Papers

In this article, we develop high-order, entropy-dissipative schemes for a hyperbolic system of conservation laws describing the first-order dynamics of two-layer thin-film flows of immiscible fluids with perfectly soluble solute particles. The key aspect is to construct entropy-conservative fluxes in the sense of Tadmor. Here, we consider and compare two different construction processes: an exact formulation and a commonly used simplified approximation in the flux evaluation. While the approximate approach is simpler at the level of construction and is frequently employed in practice (also in other contexts), it is less structured, leading to increased computational cost in the implementation compared to the exact formulation, which has been much more complicated to derive. We employ these fluxes within both an entropy-dissipative finite-difference framework and an entropy-dissipative discontinuous Galerkin spectral element method. Through numerical experiments using two distinct spatial discretizations, we investigate the performance and robustness of the proposed methods and demonstrate that the choice of numerical flux has a noticeable impact on the efficiency of the resulting solvers.

Despite the success of Time Series Foundation Models (TSFMs) on broad benchmarks, their ability to internalize basic temporal logic, especially in settings supported by exogenous covariates, remains under-examined. We introduce SimpleTimeBench, a diagnostic univariate and multivariate "unit test" suite for primitives such as monotonic trends, periodic signals and leading indicator covariates, scenarios where near-perfect forecasts should be trivial. Surprisingly, prominent multivariate TSFMs (Chronos-2, Moirai and Toto) frequently produce suboptimal zero-shot forecasts for these inputs. While fine-tuning Chronos-2 improves its behaviour on specific tasks, we show that this adaptation degrades performance on other fundamental patterns rather than enhancing its generalizable foundational capabilities. This reveals a gap between pre-training scale and basic temporal reasoning, suggesting that current TSFMs could potentially lack the inductive biases needed to capture simple predictable functions. We further demonstrate that these failures are not merely synthetic curiosities: they persist in real-world sensor forecasting, where TSFMs consistently underutilize leading indicators available in observed covariates. This inability to capture simple relationships limits the practical utility and reliability of current multivariate models.

Lifecycle overhead silently consumes accelerator capacity across large-scale recommendation training fleets. Our largest recommendation workloads process tens of billions train- ing examples per day on thousands of GPUs. Before this work, only 50-60% of their end-to-end wall time advanced training on new data. We present a fleet-scale study of this lifecycle overhead and a set of optimizations spanning the full training stack. We use Effective Training Time (ETT%) as an operational framework to instrument lost time, localize it to independently owned infrastructure components, and expose work repeated across job restarts. This analysis guides optimizations like communication elimination and pipeline overlap during trainer initialization; dynamic-shape handling, autotuning pruning, and reusable Py- Torch 2 compilation caches; asynchronous checkpointing; stan- dalone model publishing; and reductions in recovery cost. We evaluate the optimizations on representative models and measure their impacts in our training fleet. ETT% improves on every benchmark, by 15.5% on average, and reaches 85% on our largest workload. Fleet-wide ETT% rose from about 80% to above 90% after deployment.

Neural operators approximate PDE solutions within a geometry family, but independently learned local operators need not form a consistent global simulator. We study frozen, single-pass composition for steady incompressible flow in idealized two-dimensional airway trees. Separate Tube, bifurcation, and trifurcation DeepONets are trained on 4,872 primitive CFD cases using field supervision and auxiliary divergence, port-flux, component-balance, and port-pressure penalties. The validation-selected deployment is frozen before whole-tree CFD fields are inspected and assembled without tree training, iterative coupling, flux correction, or CFD-informed adjustment. It retains major flow patterns and controlled pathology responses with 0.204-0.215 s CPU inference, but has a 22.68% prescribed-inlet-normalized external residual. A post-hoc sensitivity protocol, frozen before new training and evaluation, repeats Data, Div, and Full models across three seeds with Tube fixed. Relative to Data, Full reduces primitive composite scores by 26.7% for Y2 and 26.4% for Y3 and reduces assembled component-residual and interface-mismatch RMS by 7.2% and 16.6%, respectively. Nevertheless, mean tree velocity error increases by 7.5%, while external residual increases from 17.49 +/- 4.38% to 26.77 +/- 3.65%. Local regularization can therefore improve primitive and assembled local diagnostics without ensuring accurate global fields or conservation.

Distributed state estimation is critical for applications such as surveillance, autonomous navigation, and wide-area monitoring, where sensor agents must cooperatively track targets using only local measurements and neighbor-to-neighbor communication. Existing distributed filters have been shown to achieve accurate estimation even under sparse inter-agent communication and limited sensing ranges. However, many of these methods rely on consensus parameters that depend on global properties of the communication graph, such as the maximum degree of the graph, and are therefore sensitive to changes in network topology. This limitation is particularly significant in sensor networks with mobile agents, where communication links change over time. This paper presents a Dynamic Generalized Kalman Consensus Filter for target tracking in sensor networks with switching communication topologies. The proposed algorithm computes information-based consensus weights using only locally available quantities, eliminating the need for global network parameters. Numerical simulations demonstrate that the proposed algorithm maintains estimation accuracy under switching network topologies and outperforms existing distributed filters in the given tracking problem.

Vision-language-action models benefit from the understanding and reasoning capabilities of pretrained vision-language models, but action-only supervision provides limited grounding in world dynamics. Conversely, world-action models inherit spatiotemporal priors from video generation models, yet remain limited in semantic understanding and reasoning under distribution shifts. We introduce UniWAM, a unified architecture that integrates a physical reasoner, a world generator, and an action predictor to jointly learn semantic understanding of the physical world, visual generation, and action prediction. To ensure the quality of the training data, we developed a rigorous data cleaning and annotation pipeline for both human egocentric data and robot data. To adapt the vision-language component to embodied tasks while preserving its inherited language capabilities, we represent low-level actions in natural language and introduce a pre-training recipe that assigns complementary supervision from visual question answering (VQA) data, human egocentric data, and robot demonstrations to the appropriate model components. During post-training, future visual noise augmentation reduces reliance on precise future predictions, while history-conditioned flow matching uses encoded action history to initialize action generation. Together, these designs significantly reduce denoising steps while maintaining performance. UniWAM achieves state-of-the-art (SOTA) performance across multiple evaluations, including in-distribution performance, robustness, generalization, instruction following, and long-horizon task execution. Furthermore, we uncover a log-linear scaling law of unified human-robot co-training, demonstrating the effectiveness of large-scale pre-training on a mixture of human and robot data.

We prove that there is an absolute constant $c>0$ such that every connected vertex-transitive graph $G$ on $n \ge 3$ vertices contains a cycle of length at least $cn$. Moreover, every such graph with sufficiently large degree $d$ contains a cycle of length at least $(1-d^{-1/100})n$. This gives the first linear bound towards Lovász's Hamiltonicity conjecture. The proof combines a structural result of DeVos and Mohar on vertex-transitive graphs with a general framework for finding long cycles, which may be of independent interest.

A new method of analyzing grid, or aliasing, instabilities is described, in particle-in-cell (PIC) codes for plasma kinetic theory. It starts with a meshfree approach with $N_{p}$ macroparticles, with $N_{p}<\infty$. Linearization of these equations is done about a uniform density non-drifting equilibrium prescribed by macroparticles on a uniform lattice. Macroparticle positions perturbations are induced about this lattice. The resulting linear equations are analyzed for stability and dispersion relations. The linearized equations are then discretized on a grid of $N_{g}$ points with $N_{g} \le N_{p}$, in both momentum conserving (MCP) and energy conserving (ECP) formulations. For a cold stationary plasma, this leads a dynamical matrix. For ECP, the matrix is symmetric and positive definite (SPD) and immediately shows stability. For MCP, the dynamical matrix is neither symmetric nor positive definite, preventing immediate conclusions on stability. For both MCP and ECP and for a cold stationary plasma, the resulting matrix elements vary relative to the meshfree value, a result of aliasing. This deviation is periodic in the displacement of the particle lattice relative to the grid. In the MCP discretization, eigenvalues occur in complex conjugate pairs for general placement of the particle lattice relative to the grid. These conjugate pairs indicate nonnegative growth rates. The nature of the aliasing is studied and shown to be related to the trapezoidal rule error over the grid. The scaling of the linear growth rates with respect to $N_{g}$ and especially with respect to $N_{ppc}$ is studied. These analytical results are compared with PIC simulations and found to be in excellent agreement. The connection with a cold drifting beam is discussed briefly, specifically, grid-induced instabilities for both the MCP and ECP.

Adverse weather image restoration aims to recover images degraded by rain, haze, snow, and other weather-induced artifacts, thereby improving the robustness of outdoor vision systems. Existing unified restoration models exhibit limited generalization to real-world scenes due to their reliance on synthetic supervision and insufficient semantic constraints. In this paper, we propose a novel student–teacher semi-supervised framework that addresses both challenges. Specifically, we introduce an unreliable database that preserves failed teacher predictions as informative negative samples for contrastive learning, while a reliable database stores high-quality teacher predictions as positive samples. By jointly exploiting reliable pseudo-ground truths and unreliable teacher outputs, the proposed framework learns to enhance desirable restoration characteristics while avoiding common failures. We further propose a phase spectrum-based semantic constraint that replaces computationally expensive text-based supervision with an efficient and naturally aligned semantic prior. An adaptive phase consistency loss is also designed to dynamically balance supervision between the degraded input and teacher pseudo-ground truths according to degradation severity. Extensive experiments on real-world benchmarks demonstrate that the proposed method consistently outperforms existing state-of-the-art approaches in restoration quality and perceptual fidelity while exhibiting stronger generalization to real-world adverse weather conditions.

Deciding whether an unknown quantum state either belongs to, or is far from, a given family of states is a natural question of quantum information theory. In many such cases, there is a natural 2-copy test which always accepts whenever the state indeed belongs to the target family; it is often much more difficult, however, to bound the probability of acceptance for states that are far from the family. Here we develop a simple new technique for upper bounding this probability for general families, and therefore upper bounding the sample-complexity of the decision problem itself. As a particularly striking example of this framework, we show that deciding whether an unknown pure $n$-mode state is fermionic Gaussian, or at least $\varepsilon$-far in trace distance from all Gaussian states, can be accomplished using the optimal number $\Theta(\varepsilon^{-2})$ of copies. Remarkably, our analysis applies to the well-known Bell sampling procedure for testing fermionic Gaussianity, which we therefore show to be optimal, even compared to protocols making arbitrary collective and adaptive measurements. As a second example, we show that the analogous decision problem for the family of Slater determinant states can also be solved with mode-independent sample-complexity.

We study quasi-modularity of normalized $q$-traces on bosonic Fock spaces associated with finite-dimensional quadratic spaces and superspaces. For a natural class of operators obtained from free-boson fields and their descendants, we prove that their normalized $q$-traces are quasi-modular, with weight bounded by the sum of the weights of the insertions. As applications, we prove Qin's quasi-modularity conjecture for tautological integrals on Hilbert schemes of points of a surface with numerically trivial canonical class, obtain quasi-modularity of arbitrary zero-mode correlation functions in the Heisenberg vertex operator algebra, and give a new proof of the Bloch–Okounkov quasi-modularity theorem as a rank-one specialization of our general result.

When a SCADA alarm is raised in a water distribution network, operators must decide quickly whether it reflects a cyberattack, a physical fault, a normal transient or a faulty sensor. Supervised classifiers need labelled incidents that utilities rarely have, and frontier large language models (LLMs) take tens of seconds per decision. We tested whether Jev, a training-free model that returns class probabilities in about one second, can serve as the first tier of this triage. On a four-class cause-attribution benchmark built on the C-Town network in EPANET, Jev was compared with a hand-written rule tree, a supervised classifier and seven cloud LLMs on identical evidence in four sealed, pre-registered rounds. With only a label-free prior correction, Jev matched the rule tree (macro-F1 0.62-0.64 against 0.56-0.61 in distribution) and exceeded the supervised classifier by 0.36-0.42 on event subtypes absent from its labels, in all four rounds, and it outperformed the classifier whenever fewer than about four labelled events per class were available. Jev also decided 20-40 times faster than frontier LLMs. Accepting only benign Jev verdicts confirmed by the rule tree spared an LLM reviewer 35-38% of windows on fresh sealed sets without loss of macro-F1. Transferred unchanged to two further networks, this gated cascade stayed within the non-inferiority margin of its reviewer on all four sets. A fast, training-free screen can therefore take over about a third of the review load in SCADA anomaly triage while preserving the accuracy of deliberate review.

It is an open problem in proof complexity whether every unsatisfiable CNF formula has an FPT-sized resolution refutation parameterized by incidence treewidth. In this paper, we establish several upper bounds on resolution refutation length related to this problem. Consider an unsatisfiable CNF formula $F$ with $n$ variables, $m$ clauses, maximum clause width $k$, and incidence treewidth $\mathrm{tw}^*(F)$. In this paper, we introduce two variants of incidence treewidth. Their definitions can be stated informally as follows. The first is log-weighted incidence treewidth $\mathrm{tw}_{\log}^*(F)$, which is the treewidth of the weighted incidence graph, in which variables have weight one and each clause has weight equal to the logarithm of its width. The second is partially log-weighted incidence treewidth $\mathrm{tw}^*_{\mathrm{plog}}(F)$, which is a refinement of log-weighted incidence treewidth. In this variant, for a nice tree decomposition of the incidence graph, each clause has weight one along a path selected for that clause and elsewhere has weight equal to the logarithm of one plus the number of its literals whose variables do not appear in any bag on that path, and variables have weight one. For every unsatisfiable CNF formula $F$, we prove the existence of (i) an FPT-sized resolution refutation parameterized by log-weighted incidence treewidth, with width at most $\mathrm{tw}_{\log}^*(F)+k$; (ii) a resolution refutation of length $(n+m)k^{O(\mathrm{tw}^*(F))}$ and width at most $\mathrm{tw}^*(F)+k$; (iii) an FPT-sized resolution refutation parameterized by partially log-weighted incidence treewidth; and (iv) an FPT-sized regular resolution refutation parameterized by log-weighted incidence treewidth. Our main idea is to construct FPT-sized $k$-DNF resolution refutations parameterized by incidence treewidth, and then convert them into resolution refutations.

Semantic database systems extend SQL with foundation-model inference over unstructured data, but current engines rely heavily on autoregressive LLMs for discrete relational decisions, creating high latency and monetary cost. We present JEVDB, a scalable semantic database system that uses fast, typed decision models for semantic filters, joins, classification, and ranking, while selectively escalating uncertain cases to generative LLMs. To reduce semantic-join work, JEVDB combines exact Yannakakis-style semijoin reduction over relational structure with Semantic Bloom Filters (SBFs), which use registered necessary conditions to screen candidates across latent semantic edges. We evaluate JEVDB on SemBench and Shelob, a TPC-DS-derived semantic-join workload. On SemBench, JEVDB-Flash achieves the lowest latency on all 21 evaluated queries and the lowest cost on 19, while maintaining competitive answer quality. On Shelob, where joins scale to 540K candidate pairs, JEVDB completes all queries with 95.7%-97.5% mean F1. SBF screening removes 87.4% of candidate pairs before semantic evaluation, and reusable condition-index scoring further reduces reasoning-model escalations by 55.2%. An interactive query simulator, source code, and benchmarks are available at https://jevdb.org.

Positive and negative space is a fundamental principle in visual composition, supporting visually coherent forms and layered semantic relationships. Generating such compositions is challenging because it requires coordinated control over two semantic concepts that share a common boundary. Although recent text-to-image models and multimodal large language models (MLLMs) have achieved strong performance in image generation and visual understanding, positive-negative space generation remains difficult, particularly under direct single-pass prompting. In this work, we present the Form and Void Agent (FaV-A), a multimodal agent designed for staged positive-negative space generation. FaV-A follows a progressive workflow: it first generates a base object, then analyzes its shape and spatial structure to identify candidate negative-space semantics, and finally produces compositional instructions for the final image generation stage. Experimental results and ablation analyses suggest that FaV-A provides a more effective framework than direct zero-shot MLLM baselines for producing visually coherent and semantically aligned positive-negative space compositions.

Recent advances in rectified flow-based image-to-3D generative models have enabled high-fidelity 3D asset generation. Building on this, a growing line of work has exploited these strong 3D priors for training-free stylization, transferring visual attributes from a reference image onto a generated 3D asset. However, existing methods enforce an all-or-nothing paradigm: color and texture are transferred jointly, with no mechanism to control them independently – a limitation we formalize as Disentangled 3D Stylization(Disen3D). To address this, we propose DiDE, the first training-free framework for Disen3D. Key to our approach is the observation that the structured latent space of image-to-3D models is overcomplete with respect to texture: texture information occupies only a small subset of the style-significant channels, leaving a free subspace available for independent color encoding. DiDE exploits this via a channel partition mechanism that processes a content image, a texture reference, and a color reference through dedicated branches and composes both style signals interference-free at every self-attention layer, preserving content geometry throughout. Experiments on Disen3D-Bench, our newly collected multi-reference benchmark, show that DiDE consistently outperforms 2D and 3D stylization baselines in color fidelity, texture transfer, and content preservation.

Schrödinger bridge (SB) learns stochastic transport between prescribed initial and target distributions. When the initial distribution shifts at test time, the learned dynamics can fail to recover the target distribution. We introduce the Distributionally Robust Schrödinger Bridge (DRSB), which learns a single controller that accounts for uncertainty in the initial distribution. The DRSB objective consists of control energy and a KL penalty between the resulting terminal distribution and the target distribution. DRSB seeks a single controller that minimizes the worst-case value of this objective as the initial distribution varies within an ambiguity set around the nominal distribution. We derive an exact variational formulation of this objective and connect its fixed-terminal-cost subproblem to stochastic optimal control and distributionally robust optimization. This formulation motivates an alternating algorithm that updates the adversarial initial distribution, estimates the terminal log-density ratio, and trains the controller. We develop Wasserstein and Sinkhorn variants using stochastic control optimality conditions to approximate the gradients required for adversarial updates. Experiments on two-dimensional transport tasks and image-to-image translation show improved robustness to input perturbations relative to standard SB, with a tradeoff in nominal performance. On Gaussian mixture transport, Sinkhorn DRSB also achieves lower mean sliced Wasserstein distance than fixed-level noise augmentation at both tested unseen noise levels.

We show that, unlike the lower central series, the dimension series of a Lie ring need not stabilize when two consecutive terms coincide; in fact, arbitrarily long finite plateaux occur. We prove that $D_n(L)/\gamma_{n+1}(L)$ is central in $L/\gamma_{n+1}(L)$ for every $n\geq1$, in contrast to the group case. If $c\geq2$ and $L$ is metabelian and nilpotent of class at most $c$, we prove that $D_{2c-1}(L)=0$. In particular, our results imply that $D_5(L)\subseteq\gamma_4(L)$ for every Lie ring $L$.

In certain clinical areas, relative effect measures are believed to remain more constant across populations than absolute measures. This suggests that exchangeability assumptions on the relative scale may be more plausible than those on the absolute scale. Despite this, most methods for extending trial results to a target population rely on strong and often implausible distributional exchangeability assumptions between the trial and target population (distributional transportability). We propose identification results for failure-time outcomes under a more plausible assumption of exchangeability on the relative scale, focusing primarily on the risk ratio (risk ratio transportability). We applied these methods to estimate the effect of screening strategies on all-cause mortality, using data from the National Lung Screening Trial (NLST) to a nationally representative target population from the National Health Interview Survey (NHIS). All-cause mortality data was available from NHIS, along with no confounding of screening, allowing a falsification assessment of the distributional transportability analysis against the observed baseline risk.We found that this approach substantially underestimated mortality risk. In comparison, the risk ratio transportability approach produced reasonable estimates that matched the baseline risk.Thus, assumptions on relative scales may be more plausible in certain settings where distributional transportability fails.

Some properties of languages, e.g., subject-object-verb (SOV) word order, are more prevalent than others among the thousands of attested natural languages (NLs). Such typological commonality is often attributed to learning biases. Computational simulations, recently with language models (LMs), have facilitated the exploration of this theory. In this paper, we extend existing analyses of the relationship between LMs' learning biases and typological commonality on both data and model sides, focusing on: (i) cross-serial dependencies, the upper limit of attested syntactic complexity, and (ii) stack-based LMs (SLMs), potentially facilitating learning of hierarchical patterns. We first evaluate generalization of SLMs on cross-serial dependencies across diverse artificial languages and confirm that they struggle with such constructions. However, SLMs with limited working memory generalize better suggesting a possible basis for such inductive bias and thus the typological commonality of some word order configurations.

Recent years have witnessed the rapid adoption of reinforcement learning (RL) in large language model (LLM) post-training, with substantial gains in mathematical reasoning and code generation. In practical systems, however, policy updates and differences between rollout and training engines can make sampled responses off-policy. Sequence-level masking addresses this mismatch by deciding whether an entire response should contribute to optimization. A common masking rule uses the length-normalized geometric mean of sampled token probability ratios. Its signed log-ratios can cancel across positions, concealing substantial bidirectional policy drift. We propose Cancellation-Aware Response Masking (CARM), a sequence-level mask that takes the absolute value of each token log-ratio before averaging, preventing opposing probability changes from canceling. We prove that accepted responses satisfy a joint bound on the fraction of sampled-token ratios outside a prescribed band and their mean log-distance beyond its boundaries. Experiments on mathematical reasoning and code generation show that CARM improves mean@16 averaged over AIME 2024/2025/2026 and BeyondAIME by up to $3.13$ percentage points over geometric-mean masking, and increases average pass@1 across four code benchmarks by $2.88$ points over the strongest evaluated baseline. These findings support CARM as a theoretically grounded and effective method for response-level off-policy control in LLM reinforcement learning.

Large language model (LLM) agents increasingly combine reasoning, tool use, and action, but most evidence comes from episodic tasks with relatively immediate feedback and reset failures. Long-running physical control operates in a different regime: actions alter future states, errors compound across decisions, and an agent must improve from experience without being allowed to rewrite the physical rules that make execution safe. We study this regime through irrigation, where daily decisions interact with soil-water dynamics over entire growing seasons. We present Mimir, a physics-grounded LLM agent organized around two repair timescales. At the fast timescale, a structured physical interface and deterministic simulator turn an LLM output into a proposal that we numerically check, revise, and subject to bounded deterministic action selection before execution. At the slow timescale, recurrent failure patterns are consolidated into persistent contextual principles that condition future proposals, while the physical model, evaluator, and execution constraints remain immutable. Under a common retrospective evaluator across multiple sites, crops, and years, Mimir attains the lowest reported aggregate control cost among the evaluated references and uses about 51% less irrigation than the historical schedule replay. The ablation study show higher control cost when forward simulation, verified revision, or persistent context is removed; model-scale and model-family studies show no monotonic gain from increasing LLM size. The resulting lesson show that persistent physical agents can combine semantic reasoning with bounded, evidence-driven self-improvement while reserving physical truth and actuator authority for explicit numerical mechanisms.

Consider the following optimization problem over stabilizer product states: given an $n$-qubit stabilizer state $\left|\psi\right\rangle$ and a set of single-qubit stabilizer states $S$, maximize $\left|\langle \psi | \phi_1, \ldots, \phi_n \rangle\right|^2$ over single-qubit stabilizer states $\left|\phi_i\right\rangle \in S$. By varying the set $S$, we show that solutions to this problem can be useful in a variety of settings: tighter runtime bounds for certain classical simulation algorithms; measures of entanglement; and the complexity of low-rank matrix completion. Moreover, we give a complete complexity classification of this nearest stabilizer product state problem. After accounting for the symmetries in the Clifford group, there are $9$ distinct possible sets $S$, and we show that all but the two simplest of these are $\NP$-complete.

AI agents share code, documents, tools, and analyses. No participant sees the whole state, so every step can look right while the combined result is wrong. We call this the global coherence problem. It is a problem of state, not only of intelligence: a stronger model decides better locally, but cannot see what is missing from its context. The Observation-Aliasing Impossibility Theorem gives the exact condition. An agent can always act validly exactly when every world consistent with its context allows a common action. When look-alike worlds need different actions, no reasoning, role, message, or sample can guarantee the right one; with k such worlds whose valid actions are disjoint, the best randomized policy succeeds with probability 1/k. Finding the smallest sufficient context is NP-hard, but refinement finds one and keeps it current as rules change. A second failure survives full information: valid pieces can fail to fit into one world. The same theorem sets the conditions for coherence; sheaves and groupoids are one way to meet them. Models propose, and the harness decides what is valid. Ten studies test it. On TeamBench, teams overspend a shared budget in 5/5 runs; showing them the live count still leaves 4/5, and a harness that owns the budget leaves 0/5. Identity collisions that no pairwise check can see appear in 23 of 45 public alignment networks; split-view agents create them in 9 of 40 merges, and a network check removes all nine. A frontier LLM solves 40/40 revision tasks when it sees the deciding event; with the event hidden, no arm that reasons longer, votes, or splits into roles significantly beats chance, and a companion study replicates this on models from a second provider. In tau2-bench Telecom, after a silent revert, the harness scores 1.00 against 0.07 for call-time policy checks. Refinement keeps a sufficient context at 28% of the cost of sharing every field.

In this paper, we prove Borcea's 2-variance conjecture. The Lean 4 formalization of the main results are also provided.

Let $G$ be a simply connected semisimple algebraic group. On the (undecorated) braid variety associated with a power of a Coxeter element, there is a finite-order autoequivalence, called the Zamolodchikov transformation, induced by cyclic rotation of words. In this paper, we show that the coarse moduli space of the fixed-point stack of this autoequivalence is isomorphic to the spectrum of the fusion ring of the corresponding affine Lie algebra. The above results also extend to twisted Coxeter elements, and the fusion rings of all affine Lie algebras are obtained in this way.

Individual mobility trajectories support urban analysis and location-based services, yet most trajectory generators require observations from their deployment city. This assumption excludes precisely the cities where trajectories are unavailable even though points of interest (POIs) and their attributes can be obtained from public maps. We study target-trajectory-free generation: learning from POIs and trajectories in source cities while utilizing only POI coordinates and categories in a target city, with no target trajectory or trajectory-derived statistic available for training, model selection, or generation. Existing trajectory generators typically predict absolute destinations, entangling reusable movement behavior with city-specific POI identities and spatial layouts. Our core insight is to replace this city-bound output with context-conditioned relative transitions. We propose Nomad, a transfer-and-ground framework that separates learning how people move from determining where those movements are realized. Specifically, a history-conditioned flow-matching model learns from source trajectories a transition prior over semantic displacement between POI contexts, geographic displacement, and elapsed time; at inference, a behavior graph and an exploration–return walk ground sampled transitions onto the target POI map. This factorization enables a direct test of representation level transferability without assuming invariance of the full mobility distribution. Extensive experiments across ten cities and 14 transfers show that Nomad outperforms adaptation baselines in trajectory fidelity and downstream utility, lowering the average error over the best baseline of each metric by about 15% in distributional fidelity and about 3% in downstream utility.

We show that a pair of two-qubit product measurements can be perfectly distinguished when accessed jointly, yet cannot be perfectly distinguished when their local components are distributed between distant parties restricted to local quantum operations and classical communication (LOCC). This establishes a measurement analogue of nonlocality without entanglement that, unlike its state-based counterpart, emerges in a remarkably simple setting. We further uncover a hierarchy of LOCC discrimination strategies: adaptive protocols, in which the probe used at one site may depend on classical information obtained from another, can strictly outperform restricted non-adaptive protocols, as demonstrated by a set of six bipartite qutrit product measurements. We also show that LOCC distinguishability of bipartite measurements can be intrinsically directional, depending on which party initiates the protocol. More generally, we construct pairs of $n$-qubit product measurements that are globally perfectly distinguishable but cannot be perfectly distinguished across any bipartition, even when all parties on either side of the bipartition are allowed arbitrary joint quantum operations. Finally, we show how quantum data hiding based on quantum-process nonlocality without entanglement can be realized using elementary optical components.

Stabilizer states are central to quantum computing, underlying quantum error correction, benchmarking, and efficient classical simulation. Yet their learnability exhibits a striking gap: an $n$-qubit stabilizer state can be learned from $\Theta(n)$ copies using two-copy Bell measurements, whereas non-adaptive single-copy measurements require $\Omega(n^2)$ copies. Here we show that adaptivity completely closes this gap. We give a polynomial-time adaptive algorithm that learns an arbitrary $n$-qubit stabilizer state from $\Theta(n)$ single-copy Clifford measurements, matching the optimal sample complexity of Bell sampling without any multi-copy measurements. The same ideas yield a sample-optimal single-copy tolerant tester and, with $k$ qubits of quantum memory, the optimal testing tradeoff $\Theta(n-k+1/\varepsilon)$ at infidelity $\varepsilon$. Finally, we show that this adaptive mechanism extends beyond exact stabilizer states: states of stabilizer nullity at most $r$, including states prepared by Clifford circuits with a bounded number of $T$ gates, can be learned using $O(n2^{r})$ single-copy measurements.

We give a quantum algorithm for simulating a $d$-sparse Hermitian Hamiltonian $H$, assuming a known upper bound $\Lambda$ on its maximum column Euclidean norm $\|H\|_{1\to2}$. For $t\Lambda\ge1/2$, simulation with operator-norm error $\epsilon$ uses \[ O\!\left(t\Lambda\sqrt d+\sqrt d\log(2/\epsilon)\right) \] sparse-oracle queries. This removes the subpolynomial overhead in Low's algorithm [STOC 2019], replacing it with an additive logarithmic precision term. For $d>1$ and $t\Lambda\ge\log(2/\epsilon)$, the bound matches the worst-case lower bound. A known spectral-norm upper bound may also be used in place of $\Lambda$. The number of 1- and 2-qubit gates is linear in the query scale, up to oracle costs and polynomial overhead in the input bit lengths and logarithmic precision parameters. As applications, we obtain $O(\kappa\sqrt d\,\mathrm{polylog}(\kappa/\epsilon))$ queries for solving $d$-sparse quantum linear systems with $\|A\|\le1$ and $\|A^{-1}\|\le\kappa$, under standard sparse and state-preparation access. We also give a gate-efficient implementation of black-box unitaries with at most $d$ nonzero entries per row and column using $O(\sqrt d\log(2/\epsilon))$ queries, given sparse access to the unitary and its adjoint. At constant error, the query bound is optimal and yields $\Theta(\sqrt N)$ queries for arbitrary $N\times N$ unitaries, resolving the open question on black-box unitary implementation posed by Berry and Childs [QIC 2012].