arXiv:2606.24218v1 Announce Type: new Abstract: We establish that the two-dimensional ray tracing problem with thin lenses and plane mirrors is Turing-complete, thereby resolving an open question posed by Reif et al. in 1994 as to whether three-dimensional space is necessary for computational universality in optical systems. To this end, we consider the standard approximation of reflection and refraction, namely the ABCD model for paraxial optics, which describes ray propagation through lenses (refraction) via a 2 x 2 matrix, combined with the geometric reflection model for plane mirrors. In the absence of mirrors, two-dimensional ray tracing using any combination of lenses in this ABCD matrix model can be described by a single 2 x 2 matrix-vector product, where the matrix has real entries and determinant 1. Conversely, we show that any such matrix with determinant 1 can be represented as a composition of exactly three appropriately spaced thin lenses. When mirrors are combined with lenses, the ray tracing problem can be described by a flowchart using only two variables, which establishes Turing computability for rational-valued inputs, spaces and matrix entries. Building on this observation, we present a construction of ray tracing that simulates a reversible Turing machine. We begin with a restricted version of the reversible flowchart problem, in which only two variables and certain linear functions are permitted. We prove that this restricted variant is Turing-complete. We then show that such a flowchart admits a geometric realization using lenses and mirrors in our model, thereby establishing the main result: Turing-completeness of the two-dimensional ray tracing problem with ABCD-model lenses and mirrors.
Science Journals
arXiv:2606.24381v1 Announce Type: new Abstract: Prompt-based interaction has become a dominant paradigm for using large language models (LLMs), where multiple candidate prompts are evaluated and the top-ranked one is selected for downstream use. This workflow implicitly assumes that prompt rankings are stable under minor variations in evaluation conditions. In this paper, we systematically study prompt ranking stability under common sources of variability, including random seeds and limited evaluation subsets. Across three open-weight LLMs and two benchmark tasks, we find that while overall rank correlations are often moderate to high, the identity of the top-performing prompt frequently changes, leading to unreliable selection decisions. To address this issue, we propose a simple stability-aware selection strategy based on a lower confidence bound, which accounts for both performance and variance. Our results show that this approach improves robustness in unstable settings while remaining competitive in more stable regimes. These findings highlight the importance of accounting for evaluation uncertainty in prompt selection and LLM benchmarking.
arXiv:2606.24295v1 Announce Type: new Abstract: This paper addresses non-physical artifact, specifically spontaneous droplet shrinkage, in Cahn-Hilliard-based simulations of immiscible two-phase microflows. That artifact arise from the energy functional's preference for reduced interfacial area, leading to shifts in equilibrium phase fractions away from the physical bounds of 0 and 1. A curvature-dependent correction is proposed that shifts the double-well potential to counteract this drift. This method is validated on the following test cases: an isolated droplet in a cubic cavity, drainage in a synthetic porous medium, and flow through a T-shaped junction. Results demonstrate significant suppression of phase fraction overshoot/undershoot and improved droplet volume conservation.
arXiv:2606.24350v1 Announce Type: new Abstract: Legged robots rely on accurate ground interaction awareness to traverse variable terrains, such as slippery surfaces. Existing slip detection methods often rely on kinematics and proprioception, which lack the sensitivity to detect early-stage slips that occur prior to catastrophic instability. Thus, this paper presents SlipSense, a novel framework for online force-based slip detection using a custom lightweight sensorized foot for quadrupeds to detect slip. The framework integrates a multimodal sensor design with a LSTM-based model to infer ground reaction forces and detect slip-indicative anomalies during locomotion. The proposed framework is deployed on a Unitree Go1 quadruped to demonstrate blind online slip detection over a slippery terrain. Our method detects early-stage slips down to an average displacement of 24.1 +/-6.4mm with an overall accuracy of 85.9%. This represents a 3.3-fold finer detection resolution and a 24% relative accuracy improvement over a standard kinematic baseline that uses foot velocity inferred through state estimation. The work in this paper serves as a foundation for force-aware gait adaptation in legged robotic locomotion, allowing future controllers to estimate terrain friction and adjust constraints, thus improving the overall stability of the system.
arXiv:2606.24418v1 Announce Type: new Abstract: Data augmentation is a simple and model-agnostic approach for exploiting known invariances in learning problems. Given a group acting on the input space, one augments the training set with transformed copies of each sample. Because it exploits symmetries without modifying the underlying learning algorithm, data augmentation can be applied broadly across learning methods. However, this universality comes at a computational cost: when the group is large, full group-sized augmentation quickly becomes computationally infeasible. This raises a fundamental question: Can partial data augmentation achieve the same statistical benefits as full augmentation in terms of generalization and sample complexity? We develop a general framework for investigating this question using Fourier analysis and the representation theory of finite groups. We show that, for a broad class of classical learning problems, partial data augmentation based on a randomly sampled subset of group elements achieves the same minimax rates as full augmentation, up to an approximation error that vanishes as the subset size increases. Our results provide a theoretical explanation for why partial augmentation can retain the statistical benefits of full augmentation despite enforcing symmetry only approximately, and shed light on a recently raised question in learning with symmetries: whether statistically optimal learning under general group invariances can be achieved using computationally scalable methods. Moreover, we prove a complementary impossibility result: enforcing exact invariance via data augmentation requires averaging over the entire group, and cannot be achieved by any strict subset when the hypothesis space is sufficiently expressive. Together, these results provide a unified perspective on full and partial data augmentation, as well as exact and approximate symmetry enforcement.
arXiv:2606.24423v1 Announce Type: new Abstract: We develop a sparse spectral method for solving partial differential equations on a class of two-dimensional geometries bounded by algebraic curves. The numerical method uses generalised bivariate Koornwinder polynomials which form a complete orthogonal basis, but one which is not graded in terms of polynomial degree. The polynomials are built from new families of univariate semiclassical orthogonal polynomials whose associated operator matrices (Jacobi matrices, raising matrices and differentiation matrices) are computed with optimal linear complexity in the number of basis functions. When used to discretise partial differential equations the resulting matrices are sparse enabling efficient numerical solution. Moreover, we develop fast transforms from values on a grid to expansion coefficients. The efficiency and accuracy of the resulting spectral method are illustrated through a series of numerical experiments on geometries whose boundaries are smooth and piecewise smooth including non-convex geometries. We observe algebraic convergence for geometries with corners, which accelerates to exponentially fast (spectral) convergence when the boundary is smooth.
arXiv:2606.24358v1 Announce Type: new Abstract: The Earth's climate is an ensemble of interacting, spatially extended oscillatory media ('climate systems') whose slow-changing averages coexist with chaotic, high-frequency weather fluctuations in quasi-equilibrium. The limit of deterministic predictability (LDP) for any climate system is determined by its fastest-growing errors. However, recent findings show that the Indian Summer Monsoon Rainfall (ISMR) can be predicted up to 18 months in advance-far beyond its LDP. Using a model of two interacting oscillatory media, we show that this extended predictability arises from lag synchronization between ISMR and its predictor, the Global El Nino-Southern Oscillation (G-ENSO), to which it is strongly coupled. We introduce complex order parameters representing the internal dynamics of the two climate systems. Their spatiotemporal evolution is governed by coupled Complex Ginzburg-Landau Equations, producing aperiodic yet strongly correlated time series at long lead times. Our findings have far-reaching consequences in advancing seasonal prediction across climate systems.
arXiv:2606.24359v1 Announce Type: new Abstract: This paper proposed an algorithm for part-of-speech (POS) tagging senses of a bilingual dictionary. The algorithm is applied on the Al-Mawrid Arabic-English dictionary. The tagging task is accomplished by transferring the POS tags of the English translation equivalences (TEs) to the dictionary senses after dis-ambiguities process. The English POS tags of senses are acquired from the Princeton WordNet. POS tagging of bilingual dictionary senses is prerequisite to link a bilingual dictionary to WordNet and/or standardizing that dictionary into WordNet-LMF format where the synset (set of synonyms), not word, is the basic brick. The registered accuracy is high though the cost is little. Building NLP/HLT tools needs linguistic experts, large investments, and long time. For statistical approach, we need large annotated corpora and for rule-based approach, we need large lexicon that contains rich linguistic and world knowledge. That motivates the appearance of what are called resource-light approaches to develop natural language processing (NLP) tools for poor-resource languages.
arXiv:2606.24437v1 Announce Type: new Abstract: Mixture-of-Agents (MoA) architectures improve inference-time scaling by organizing multiple LLM agents into layered reasoning pipelines. However, existing MoA variants fail to sustain gains as depth increases, exhibiting degradation, early plateauing, or saturation. We propose ReM-MoA, a memory-augmented MoA framework that sustains scaling through two mechanisms: (1) a Ranked Reasoning Memory that persistently stores and ranks reasoning traces from all layers using a comparative Reviewer Agent, and (2) a Curated Diversified Memory Routing scheme that exposes different agents to distinct combinations of successful and failed traces, preserving exploration diversity while propagating high-quality reasoning. We further introduce an optional multi-domain Reviewer distillation pipeline that improves ranking quality through frontier-model supervision. Across five reasoning benchmarks spanning math, formal logic, code, knowledge, and commonsense, ReM-MoA consistently outperforms prior MoA variants across both depth and width scaling, and its advantage widens with depth, establishing structured cross-layer reasoning memory as a key missing mechanism for scalable multi-agent inference.
arXiv:2606.24438v1 Announce Type: new Abstract: Kubernetes has become the industry standard for orchestrating containers in microservice-based software architectures. While several hardening guidelines and scanning tools for securing Kubernetes clusters and deployments have emerged in recent years, their differing guidance and outputs often lead to inconsistent configuration and prioritization decisions. This work presents a systematic comparison of eight commonly used Kubernetes hardening guidelines. Through this comparison and the inclusion of best practices, we established a benchmark of 79 Kubernetes configuration recommendations and conducted the a structured empirical evaluation of ten popular static configuration scanning tools and their scoring outputs. Our findings reveal substantial disparities in the coverage of configuration issues across hardening guidelines and scanners, as well as inconsistencies in how configuration issues are scored and ranked by different scanners. These results highlight the need for more standardized, transparent, and consistent approaches to risk and severity assessment of Kubernetes configuration issues.
arXiv:2606.24467v1 Announce Type: new Abstract: Long-context large language model (LLM) inference is increasingly constrained by the memory footprint and decoding cost of key-value (KV) caches, limiting sustainable deployment on resource-constrained hardware. Existing KV cache eviction methods typically apply heuristic token scoring over all heads in GQA-based LLMs. These methods ignore the different functionalities of attention heads, leading to the eviction of critical tokens and thus degrading the performance of LLMs. To address this issue, we propose CompressKV, a resource-efficient KV-cache compression framework for GQA-based LLMs. Instead of aggregating attention scores from all heads, CompressKV identifies Semantic Retrieval Heads (SRHs) that capture both the initial and final tokens of a prompt and semantically important mid-context evidence, and uses them to select tokens whose KV pairs should be retained. Furthermore, CompressKV allocates cache budgets across layers according to offline estimates of layer-wise eviction error. Experiments on LongBench and Needle-in-a-Haystack show that CompressKV consistently outperforms existing KV-cache eviction methods across memory budgets. Notably, it preserves over 97\% of full-cache performance using only 3\% of the KV cache on LongBench question-answering tasks and achieves 90\% accuracy with just 0.7\% KV storage on Needle-in-a-Haystack. These results demonstrate an improved resource--performance trade-off for long-context LLM inference. Our code is publicly available at: https://github.com/TUDa-HWAI/CompressKV
arXiv:2606.24489v1 Announce Type: new Abstract: Pose graph optimization (PGO) is a key back-end component for state estimation in networked multi-robot simultaneous localization and mapping (SLAM). In object-based multi-robot SLAM, the problem becomes more tightly coupled because robots must jointly estimate both their trajectories and the poses of persistent objects observed by multiple agents. Existing decentralized solutions often assume that the communication graph closely matches the physical interaction topology, which is restrictive in realistic deployments where communication is sparse, intermittent, or time-varying. This paper presents a fully decentralized Riemannian optimization framework for object-based multi-robot PGO that decouples the coupled estimation problem via a consensus mechanism, enabling flexible communication topologies. To improve convergence under limited communication budgets, we further develop a distributed approximate-Newton scheme that exploits local second-order information while operating directly on the SE(d) manifold to preserve geometric consistency, and we establish the convergence to Riemannian first-order stationary points and provide a local condition-number analysis explaining the benefit of approximate second-order information over first-order Riemannian descent. The resulting method reduces iteration count and communication overhead without sacrificing estimation accuracy. Extensive evaluations on public benchmarks, large-scale simulations, and real-world multi-robot experiments demonstrate improved accuracy, runtime efficiency, scalability across network topologies, and robustness to communication failures.
arXiv:2606.24535v1 Announce Type: new Abstract: Multi-agent LLM environments require robust mechanisms for shared knowledge management. This paper formalizes the fleet-memory problem and identifies four foundational failure modes: unauthorized leakage, stale propagation, contradiction persistence, and provenance collapse. To address these, we define explicit systems-level primitives: scoped retrieval, temporal supersession, provenance tracking, and policy-governed memory propagation. These primitives are implemented in MemClaw, a production multi-tenant memory service, and evaluated via ArgusFleet, a reproducible harness testing four governance dimensions. Rather than a baseline comparison, this study measures a live production service, emphasizing real-world architectural insights and negative results. Key Evaluation Results Provenance: Successfully reconstructed 100% of depth-four derivation chains with correct writer identity at sub-second per-hop latency. Propagation: Demonstrated high intra-fleet visibility with zero cross-fleet leakage. Under strong write mode, write-to-visible latency was optimized to a single search round-trip. Production Architectural Issues Discovered Asymmetric Scope Enforcement: Tenant isolation held, but sub-tenant scope was initially bypassed on direct GET-by-id requests for agent-scoped credentials (disclosed and remediated during the study). Pipeline Ordering Conflict: While contradiction supersession works for admitted writes, a synchronous near-duplicate gate can prematurely reject contradictory writes before the asynchronous contradiction detector can evaluate them. Conclusion: Long-context retrieval alone is insufficient for production multi-agent memory. Governed shared memory demands explicit systems-level abstractions, and live evaluation is vital to expose enforcement and pipeline-ordering failures missed by design-only treatments.
arXiv:2606.24596v1 Announce Type: new Abstract: As Large Language Models are increasingly deployed in critical applications, robustly evaluating their social biases is paramount. However, the current literature suffers from widespread methodological fragmentation, which yields contradictory conclusions. This stems largely from ignoring the structural framing of benchmark-level evaluations. To resolve this, we introduce a unified and controllable framework that standardizes heterogeneous benchmarks to systematically contrast isolated demographic assessments with forced-choice comparative settings. Crucially, this allows us to disentangle the confounding effects of Chain-of-Thought reasoning, neutral fallback options, and other structural artifacts in social bias evaluations. Our evaluation across multiple model families reveals a massive, systematic paradigm gap: while isolated assessments limit prejudice activation, comparative settings act as aggressive catalysts for latent discrimination, a shift primarily driven by underspecified contexts. Alarmingly, CoT reasoning exacerbates social biases under comparative settings, and this systemic bias persists as a deterministic prejudice even when models are provided neutral fallback options or claim to answer randomly. Finally, we demonstrate that this comparative prejudice is a generalized phenomenon that scales positively with model size. Ultimately, we offer a crucial methodological guideline: while researchers must leverage comparative settings to robustly audit hidden biases, practitioners cannot safely rely on comparative deployments in ambiguous real-world tasks.
arXiv:2606.24619v1 Announce Type: new Abstract: Competency Questions (CQs) are the central component of CQ-verification, an established process in which an ontology is evaluated against a set of natural language questions to determine whether the intended purpose of the ontology has been properly modelled. However, CQ-verification is often time-consuming and error-prone, as it requires careful interpretation of linguistic nuances and precise alignment with formal ontology constructs. Ambiguities and complexity in CQs can further complicate this process, leading to inconsistent modelling decisions and verification outcomes. In this paper, we investigate what makes a CQ challenging and possible solutions to enhance the users' performance in the CQ-verification process. We experimented with the data of 19 participants who performed CQ-verification on 20 tasks using an LLM assistant to support ontology evaluation. The results show the necessity of a tool to refine CQs before publishing them to avoid ambiguity or excessive complexity in later phases of the ontology engineering process.
arXiv:2606.24627v1 Announce Type: new Abstract: Fact-checking systems built on LLMs achieve high verdict accuracy on standard benchmarks, yet routinely output Supports labels whose cited evidence does not license the claim. Structured decomposition is the natural way to inspect those warrants, but rigid extraction protocols strip the full-claim context that facets need. We introduce SIFT -- claim-conditioned re-scoring of extracted evidence spans against the full claim -- paired with WSP (Warranted Supports Proportion), an automatic NLI check that the cited warrant entails the claim. We evaluate on FEVER, SciFact, 5PILS, and DP across four open-source backbones. SIFT recovers accuracy on cells where naive decomposition costs up to 27.6 points, while raising WSP above direct prompting; WSP itself calibrates against human gold evidence at AUC 0.92 and precision 0.98.
arXiv:2606.24496v1 Announce Type: new Abstract: The use of agentic systems to perform offensive security operations has moved from a theoretical possibility to a commoditized capability. However, while the community has focused on creating more and more capable agents, less attention has been allocated to assessing the security of those systems. In this work, we present the first in-depth security analysis of the most widely used agentic systems for offensive security operations. We show that most of these tools share common design flaws that enable an active adversary to exfiltrate API keys, establish persistent footholds, and fully compromise the operator's machine, even when the agent operates inside a sandboxed container. To support our analysis, we introduce a full cyber kill chain for such agentic systems, capturing the progression from initial LLM manipulation to lateral movement, persistence, guardrail bypass, and sandbox escape. Building on our security analysis, we derive a robust architecture for agentic offensive-security tools and propose actionable, broadly applicable design principles that mitigate the disclosed attack paths at the architectural level.
arXiv:2606.24636v1 Announce Type: new Abstract: Cinematographic captioning aims to describe how a video is filmed using professional film-language concepts such as camera movement, shot size, depth of field, composition, and shooting angle. This capability is important for fine-grained video understanding and controllable movie-quality video generation, yet remains underexplored in existing multimodal large language models. Unlike question-answering-based evaluation of cinematic understanding, cinematographic captioning requires a unified open-form description over multiple cinematographic dimensions. This task is challenging for two main reasons: the model must infer professional cinematographic concepts from subtle visual evidence, and it must generate captions that are both comprehensive and accurate. Accordingly, we propose CineCap, a framework that combines structured reasoning with spatio-temporal anchors and reinforcement learning with comprehensiveness, accuracy, and gated coverage rewards. The former grounds professional cinematographic descriptions in explicit visual evidence and organizes them into compact atomic reasoning for supervised fine-tuning, while the latter improves the balance between descriptive completeness and factual correctness. In addition, we construct CineCap Bench, a benchmark of 472 manually annotated video-caption pairs for systematic evaluation. Extensive experiments show that CineCap consistently outperforms strong proprietary and open-source baselines, establishing a new state of the art for cinematographic captioning. The code, model checkpoint, and benchmark are publicly available in https://github.com/Hectormxy/CineCap.git.
arXiv:2606.24639v1 Announce Type: new Abstract: Photonic crystal waveguides (PCWs) are a powerful platform for optical technologies because they can spatially confine light on sub-wavelength scales and manipulate the group velocity of propagation modes, both of which enhance light-matter interactions. Many applications in photonics require a large bandwidth of low-loss and constant-velocity slow light, a significant challenge for previous dispersion and Bloch mode engineering techniques. By combining inverse design with an efficient mode solver and physics based formulas, we reduce the computational time of PCW designs by more than 100 times, allowing for the realization of PCWs with up to an order of magnitude increase in bandwidth and up to 4 times decrease in loss. We then explore the trade-offs between bandwidth, disorder-induce loss, group index, and dispersion. As examples, we apply this approach to two active and practical areas of research for PCWs design: broadband, position-tolerant Purcell enhancement, and compact phase shifters for optical communications. Our results significantly improve state-of-the-art PCW designs and provide a general method to optimize PCWs integrated technologies.
arXiv:2606.24531v1 Announce Type: new Abstract: Random access into compressed data is normally confined to a single layer. Entropy-layer methods (Recoil) seek within rANS by storing intermediate decoder states; dictionary/match-layer methods seek within LZ-style references. We are not aware of a format that supports a single position-invariant seek through both an entropy layer and a match layer addressed by one coordinate. We show that ACEAPEX's absolute-offset design provides exactly this: because the match layer resolves every back-reference to an absolute position at encode time, and the entropy layer is applied per block, an arbitrary block can be decoded through both layers using one coordinate, bit-perfect, in isolation. We prove this with a three-phase verification that closes the empty-buffer trap. The seek of one 16KB block through ANS-entropy and match completes in 0.334ms. We verify the full entropy+match pipeline end-to-end on four data profiles and characterize the hardware ceiling the format reaches: the absolute-offset structure unrolls to as many as 25,344 independent parsers on one H100, which sequential LZ77 cannot do. We state explicitly what is not claimed: this is a round-trip correctness proof, not a disk-archive format; throughput figures are match-phase; and the unified-seek result is demonstrated for two layers, with three-layer generalization left as a hypothesis. Code and the verification harness are in the project repository.
arXiv:2606.24537v1 Announce Type: new Abstract: Traditional importance sampling (IS) is designed to estimate rare-event probabilities by minimizing estimator variance. However, many applications prioritize rapid discovery: the generation of a trajectory within a rare set $A_n$. This requires a shift from ensemble-based estimation to a design principle focused on the hitting time $\tau_{A_n} := \inf\{t \ge 1 : Y_t^n \in A_n\}$. We formalize a Quality of Discovery problem as the problem of minimizing the description length (surprisal) of the discovered trajectory under the nominal model $p$. We prove that minimizing this description length is equivalent to minimizing the nominal rank exponent $J_{\mathrm{rank}}(q_n) := \lim_{n\to\infty} \frac{1}{n} \log G_n(Y^n)$, where $G_n(x^n)$ is the guesswork of sequence $x^n$. For i.i.d.\ models and type-defined rare sets $\Gamma$, we show that while classical IS targets the mass-dominating type $Q_{\mathrm{IS}}^* \in \arg\min_{Q \in \Gamma} D(Q\|p)$, discovery optimality is achieved by $Q_{\mathrm{GW}}^* \in \arg\min_{Q \in \Gamma} [H(Q) + D(Q\|p)]$. This framework identifies a fundamental rule: minimizing the guesswork exponent ensures the discovered sequence is the "least surprising" representative of the set relative to the nominal model's search order. We further demonstrate that under budgetary constraints, this exponent serves as a lexicographic tie-breaker when the hitting-time minimizer is not unique. This establishes $H(Q) + D(Q\|p)$ as a natural objective for discovery-based importance sampling, providing a formal bridge between randomized sampling and systematic search.
arXiv:2606.24579v1 Announce Type: new Abstract: Parametric knowledge in Large Language Models is not equally accessible across languages. As a result, standard inference techniques often struggle to surface localized facts, leading to failures in cross-lingual knowledge transfer and consistency. In this work, we investigate techniques for accessing hidden factual knowledge by exploring cross-lingual prompting strategies. We identify four inherent dimensions of cross-lingual exploration that directly govern parametric knowledge retrieval and evaluate them on multilingual factual benchmarks covering 17 typologically diverse languages. Our results demonstrate that cross-lingual exploration significantly improves knowledge transfer and factual recall, representing a more efficient compute Pareto frontier than native-language scaling. Furthermore, we observe corresponding improvements in cross-lingual consistency, exceeding what can be explained by accuracy gains alone. Overall, our work establishes multilingual prompt exploration as a highly effective inference-time strategy for unlocking latent parametric knowledge.
arXiv:2606.24630v1 Announce Type: new Abstract: We investigate how the influence of a free surface is transported in turbulent open channel flow by analysing matched open- and closed-channel direct numerical simulations up to $Re_\mathrm{\tau} \approx 900$ in a domain large enough to accommodate very-large-scale motions (VLSMs). The turbulent kinetic energy (TKE) budget shows that the surface influence is communicated primarily through transport terms. Near the free surface, pressure transport supplies energy towards the interface, whereas turbulent transport and dissipation are reduced; the resulting energy surplus is exported away from the surface predominantly by viscous diffusion. The near-surface budget terms do not exhibit a single universal similarity scaling: viscous diffusion is organised over the near-surface viscous scale $\ell_\mathrm{V}$, dissipation over the Kolmogorov sublayer scale $\ell_\mathrm{K}$, and pressure-related terms require the mixed velocity scale $u_\mathrm{b} u_\mathrm{\tau}^2 /h$. The pressure-strain redistribution further reveals outer-inner coupling: although intense pressure-strain events remain small-scale, their magnitude and directional bias are organised by low-velocity VLSM streaks. The free-surface influence is therefore best understood as a coupled multi-scale process involving local kinematic constraints, Reynolds-number-dependent surface layers, and outer-layer coherent motions.
arXiv:2606.24666v1 Announce Type: new Abstract: Approximate agreement tasks on graphs are discrete relaxations of consensus, where each process in a distributed system is given as input a vertex on a graph $G$, and processes have to output vertices that lie on a clique of $G$ contained in the convex hull of the input vertices. Although such tasks have been widely studied in a variety of models, graph classes and notions of convexity, it remains largely open for which classes of graphs these problems are solvable in asynchronous systems. In this work, we give a complete topological characterisation of the $t$-resilient solvability of approximate agreement on graphs and simplicial complexes in asynchronous shared-memory systems with read-write registers. As a result, we answer several open problems related to different variants of approximate agreement on graphs. For example, we give the first proof of Ledent's conjecture [PODC 2021] about the wait-free solvability of clique agreement. In fact, we show a more general result: clique agreement is $t$-resilient solvable on a graph $G$ if and only if its clique complex is $(t-1)$-connected in the homotopical sense. We also show that clique and monophonic agreement are solvable on the same class of graphs, but there exists a separation between monophonic and geodesic agreement, answering a question by Alistarh et al. [TCS 2023]. In the message-passing setting, our results imply new resilience bounds for asynchronous approximate agreement and round lower bounds for synchronous approximate agreement on graphs.
arXiv:2606.24669v1 Announce Type: new Abstract: Large language models (LLMs) have shown strong potential for planning and sequential decision-making, but prior work often relies on using them as direct controllers, which requires precise action generation and can be unreliable in practice. This paper proposes Latent Action Guidance for Online Reinforcement Learning (LaGO), a framework that uses a pretrained LLM as a latent action prior to softly guide online policy optimization, rather than treating the LLM as an explicit planner or controller. Experiments on both a discrete-control benchmark, CLEVR-Robot, and a continuous-control benchmark, Meta-World, demonstrate that LaGO consistently improves both reward and success rate over Vanilla PPO. In particular, LaGO increases the average success rate from 15.1% to 27.2% on CLEVR-Robot and from 2.7% to 15.2% on Meta-World. Our analysis further shows that stronger pretrained LLMs provide more effective guidance, suggesting that LLM knowledge can improve planning and online decision-making.