Papers

Recovering Partial Differential Equation (PDE) coefficient fields from extremely sparse observations is a severely ill-posed inverse problem for which generative machine learning methods (e.g., diffusion models) have become a leading way to encode the prior. Recent state-of-the-art diffusion solvers lift these priors to function spaces, finding a physics-consistent reconstruction in the output space of the diffusion denoiser. We prove that, in a discontinuous PDE setting, output space methods can result in failure to appropriately minimize the unobserved error with the correct coefficient field. Consequently, we propose Function Space Backward-Consistent Sampling (FunBCS), an input space optimization approach for solving PDE problems which aims to find the best input such that the denoiser reconstruction is physics-consistent. We then prove that FunBCS appropriately minimizes the unobserved error, unlike output space optimization methods. Per our theoretical analysis, we also provide insights on how to dynamically allocate the number of input space optimization steps used throughout the sampling process. Our evaluations, across four PDE inverse problems (including the discontinuous Darcy flow), demonstrate that FunBCS reduces the reconstruction error by $27$-$64\%$ while running $1.4$-$2.1\times$ faster when compared to the current state-of-the-art.

We provide a necessary condition for integral polytopes to satisfy subspace concentration type inequalities, by mean of a convex geometric interpretation of the Bogomolov–Gieseker inequality.

We investigate Campanato and Morrey spaces on metric-measure spaces and establish their relationships with Hölder spaces. In particular, we show that the embedding of a Campanato space into a Hölder space is equivalent to the existence of a lower bound for the underlying measure. Several examples are provided to illustrate the results.

Entangling measurements can reduce the cost of learning many-body correlations. We consider classical shadows in which a fixed unitary on a $k$-qubit region is sandwiched between two layers of random single-qubit Clifford gates, and ask which middle unitary best estimates Pauli strings with full support on the region. Combining symplectic support counting with a constraint from operator-size parity, we prove that within this architecture the minimum squared shadow norm over all Clifford middle unitaries is $C_k^{\rm opt}=4\cdot 9^k/(3\cdot 5^k+3^k-6)$ for odd $k$ and $C_k^{\rm opt}=4\cdot 9^k/(3\cdot 5^k-3^k+2)$ for even $k$. A dual-axis rotation circuit $U_*$ attains this minimum for every $k$. Asymptotically $C_k^{\rm opt}\simeq(4/3)\cdot(9/5)^k$: the exponential base of Wu et al.'s contractive unitary is optimal, and the prefactor improves from $2$ to $4/3$. For $1\leq k\leq7$, exact certificates show that $U_*$ is optimal over the entire unitary group $\mathrm U(2^k)$, and we conjecture that this holds for every $k$.

Large language models (LLMs) increasingly mediate human communication, from drafting emails to summarizing scientific reports, yet whether they faithfully preserve a speaker's position remains largely untested. We model AI-mediated communication as a two-step generation-extraction pipeline: one LLM produces an argument from a specified stance, and a second LLM extracts the stance from that argument. We represent the pipeline as a probabilistic state transition over five Likert-type stance categories and define the stance preservation rate (SPR) as the average probability that the extracted stance matches the initial stance. Across 112 debate propositions, none of the nine LLMs tested exceeded an SPR of 0.7 under the default configuration. Three drift patterns accounted for most of the drift: polarization, deviation from neutrality, and flipping. Among the mitigation strategies tested, including in-context learning, multiple extraction with shuffled options, assertion, and reflection, only adding medium reasoning effort to a reflection prompt for GPT-5.4 substantially improved the SPR, to 0.775, yet polarization remained the largest pattern, with 0.119 of the transition mass. An exploratory comparison with human extraction on a single proposition suggests that drift arises at both the generation and the extraction stage. These results point to a fidelity gap in AI-mediated communication, with implications for journalism, policy deliberation, scientific communication, and other domains where opinion-laden messages pass through language models.

Many physical inverse problems are mediated by expensive stochastic simulators for which response gradients, adjoint sensitivities, or a differentiable simulator interface are unavailable. We introduce Multiple Target-based Confident Acquisition (MUTACO), an uncertainty-aware sequential-design method for response matching that requires only noisy forward evaluations and learns the multicomponent response together with its predictive uncertainty. We develop and evaluate MUTACO using a heterogeneous network of stochastic phase oscillators. The inverse task is to infer statistical properties of the local potential and interactions from macroscopic rotation and synchronization curves under multiple driving conditions. Rather than requiring unique recovery of these statistical properties, MUTACO searches for parameter configurations whose predicted rotation and synchronization responses are compatible with the target response while accounting for predictive uncertainty. This response-centered formulation is appropriate when experimentally accessible observables characterize ensemble statistics rather than a particular microscopic realization. Under strictly limited simulation budgets, MUTACO achieves the lowest held-out response error among the tested adaptive-search, space-filling, and simulation-based inference methods, while also yielding lower parameter-recovery error than the compared methods. These results demonstrate that response-targeted sequential design is a simulator-efficient approach to inverse modeling from finite noisy forward evaluations and suggest broader applicability to stochastic physical systems with correlated multicomponent responses and weakly constrained parameter directions.

Spatiotemporal microwave magnetic-field imaging reveals current flow in high-frequency circuits and nonequilibrium spin dynamics, yet probes rarely combine calibrated spectral readout, optics-free operation and transient mapping at room temperature. Here ferrimagnetic order in yttrium iron garnet supports coherent coupling from a pump-induced magnon mode, converting target-field amplitude into a spectral splitting with all-microwave readout. Sampling the calibrated splitting over position and delay reconstructs spatiotemporal imaging of magnetic fields. Continuous-wave measurement reaches a sensitivity of 58 pT/$\sqrt{\mathrm{Hz}}$ and recovers phases across various powers. Combined with time-resolved frequency-comb spectroscopy, the method reconstructs transient fields with a 130-ns response time. Coplanar-waveguide imaging validates the magnetic selectivity of the mode-splitting readout, where measured maps agree with simulated magnetic-field distribution. In a microwave amplifier, our reconstruction resolves nonuniform switching dynamics and detects downstream field suppression from an open-contact fault. Magnonic coherent splitting provides a scalable route for optics-free imaging of spatiotemporal field evolution in functional devices.

In this paper, we present a method for constructing linear codes derived from book graphs. Applying such a method, we construct binary codes that have the greatest possible minimum distance for their length and dimension by means of the $2$-sum of two equal book graphs. We then utilize matroid and graph theory together to investigate some properties of the resulting linear codes. Furthermore, we show that, from the incidence matrix of any graph, we can obtain a linear code over any finite field maintaining the same parameters. Furthermore, we show how the condition for two linear codes to generate a Calderbank-Shor-Steane (CSS) code translates into matroid theory and, utilizing cycle graphs, we exhibit a way to generate codes that meet this condition.

A vision–language–action (VLA) policy can complete complex tasks while ignoring the evidence that should determine its actions. An object held near the wrist camera can displace the instructed target. Language and action show the same pattern: a familiar noun can trigger the operation it was paired with in training even after the verb changes, and a gripper that closed on nothing may lift anyway. We call these dependencies modality shortcuts: regularities in successful demonstrations make visual, lexical, or motor cues sufficient to predict expert actions without the task evidence needed for the underlying decision. More demonstrations of the same kind can raise task success while leaving these shortcuts intact. We propose Perturbot which makes task-relevant evidence easier to use and shortcuts insufficient on their own: it applies task-preserving wrist-view perturbations, enriches instructions with decision-relevant captions, and adds random and failed trajectory segments relabeled with the behavior they contain. It complements scaling by changing what is scaled, and leaves inference unchanged. Moreover, we propose GroundingFscore, an offline score that diagnoses how severely a policy relies on modality shortcuts. Task success rate shows whether a policy improves, while GroundingFscore reveals whether the policy scales healthily, relying on task evidence rather than shortcuts. Together, Perturbot and GroundingFscore provide a training-and-evaluation framework for disentangling VLA decisions from shortcut priors while preserving responsiveness to task-relevant evidence.

Datacenter services must meet tight tail latency service-level objectives. Research on improving tail latency focuses on reducing queuing delay by approximating optimal request scheduling policies. As request scheduling nears optimality, the primary way to further improve tail latency is to reduce the service time of requests. Unfortunately, datacenter services lack obvious hotspots for general service time optimization. We point out a new optimization opportunity in targeting the tail service time of services with dispersive service times, which are common in datacenters. To show the feasibility and benefit of this approach, we present PonyTail, a performance analysis methodology and toolkit for analyzing service-level outlier behaviors associated with tail service time. PonyTail helps performance engineers identify control-flow and microarchitectural patterns responsible for service time outliers, as well as their root causes. We apply PonyTail to analyze five latency-critical services, including an in-memory database system and an online search engine. Based on PonyTail's analysis, we optimize some of the services, improving their 99th percentile service time and latency by 10.7%–46% and 21%–$5\times$, respectively.

Physical human–machine interaction and other multi-agent control settings require decision-making policies that adapt online. Differential games provide a principled framework where each agent optimizes an individual objective while anticipating the other's response. The relevant solution concept in many applications is the feedback Nash equilibrium (FNE), which yields time-consistent state-feedback strategies. However, computing the FNE is demanding and becomes intractable when state and input constraints must be enforced, motivating the need for approximate methods. This paper presents a Model Predictive Control (MPC) approach that approximates infinite-horizon FNE trajectories through repeated solution of finite-horizon open-loop games. An auxiliary-game formulation is introduced that selects prediction horizons and terminal costs to approximate the feedback-game optimality conditions. The approach is extended to incorporate hard constraints via a constrained open-loop game formulation. For the unconstrained setting, an analytic upper bound on the state-trajectory deviation between the MPC-induced and FNE trajectories is derived, enabling quantitative performance certification. Numerical examples illustrate the effectiveness of the proposed method compared with baseline approaches from the literature.

The surface code is the leading candidate for fault-tolerant quantum computation owing to its planar nearest-neighbor connectivity, high threshold, and efficient decoding, but its low encoding rate demands on the order of a thousand physical qubits per logical qubit in the teraquop regime. Yoked surface codes improve the density by a factor of two or three by concatenating a high-density parity check code on top of the surface code while retaining planar nearest-neighbor connectivity. In this work, we generalize this idea to multiple levels of concatenation and introduce multi-yoked surface codes. Our construction rests on two new ingredients. First, we propose a family of outer codes called chain codes, built by chaining copies of a seed code that detects the block errors of the code one level below; the resulting codes use all logical qubits of the lower level and achieve a high encoding rate within a few concatenation levels. Second, we design a patch allocation in which movable workspaces perform the yoking checks by lattice surgery with a hierarchy of yoking intervals, so that lower-level checks are performed frequently while higher-level checks are performed less often, which avoids the long yoking intervals that a single large-distance outer code would require. As a benchmark, we construct a three-yoked surface code with a $[[256,166,8]]$ outer code and evaluate it numerically under the SI1000 noise model using soft information from the surface code decoder. The logical error rate is suppressed exponentially in the inner code distance, and in the teraquop regime the three-yoked surface code is about 4 to 4.5$\times$ denser than the unyoked surface code.

Soft robots present significant modelling challenges due to their non-linearity, complex dynamics and potentially intricate geometries. These difficulties in accurate system identification and dynamics modelling limit their applications in precise robotics tasks. Prior modelling approaches typically suffer from trade-offs in accuracy, computational efficiency, or speed. The differentiable finite element method (FEM) offers a promising balance between these desiderata for soft robot modelling, and enables the use of gradients for efficient calibration and trajectory optimisation. In this paper, we propose an end-to-end differentiable FEM-based framework designed to streamline modelling and system identification for pneumatic soft robots, enabling the generation of reliable models for downstream tasks. The framework automates the conversion of computer-aided designs into voxelised tetrahedral viscoelastic FEM meshes that accurately represent the robot's geometry and actuation mechanism. By integrating easily acquired point cloud data with differentiable FEM, the framework achieves precise identification of material and dynamic actuation parameters using a minimal experimental setup. Additionally, the differentiable nature of the model facilitates trajectory optimisation by leveraging gradients from robot dynamics and contact interactions. We validate the framework by modelling a complex bellow-shaped pneumatic soft robot and demonstrate its efficacy in real-world motion planning tasks. Experimental results indicate high modelling accuracy, with a maximum positional error of less than 3 mm, and successful application in tasks such as path following and grasping.

Runtime enforcers observe a system's behavior and exert control over it to ensure that the system always adheres to its requirements. Many natural requirements not only formulate restrictions on the system's present behavior, but also impose obligations on its future behavior; for instance, agentic security may require personal data collected during a run to be erased by some deadline. In an ever-growing compliance landscape, real-world systems may be subject to hundreds of such requirements. However, existing enforcement mechanisms supporting complex policies are often too slow for production software; instead, developers may resort to non-temporal access control mechanisms and ad-hoc instrumentation, but these scale poorly with requirement complexity. To address this problem, we introduce an efficient algorithm and tool for enforcing complex temporal requirements and demonstrate its performance. Specifically, we identify a fragment of Metric First-Order Temporal Logic (MFOTL) that can be enforced with low runtime complexity while supporting a rich family of practically relevant requirements, including obligations. We then design an enforcement algorithm for this fragment and implement it in EnfFlash, a novel tool that enforces requirements with latency up to 44x lower than EnfGuard, the previous state-of-the-art enforcer, on standard benchmarks, and up to three orders of magnitude lower on security policies for LLM agents. This performance is achieved by compiling requirements into imperative programs that we efficiently interpret. We evaluate EnfFlash both standalone, on existing benchmarks, and integrated in web applications as an enforcement backend. We demonstrate that it can enforce a substantial 400-line MFOTL formula specifying the GDPR on a social network while adding under 15 ms to each page view, which is sufficient for most interactive and real-time applications.

We introduce a tensor envelope (TEE) for composite objectives $\varphi=f+g$, built from a $q$th-order Taylor model of the smooth term $f$ regularized by a $p$th power with $p>q$. To construct it, we first establish a tensor descent lemma and characterize its behavior in the three regimes $q<p<q+1$, $p=q+1$, and $p>q+1$. Under suitable prox-boundedness and parameter conditions, the associated tensor operator (TOP) has nonempty compact values, and TEE is finite-valued and continuous, preserves global minimizers, and inherits the level-boundedness of $\varphi$. We further show that TEE is locally Lipschitz continuous and directionally differentiable, characterize its Fréchet differentiability, and prove that it is $C^1$ whenever TOP is single-valued. As such, TEE preserves the essential optimization landscape properties of $\varphi$ while enjoying a richer analytical structure, which facilitates the design and analysis of tensor-based optimization methods. Finally, TEE serves as a Lyapunov function for the exact tensor iteration: every cluster point is critical, and, for bounded trajectories with $q<p\le q+1$, an $\epsilon$-stationary point is reached within $\mathcal{O}(\epsilon^{-p/(p-1)})$ iterations. To our knowledge, both the tensor descent lemma and this complexity bound are the first of their kind obtained without assuming global Lipschitz or Hölder continuity of the $q$th-order derivative of $f$.

Hierarchical control architectures are widely used to decompose complex control problems into interacting control levels and are particularly important in robotics, where planning, whole-body motion, and lower-level control must be coordinated across different levels of abstraction and time scales. Their overall closed-loop performance, however, depends strongly on parameters distributed across the hierarchy, such that tuning controllers on different levels independently may neglect relevant cross-layer interactions. We propose a contextual Bayesian optimization framework for joint parameter learning in hierarchical control systems. Rather than modeling closed-loop performance only as a scalar black-box function, we retain separate observations of task performance, realization quality, and control effort. A correlated multi-output Gaussian process models these performance components, while their known aggregation into the overall closed-loop objective is evaluated analytically. The formulation exploits three complementary consequences of hierarchical control: informative performance quantities exposed by the hierarchy, coupling between parameters of different controller levels, and variations of these relations with operating conditions. We evaluate the approach for humanoid loco-manipulation, jointly tuning a centroidal predictive controller and a whole-body controller for physical box pushing under varying box mass. The proposed method achieves the lowest mean empirical regret during both training and adaptation among the considered baselines.

For $0<\theta<\pi$, let $K_\theta=\{e^{is}:|s|\le\theta\}$ and $E_\theta=\operatorname{span}_{\mathbb C}\{1,z\}\subset C(K_\theta)$. We prove that every contractive linear map from $E_\theta$ into $\mathcal B(H)$ admits a factorization through a unitary operator whose spectrum is contained in $K_\theta$, and is therefore completely contractive. Consequently, $E_\theta$ has a unique operator space structure. For $0<\theta,\varphi<\pi$, we also show that $E_\theta$ and $E_\varphi$ are isometrically isomorphic if and only if $\theta=\varphi$, and that none of these spaces is isometrically isomorphic to $\ell_1^2$ or $\ell_\infty^2$. Thus we obtain uncountably many mutually non-isometric two-dimensional complex Banach spaces with a unique operator space structure, giving a negative answer to a question of Pisier.

Robots need to anticipate how their actions will change the world, since manipulation success hinges on the resulting contacts and object motions. However, existing Vision-Language-Action (VLA) policies that predict future observations from shared features leave the forecast decoupled from the actions the policy will actually execute, and impose no physical constraints on how the scene may evolve. We introduce ForeAct3D, a framework for policy-grounded future world modeling within VLA policies. Learnable geometric queries decode depth, semantic segmentation, and camera pose from the policy representation into current and future semantic 3D scene states, and the future queries are conditioned on the policy-generated action chunk to ground the forecast in the planned interaction. A physical-consistency closure relates the two states through background staticity and instance-level rigidity, and anchors the wrist-camera pose to end-effector kinematics. These objectives shape the shared representation used for action generation during training, and no future prediction is required at inference. Without robot pretraining, ForeAct3D achieves 98.3% average success on LIBERO and an average task length of 3.73 on CALVIN, outperforming its base policy on every suite. Ablations show that semantic 3D supervision, physical consistency, and action conditioning each improve manipulation performance, and that action conditioning substantially improves future object localization. Real-world experiments on spatial placement, object insertion, and sequential manipulation further raise average success from 6.7% to 37.8% over the base policy. The project page and code are available at https://github.com/anthonytao80-crypto/ForeAct3D.

We present a 4D Gaussian Splatting framework for the Sparse-View Track of the SIGGRAPH Asia 2026 Volumetric Video Challenge, which requires dynamic scene reconstruction from only six cameras with wide baselines. To achieve robust dynamic reconstruction under such sparse views, our framework integrates three components. (1) Region-adaptive spatial priors: We use foreground masks to guide Gaussian initialization and mask voting to control densification separately for the dynamic foreground and static background. Background geometry is regularized using monocular depth aligned to metric scale. (2) Motion-consistent temporal priors: We provide supervision at intermediate times through frame interpolation and constrain projected Gaussian motion with estimated optical flow. (3) Generative assistance: We place virtual cameras in the widest angular gaps and restore their rendered images using a diffusion-based model conditioned on camera poses. The restored images are iteratively incorporated into training as pseudo-supervision. On the validation set, our framework improves full-frame PSNR from 25.60 dB for the baseline to 29.75 dB. On the official test benchmark, it achieves 30.04 dB full-frame PSNR and 27.88 dB foreground PSNR, ranking first overall in the Sparse-View Track.

Many visual explanation methods in computer vision highlight pixel importance but struggle to link these low-level cues to semantically meaningful concepts, limiting their interpretability and trustworthiness. We introduce Concept-based Explanations (ConEx), a novel framework that bridges saliency visualization with concept-based reasoning to provide both faithfulness and interpretability. ConEx automatically discovers class-specific concepts and represents them through concept activation vectors (CAVs), learned without manual supervision using an architecture-specific masking mechanism that reduces noise introduced by the segmentation masks to enhance concept purity. ConEx generates faithful saliency maps that reveal where each concept appears in the image and how it contributes to the prediction. To evaluate the reliability of these learned concepts, we propose two complementary metrics, Vector-Concept Match (VCM) and Concept-Class Match (CCM), that quantify concept alignment and enable direct comparison with existing methods. Extensive experiments across diverse settings demonstrate that ConEx achieves state-of-the-art performance on faithfulness, segmentation, and concept-quality benchmarks. Overall, ConEx advances the field toward truly interpretable and concept-grounded explanations in vision models.

Automatic curriculum learning can improve the effectiveness of reinforcement learning by selecting the training experiences presented to the agent over time. Predicting the consequences of such decisions can, however, be difficult. We analyze automatic curriculum learning as a sequential decision-making problem, highlighting a gap between the quantities that determine the value of curriculum decisions and the information captured by local learning signals commonly used to guide them. We then investigate whether Large Language Models (LLMs) can exploit richer information about the learning problem to better anticipate the consequences of curriculum decisions. We introduce a method that combines online learning-progress estimates with LLM-informed estimates of (i) the potential downstream benefits of learning on each task and (ii) whether direct training on a task is currently likely to produce progress. We evaluate the approach on a custom benchmark of 256 textual goals in Craftax under different curriculum objectives. We observe the strongest gains when optimizing for individual target tasks. When optimizing across the full task set, the benefits vary across learners with different mechanisms for cross-task transfer, ranging from modest improvements in learning speed to larger gains that persist through the end of training.

We show that the abelian category of coherent toric sheaves is generated, as a Serre subcategory, by pushforwards of rank one reflexive sheaves supported on invariant subvarieties. As an application, we extend previous results by Klyachko on cohomology of toric vector bundles to coherent toric sheaves.

Primitive-based 3D segmentation offers a compact and explicit alternative to dense surface prediction, naturally supporting structural abstraction and boundary localization. However, geometric decomposition alone does not determine how primitives should be organized into semantic parts: a single part may span multiple primitives, while geometrically similar or touching primitives may belong to different parts. We therefore introduce RePart (Reinforcement Part Reasoning), which formulates primitive-to-part organization as a finite-horizon Markov decision process and learns semantic organization through trajectory-level reinforcement reasoning. RePart constructs a Composable Primitive Workspace from fine-grained superquadrics and applies a merge-and-stop policy whose decisions are optimized by their downstream effects on the resulting partition rather than local primitive compatibility. The inferred part identities are then mapped back to the original mesh through Boundary-Aware Surface Labeling, preserving accurate surface boundaries beyond the primitive approximation. On PartNet, RePart achieves the strongest results across all four aggregate partition metrics; on 3DCoMPaT++, it obtains the highest RI and SC without target-dataset fine-tuning. These results demonstrate that reinforcement reasoning provides an effective mechanism for organizing geometric primitives into semantic parts while retaining dense segmentation accuracy. Code is available at https://github.com/EngineeringAI-LAB/RePart.

Magnetic Resonance Imaging (MRI) is widely regarded as the optimal sensor for fetal brain analysis due to its superior soft-tissue contrast and anatomical detail. However, its high cost and operational burden make it invasive and difficult to obtain at scale. Ultrasound (US), in contrast, is cheap, safe, and routinely acquired, and as a result it has produced substantially larger datasets and a growing ecosystem of pretrained models. This asymmetry raises a natural question: Can we teach a US-only model to understand fetal MRI from only a limited set of examples? The standard recipe, training a foundation model on subject-to-subject paired MRI-US scans, is not viable since no such paired fetal dataset is publicly available. In this paper we address this gap with Weakly Aligned Spatiotemporal Pairs (WASP), a framework that formulates cross-modal correspondence as an entropic Optimal Transport problem driven by clinical metadata, in particular Gestational Age (GA) and diagnostic planes, enabling the fitting of a lightweight alignment module that lifts MRI representations into the US latent space, without fine-tuning the backbone. Empirically, WASP yields its largest gains when MRI is unseen by the model during pretraining (on USFM, GA estimation error drops from 21.9 to 17.4 days and standard plane classification accuracy climbs from 61.9% to 69.0%), while providing smaller, backbone-dependent refinements for backbones pretrained on both modalities (e.g., BioMedParse GA estimation error from 6.5 to 6.0 days and SAM-Med2d plane accuracy from 83.3% to 88.1%). Code is available at https://github.com/miccunifi/WASP.

Best arm identification under differential privacy is a pure-exploration problem in which both statistical efficiency and privacy protection must be achieved simultaneously. We study fixed-budget best arm identification for bandits under pure $\epsilon$-differential privacy, where the learner must recommend an arm after a prescribed sampling budget while protecting the full transcript. We prove that the optimal exponential decay rate of the error probability is upper bounded by an instance-dependent privacy-aware transportation exponent that differs from the analogous quantity used to characterize the stopping time in fixed-confidence analysis by Jourdan and Azize [2025]. Guided by this exponent, we propose AO-Pri-BAI, an adaptive algorithm that maintains private running estimates through Laplace-tree mechanisms and learns a sampling design through a min–max interaction between hard alternatives and arm allocations. We prove that AO-Pri-BAI satisfies pure $\epsilon$-differential privacy. We also establish that the exponent of the failure probability of AO-Pri-BAI matches the privacy-aware benchmark. Numerical studies show that even in the non-asymptotic setting, AO-Pri-BAI outperforms benchmark algorithms on various instances, complementing the theoretical analyses.

This paper reports about development of a dynamic lock-in based magnetoelectric (ME) coupling measurement system and its application to investigate strain-mediated coupling in 0.65Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$-0.35PbTiO$_3$/NiFe$_2$O$_4$ (PMN-PT/NFO) and CoFe$_2$O$_4$/BaTiO$_3$ (CFO/BTO) composites. The PMN-PT/NFO composite exhibits a significantly enhanced ME coefficient ($\alpha_{\mathrm{ME}} \approx 1.85$~mV\,mm$^{-1}$\,Oe$^{-1}$) compared to CFO/BTO ($\approx 0.147$~mV\,mm$^{-1}$\,Oe$^{-1}$). The antisymmetric field dependence and $180^\circ$ phase reversal confirm the strain-driven origin of coupling in both the samples. The superior response of PMN-PT/NFO arises from the combined effect of high piezoelectric strength in PMN-PT and low magnetic anisotropy of NFO, whereas the high magnetic anisotropy of CFO and weaker piezoelectricity of BTO limit the ME output. These results highlight the decisive role of magnetic softness and piezoelectric strength in optimizing strain-mediated ME coupling.

In this paper we study the constant speed, biased random walk in dynamical random conductances. In certain regimes of the parameters of the model, we prove that the random walk is ballistic. We show annealed and quenched CLT in the full parameter range. Furthermore, as a consequence of the non-reversible nature of this model, we show that the classical Einstein relation does not hold.

We study the following quantum state identity problem: given access to copies of $n$ unknown pure quantum states, the goal is to determine whether every pair has fidelity at least $1-\varepsilon$ or some pair has fidelity at most $\varepsilon$. This problem relaxes the identical-or-orthogonal promise considered in previous work. For any fixed overlap parameter $\varepsilon\in(0,1/4)$, we present two quantum algorithms with complementary guarantees on circuit depth and sample complexity. The first runs in constant depth using parallel swap tests and takes $O(\log(n/\delta)\log(2/\delta))$ copies of each input state to succeed with probability at least $1-\delta$. The second uses the Schur transform to reduce the sample complexity to $O(\log(n/\delta))$, through an analysis relating Jucys–Murphy elements to Schur sampling. We also prove a matching sample complexity lower bound of $\Omega(\log(n/\delta))$ for any quantum algorithm with failure probability at most $\delta\le 1/2-c$, for any constant $c>0$, establishing that the second algorithm achieves the optimal dependence on both $n$ and $\delta$ for fixed $\varepsilon$.

On-policy distillation (OPD) has emerged as a widely used paradigm for post-training large language models, reducing the train–test mismatch of conventional distillation by supervising the student on its own generated trajectories. However, existing OPD objectives remain largely token-local and outcome-agnostic, optimizing teacher–student agreement at each prefix despite reasoning quality being determined at the trajectory level. Reinforcement learning with verifiable rewards (RLVR), particularly Group Relative Policy Optimization (GRPO), provides complementary outcome-level supervision but suffers from sparse rewards and coarse credit assignment. We show that OPD and RLVR exhibit complementary blind spots: teacher signals provide dense local guidance but are weakly aligned with rollout correctness, whereas group-relative rewards capture task success but provide coarse token-level credit and vanish on all-failure groups. We introduce DiffGate, an outcome-gated objective that combines GRPO with selective, bounded teacher guidance. Teacher supervision is applied only to failed trajectories, scaled by group difficulty, and smoothly bounded to prevent extreme teacher–student discrepancies from dominating optimization. The verifier therefore determines which trajectories receive teacher guidance, while the teacher provides dense token-level update directions within those trajectories. Across Qwen3-0.6B and Qwen3-1.7B students, DiffGate improves code avg@8 over matched GRPO by $+1.7$ and $+1.8$ points and pass@8 by $+1.6$ and $+5.7$ points, respectively. On mathematics, avg@8 remains within $0.5$ points of GRPO while pass@8 improves by $+1.1$ and $+3.9$ points. Overall, DiffGate improves pass@8 across all four model–domain settings, demonstrating improved solution coverage under our evaluation protocol.

Black-hole (BH) quasinormal modes encode the properties of merger remnants and provide powerful tests of strong-field gravity. The BH spectroscopy has predominantly treated them as independent linear oscillations. Nonlinear ringdown can additionally reveal how these modes interact and which intermediate states mediate their interactions. Inspired by cosmological collider physics, we introduce quasinormal-mode collider spectroscopy (QCS), a framework for organizing and predicting nonlinear BH responses. We establish two structural results. First, at an isolated, nondegenerate intermediate pole, a cubic strain residue factorizes into an excitation amplitude and a quadratic conversion coefficient. This factorization imposes rank constraints across output channels and choices of second-order initial data, providing consistency tests of the intermediate-mode description. Second, the intermediate pole residue can be reconstructed from its horizon and infinity radiation. With the first-order field and third-order data held fixed, this reconstruction extends to the full cubic waveform difference generated by changing the second-order initial data. QCS thus connects lower-order radiation to higher-order observables and provides a framework for probing the interaction structure of nonlinear ringdown.