arXiv subjects

Qixin Zhang

Publications and source records attributed to Qixin Zhang.

At least 19 recordsLinked to original sources

arXiv2026

A Sharp Barrier of Consistent Submodular Maximization: Any Improvement over $2-\sqrt{2}$ Entails Exponential Queries or Linear Recourse

Consistent submodular maximization aims to maintain a high-utility subset of size at most $k$ as new elements arrive one by one, while changing only a limited number of elements per update. Previously, [DFL+25](STOC '25) established an information-theoretic bound of $2/3$ and gave the first polynomial-time randomized algorithm with a $0.51$-approximation guarantee. However, a fundamental question remained open: Is it possible to design an efficient algorithm for consistent submodular maximization that matches the classical offline $(1-1/e)$-approximation? In this paper, we answer this question in the negative by proving that the sharp approximation threshold achievable with polynomially many value queries and worst-case constant recourse is \[β:=2-\sqrt{2}\approx0.5858<1-1/e.\] Specifically, we develop an improved poly-time randomized algorithm, which can attain a $(β-\varepsilon)$-approximation in expectation at each fixed time with $O(\varepsilon^{-2})$ worst-case recourse. The cornerstone of this algorithm is a novel anchored sampling scheme, which uses only value queries on subsets of the elements seen so far to construct a solution that remains competitive under unknown future arrivals. Conversely, we establish a matching lower bound by showing that any fixed improvement over $β$ requires either exponentially many value queries or $Ω(k)$ changes per update. Furthermore, we characterize the impact of curvature by establishing a sharp threshold of $1-(\sqrt{2}-1)\vartheta$ for consistent submodular maximization, where $\vartheta\in[0,1]$ denotes the total curvature. Surprisingly, for weighted coverage objectives, we devise a poly-time randomized algorithm that can match the optimal $(1-1/e-\varepsilon)$-approximation with $O(\varepsilon^{-1})$ worst-case recourse, thereby separating coverage maximization from general submodular maximization in the consistent settings.

cs.DS↗

arXiv2026

From Visual Matching to Textual Conditioning: Cross-Domain Few-Shot Segmentation via Reference Inversion

Cross-Domain Few-Shot Segmentation (CD-FSS) aims to segment objects from unseen domains using only a few annotated references. Recent Segment Anything Model (SAM)-based methods have advanced CD-FSS, yet their reference-target visual matching is highly sensitive to target appearance variations. SAM3 introduces text-conditioned segmentation, enabling natural-language descriptions to guide segmentation across target images, but directly using the category name as the condition still yields unstable performance under severe domain shifts. We propose Reference Inversion for SAM3 (RI-SAM3) that leverages SAM3's large-scale vision-language pre-training to learn suitable textual tokens for each target category. RI-SAM3 comprises three core designs: (i) Bi-level Reference Inversion that learns complementary tokens before and after the frozen text encoder: the former remain anchored in SAM3's text space while the latter represent the category more flexibly; (ii) Layer-adaptive Textual Conditioning combines these tokens differently as object queries evolve across decoder layers; and (iii) Presence-aware Confidence Supervision that jointly supervises query confidence and target presence for reliable predictions. With SAM3 frozen, RI-SAM3 optimizes around 12K parameters only per category and it efficiently segments each target in a single forward pass with reusable textual conditioning without per-sample reference-target visual matching. Extensive experiments over multiple widely adopted benchmarks show that RI-SAM3 achieves superior performance consistently in CD-FSS tasks, together with strong robustness, efficiency, and generalization.

cs.CV↗

arXiv2026

Structural Dual Adaptation for Safe Reinforcement Learning

Primal-dual methods enforce safety constraints in reinforcement learning through Lagrangian relaxation. For a fixed policy, the exact bounded multiplier response exhibits bang-bang switching at the constraint boundary. Practical gradient updates can oscillate through coupling with policy optimization. We propose Structural DuaL Adaptation (SDLA), which replaces this bang-bang response with a unique continuous response through current-cost centering, trajectory weighting, and quadratic regularization. We characterize activation thresholds and response sensitivity. Ternary search computes multipliers without a dual gradient stepsize. For entropy-regularized tabular policies, we bound equilibrium constraint violations alongside reward gaps. We establish convergence of delayed updates under mild assumptions. Neural PPO/SAC experiments on OmniSafe and HASARD demonstrate competitive rewards with improved constraint tracking. On HASARD, PPO-SDLA achieves higher reported mean reward than the human baseline in six of eighteen settings while meeting the respective mean-cost budgets, including four with lower mean cost. To the best of our knowledge, this is the first report of higher mean reward at lower mean cost than the human baseline across multiple HASARD settings.

cs.LG↗

arXiv2026

When Weak Submodularity Meets Matroids: How Does Standard Greedy Behave?

Weakly submodular maximization finds numerous applications in machine learning, data mining and statistics. In particular, under a cardinality constraint, the standard greedy algorithm is known to attain the tight $(1-e^{-γ})$-approximation guarantee, where $γ$ denotes the submodularity ratio. However, when considering general matroid constraints, \emph{how well standard greedy can perform} has remained a longstanding open question. In this paper, we resolve this question by studying the worst-case approximation guarantee $R_{\mathrm{gr}}(γ,r)$ of standard forward greedy, where $r$ is the rank of matroid. Specifically, our first contribution is the following refined lower bound \begin{equation*} R_{gr}(γ,r)\ge \max\left\{ \fracγ{r}, \frac{γ^2} {B_γ+\sqrt{γ(r-1)}}, \frac{γ^{r+1}} {2-γ+γ^{r+1}}, \frac{γ^2} {14\left(B_γ+\sqrt{γ(1-γ)(r-1)}\right)} \right\}, \end{equation*} where $B_γ\triangleq2-γ+γ^2$. This lower bound not only strictly improves upon the previous guarantee of $0.4γ^2/(1+\sqrt{γr})$, but also can recover the classical $1/2$-approximation guarantee at $γ=1$. Subsequently, a corresponding upper bound is established for $R_{\mathrm{gr}}(γ,r)$, namely, \begin{equation}\label{eq_upper_abstract} R_{gr}(γ,r) \le\min\left\{\frac{1}{2},20\max\left\{\fracγ{r}, \frac{γ^2}{B_γ+ \sqrt{γ(1-γ)(r-1)}}\right\}\right\}. \end{equation} For every fixed $γ\in(0,1)$, this equation effectively sharpens the recent $O_γ(1/\log(n-1))$ upper bound to $O_γ(r^{-1/2})$, where $n$ is the size of ground set. Putting all these results together, we eventually can obtain \[R_{gr}(γ,r) = Θ\left( \max\left\{\fracγ{r}, \frac{γ^2} {1+\sqrt{γ(1-γ)r}}\right\} \right).\]

math.OC↗

arXiv2026

PhaseBreak: Proactive Temporal Protection against Unauthorized Image-to-Video Animation

Image-to-Video (I2V) diffusion models can animate a single portrait or photograph, enabling shared images to be repurposed for motion synthesis without the subject's authorization. We study proactive visual protection against such use: before an image is released, its owner applies a bounded perturbation that preserves the sharing workflow but disrupts downstream motion generation. Existing spectral disruption objectives globally attenuate temporal representations and therefore provide limited control over subtle or spatially localized motion. Our key idea is that generated dynamics depend not only on temporal feature strength, but also on the order in which feature events occur. We propose PhaseBreak, a white-box spectral retiming protection method that matches intermediate denoiser features to a constrained temporal rearrangement of their clean counterparts. PhaseBreak operates along the true temporal axis and uses a subject-aware mask to confine the protective perturbation to the depicted subject. Evaluations on Stable Video Diffusion and DynamiCrafter show that protected images induce greater short-term motion variation and lower temporal regularity, impeding stable motion customization from the released image.

cs.CV↗

arXiv2026

Probabilistic Multi-Source Data Selection via Learnable Categorical Priors: Variance Reduction and Guaranteed Derandomization

Bilevel data selection is a fundamental task with numerous applications in machine learning and statistics. A common strategy for tackling this problem is to relax the original bilevel combinatorial optimization into a continuous one. However, existing methods, including 0-1 relaxation and probabilistic relaxation, still suffer from several limitations, such as unstable gradient estimation and infeasible rounding. To address these issues, this paper proposes a new probabilistic relaxation for the multi-source bilevel data selection problem. Our key idea is to introduce multiple learnable categorical priors to parameterize a probability distribution supported only on feasible data subsets, thus naturally yielding a lossless rounding scheme. We further show that our proposed relaxation admits an effective two-point gradient estimator, which can simultaneously avoid the inverse-Hessian computation required by existing 0-1 relaxation and the unbounded score term appearing in prior probabilistic relaxation. Furthermore, we develop a reducible representation of this estimator, which substantially reduces the number of lower-level retrainings required for gradient computation. Built upon this reducible two-point estimator, we then design a novel stochastic gradient algorithm, termed ReSGD, for multi-source bilevel data selection problem, and establish a rigorous approximation guarantee for the subset returned by ReSGD under weak submodularity. Finally, extensive experiments are conducted to validate the effectiveness of our proposed ReSGD.

cs.LG↗

arXiv2026

Improved E-Value Thresholds with Applications to Multiple and Sequential Testing

E-values provide a flexible framework for statistical inference, but the universal threshold $1/α$ can be conservative when the null distribution has additional structure. We study how structural restrictions limit the worst-case concentration underlying Markov's inequality, using a nondecreasing density model to constrain tail allocation and an $L$-Lipschitz density model to control local concentration. The nondecreasing model gives the minimax rejection threshold, and the Lipschitz condition yields a sharper closed-form threshold with an $O(L^{-1/2})$ relative improvement over $1/α$. We further show that this threshold is asymptotically sharp as $α\to0$, in the sense that no uniformly valid threshold can improve on it by a fixed positive $L$-dependent amount. We then incorporate the Lipschitz calibration into multiple testing procedures with FDR control and use the same structural information to construct calibrated conditional e-values for anytime-valid sequential inference. Numerical experiments illustrate the resulting gains in discoveries and the trade-offs of the sequential procedures.

stat.ME↗

arXiv2026

Beyond Reward Suppression: Near-Optimal Offline Attacks on Warm-Start Bandits with Bounded Rewards

Adversarial attacks on bandits aim to mislead a learner toward a target arm while keeping the attack cost small. Existing attacks typically achieve this by suppressing non-target arms. In practice, however, manipulation such as fake reviews often directly promotes the target item. We study this gap through bounded offline attacks on warm-start bandits, where an attacker can inject only valid action-reward pairs into the warm-start history before deployment. We show that target promotion is not merely a heuristic: when the target arm lies near the lower reward boundary, any order-optimal-cost attack against UCB that makes it selected in nearly all online rounds must allocate a nonvanishing fraction of its cost to the target arm. We then design an attack that achieves the optimal sublinear cost and characterize its allocation between target promotion and non-target suppression. We further extend the attack to Thompson Sampling, $ε$-greedy, and a broader class of bandit algorithms. Experiments on real-world and synthetic data validate the effectiveness of our attacks.

cs.LG↗

arXiv2026

QuSema: Detecting Silent Bugs in Quantum Libraries via Quantum-knowledge-enhanced Agents

Quantum libraries are now critical infrastructure for quantum algorithm development, yet their correctness remains difficult to test. Existing testing techniques mainly rely on failure-based or comparison-based oracles, exposing bugs only when executions fail, violate runtime checks, or disagree with another implementation. Their applicability is limited when suitable execution-based oracles are unavailable, leaving some silent bugs undetected. Such missed bugs can produce incorrect results that propagate into experimental conclusions, simulation studies, and algorithmic designs. Here we present QuSema, an autonomous testing agent for finding silent bugs in quantum libraries. QuSema uses constraints from quantum semantics and documentation as a source-level semantic oracle to assess whether implementation logic can produce invalid outputs from valid inputs. It operates through an agentic loop that repeatedly inspects library API documentation and source code, reasons about the intended behavior of quantum operations, identifies potential semantic deviations, and validates them by generating executable tests through library APIs. Guided by quantum-domain reasoning, QuSema turns high-level behavioral mismatches into concrete, user-triggerable bug reports, enabling it to uncover non-crash defects. We implement QuSema for Qiskit and PennyLane. On a benchmark of 20 historical silent bugs, QuSema achieves higher mean bug relocation counts than Claude Code and Codex, with the DeepSeek configuration costing less than Claude Code. QuSema also discovers 40 previously unknown bugs confirmed by the developers, including 30 silent bugs.

cs.SE↗

arXiv2026

Learning to Outgrow a Theory: Experimental Discovery Beyond the Initial Hypothesis Space

Scientific discovery systems typically optimize experiments within a fixed hypothesis space. This creates a failure mode when all available candidates omit the same missing mechanism: candidate disagreement can collapse even while the model class is systematically wrong. We formulate experimental model-class revision, in which a discovery policy jointly proposes a structural edit and a diagnostic experiment that tests whether that edit is necessary. The method couples a class-level distinguishability objective, in which one shared parameterization must explain all selected experiments, with anytime-valid sequential evidence that triggers structural revision only after the current class is rejected. On 400 held-out controlled dynamical environments, the joint policy reaches 89.5% exact recovery with a budget of 32 real experiments, improving the strongest matched baseline by 10.0 percentage points while requiring fewer executed experiments and candidate fits. The learned revision-experiment pairing transfers across unseen mechanism combinations, held-out but expressible primitives, parameter extrapolation, and shifted experiment costs; when the true mechanism is outside the edit grammar, it detects library insufficiency in 88% of cases with a 5.5% false-support rate. Revision gains also transfer to ODEBench and ODEBase model-library tasks, as well as DiscoverPhysics worlds. These results support a view of scientific discovery in which deciding what mechanisms a theory should make expressible and where to collect evidence are treated as a single sequential decision problem.

cs.AI↗

arXiv2026

Decompiling Quantum Assembly into Structured Programs

Quantum compilers translate programs into native gates, insert SWAP gates to route interactions onto a device, and optimize the result. The output is quantum assembly, a flat gate list that hides the algorithm's structure (QFT, Grover iteration, QAOA layers). Understanding, auditing, porting, or reusing such assembly requires recovering a program that exposes this structure. We present Quelle, a decompiler that recovers structured programs (library calls, loops, functions, symbolic angles) from routed and optimized quantum assembly (OpenQASM) and checks every output for equivalence with its input. Quelle is built on one invariant: every step is either an exact rewrite, checked where it is applied, or a hypothesis, checked against the input before use. It first lifts the assembly into a circuit by removing compilation artifacts, notably un-routing, which recovers the SWAPs that routing inserted, including those merged into other gates. It then recovers algorithm templates (sketches) whose parameters are solved from quantities preserved by compilation, and, for algorithms without a template, library calls and loops by anti-unification. Failed hypotheses are rejected; the corresponding operations remain in gate-level form. On 816 assembly programs from 22 algorithm families and a random-circuit control, compiled at four routing and optimization levels with native two-qubit gates CX, ECR, or CZ, Quelle's output is equivalent to the input for 100% of the inputs, and it fully decompiles 94% of them; compared on the same inputs, it fully decompiles 1.7x as many as the best LLM-based decompiler, which spends 15K tokens per input. On nine algorithm families for which it has no template, the structure it recovers without templates explains 60% of the gates. It checks inputs of up to 2.3 million gates and emits no inequivalent output on 237 real-world QASMBench assembly files.

cs.PL↗

arXiv2026

Near-Oracle KV Selection via Pre-hoc Sparsity for Long-Context Inference

A core bottleneck in large language model (LLM) inference is the cost of attending over the ever-growing key-value (KV) cache. Although near-oracle top-k KV selection can preserve the quality of dense attention while sharply reducing computation and bandwidth, existing sparse methods generally rely on posterior heuristics, i.e., selectors conditioned on observed attention or proxy scores. Such conditioning introduces posterior bias: it tends to distort true token importance and miss salient tokens, thereby impairing long-range reasoning. To tackle this problem, we propose Pre-hoc Sparsity (PrHS), which selects KV entries before attention scoring and provides explicit accuracy control. Let the attention mass of discarded entries be delta (the dropped mass). Through a marginal-to-mutual-information analysis, we derive an upper bound on the mutual-information loss that depends only on the dropped mass. This relation explains failure modes of posterior heuristics and enables verifiable guarantees by controlling the dropped mass in advance. Within PrHS, we instantiate three orthogonal pre-hoc selectors along the axes of time, depth, and layer. Extensive experiments on LLaMA and Mistral families validate PrHS. Across GSM8K and CoQA, PrHS reduces retrieval overhead by over 90%, achieving 3x higher retrieval sparsity than HShare at matched or better accuracy. It incurs under 1% average degradation on LongBench, lowers attention FLOPs by about 15% versus prior sparse baselines, and yields a 9.9x speedup in attention-operator latency and 2.8x higher throughput on NVIDIA A100-80GB GPUs than the dense baseline.

cs.LG↗

arXiv2026

Poisson Exchange Beyond Submodularity: Effective Approximation Algorithms for Offline and Online Subset Selection over Matroids

Over the past decade, a growing body of research has shown that $γ$-weak submodularity broadly arises in numerous subset selection tasks, including feature selection, neural network pruning, and video summarization. Despite its prevalence, maximizing a $γ$-weakly submodular function subject to a general matroid constraint remains challenging. To date, the only known approximation guarantee is the conservative $(1+1/γ)^{-2}$ factor established by \citet{chen2018weakly}. To improve upon this result, this paper proposes a novel algorithm called \MGPE, which repeatedly performs maximum-gain local exchanges through careful control of a non-homogeneous Poisson clock, and proves that this \MGPE\ can attain an approximation ratio arbitrarily close to $ρ_γ=1-\left(γ/(2-γ)\right)^{ \frac{γ^2}{2(1-γ)} }$. In sharp contrast to the previous guarantee, our obtained factor $ρ_γ$ not only strictly improves upon $(1+1/γ)^{-2}$ for every $γ\in(0,1]$, but also can asymptotically approach the optimal $(1-1/e)$-approximation for submodular maximization as $γ\to1$. Furthermore, we surprisingly find that when the matroid constraint reduces to a cardinality or the objective satisfies the stronger notion of $α$-weak DR-submodularity, \MGPE\ can automatically recover the tight approximation ratios of $1-e^{-γ}$ and $1-e^{-α}$, respectively. Here, $α\in(0,1]$ denotes the DR ratio.

cs.DS↗

arXiv2026

Multi-Agent Video Prediction: Self-Correcting Conditional Frames for Dynamic Scene Forecasting

Transmission latency significantly degrades user quality of experience in real-time interactive perception systems. In remote driving, maintaining reliable visual feedback is critical for safe operation under dynamic network variability. Although video prediction offers a promising approach to compensate for short-term transmission delays and approximate near-zero-latency streaming, prediction-only methods remain vulnerable in highly dynamic scenes, especially when newly emerged objects appear during uplink outages. To address these challenges, we propose a multi-agent video prediction framework that combines continuous edge-side video prediction with lightweight mask-guided conditional frame reconditioning. The framework consists of three role-specialized agents: a continuous prediction agent for low-latency visual continuity, a vehicle-side trigger agent for detecting newly appeared objects, and a conditional reconditioning agent that repairs the predictor conditioning state using sparse mask guidance. This design enables semantic recovery of exogenous scene changes without requiring full-frame retransmission. We validate the proposed framework through extensive experiments on benchmark video data under realistic 5G communication traces. Results show that our method improves semantic recovery of novel objects while preserving perceptual quality and practical runtime efficiency under network-induced disruptions.

cs.NI↗

arXiv2026

Impact of Data Compression on Downstream AI Tasks: A Study using Teleoperated Driving over 5G

Teleoperation, such as remote driving, is considered as a key use case of 5G and Next-Generation (NextG) networks. In this context, robots, autonomous vehicles, or other autonomous agents transmit sensor data over mobile networks to edge or cloud servers, where AI systems collaborate with human operators to provide situational awareness and enable remote control. In the case of teleoperated driving, vehicles are equipped with an array of cameras and LiDAR devices, which can generate 100s Mbps (megabits per second) of data. As shown in existing measurement studies, such data volumes far exceed the \emph{uplink} capacity of currently deployed 5G networks, especially when multiple vehicles compete for radio resources. Data compression is thus imperative. In this paper, we explore the impact of sensor data compression on the performance of downstream AI tasks running in edge/cloud servers, which are crucial to alert human operators for safe teleoperation. Using object recognition and semantic segmentation as two example AI tasks, we study how data compression affects the performance of these two AI tasks using unimodal (video or LiDAR) and multi-modal (video+LiDAR) data. We find that lossy data compression generally decreases the performance of AI tasks. The performances of these AI tasks exhibit differing degrees of sensitivity based on the types of data sources and levels of compression. We also empirically identify an optimal trade-off point for the multi-modal vision tasks.

cs.NI↗

arXiv2026

Case for Vehicle-Edge Collaborative Multi-Sensor Data Fusion for Autonomous Vehicle Teleoperation

Teleoperation provides a critical safety fallback when autonomous vehicles (AVs) encounter scenarios that are outside their operational design domain. In practice, however, remote operators rely primarily on compressed camera streams over 5G, which often lack depth and spatial geometric cues for safe operation in complex dynamic environments. While multi-sensor fusion can enhance situational awareness, directly transmitting raw camera and LiDAR data is impractical due to 5G uplink bandwidth and latency constraints. In this paper, we propose SHARDED, a collaborative camera-LiDAR perception framework that deploys a feature-level fusion pipeline across the vehicle and edge to reduce uplink traffic while preserving 3D detection and depth estimation accuracy. We further design two complementary mechanisms for SHARDED: (i) A network-aware adaptive feature transmission mechanism that reduces data traffic by 50% on average (peaking at over 95%) compared to raw sensor data, and (ii) a latency-aware positional drift compensation mechanism to mitigate cross-modal misalignment induced by unstable network conditions. Evaluations on the nuScenes dataset and real-world 5G measurement traces show that SHARDED achieves competitive perception quality while reducing uplink bandwidth consumption and end-to-end latency.

cs.NI↗

arXiv2026

Hidden APIs in Language Models: Discovering Reusable Causal Interfaces from Forked Futures

Identical language-model answers can arise from hidden states that support different future computations, so current-answer probes do not establish a reusable internal interface. We introduce forked futures: future operations are sampled only after a prefix state has formed, and states are compared through the response distributions induced by those operations. This yields an empirical causal quotient over hidden states without requiring researcher-specified latent labels. Shared, Local, Mixture, and Distributed interfaces then compete under prequential causal description length subject to future-signature fidelity and matched capacity constraints. In the two detailed model evaluations, Shared has the lowest held-out description length, with gains of 0.216 nats on Qwen2.5-1.5B and 0.294 nats on Llama-3-8B, while maintaining tightly clustered mean future-signature distortion; a five-backbone sweep preserves the positive direction of Sharedness Gain. The figure-aligned transplantation analysis gives Shared the strongest joint target-correctness, locality, copy-preservation, and composite profile, and API-aligned paths mediate 0.749 of the target effect versus 0.150 for matched null paths. In the blind four-class model-organism test, 14/16 architectures are recovered, with one observed non-Shared to Shared error among 12 non-Shared organisms. These results support an economical reusable causal interface within the tested operation banks, while keeping the claim explicitly conditional on the candidate architectures, interventions, and held-out futures.

cs.AI↗

arXiv2026

Feature Priming in Online Linear Regression: Sparse-Regret Lower Bounds and Tight Coordinatewise Rates

In high-dimensional online prediction, sparse comparators motivate regret bounds that depend on sparsity rather than ambient dimension. Feature priming seeks such adaptation by reweighting features using past data and refitting a minimum-norm predictor. At COLT 2023, Warmuth and Amid posed the open problem of whether the univariate, Pearson, or multivariate priming rules admit competitive online regret guarantees. Under the natural past-only Moore--Penrose protocol, we establish sparse-regret lower bounds that refute the corresponding sparse-logarithmic guarantee. The key obstruction is cheap nuisance interpolation, which permits exact interpolation of the history while assigning insufficient weight to the truly predictive coordinate. An exact target-mass identity and a two-sign argument convert this obstruction into clipped prediction loss. Hadamard constructions yield $Ω(\min\{T,\sqrt d\})$ clipped regret for each of the three unit-power rules against a zero-loss one-sparse comparator. For every fixed power $α\ge1$, one shared paired construction further yields linear regret simultaneously for all three powered rules and selectors among them in sufficiently high dimension. A rank upper bound is tight for powered univariate priming, even with Euclidean-unit inputs, and for unit-power Pearson priming with coordinatewise bounded inputs and target-preserving totalization. A separate algebraic construction gives $Ω(\min\{T,d^{1/4}\})$ regret for unit-power multivariate priming under Euclidean-unit inputs. The univariate lower bound persists under any nonnegative second-stage ridge schedule, while a paired ridge construction yields linear lower bounds for all three powered rules. Exploratory diagnostics on frozen language-model activations are consistent with the same qualitative mechanism. The exact multivariate frontier remains open.

stat.ML↗