment transformer layers with lightweight SubExperts and a learned sub-routing function that dynamically selects and composes a sparse subset of modules conditioned on task inputs. This induces a structured decomposition of the parameter space where knowledge is localized yet accessible, mitigating interference while preserving reuse. Specifically, MoSEs balance the dilemma via three pillars: (i) stability by isolating knowledge within sparsely activated modules, (ii) plasticity through routing-driven recombination and selective expansion, and (iii) scalability via sublinear growth in effective capacity. Notably, the routing mechanism enables compositional generalization, allowing new tasks to be represented as combinations of previously acquired sub-functions. We empirically validate MoSEs on TRACE and SuperNI, showing reduced forgetting, improved forward transfer, and better parameter efficiency over strong PEFT baselines. MoSEs establish a new Pareto frontier, achieving state-of-the-art performance while maintaining strict parameter budgets. Our results suggest that modular sparsity and compositional routing are key inductive biases for building foundation models that continually learn without saturation.
arXiv:2607.14937v1 Announce Type: new
Abstract: Recent foundation models (FMs) for zero-shot reconstruction of dynamical systems (DS) achieve strong out-of-domain generalization but provide little insight into the mechanisms that underlie their forecasts. Such an understanding could help to strip down overladen FM architectures to their bare essence and expose the minimal requirements for in-context learning in the DS domain. Toward this goal, here we iteratively reduce a recent powerful SOTA model for DS reconstruction, DynaMix (Hemmer & Durstewitz, 2025), to a minimal interpretable two-parameter form, which we call DynaBase. DynaBase produces forecasts through a linear blend of the current latent state and the nearest in-context neighbor and its temporal successor. Surprisingly, despite its extreme simplicity, DynaBase produces highly competitive zero-shot DS reconstructions across chaotic and cyclic systems, with a negligible parameter load, many orders of magnitude below that of other FMs. Even more, this extreme simplicity permits direct model optimization on DS reconstruction measures, as well as closed-form one-step analytical solutions on prediction MSE. Theoretical and empirical analysis of DynaBase further leads to a 1-parameter family of maps, with the context-parroting algorithm of (Zhang & Gilpin, 2026) recovered at one end, and chaotic (divergent but bounded) behavior at the other. We further show how different training strategies lead to models either optimal for short-term prediction or for DS reconstruction. Thus, DynaBase not only exposes the minimal mechanisms required for producing zero-shot DS reconstruction, but also reconciles within an accessible mathematical frame divergent observations in the literature.
arXiv:2607.15247v1 Announce Type: new
Abstract: Evidence synthesis is crucial for turning primary research into reliable knowledge for science, medicine, education, and policy. Yet, quantitative evidence synthesis remains largely manual and difficult to scale. Here, we introduce AutoSynthesis, an end-to-end multi-agent system for automated meta-analysis. Given a research question in natural language, AutoSynthesis formulates a search strategy, retrieves scientific literature, screens candidate studies, assesses full-text eligibility, extracts quantitative statistics, computes standardized effect sizes, and finally performs random-effects meta-analysis. AutoSynthesis further supports heterogeneity analysis to examine how effect sizes vary across moderators, as well as risk-of-bias assessment. As output, AutoSynthesis produces a transparent report aligned with PRISMA guidelines. In our application, AutoSynthesis screened over 28 studies and extracted more than 20 quantitative claims. The pooled effect estimates produced by AutoSynthesis are similar to Hedges' $g$ of expert-conducted meta-analyses, indicating close agreement with manual evidence synthesis. Together, these results show that AutoSynthesis can make quantitative evidence synthesis more scalable, thereby supporting evidence-based decision-making across disciplines.
arXiv:2607.15253v1 Announce Type: new
Abstract: Retrieval systems are trained and evaluated on a static idea of usefulness: hand a document and a question to a reader model, see whether the answer improves, and score the document accordingly. The idea holds up when a document is read on its own. It breaks when a language model works as a search agent, issuing several queries and reasoning across turns, because a document can matter for what it lets the agent do next rather than for what it says about the current question.
We measure that gap rather than argue it. Using a ReAct style agent over HotpotQA, we replay 1000 development questions and, for every document the agent read, delete it and re-run the rest of the trajectory from that point. Comparing the original run against its counterfactual gives a Counterfactual Trajectory Utility (CTU) score from three deltas: final answer quality, next query retrieval quality, and turn count. Crossing CTU against Static RAG Utility (SRU) over 23,322 document observations, the two are close to statistically independent (Spearman rho = -0.026). Roughly a third of the documents the agent reads are causally load bearing while looking useless to a static reader; we call these bridge documents. The pattern survives when the reader based axis is swapped for a BM25 and cross encoder proxy, giving a bridge cell of 27.2% on an evenly spread axis.
A second experiment pins down the mechanism. Using the Observable Entity Relevance (OER) measure from prior work, entities that discriminate relevant from non-relevant candidates appear in the agent's next query 4.02 times more often than entities found only in non-relevant documents (6.1% vs 1.5%, n = 227,139). A bridge document earns its keep by handing the agent a discriminative entity that redirects the search. Static relevance and causal usefulness are different quantities in agentic retrieval, and optimizing the first does not deliver the second.
arXiv:2607.15035v1 Announce Type: new
Abstract: Principal component analysis (PCA) is optimal for the linear reconstruction of Gaussian data, a foundational property underlying its central role in algorithms and signal processing. Its nonlinear analogue, however, is notoriously subtle: in 2011, Mallat and Zeitouni conjectured that the Karhunen--Lo\`eve (KL) basis remains optimal even when the retained coordinates are chosen adaptively per sample, a property that would theoretically justify the ubiquitous pipeline of PCA followed by sparse thresholding. In this paper, we establish a $1+O(1/\sqrt{d})$-approximate version of the retained-energy form of the Mallat--Zeitouni conjecture, showing that the KL basis is within this factor of the optimal basis. This dimension-free comparison depends only on the number of retained coordinates and shows that the possible advantage of optimizing over all orthonormal bases vanishes as $d$ grows. It complements the universal-constant reconstruction-error comparison of Litvak and Tikhomirov (Ann. Appl. Probab., 2018), while providing a comparison naturally suited for algorithmic analysis. Our proof rests on a clean, conceptual reduction: we relax arbitrary rotations to a deterministic threshold bound via Schur--Horn majorization, and identify the remaining loss with the correlation gap of the rank-$d$ uniform matroid over Gaussian level sets.
arXiv:2607.15036v1 Announce Type: new
Abstract: Navigating dynamic and crowded environments presents significant challenges for quadruped robots due to severe sensor occlusion and unpredictable human motion. Existing approaches face a trade-off: model-based methods, such as Velocity Obstacles (VO), theoretically guarantee safety but rely on accurate obstacle motion estimates that often fail in dense crowds, while end-to-end learning methods offer robustness but lack motion prediction capability of obstacles, leading to collisions or conservative behaviors. To solve this, we propose VOP-Nav, a novel navigation system that combines the geometric safety of VO with the agile adaptability of end-to-end learning. Using only local onboard observations, our system avoids explicit obstacle detection and tracking pipelines. The VOP-Net processes multi-frame LiDAR data to implicitly encode dynamic constraints and predict a safe velocity region derived from Velocity Obstacle theory. Importantly, the VO predictions serve a dual role: they are used as input to the navigation policy during inference and as a reward signal during training to encourage safe motion. Evaluations in Isaac Gym demonstrate that VOP-Nav achieves higher success rates than all baselines while balancing locomotion speed and collision avoidance. Real-world deployment on a Unitree Go2 quadruped robot further validates the system's robustness and efficiency in complex indoor and outdoor dynamic environments.
arXiv:2607.14193v1 Announce Type: cross
Abstract: The Helmholtz equation governs time-harmonic wave propagation, and in dissipative media a complex modulus renders its squared wavenumber $\kappa^2$ complex. Inferring such fields from sparse, noisy data calls for solvers that also quantify their own uncertainty. Physics-informed Gaussian-process (GP) regression supplies this by returning a posterior over the solution, yet operator-conditioned formulations have been developed almost exclusively for real-valued fields. We extend operator-informed GP regression to complex-valued Helmholtz problems by realifying the complex operator into an equivalent coupled real block, which enables inference with standard real-valued GP conditioning. The construction admits a family of priors, from a proper diagonal prior to coregionalized and multiscale variants, and conditions on PDE residuals and boundary traces. On benchmark problems in one to three dimensions, the solver is competitive with finite-difference and neural-network baselines at a far smaller interior-constraint budget. Unlike those deterministic baselines, it returns a posterior over the complex wavefield rather than a point estimate. Applied to \textit{in vivo} brain magnetic resonance elastography, a proper multiscale prior reconstructs the shear curl field to a correlation of $0.77$ with measurement, above a $0.75$ target. The gain arises from the multiscale kernel rather than from real--imaginary coupling. We further identify a low-frequency accuracy ceiling set by model mismatch and a posterior uncertainty that is not yet calibrated. Calibrated uncertainty therefore emerges as the central next step for probabilistic wavefield inference in dissipative media.