Papers

We study positive $(n-1)$-convex entire subsolutions of the normalized real $(n-1)$ Monge–Ampère equation $\operatorname{det}^{\frac1n}\bigl(\Delta uI-D^2u\bigr)=f(u)+g(u)|Du|^q$ in $\mathbb R^n$. Under two sets of structural assumptions on the continuous, non-decreasing coefficients $f$ and $g$, we establish necessary and sufficient conditions for the existence of entire subsolutions when $q<2-\frac1n$. Our results cover the pure-gradient degenerate case $f\equiv0$ with $0<q<1$, the gradient-singular case $q<0$, and the case where $g$ changes sign. For $q=2-\frac1n$, we recover the Keller–Osserman condition for the gradient-independent equation, prove nonexistence when $g$ is eventually positive, and obtain an exponentially weighted condition when $g$ has a nonpositive limit at infinity. This is the first of two companion papers and treats the determinant case.

Large language models can produce fluent tu- toring dialogue, but whether they actually help students learn remains unclear. We present a process-centered synthesis of LLM tutoring that follows the path from learner-state infer- ence to pedagogical action, tutor training, eval- uation, and student simulation. This view ex- poses a central gap: implementing a tutoring component does not establish that it works or that its outputs meaningfully affect later stages. A structured study-level audit shows that peda- gogical evaluation is common, while evidence becomes much thinner for learner-conditioned intervention, human learning gains, and espe- cially transfer or delayed retention. Human studies nevertheless provide a conditional posi- tive result: LLM tutors can improve learning, but benefits depend on pedagogical structure, learner engagement, and how learning is mea- sured. We argue that progress requires validat- ing the interfaces between tutoring stages, not only improving individual components.

Existing reinforcement learning (RL) largely focuses on optimizing learning algorithms within a pre-defined task formulation, while applying RL to new tasks still relies heavily on human expertise to design the learning pipeline: what an agent observes, how it is rewarded, which algorithm it uses, and how training is configured. Automating these choices is challenging because they are tightly coupled. We introduce FARL (Fully Automated Reinforcement Learning), a framework that automates RL design by jointly searching observation and reward programs, learning algorithms, and training settings. FARL uses training statistics and observed behavior to diagnose failures, propose changes, and test whether they improve learning. Its search preserves diverse candidates and the controls needed for these tests, using a staged budget to screen designs before investing in longer training. Experimental memory records each finding together with its conditions, so an unsuccessful component can be reconsidered in a different combination. Across expert-withheld and expert-available settings, FARL outperforms the evaluated automated baselines on challenging navigation, locomotion, and manipulation tasks. On Adroit Hand Relocate, FARL achieves 97.1% success at 5M training steps per policy, compared with 0% for Eureka and LiMEN and 1.0% for native Proximal Policy Optimization (PPO) under the same policy training budget.

We establish uniform score bounds and Lipschitz continuity for truncated Gaussian, Cauchy, Boltzmann, and softmax policies under explicitly stated parameterizations.

Flow matching can learn structure directly from data, raising the question of when additional constraints improve generation. We study penalties that encode such constraints, with physics-informed flow matching as a motivating example. Satisfying a constraint more closely need not make the generated distribution more accurate. We therefore compare penalised and unpenalised generative modelling through their expected squared $2$-Wasserstein error. Our analysis covers both vector-valued and functional data in a Hilbert-space setting. We first derive geometric criteria that account for constraint violations and the distribution of samples after projection onto the constraint set. We then solve the statistical comparison explicitly for specific velocity-field classes and constraints via flow matching. In this model, penalisation improves accuracy exactly when the reduction in estimation variance outweighs the increase in squared bias. The resulting formula shows how this trade-off depends on sample size, the model class, the noise schedule, and the penalty weight.

We generalize Nakajima's theory of Hilbert schemes of points on surfaces to Hilbert schemes of points on orbisurfaces, and obtain initial factorization based on stratification by stabilizers. While the usual formula is retained for the trivial stabilizer stratum and for those strata of codimension $1$, genuine difficulties arise with stacky points strata. In the local picture of an isolated stacky point, the theory reduce to the study of $\Quot^\bfv[\CC^2/G]$ for a small finite subgroup of $GL_2(\CC)$. The generating series for their total cohomology is a geometric correction of the generating series for total cohomology of ordinary smooth surface schemes. In addition, we obtain an action of the Borel-Moore homology of the punctual fibre stacks on the total Hilbert cohomology by virtual correspondences, in analogy with the Fock space description in Nakajima's theory. The punctual fibre stacks are genuinely different from the symmetric stack, and has natural realizations via motivic integration.

The explosive growth of short videos has presented significant challenges to content governance. Traditional manual labeling is inefficient, slow to iterate, and costly. Therefore, we explore and develop a multi-stage autopilot labeling framework aimed at progressively increasing the level of automation in short video content annotation. To move beyond the heavy reliance on human expert labeling at the initial L0 stage, we first introduce a discriminative MLLM labeler at the L1 stage, which is fine-tuned with supervised data to directly predict labels for short videos. Advancing to the L2 stage, we shift to a domain-adaptive MLLM pretrained on short video data and use it for zero-shot labeling, enabling flexible generalization without task-specific supervision. In the L3 stage, we propose an agentic annotation workflow, and equip the agent with several key tools, which empower the agent to handle complex, unfamiliar, or vaguely defined cases, significantly reducing the need for human intervention. We conduct extensive experiments across various content issues, and results demonstrate that each stage of the autopilot labeling framework progressively improves labeling accuracy, and has significantly reduced manual labor costs in real-world applications by up to 85%.

We prove that two completely different oscillators synchronise through arbitrarily weak reciprocal impulses. Any two planar oscillators with hyperbolic attracting limit cycles and equal natural periods lock stably one-to-one under translation impulses with generic directions and a suitable range of positive strength ratios, whatever their vector fields, limit cycles and transverse contraction rates. The mechanism is topological: the winding of the asymptotic phase gradient forces phase advances and delays, and the relative winding number of an effective impulse field gives lower bounds on attracting and unstable locked states. Equal periods are not essential: locking persists under small nonzero mismatches, with persistence and loss governed by a shifted phase balance. The analysis covers the full state-dependent impulsive dynamics, including transverse stability. Nearly simultaneous emissions may make the return discontinuous; under an explicit regularity condition the global return has a normally attracting Lipschitz invariant circle with topologically Morse–Smale dynamics.

Conventional distillation transfers capability through teacher-generated demonstrations. LLM-as-a-Judge knowledge distillation offers a distinct and increasingly practical alternative. In the label-only variant studied here, the student generates every response and improves from scalar scores alone. Prior work shows that this non-demonstrative feedback can improve student capability, but it creates a fundamentally different provenance problem. No teacher-generated answer enters the student's training set, so any evaluator-specific trace must pass through a low-bandwidth reward signal rather than copied text. Existing watermarks and distillation detectors do not cover this score-only channel. We introduce Radioactive Feedback, which encodes a registered pattern of behavioral preferences in the rewards themselves. The evaluator applies bounded pointwise adjustments to quality-qualified responses, allowing repeated optimization to transfer the pattern to a student trained by another party. Experiments on code and mathematics show that the registered preferences transfer through scores alone and across datasets, enabling black-box detection against a fixed reference pool.

Magnetic circular dichroism (MCD) is an optical probe of orbital time reversal symmetry breaking. Although frequency integrated MCD is related to the self-rotation contribution to orbital magnetization at zero field, its magnetic response generally differs from the thermodynamic orbital susceptibility. Here, we define the MCD susceptibility and derive general expressions for multiband systems using an electromagnetic $U(1)$ gauge invariant approach. For insulators, the response contains contributions from the non-Abelian quantum metric, Berry curvature, and field induced interband mixing. For metals, a finite temperature Green function formulation separates the smooth response into Fermi sea and Fermi surface contributions. An independent Landau level calculation confirms the expressions for the zero-field MCD moment and its linear magnetic response. In a continuum model for twisted bilayer graphene, the MCD susceptibility vanishes within the charge neutrality gap, while the thermodynamic orbital susceptibility remains markedly diamagnetic. Near the gap edges, the orbital moment term dominates the response. Features near the van Hove energies are associated with density of states enhancement. These results clarify how the two susceptibilities reflect different orbital processes even for the same electronic structure and thus establish the MCD susceptibility as a distinct probe of orbital magnetic response.

Magnetic frustration is commonly quantified by the frustration index, calculated from the Curie-Weiss and Neel temperatures. Because both quantities are not simultaneously available for most materials, direct prediction of the magnetic frustration index remains challenging. Here, we propose a machine learning workflow for indirect prediction of the frustration index and consequent screening of potential frustrated magnetic compounds through independent prediction of Curie-Weiss and Neel temperatures. In our work, composition-based models implemented via the CatBoost algorithm, trained on experimental data were optimized using chemically informed dataset subdivision. The highest predictive accuracy was achieved for the rare earth-oxide model in predicting Neel and for the rare earth model in predicting Curie-Weiss. Ensemble uncertainty was incorporated through a conservative frustration index to improve the reliability of candidate selection. Screening of approximately 67000 Materials Project compounds identified 20 high-confidence frustrated magnetic candidates, including several experimentally known frustrated magnets and previously unexplored oxide systems potential for further investigation.

A key milestone in algorithmic graph theory is Hopcroft and Tarjan's 1974 linear-time algorithm for graph planarity testing. At a workshop in 2002, Linial and Rabinovich asked for either a polynomial-time algorithm or an NP-hardness proof for metric planarity testing: given a metric space $(X,d_X)$, determine whether there exists an edge-weighted planar graph $G=(V,E,w)$ with $X\subseteq V$ that realizes the distances in $X$, meaning that $d_G(x,y)=d_X(x,y)$ for every $x,y\in X$. This question arose in the context of research on metric embeddings and their applications in computer science since the mid-1990s. Over the past few decades, polynomial-time algorithms have been developed for several special cases. In this work, we show that metric planarity testing is NP-hard, in sharp contrast to graph planarity testing. Our reduction yields a stronger result: under the Exponential Time Hypothesis (ETH), no $2^{o(n)}$-time algorithm for metric planarity testing exists, where $n$ is the number of points in the metric. To complement our ETH lower bound, we give two algorithmic results: (i) an algorithm for computing a metric planar embedding in $2^{\tilde{O}(n^2)}$ time and (ii) a $(1+\epsilon)$-approximation algorithm in $2^{\tilde{O}(n)}$ time for any fixed $\epsilon\in(0,1)$. The second algorithm produces a planar graph that preserves the input metric up to a factor of $(1+\epsilon)$.

Parametric Computer-Aided-Design (CAD) modeling from human intent remains challenging, particularly during the conceptual design stage, where design goals are expressed through incomplete and unstructured modalities (e.g., hand-drawn sketches and textual descriptions). In this work, we rethink the human intent-to-CAD pipeline and propose a unified method that directly maps multi-level human intents to executable codes, without assuming the prior existence of target CAD models. To support our study, we construct HiCAD, the first large-scale dataset aligning hand-drawn sketches, textual descriptions, and parametric CAD codes. Based on this, we introduce HiCAD, a two-stage framework comprising Cooperative Multi-Task Alignment to bridge the representational gap between heterogeneous inputs, and Spatial-Aware Reinforcement Learning to enforce geometric and topological consistency. Extensive experiments demonstrate that our method significantly outperforms existing baselines across multiple tasks, validating its effectiveness and robustness in transforming heterogeneous human intents into high-fidelity parametric CAD models. Our project page: https://zqwlearning.github.io/HiCAD.

We present a faithful translation from Aloni's logic BSL into a classical modal logic over semilattices combining ideas from earlier modal translations of truthmaker semantics with algebraic representation theory. We show how our method can also be made to work for other current hyperintensional logics. Finally, we place our results in a broader setting of translating hyperintensional logics into classical modal ones, and discuss applications and new challenges that arise for both areas of philosophical logic connected in this way.

The bipartite edge frustration of a graph $G$, $\varphi(G)$, is the minimum number of edges that must be removed from $G$ to obtain a graph that is bipartite. Core graphs are singular graphs on $2$ or more vertices, for which the kernel of the adjacency matrix contains a full eigenvector. A nut graph is a core graph of nullity one. Nut graphs $G$ are non-bipartite. It is proved here that $\varphi(G) \geq 2$ if $G$ is a nut graph, i.e. every nut graph requires deletion of at least two edges to produce a bipartite graph. In addition, we give a constructive proof that for every integer $k \geq 2$ there exist infinitely many chemical nut graphs $G$ with $\varphi(G) = k$. Furthermore, for $3 \leq d \leq 8$, the values $k$, for which a $d$-regular nut graph $G$ with $\varphi(G) = k$ exists, are characterised. It is shown here that for every integer $k \geq 2$ there exist infinitely many cubic polyhedral nut graphs $G$ with $\varphi(G) = k$. Two ways of producing larger nut graphs from smaller are described: the cut and frustration constructions. One straightforward consequence is that total double subdivision of a nut graph (i.e. simultaneous insertion of two degree-$2$ vertices into every edge) yields a nut graph.

Carl Jung theorised that the human psyche contains an inherited framework, the collective unconscious, populated by universal archetypes. As large language models (LLMs) are trained on vast corpora of textual data, this paper investigates whether they spontaneously construct distinct archetype-like regions within their high-dimensional latent spaces. The paper proposes that these regions function as spatial constraints that naturally organise semantically related narratives. To evaluate this, we applied cosine similarity and angular distance metrics across thirteen experiments utilising OpenAIs text-embedding-3-small model. The paper contains two experimental sections the first section explores these ideas using synthetically constructed narratives, the results of which act as a baselines for experiments conducted in the second section where the synthetic data is replaced by human-authored literature (Shmoop corpus), unedited dream reports (DreamBank corpus), and culturally distilled folklore (Andrew Langs Fairy Books). The results show that archetypal roles occupy distinct, measurable regions in the latent space. Crucially, these regions remain compact and consistent because of narrative structure rather than simple word overlap. Additionally, text category dictates spatial distribution: dream reports concentrate within Trickster and Shadow regions, while traditional folklore distributes evenly across all tested archetypes. We conclude that transformer latent spaces encode stable regions which appear to correspond to recognised Jungian archetypes.

Continual learning aims to adapt pretrained large language models (LLMs) to evolving data while preserving their pretrained capabilities. A central challenge is catastrophic forgetting: adaptation to new data can impair performance on previously learned knowledge. Since continual learning commonly changes model parameters, the model's predictions may draw on knowledge from the base model, the parameter update, and the input context. Understanding how these sources interact is essential: conflicts reveal whether new knowledge can override outdated knowledge, while multi-hop reasoning tests whether new knowledge can be composed with existing knowledge to support generalization. We study these interactions in a hypernetwork-based adaptation framework, where a shared network generates adapters from context, allowing a frozen base model to adapt without task-specific updates. We find that, under knowledge conflict, models preferentially follow the context, and their choices depend more on where knowledge is presented than on its content. We also show that context and adapter knowledge perturb the base model's representations along directions orthogonal to its clean hidden states, enabling us to derive steering vectors that control which source the model follows. In multi-hop reasoning, we find that models fail to reliably compose knowledge across the three sources, with the key breakdown arising from the interaction of the hypernetwork with both the base model and the context. Code and reproduction materials: https://github.com/missswiftie/Knowledge-Interaction-in-CL

In this paper, we develop a greedy double-block nonlinear Bregman-Kaczmarz method to efficiently find sparse solutions of nonlinear equations. The theoretical convergence rate of the proposed method is established under certain assumptions. Numerical experiments illustrate the competitive performance and superiority of the proposed method.

Quantization lowers deployment costs of vision-language-action (VLA) policies but can compromise task completion. Across five VLA models and 4,050 real-world trials, we systematically reveal that quantization-aware training (QAT) generally improves on post-training quantization (PTQ) but leaves substantial gaps to full precision (FP) on long-horizon tasks and under visual and semantic shifts, while its imitation-based objective does not explicitly use rollout success or partial completion. To exploit these outcome signals, we introduce Quantization-Conditioned Reinforcement Learning (QCRL), an offline RL method coupling progress-based advantage estimation with quantization-aware source conditioning. FP rollouts supply reference experience beyond action-level distillation, progress-scaled terminal penalty distinguishes partial completion, and quantization-aware conditioning selects advantageous reference behavior within the quantized policy. We evaluate weight-only INT4 W4A16 on $\pi_{0.5}$ and GR00T N1.5 and joint weight-activation NVFP4 W4A4 on $\pi_{0.5}$. Using only in-distribution data, QCRL reaches 99.3% of FP's mean score across three visual-shift conditions for $\pi_{0.5}$ with INT4 W4A16, alongside 42.9% model-memory savings. With NVFP4 W4A4, it reaches 100.7% of the same FP baseline, alongside a $1.73\times$ speedup using NVFP4/FP8 deployment. Hardware gains are relative to FP16 on Jetson Thor.

Let $h(x)$ be the number of pairs $1\le a<b<x$ with $\gcd(a,b)=1$ and $\sigma(a)=\sigma(b)$. Erdős Problem #824 asks whether $h(x)>x^{2-o(1)}$. By an argument of Pollack and Pomerance, this follows if for every fixed $\delta>0$ there are $y^{1-o(1)}$ primes $p\le5y$ with $p+1$ free of prime factors exceeding $y^\delta$. We write this implication out with explicit parameters and formalize it in Lean 4. We then check that the argument of the recent OpenAI preprint "Weighted dilation graphs, smooth shifted primes and totient fibers", which claims the corresponding statement for $p-1$, applies to $p+1$ after a change of sign in two of its sections. Consequently $h(x)=x^{2-o(1)}$, conditionally on the correctness of that preprint, which has not been refereed and whose main new estimates we have not independently verified.

For the degenerate parabolic equation $u_t=\nabla\cdot (u^{m-1}\nabla u)$, the homogeneous Neumann problem in smoothly bounded domains $\Omega\subset {\mathbb{R}}^n$ is considered in the (super-fast) diffusion range when $m\in (-\infty,1)$. Upper and lower estimates for solutions are inferred by means of two Moser-type iterations, and optimality properties of these bounds are derived using comparison arguments. On the basis of the accordingly obtained information on regularization into spaces of bounded and uniformly positive functions, a result on global solvability in an associated initial-boundary value problem is achieved for all nonnegative and nontrivial initial data belonging to $L^1(\Omega) \cap \bigcup_{s>n(1-m)/2} L^s(\Omega)$.

Researchers and policymakers frequently make a large number of decisions simultaneously over many units using noisy estimates of unit-level effects. Researchers often assume that unit-level effects are drawn from a common effect distribution, allowing for optimal decision-making. In applications, however, this effect distribution is unknown to the econometrician, introducing uncertainty in the ultimate decision-making problem. This paper considers the problem of quantifying this uncertainty. For instance, researchers may seek to understand how an oracle decision maker with knowledge of the effect distribution would compare different feasible decisions, or understand which decisions an oracle would plausibly make. Analyzing these questions from the perspective of an oracle decision maker involves comparing the conditional means of unit-level effects given estimates thereof, suggesting a sufficient inferential objective of uniform coverage of these conditional means. Based on an equivalence between uniform coverage of conditional means and multiple testing, I develop methods that satisfy this coverage. Finally, I consider an application to the problem of identifying high-economic-mobility neighborhoods. My methods sharpen inference relative to existing methods and identify units that can be confidently included in oracle selections.

Eyewear that senses articulation with inaudible ultrasound can now recognize silent speech over an open vocabulary, but its accuracy is limited by the cost of training data. We present SoniGAN, which synthesizes the ultrasonic echo profiles of silent articulation from text and uses them as synthetic supervision. A voice-cloned text-to-speech (TTS) model reads a text corpus, and a two-stage generator synthesizes echo profiles from representations of the spoken content of that audio. Pretraining a recognizer on 104 hours of the synthesized data improves the word error rate (WER) of a public open-vocabulary benchmark by 2.3 points. Adding the sessions the corpus discards for a faulty microphone brings the system to 22.2% without any language model. Lexicon-constrained decoding, LLM rescoring, and ensembling further bring it to 14.9%, the first minimally obtrusive silent speech interface to fall inside the error range in which users report no loss of willingness to use silent speech input.

We study multidimensional entry-exit phenomena in slow-fast systems whose fast linearization contains a nilpotent component. We show that the classical spectral balance still determines the exit point as $\varepsilon \to 0$, however the nilpotent component induces an algebraic amplification invisible to the spectrum, producing a $\varepsilon|\log\varepsilon|$-shift of the exit point for $0 <\varepsilon \ll 1$. We further extend the analysis to systems with several spectral branches and show that mode dominance follows a hierarchical, lexicographic selection principle: accumulated spectral growth determines the leading order, while the nilpotent component resolves degeneracies between spectrally equivalent modes.

Weak bag-level labels are widely available in computational pathology, whereas reliable instance-level annotations for whole-slide images remain expensive and ambiguous. Weakly supervised multiple instance learning (MIL) achieves strong bag-level classification, but instance-level supervision from attention scores, model predictions, negative bags, or spatial refinement may fail to identify class-specific local evidence. We propose ProtoPur, a prototype-purity pseudo-labeling method for weakly supervised instance-level learning in pathology whole-slide images. ProtoPur estimates class-balanced local purity over prototype regions constructed from frozen foundation-model features, and assigns pseudo-labels to high-purity regions strongly associated with a target class. This purity-first design separates class-specific evidence from negative or shared morphology, with coverage used only to ensure sufficient pseudo-label assignment. We provide a PAC-style analysis showing that the risk of an instance classifier trained with ProtoPur pseudo-labels can be decomposed into a standard uniform-convergence term and a ProtoPur-specific pseudo-label noise term, comprising selected-region mismatch and a coverage residual. Experiments on three public whole-slide image datasets with two pathology foundation encoders show that ProtoPur consistently improves instance-level performance across multiple MIL backbones while maintaining competitive bag-level performance. Pseudo-label quality comparisons on two public datasets further demonstrate that prototype-purity selection provides stronger instance supervision. These results suggest that the foundation-model features contain exploitable instance-level supervision signals, and ProtoPur is a way to reveal and use these signals from weak bag labels without requiring dense instance annotations.

A topological group, defined in terms of “composable minimal geodesics” is constructed and shown to be homotopy equivalent to the pointed loop space of a path-connected, simply connected Riemannian manifold $M$ of positive convexity radius. This construction is analogous to John Milnor's free group model for the pointed loop space of a connected simplicial complex. Related models built from composable minimal geodesics are also obtained for the free loop space of $M$ and for the space of maps from any finite two-dimensional CW-complex into $M$.

A single evaluation score can rank generation systems but rarely reveals what failed. We propose rate-resolved text evaluation, which turns the masking rate of masked diffusion language models into a diagnostic axis. By reconstructing text under different fractions of masked tokens, one diffusion score becomes a vector of band-conditioned scores that reflect reconstruction difficulty at varying levels of visible context. On SummEval, preserving this rate structure yields complementary signal: the best masking-rate band improves fusion with autoregressive likelihood over a collapsed diffusion scalar, survives a sample-shuffle control that breaks rate ordering, and adds residual signal to a fixed prompted judge. A second diffusion model reproduces the effect more weakly. On WMT MQM zh-en, roundtrip mask-and-reconstruct probing produces a tunable localization curve in which ranking-oriented AUROC and span-detection F1 peak at different masking rates. Factuality benchmarks bound the interpretation: band semantics are model- and task-dependent, so each application requires empirical validation.

Converting natural-language instructions into executable action plans conditioned on a scene image is a core capability for embodied human-robot interaction, but existing benchmarks target English, simulated or video-grounded environments, and largely assume instructions are clear and executable. We introduce the first Persian vision-language-action dataset for this task: 258 instances over 230 real household/office photographs, annotated with reference plans, deliberate ambiguity and infeasibility labels, disambiguating question-answer pairs, and an auto-generated chain-of-thought rationale for training. Using this resource, we ablate retrieval-augmentation, chain-of-thought prompting, and an agentic disambiguation step, evaluated with an LLM-as-judge protocol and a new metric, PGOS-FA, extending prior work (PG2S) with step-order sensitivity, an over-generation penalty, and Persian-adapted embeddings. Paired statistical testing across 36 comparisons shows retrieval-augmentation is a large, robustly significant effect, while finer-grained additions are directionally consistent but not statistically distinguishable from noise at this scale, and the LLM-judge metric has near-zero power where PGOS-FA succeeds. A blind human-correlation study on 79 real outputs shows PGOS-FA tracks human judgment at least as closely as the LLM-judge. Testing generalization beyond the ablation's single backbone, we find that most of the gap between an open-weight and a substantially stronger closed planner is attributable to open-weight model generation rather than to the closed model's capability specifically, and that our best configuration significantly outperforms an independently reproduced external baseline despite a weaker backbone. The dataset, PGOS-FA implementation, and evaluation code will be made available upon reasonable request.

We present AnyEdit, a unified, separation-free framework for speech and singing voice editing that preserves real-world acoustic environments, including noise, reverberation, and background music. Recent unified generative models already achieve strong speech and singing generation in clean conditions, but real-world vocal editing remains challenging because the model must revise content while simultaneously preserving speaker identity, prosody, and the surrounding acoustic scene. Directly modeling noisy audio end-to-end entangles semantic editing with environmental acoustics, weakening the core vocal generation capability. We therefore adopt a two-stage design that preserves clean-domain editing ability while deferring acoustic rendering to a separate stage: an instruction-guided autoregressive editor first predicts clean prosody and content-style tokens, supported by a teacher-student noise-robust prosody tokenizer that distills clean prosodic tokens from degraded recordings; a flow-matching acoustic model then performs in-context rendering conditioned on the source acoustic context, so the edited segment inherits surrounding noise, reverberation, and background sound while maintaining consistent speaker timbre. To stabilize unedited regions, we introduce unmodified-area-aware supervision; after pre-training, we further apply direct preference optimization on mined real-to-real singing pairs. We also release AnyEditBench, a benchmark covering both speech and singing voice editing under clean, simulated, and in-the-wild acoustic conditions. Experiments on Chinese and English speech and singing datasets showed that AnyEdit consistently outperforms strong baselines in content accuracy, subjective quality, and background consistency under noisy and reverberant conditions. Demo: https://any-edit.github.io/. AnyEditBench: https://huggingface.co/datasets/Ririiiii/anyeditbench.

The detection and quantification of quantum entanglement are central problems in quantum information science. Based on the realignment of density matrices and the vectorization of reduced density matrices, we construct a family of enhanced separability criteria for bipartite and multipartite quantum systems. Our criteria recover the previously proposed realignment-based criteria as special cases and detect more entanglement than the earlier ones. Moreover, we derive tighter lower bounds for the concurrence and the convex-roof extended negativity, criteria for detecting the genuine tripartite entanglement, and lower bounds on genuine-multipartite-entanglement concurrence. The advantages of our results are demonstrated with detailed examples.