Papers

Deterministic benchmark scores show that an agent received credit, but not whether that credit was earned, reported honestly, or would hold on a second run. We introduce a Trust Layer for Agent Evaluation, an additive post-hoc framework that reports, beside each recorded score, whether it should be believed. It verifies four properties: whether the result is supported by the benchmark's own grading logic, whether a passing answer was earned through traceable computation, whether the agent's completion claim matches what occurred, and whether the result is stable under repeated execution. The first three use only saved artifacts; the fourth re-runs the agent. Model judgments only label evidence under majority voting; all verdicts follow deterministic rules and never modify the recorded score. Applied to five agent configurations on 108 tasks from Agents' Last Exam, every model shows passing runs with no traceable computation (at rates varying tenfold), confirmed false completion claims, and unstable results: 18-46% of tasks do not stay in one score band over five runs. Only 22.6% of recorded passes clear all four checks (95% CI 15.0-32.6, n=84). Measuring what an agent can do and verifying that it did it are different problems, and current benchmarks address only the first.

We report an interesting line of sight towards the blazar PKS 1158+007 (J1201+0028) ($z_{\rm em}$ = 1.369), revealing the rare detection of two intervening HI 21-cm absorption systems within a narrow redshift interval ($\Delta z \sim 0.04$) using the MeerKAT radio telescope. The stronger absorber at $z_{\rm abs}$ $=0.5653$ ($\int\tau dv = 1.31\pm0.04$ \kms) is associated with a strong MgII $\lambda2796$ system seen in the Sloan Digital Sky Survey (SDSS) and Dark Energy Spectroscopic Instrument (DESI) spectra, with rest-frame equivalent widths of $W_{2796} = 1.40\pm0.07$~Å\ and $1.21\pm0.11$~Å, respectively. In stark contrast, the second detection at $z_{\rm abs}$ $= 0.5305$ reveals a distinct HI 21-cm absorption feature ($\int\tau dv = 0.31 \pm 0.04$ \kms) with no associated metal absorption detectable in the optical spectra. This system represents a prime example of a "metal-poor” HI 21-cm absorber. Using photometric redshifts from Hyper Suprime-Cam (HSC) PDR3 and DESI Legacy Surveys DR10, we identify a broad galaxy overdensity (at $z \sim0.53\pm0.06$) coincident with these absorbers, suggesting the sightline pierces a complex large-scale structure or filament, which would be interesting to confirm with follow-up observations. These results underscore the power of blind HI 21-cm surveys to uncover the "invisible” cold gas phase of the Universe that optical/UV metal-line selection may systematically miss.

We analyze the level lines of the Gaussian Free Field with logarithmic singularities in polygonal domains. We focus on the (none-zero) singular case and compare it to the singular-free setting. The law of the level lines for the field in singular case is absolutely continuous with respect to the law for the singular-free case, with a Radon-Nikodym derivative related to the reduced Green's energy which is introduced by F. Viklund and D. W. Nyström~[VN24]. These level lines admit a Brownian motion representation. In the singular-free case, such representation involves Poisson point processes of Brownian loops and excursions; while for the singular case, it additionally includes Poisson point processes of Brownian bubbles and bridges. The special cases of one or two singularities yield moment-generating functions of the conformal radius, which can be interpreted as one-point and two-point correlation functions of vertex operators in conformal field theory at the free-boson point. While the Radon-Nikodym derivative is bounded away from the singularities, the behavior of the level lines near the singularities is markedly different from the singular-free case, with different asymptotic probabilities for all level lines to remain close to the singularity.

Linkage algorithms for hierarchical clustering (HC) are a powerful and efficient framework for constructing clustering trees, yet it is often unclear which merge rule best suits a given dataset or task. In contrast, neural approaches can learn from data, but often fail to retain the efficiency and size generalization of classical algorithms. We introduce NN-linkage, a neural network (NN) model that can learn task-specific and locally dependent merge rules while retaining the recursive structure and efficient inference of classical linkage algorithms. In particular, our model is algorithmically aligned with the Lance-Williams (LW) recurrence, a parameterized framework for defining a broad, continuous family of linkage rules for agglomerative HC. Classical methods such as single linkage (SL), complete linkage (CL), and average linkage arise as discrete choices within this broader family. We show that NN-linkage is a universal approximator for continuous linkage functions, including LW recurrences, and, when paired with a transformer encoding, can also approximate globally dependent rules such as robust single-linkage. We further show that NN-linkage can exactly implement any symmetric constant-coefficient LW recurrence across all input sizes. On the empirical front, we evaluate NN-linkage in real-world applications, clock-tree routing and phylogenetic reconstruction, using both synthetic and real datasets, demonstrating its effectiveness over both classical algorithms and other neural approaches. By learning merge rules directly from target trees, NN-linkage extends efficient HC to scientific and engineering objectives not adequately captured by existing hand-designed linkage rules.

Internal features in LLMs are often interpreted as mechanisms when they track a concept and their manipulation changes a related behavior. Yet steering can push a feature far outside its natural range, where its effects need not reflect the model's own computation. We examine this inference and propose an empirical contract whose tests evaluate features at values observed on natural inputs. One test copies a feature's value from an input that shows a behavior into a matched input that does not (installation) or the reverse (removal); the other restores the feature after an upstream edit (downstream rescue). Installation measures how far the feature suffices for the behavior; removal and downstream rescue measure how much the model uses it. Applied to three kinds of representations, the two strengths separate sharply. The published unknown-entity latent strongly steers knowledge abstention, yet installing observed values from either published latent into matched prompts transfers only a small fraction of the natural known–unknown abstention contrast. Dense known–unknown directions show opposite asymmetries between installation and removal in Gemma and Llama, and how fully a released subject–verb agreement feature set reproduces and restores the behavior depends on how its values are written into the model. Tracking a concept and steering a behavior therefore do not by themselves show that the model uses a feature, and each conclusion holds only for the intervention tested.

Cross-view geo-localization is commonly solved as an image retrieval problem, matching a ground-level image against a database of satellite tiles through a jointly trained embedding. Such models are accurate, but they need large paired supervision and cannot show what evidence supports a match. In this paper, we study a different question: how much of this task can be solved through language alone? We prompt a multimodal large language model (MLLM) to describe each ground panorama and each satellite tile as structured text, and localize by comparing these descriptions. No component is trained. We evaluate on 9,826 VIGOR pairs from four U.S. cities, in three settings. First, the descriptions are faithful but not discriminative. They agree closely across the two views, yet ranking the full pool by description similarity almost never returns the correct tile (0.39% Recall@1). Second, we narrow the pool to ten neighboring tiles, as a coarse prior would do. The same descriptions now become useful: an MLLM judge that scores structural consistency doubles random ranking and matches a strong lexical baseline. It also states which fields of the two descriptions agree and which conflict, which an embedding distance cannot do, and which we see as a step toward interpretable localization. Third, we place the judge on a trained visual retriever. On the queries it ranks wrongly, reranking from images works, while reranking from our descriptions does not (23.5% against 10.7% Recall@1). Scene structure survives the conversion into language, while the fine appearance detail needed to separate nearby places does not. Code and prompts are publicly available at https://github.com/AyeshAbuLehyeh/GeoLingual.

The log-rank test is the standard tool for two-sample survival comparison and has good power against proportional-hazards alternatives, but it loses power against sparse hazard departures, in which the hazard difference is concentrated in a small number of time intervals whose locations along the follow-up are unknown a priori (Kipnis, Galili and Yakhini, Biometrika 2026). Weighted log-rank tests – Gehan-Wilcoxon, Tarone-Ware, Peto-Prentice, Fleming-Harrington – each impose a pre-specified temporal emphasis. Combination procedures such as MaxCombo and the Yang-Prentice short-term/long-term hazard-ratio model relax that choice, but still scan only a small dictionary of global temporal shapes and remain insensitive to sparse departures occurring outside them. We introduce lifelines-hc, a Python package extending the lifelines survival library with the HCHG test: Higher Criticism applied to per-interval hypergeometric p-values. HCHG applies to right-censored two-sample data and detects sparse hazard departures at unknown locations without committing to any temporal pattern. Across four clinical case studies – CheckMate 057 PFS (n=582), COMET-1 OS (n=1028), AZURE DFS (n=3359), and the Copenhagen Study Group for Liver Diseases cirrhosis trial (n=446, fully public individual patient data) – HCHG achieves p <= 0.014 in every dataset, while the log-rank test is non-significant throughout (p >= 0.26). MaxCombo and the Yang-Prentice adaptive log-rank test detect the delayed-benefit crossing in CheckMate 057 (p < 0.001) but are non-significant on the remaining three (p >= 0.24), where the departure is sparse or multi-window rather than a smooth short-term/long-term hazard-ratio pattern. lifelines-hc is freely available under the MIT license at https://github.com/alonkipnis/lifelines-hc and via pip install lifelines-hc.

This paper presents Chana, a GPU-accelerated, block-structured adaptive-mesh code for general relativistic magnetohydrodynamics, multigroup M1 neutrino transport, and dynamical spacetime evolution using the Z4c formulation. Each physical module uses independently selected spatial discretizations and ghost-zone widths to balance accuracy and computational cost. Stiff radiation-matter interactions are treated implicitly, with Jacobians calculated analytically from the chain-rules. The code is written in C++20 and it uses MPI and Kokkos 5 for distributed-memory and performance-portable parallelism. The code is validated through a number of GRMHD, radiation transport, and dynamic spacetime tests. For a representative core-collapse supernova configuration with three neutrino species and 12 energy groups per species, the code achieves approximately $1.1 \times 10^6$ cell updates per GPU second on NVIDIA A100 GPUs using four-stage RK4 integration. Weak-scaling efficiency remains above 85% up to 256 GPUs on Perlmutter.

Retriever upgrades are typically evaluated using aggregate metrics, which can hide regressions on queries the previous retriever already served correctly. We study these regressions as negative flips: queries for which BM25 retrieves a judged relevant passage and the replacement does not. We evaluate BGE-large, E5-large-v2, and SPLADE on three BEIR collections: Natural Questions, HotpotQA, and FiQA, across five retrieval depths. All replacements improve overall retrieval coverage. Negative flips occur in every setting and vary substantially by corpus, retriever, and depth. At k=1, 8.6-37.5% of BM25 successes are lost across the evaluated settings. Negative-flip rates are lower in the larger-depth settings, where the BM25-supported cohort is defined separately at each depth. These rates use the any-relevant support label. On HotpotQA at k=10, requiring every positive qrel passage raises the negative-flip rate to 12.3-17.3%. Simple fixed-budget combinations with BM25 reduce these regressions, and a HotpotQA reader experiment provides a limited downstream check in which some retrieval flips are accompanied by answer regressions. These results motivate evaluating retriever updates using query-level compatibility alongside aggregate retrieval quality.

Estimating small area prevalence of opioid misuse is critical for targeting public health interventions, yet direct measures are unavailable and related surveillance data are often reported on misaligned areal units. We propose a Bayesian Multiscale Integrated Abundance (MIA) model for estimating latent opioid misuse prevalence by jointly analyzing multiple indirect surveillance indicators observed on different geographic supports. The model extends existing integrated abundance models by representing all source geographies through a common set of atomic spatial units formed by the intersections of observed areal supports. Latent prevalence at the atomic level is modeled using a Fisher noncentral hypergeometric distribution, which preserves county-level prevalence totals while respecting local population constraints. To enable scalable inference, we develop a two-stage compositional Markov chain Monte Carlo algorithm that combines customized sampling strategies and parallel computing. Simulation studies show the proposed approach reduces bias and root mean squared error relative to common downscaling methods. We apply the model to Ohio data from 2010-2023, integrating state-level survey estimates, county-level counts of opioid overdose deaths and treatment admissions, and ZIP code tabulation area-level counts of emergency medical services naloxone administrations. Results reveal substantial within-county heterogeneity and identify localized areas of elevated opioid misuse prevalence that would be missed by county-level analyses.

In this note, we establish quantitative stability of aggregation-diffusion energy for compactly supported data. Our consideration focuses on the degenerate diffusion with local attraction that are asymptotically flat at infinity, such as Riesz kernels. We characterize the spectral gap of the Wasserstein Hessian at steady states.

We study leading tensor propagation in a specified first-order Einstein–Cartan–Dirac theory with the parity-even quadratic torsion invariant $\zeta T_{\lambda\mu\nu}T^{\lambda\mu\nu}$. Eliminating the nondynamical Lorentz connection on the regular algebraic branch gives a metric description containing the Einstein–Hilbert term, the Dirac action, and a $\zeta$-dependent axial–axial fermion contact interaction. We evaluate the transverse-traceless (TT) Hessian under an explicit factorized mean-field closure, with vanishing connected-current TT response, vanishing first- and second-order TT response of the factorized current scalar, and zero intrinsic TT anisotropic stress. Under these imposed conditions, the leading two-derivative tensor action has $Q_T=M_{\rm Pl}^{2}$ and $c_T=1$, with no leading dispersion or propagation-induced polarization splitting. These conditions do not follow from isotropy of the one-point axial current, and the present calculation does not derive them from a microscopic fermionic state. The result is therefore conditional and does not establish a general Einstein–Cartan–Dirac no-go theorem. We identify the connected-current TT response that must be calculated to extend the result beyond this closure. Published NANOGrav summaries are used only to check consistency with the GR-like prediction; no new timing-data likelihood or constraint on $\zeta$ is obtained.

In this paper, we propose an alternating numerical scheme for constructing quasi-periodic solutions to a class of nonlinear partial differential equations (PDEs) with bounded perturbations, including the one-dimensional nonlinear Schrödinger (NLS) equations and nonlinear wave (NLW) equations under periodic and Dirichlet boundary conditions. A key observation concerning the resonant $Q$-equations allows us to establish directly a local diffeomorphism between the amplitudes and the drifted frequencies. This renders the proof considerably cleaner, since it avoids the Birkhoff normal form and the associated coordinate transformations required in classical KAM theory for PDEs.Unlike in the finite-dimensional setting, the lattice boxes must also include the spatial index, so that the multiscale induction has to be carried out in one additional dimension. This introduces two difficulties. First, the measure estimate for the excluded set of “bad” frequencies must account for the spatial index. For both the NLS and NLW equations, the linear frequencies and their differences are integers or close to integers; this allows the spatial dependence to be controlled through the modulus of the temporal index, so that the excluded measure remains under control. Second, a singular set may contain sites with the same temporal index but widely separated spatial indices, which obstructs the “inversion implies localization” process. For the one-dimensional NLS and NLW equations, however, such sites occur only in pairs with opposite spatial indices. They can therefore be separated by small boxes, after which the global inverse is obtained from the local inverses via the resolvent identity. Numerical experiments illustrate the scheme for nonlinear traveling and standing waves, exhibiting both the computed quasi-periodic solutions and the convergence of the iteration.

A team of coding agents can look fine agent by agent yet fail as a team: each passes its own tests while the merged result is broken, and single-agent evaluation never catches it. As teams run several LLM coding agents in parallel on one codebase, the agents collide: two rewrite the same function, one codes against a contract a teammate just changed, and integration fails after the work is done. Most coordination tools react (watch for a conflict, then warn), but at agent speed the warning arrives after the wasted edit. We recast the problem as scheduling: take each work item's declared scope, partition the work into disjoint scopes, and order merges along the producer->consumer graph, all up front. We build this planner into Nerveplane and evaluate it with NP-Bench, an environment-grounded three-arm benchmark (no coordination; reactive detection; proactive planning) that verifies integration off a real git merge, both in a deterministic simulation and with live agents. The planner lifts clean-integration from 1/9 to 9/9 scenarios and cuts merge conflicts from 13 to 0, with a gap that grows in the number of agents. On a live breaking contract change it rescues an outcome both baselines miss on every seed: the clean-integration rate rises from 0 (no coordination and reactive detection) to 1.0 on a frontier model and 0.6 on a small one, while agents respect assigned scopes (0/5 leakage). A cross-session memory drops the repeated-mistake rate from 1.00 to 0.00 on strong and weak models alike. We also report a negative result: routing facts to agents does not rescue long-context accuracy at window-fitting scales; its value is cost and capacity, not attention. Across two capability tiers and two vendors, the benefit did not shrink as models got stronger, because it comes from how work is allocated, not model reasoning.

We prove that every smooth quartic double $n$-fold, $n\ge2$, over an algebraically closed field of characteristic zero is algebraically elliptic in Gromov's sense. In particular, every smooth quartic double solid is algebraically elliptic, which answers Question~4.28 in [M. Zaidenberg, Algebraic Gromov ellipticity: a brief survey, Taiwanese J. Math. 29 (2025), no. 6, 1681-1705]. We also prove that removing any closed subset of codimension at least two preserves algebraic ellipticity for smooth quartic double spaces and smooth cubic hypersurfaces of dimension at least two.

We construct self-similar solutions to a nonlinear convection–diffusion equation posed on the whole Euclidean space, for a class of homogeneous initial data. The corresponding self-similar profiles solve a nonlinear elliptic equation on $\mathbb{R}^N$. We obtain these profiles as limits of solutions to Dirichlet problems on bounded domains with truncated nonlinearities, using a priori estimates that are uniform with respect to both the domain size and the truncation level. Our approach is inspired by recent constructions of large self-similar solutions for the Navier–Stokes system. The convection–diffusion equation considered here shares some structural features with the Navier–Stokes equations, but its scalar parabolic nature allows us to exploit tools such as the maximum principle and thereby obtain a more direct construction of self-similar solutions.

Enterprise AI agents that share a memory store face two unaddressed risks: sensitive data can leak through legitimately computed results the requester could not derive, and departments can silently compute a same-named key performance indicator (KPI) through conflicting logic. Existing agent-memory systems (e.g., MemGPT, Zep, A-MEM) gate retrieval by content, ownership, and role, not derivation, missing a cached insight that embeds a forbidden column. We introduce the Analytical Memory Unit (AMU), a memory schema that attaches a full derivation (lineage) graph to every cached result, gated by a retrieval policy that serves a hit only when the requester is authorised for every column touched. Provided lineage recording is complete, we prove by construction that the policy blocks retrieval of results derived from a sensitive column outside the requester's permissions, at O(n) worst case – a conditional design guarantee, not an empirical claim, that excludes derived features encoding sensitive information without naming their source. Eliminating measured leakage required 75-90% recorded lineage completeness, so we treat 90% as a conservative deployment target. Across six experiments, lineage-gated retrieval removes the 18.8-25.5% cross-department leakage naive content-gated memory suffers, keeping 81.5-82.6% of memory reuse at 13.8 microsecond worst-case overhead. A real-agent proof-of-concept with LLM-generated SQL is consistent with the guarantee: zero leaks over 9 round-trips, two conflicts caught automatically – though a feasibility demonstration, not evidence of production viability. This offers a practical governance layer for shared agent memory, complementing source-layer access control and supporting EU AI Act compliance.

Developers increasingly run a fleet of coding agents side by side on one workstation. Terminal multiplexers like tmux and a new generation of agent managers were built to arrange windows, not to govern memory. When ten agents each spawn language servers, test runners, and browsers, no standard tool can say how much memory belongs to which agent, confirm that a terminated agent's descendants are gone, notice a child that has escaped its agent, or keep the machine off the swap cliff when an out-of-memory (OOM) kill would silently discard uncommitted work. We treat these as runtime-verification problems: a hosting substrate should emit signals an operator can check while agents run. We present MemMux, an unprivileged local runtime (no kernel control groups) turning resource governance into checkable signals: per-agent attribution, complete reclamation, escaped-process visibility, bounded footprint under overcommit, and monitoring overhead. A claims-disciplined benchmark measures each against tmux and a raw-process baseline on identical workloads. Under a binding memory budget on a Linux host, MemMux holds the fleet under budget (7500 MiB) with zero swap by admitting a subset and reclaiming under pressure, while the ungoverned tools run every agent, pin the machine at its RAM ceiling (2x over budget), and spill about 2 GiB into swap. MemMux reclaims 100% of a terminated agent's process subtree where the raw baseline strands half of it (tmux matches us here; the raw baseline does not), and it is the only launcher we compare against that surfaces escaped children (10 of 10 detected). The cost: the always-on 1 Hz monitoring loop runs near 0.6% CPU at one agent but 2.7% at ten, above our 2% target. Running the harness on real Claude Code sessions shows 100% attribution and low overhead carry over to live agent trees. We release the engine, benchmark, and reproducer.

AI agents powered by large language models (LLMs) can perform complex tasks but may harm the systems they operate in, either intentionally or unintentionally. Existing agent monitoring approaches rely on rule-based guardrails or LLM-based trace auditing. However, rule-based guardrails can be bypassed through obfuscation and may miss harmful actions beyond their predefined rules, whereas applying an LLM to audit every action is costly. We present a two-stage agent trace auditing framework. The first stage uses single-event and trace-sequence rules to select pending actions for inspection; the second uses an LLM audit agent to examine each selected action in the context of the agent's preceding trace before execution. We jointly refine the gate rules and audit instructions using training data, allowing the framework to adapt to complex agent behaviors rather than relying solely on predefined rules. On the public benchmark OpenAgentSafety, our framework reduces the average number of LLM audits from 8.15 to 2.33 per run and token usage from 47.8k to 14.6k, with a detection rate of 72.8% compared with 81.5% when every action is audited. In two simulated multi-agent case studies, the framework flags all malicious traces while reducing audit token usage by more than 80%.

Neural algorithmic reasoning, or aligning a neural network with an algorithmic paradigm, has emerged as an approach to solving polynomial-time-solvable and computationally harder combinatorial optimization problems. We propose a new message-passing framework based on the Chambolle-Pock Primal–Dual Hybrid Gradient (PDHG) method called GraphPDHG for solving general graph saddle-point problems. Theoretically, we show that GraphPDHG can efficiently solve a family of graph saddle-point problems by simulating PDHG. We also show that our network can learn an accelerated PDHG algorithm. Experimentally, we support our results on accelerated PDHG by evaluating the performance of our model as a learned warm start for second-order optimization techniques (SSNAL). We also show that alignment with PDHG leads to stronger size generalization than non-aligned graph neural network (GNN) baselines. Overall, we propose a novel architecture for solving a general family of optimization problems on graphs.

The 'unreasonable effectiveness of mathematics in the natural sciences' may at times give the impression that natural science, especially modern theoretical physics, is all but a formal apparatus. However, a key challenge of physics remains to align everyday notions of experience – be it directly or mediated through instruments of arbitrary sophistication – with their mathematical formalisation. This applies in particular to quantum theory, arguably the most successful theory of physics ever invented. One of its core assumptions postulates: $Observables\ correspond\ with\ self-adjoint\ operators.$ Here, we argue that already this most basic premise about the quantum formalism falls apart under careful scrutiny, at least when understood for all observables at once. In other words, we challenge the role of the noncommutative algebra of bounded operators as an adequate formalisation of the 'algebra of observables', understood as (equivalence classes of) measurement procedures that admit a coherent empirical interpretation.

Neural fields are usually evaluated by how well they reconstruct an observation. We show that this misses two useful properties of a fitted network: how easily it can adapt to new observations, and what its weights retain from earlier ones. We study these properties as adaptation geometry. For images, we meta-learn class-specific initializations, adapt each one to a new image, and measure how much the network must change to fit it. A simple local linear model closely predicts this adaptation cost, while replacing one network's tangent kernel with another's substantially worsens the prediction. Adaptation thus depends on the local geometry of the fitted network, not only on its current reconstruction. For physical fields, we repeatedly fit the same network to observations from a sequence. Its weights then retain information about that history. When two wave histories end at exactly the same observation, the final weights recover the sign of the wave velocity with 68.6% accuracy, whereas the current observation alone contains no such information and gives 50%. These two phenomena are quantitatively linked: tangent-kernel eigenvalues predict both which changes are easy to learn and how quickly they are overwritten by later fitting. Together, these results show that neural fields contain useful information beyond what they currently reconstruct: in how they can change and in how they got there.

The Minimum Vertex Cover (MVC) problem is a fundamental NP-hard combinatorial optimization problem with applications in network analysis and resource allocation. Grover's algorithm provides a quadratic reduction in query complexity for unstructured search, but existing Grover-based MVC formulations can incur substantial quantum resource overhead due to costly vertex-counting circuits and complex oracle constructions. We develop and evaluate several encoding and oracle-design strategies for reducing the qubit count, circuit depth, and gate complexity of Grover-based MVC search. First, we construct a Dicke-Parallel formulation that restricts the search to fixed-cardinality subsets, eliminating explicit vertex counting, together with a parallel edge-verification oracle that reduces feasibility-checking overhead. We then develop an Edge-Counting formulation that replaces per-edge auxiliary storage with a logarithmic-size counting register, substantially reducing ancillary-qubit requirements. Finally, we propose an Edge-Centric encoding that represents endpoint selections directly and derives vertex-selection states through incident-edge Boolean operations, enabling more depth-efficient oracle construction. Our resource analysis reveals complementary trade-offs among qubit width, circuit depth, gate count, and Grover iteration count. Edge-Counting is particularly attractive under tight qubit constraints, while Edge-Centric can reduce both circuit depth and Grover iteration count when the graph has a moderate edge count and sufficient representation multiplicity. Dicke-Parallel provides a more robust choice when such multiplicity is limited or graph density makes the edge-based search space large. These results provide practical guidance for selecting Grover-based MVC formulations according to hardware constraints and graph structure.

GHZ-based conference key agreement distributes a shared key to $N$ parties in one network use, whereas pairwise BB84 needs $N-1$. The survival of that advantage has been studied against party number, loss, and topology, but almost always with the channel fixed at depolarizing. Simulating both protocols exactly for $N = 3, 4, 5$ under dephasing, amplitude damping, and depolarizing noise, we find the crossover is set by the channel's Pauli error composition, not its identity: normalized to average infidelity, amplitude damping and depolarizing agree to within about 1% at each group size, while dephasing can tolerate roughly $2.4\times$ more at $N = 3$. We derive a closed-form rate for arbitrary per-party Pauli noise and use it to prove that concentrating a fixed noise budget on one arm is strictly worse than spreading it, and that giving the dealer role to the cleanest arm improves the rate by roughly 18%. One structural fact drives every result: the phase-error term is a product over all $N$ arms, while the bit-error term stays local to a pair.

Wrapping an image generation model in an agentic harness can effectively boost Text-to-Image task performance: the harness can leverage memory, skills, workflow orchestration, result verification, and iterative refinement to continually construct and revise prompts, thereby eliciting better images. These gains, however, remain external to the diffusion model and are realized only while the full harness runs. We propose Diffusion On-Policy Context Distillation (D-OPCD), which treats the agent-improved prompt as privileged context and distills the knowledge encoded in the agent harness into the weights of the diffusion model, so that the model retains part of the harness's benefit when conditioned on the original query alone. Using a Text-to-Image agent equipped with our proposed Auto Skill Evolver (ASE), we show that D-OPCD can internalize harness capabilities into the generator's weights, raising the average direct-generation score from 60.52 to 65.09 across four benchmarks. With this knowledge absorbed into the weights, the harness can shed its saturated skills and resume evolving: a second ASE round on the updated generator improves on a skill-free harness by additional 1.83 points, pointing toward text-to-image systems in which harness and model keep improving each other through continual co-evolution.

How can an AI agent determine what rules to follow? One rule permits an action. Another imposes a condition, exception, or conflicting obligation. Deterministic systems can resolve those relationships when they have been specified. When they remain implicit in language, an agent can follow one rule while missing another that should stop it. Refusing every unresolved action avoids that risk, but also blocks permissible actions. We wanted the agent to make the distinction and still act. Our initial hypothesis was that geometric measurements could supply a basis for judgment. We represented actions and policies as vectors, then tested whether their geometry could identify governing policies and interpret the action's relation to them. Across four studies, the tested approaches did not establish reliable pre-action judgment. In the final synthetic study, a lexical router recovered every governing and blocking policy while reducing median policy checks by 97.7%. The composed pipeline nevertheless escalated all 2,304 test actions, including those it should have allowed. Supplying every policy to the same downstream mechanism changed no decision. Finding the policies had not solved the problem of interpreting them. This result led us to revise our hypothesis: judgment in AI agents requires developing a consequence graph. Such a graph would connect the actor and authority to policy conditions, exceptions, and the changes an action would produce. Follow-on studies will ask whether making those relationships explicit helps the agent distinguish when to act, stop, or seek review.

We study a Poincaré-type inequality for Gaussian measures restricted to origin-symmetric convex sets. The inequality arises from the second variation at $t=0$ of the function $t\longmapsto \gamma_{\Sigma}\left(e^{tA}K\right)$, where $\Sigma$ and $A$ are symmetric matrices. The relevance of this function comes from Saroglou's reformulation of the log-Brunn–Minkowski conjecture. We show that $\Sigma$ and $A$ commute if and only if the inequality holds for every box of the form $UD B_\infty^n$, where $U$ is orthogonal and $D$ is diagonal. In the non-commuting case, this yields counterexamples for orthogonal boxes whose axes can be chosen arbitrarily close to the coordinate axes. We also show that the inequality holds when $K$ is unconditional with respect to an eigenbasis of $\Sigma$ and $A$ is an arbitrary symmetric matrix.

Large language models have shown strong reasoning capabilities, but their high inference costs make knowledge distillation an important approach for transferring such capabilities to compact models in resource-constrained scenarios. On-policy self-distillation further reduces the reliance on external large teacher models while improving the reasoning ability of compact language models. However, existing methods typically either distill all token positions uniformly or select tokens using fixed heuristic criteria, assigning the same distillation strength to the selected positions rather than adaptively learning which tokens are most beneficial for distillation. To address these limitations, we propose BiToK-SD (Bilevel Top-K Token Selection for Self-Distillation), a bilevel-optimization-based token selection method that learns where distillation should be applied during on-policy self-distillation. Specifically, BiToK-SD is formulated as a bilevel optimization problem, where the lower-level problem models Top-K token selection as a differentiable threshold-based relaxation, allowing the selected positions to adapt as the student policy evolves, while the upper-level problem performs knowledge distillation on the selected positions. Experiments on mathematical reasoning benchmarks show that BiToK-SD achieves the best average performance among all compared methods while requiring only lightweight additional computation.

We introduce contact monopoles on contact metric $5$-manifolds and study their basic geometric properties. We construct natural examples from Boothby–Wang fibrations over Kähler surfaces and relate the equation to contact instantons on Sasakian $5$-manifolds. In particular, we show that anti-self-dual contact instantons with a parallel Higgs field provide contact monopoles. We also prove a compact rigidity result: on compact contact metric $5$-manifolds, every smooth contact monopole has parallel Higgs field and satisfies the reduced curvature equation $F_A\wedge\omega=0$. In the Sasakian case, this relates compact contact monopoles to anti-self-dual contact instantons under the usual transverse type condition. We also explain why the associated deformation complex is not elliptic in the usual sense. We then focus on unit tangent sphere bundles of oriented Riemannian $3$-manifolds, endowed with their canonical contact metric structures. In this setting, we derive a local form of the contact monopole equation with respect to the canonical adapted frame and prove that pure pullback configurations from the base are rigid. Finally, for the homogeneous Sasakian manifold $T_1S^3\cong SO(4)/SO(2)$, we use Wang's theorem to reduce the invariant contact monopole equation to finite-dimensional algebraic systems and classify the invariant solutions for homogeneous $U(1)$- and $SO(3)$-bundles. In the abelian case, the classification yields non-flat homogeneous $U(1)$ contact monopoles for nonzero topological charge. In the non-abelian case, all weights except $m=1$ reduce to the maximal torus, while the weight $m=1$ gives a genuinely non-abelian branch of homogeneous $SO(3)$ contact monopoles.

In this paper, we present a robust nonprehensile object transportation framework for quadruped robots. An uncertainty-aware trajectory optimization method generates object motions with minimal closed-loop sensitivity to uncertain parameters. The resulting reference trajectory is tracked using a coupled convex model predictive controller that jointly predicts the CoM dynamics of the quadruped and the payload followed by a whole-body QP that enforces ground reaction constraints. The approach is evaluated through extensive simulations and real-world experiments under variations in the object's inertial parameters. Its performance is compared with fixed-orientation and straight-line trajectories as baseline. The results show that the optimized object motion reduces the sliding by approximately 50% compared with the fixed-orientation baseline and 30% compared with the straight-line baseline, while also achieving lower robot CoM tracking errors.