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arXiv2026

Constrained minimization problems and FFT-based solvers: application to local Dirichlet boundary conditions and contact mechanics

The present paper focuses on a recent and active research axis to overcome the limitations of FFT-based solvers in order to apply various types of boundary conditions (BCs) and not only periodic BCs. A complete framework based on discrete trigonometric transforms (DTTs) of various types, possibly combined with discrete Fourier transform, has been proposed recently to account for any type of BCs defined per face of the unit-cell and per component of the displacement or traction vector. A parallel implementation by Amouzou-Adoun et al. recently proved its robustness and versatility. The main novelty consists of few modifications introduced in the displacement-based FFT/DTT iterations in order to account for Dirichlet BC on a selected part of a boundary face (and Neumann BC on the other part), or on interior points, and also to apply kinematic relations between displacements on different nodes. Introduced from the viewpoint of local equations, these modifications are then discussed from the perspective of constrained minimization and saddle point systems. The current proposition is identified as a 'null-space' method in the category of 'segregated' methods (see Benzi et al., 2005): the reaction forces (acting locally to enforce the Dirichlet BC) are evaluated a posteriori once the displacement field is found. This approach is original in the context of FFT-based solver's extension to Dirichlet BCs. Starting from this modified FFT/DTT-based algorithm to account for equality constraints, the second important novelty consists in embedding this algorithm in a conventional active-set strategy to account for inequality constraints, with an application in the context of contact mechanics. Two implementations have been proposed, in the context of small strain and finite strains. It is believed that these propositions significantly expand the field of applications of FFT-based solvers.

cs.CE↗

arXiv2026

BG-REAL: A Public Real-Data Anchored Benchmark for Background Manipulation Detection and Localization

Background manipulation is a practical but under-specified image-forensics setting: the manipulated evidence can sit outside the salient foreground object, while many evaluations emphasize object-centric copy-move, splicing, or generic synthetic edits. We introduce BG-REAL, a public real-data anchored benchmark package for background manipulation detection and localization. The current release is built from Open Images V7 instance-segmentation sources and contains 7,000 processed samples over 1,200 source groups, including 6,000 public-data anchored samples and 1,000 synthetic control samples. BG-REAL covers six edit families, matched authentic controls, source-group splits, mask and leakage QA, 599 human-assisted quality-control rows, three completed external baselines (TruFor, MVSS-Net, and HiFi-Net), and five-seed model evaluation. Beyond aggregate accuracy, we use matched-authentic-control diagnostics to measure how often baselines misclassify re-encoded authentic images as manipulated at a threshold fixed on held-out validation data; false-positive rates range from 0.57 (TruFor, the lowest) to 1.00 (several weak or mask-informed baselines), indicating that re-encoding artifacts are a shared shortcut risk across baselines rather than a problem specific to any one model. The release provides the construction pipeline, evaluation protocol, paper-ready figures, and reproduction documentation. We frame BG-REAL as a background-manipulation-focused complement to general image-manipulation-localization benchmarks, not as a fully real-only or general-purpose benchmark.

cs.CV↗

arXiv2026

The Klein-Gordon-Fock theory as a one-particle relativistic quantum mechanics

The Klein-Gordon-Fock (KGF) theory is presented as a single-particle relativistic quantum theory. A Schrodinger-type equation for a single-component wave function is derived. In addition to the KGF Hamiltonian, operators for momentum and orbital angular momentum for a scalar boson are identified, which act within the space of single-component wave functions. This theory is applicable to both massive and massless scalar bosons.

quant-ph↗

arXiv2026

Phase Retrievability of Super Operators and Measurements

We continue the study of Phase Retrieval in the Quantum Information setting in the style of \cite{liu2023phase}, in a manner which is more general in two primary ways: (a) Instead of only pure states we consider also states (and positive semidefinite operators) of bounded rank, as is done in Quantum Tomography; (b) We consider general super operators instead of only quantum channels. We show that in order to have phase retrieval with respect to positive semidefinite operators of bounded rank, it suffices to discriminate between perfectly distinguishable pairs (i.e. those with orthogonal supports). From this we prove that phase retrievability is always Lipschitz stable with respect to the trace norm, and then we use the Fuchs-van de Graaf inequalities to deduce stability with respect to the Bures--Wasserstein distance (thus generalizing the known stability results for phase retrieval in Frame Theory). For Hermitian-preserving super operators taking values in block-diagonal matrices, we characterize phase retrievability in terms of conditions inspired by the classical complement property from Frame Theory.

quant-ph↗

arXiv2026

PowerAtlas: Feasibility-Aware Language Models for Electricity-Computing Co-Scheduling

Electricity-computing co-scheduling (ECCS) decides where and when computing tasks run together with how generators are dispatched, because task placement changes nodal demand while power availability determines whether tasks can be served. Prior work addresses such coupled problems with optimization or learned controllers, and large language models (LLMs) are increasingly used to generate structured decisions for scheduling and power systems. Solver runtimes vary across instances, and LLM outputs that parse correctly can still violate grid and service constraints. We formalize ECCS as a structured decision task and release ECBench, 2,000 instances with Gurobi-optimal reference schedules and executable checks for grid limits, task service, cost, and latency. We propose PowerAtlas, which trains an LLM with supervised initialization and Feasibility-Aware GRPO on deterministic scorer feedback, and generates the joint schedule in a single response without solver calls or retrieval. On 10-40 paired instances per backbone, selected PowerAtlas checkpoints lower violations by 89-98% and penalized cost by up to 26x relative to base models, with residual supply deficits. Code and data are available at https://github.com/JAVA-Jiang/PowerAtlas.

cs.LG↗

arXiv2026

Parity-Based Time-Bin Encoding Enabling SWAP Between Polarization and Time-Bin Qubits

Multi-degree-of-freedom photonic quantum processing requires routing between degree-of-freedom (DOF) qubit encodings on a single photon. A SWAP between polarization and time-bin qubits is an advantageous primitive for such architectures, however conventional early/late time-bin encoding does not support bidirectional logical time-bin flips from late to early which limits the ability to implement certain quantum operations. We introduce a parity-based time-bin encoding in which logical $\ket{0}_T$ and $\ket{1}_T$ correspond to even and odd multiples of a spacing $Δt$, so that a physical delay of $Δt$ implements $\ket{0}_T \leftrightarrow \ket{1}_T$. This encoding is the enabling ingredient that makes a polarization-controlled delay line implement $\mathrm{CNOT}_{P \rightarrow T}$ and aligns naturally with periodic refractive index modulation for $\mathrm{CNOT}_{T \rightarrow P}$. Composing three such CNOT operations sequentially results in a deterministic SWAP between polarization and time-bin degrees of freedom. We quantify how EOM voltage errors reduce the polarization-flip probability and estimate timing requirements from modulator switching, detector resolution, and timing jitter, giving an illustrative timing budget.

quant-ph↗

arXiv2026

Inverse Learning of Latent Risk-Neutral Densities from Irregular Option Quotes

Accurate option prices do not imply accurate recovery of the latent risk-neutral density. We study this distinction with two complementary benchmarks. A controlled benchmark exposes simulator-truth densities for latent evaluation, while a chronological NIFTY benchmark tests only held-out market prices. A two-component lognormal mixture has the lowest aggregate price, $L^1$, Wasserstein, and fixed-tail errors on the synthetic benchmark. Learned operators retain narrower strengths: DeepONet reduces 1% quantile and variance error by 39.0% and 34.6% relative to the mixture, and a quote transformer reduces $L^1$ by 16.4% on the structurally misspecified Merton family. A numerical conditioning analysis explains why these rankings can differ: after enforcing mass and forward constraints, 95 of 126 pricing directions are numerically null, and two densities separated by $L^1 = 0.061$ produce identical prices on the covered strikes. On 524 held-out NIFTY calls, validation-selected test-time adaptation reduces DeepONet RMSE by 28.3%, but per-expiry mixture and SVI fits remain much more accurate. The evidence supports target-dependent inductive bias, not a universal winner.

cs.LG↗

arXiv2026

Predictability of Human Movements across Industry Sectors using Multilayer Networks

Predicting the patterns of human movement is important to applications from urban design to disease control and emergency response. In this work, we leverage machine learning (ML) to study the predictability of movements to different types of locations (e.g., movements to grocery stores, to schools, or to hospitals). Our approach relies on developing multilayer mobility networks encoding movements between census tracts with network layers associated with different industry sectors. We study the predictability of node degrees across layers, studying which industries are easier/harder to predict. Rather than treat prediction as an end in itself, we propose ML predictability as an exploratory tool to understand multilayer network organization. Our results suggest that node's out-degrees are easy to predict, since they are driven by census tract populations; whereas in-degrees are harder to predict, since persons can be drawn to diverse type of locations in a census tract. We also find that movements to certain industry types (e.g., restaurants) are easier to predict than others, and the different industrie's predictability are positively correlated with the number of movements to those types of locations. These findings provide a practical step toward using ML for multilayer mobility modeling and the many downstream application.

physics.soc-ph↗

arXiv2026

Flow Matching with Missing Data

Flow matching assumes fully observed training data, which many real-world applications rarely provide. We study Missing-Data Flow Matching, which treats the missing coordinates of training samples as latent variables and averages the flow matching loss over the values they could take. We first prove that the oracle correction is exact: completing from the true pattern-conditioned posterior recovers the complete-data flow-matching objective under any missingness mechanism. Under missing completely at random (MCAR) and missing at random (MAR), this posterior equals the ordinary complete-data conditional, while under missing not at random (MNAR) it generally depends on the missingness mechanism and may require additional structure to identify. Our finite-sample analysis then answers design questions that the algorithm leaves open. Missingness transfers estimator variance rather than adding it, and for the fixed-parameter loss estimator one completion per example matches complete-data variance and is optimal under a fixed evaluation budget. A learned completion model contributes population completion bias, which we bound by its expected conditional Wasserstein distance to the true completion law. Experiments numerically validate the theoretical predictions, show that deterministic rather than frozen imputation reduces generated conditional variability, and place our method alongside strong classical and deep imputation baselines on real tabular data.

cs.LG↗

arXiv2026

Diagnosing Compositional Generalization in Sequential Robot Tasks

Sequential robot manipulation requires policies to execute novel combinations of familiar instruction components. However, collecting demonstrations for all possible instruction tuples is combinatorially expensive, while sparsely covered datasets often fail under out-of-distribution recombination. This paper studies compositional generalization through the lens of instruction-space coverage. We decompose the generalization gap into three sources: \textit{marginal instruction shift}, \textit{instruction-compositional shift}, and \textit{context--action shift}. This decomposition allows us to diagnose when sparse training coverage is sufficient, and what structure the training set must preserve for reliable action prediction. Our results show that exhaustive tuple enumeration is unnecessary: a structured subset can recover strong out-of-distribution performance when it covers action-relevant dependencies. We further find that sparse training often fails due to instruction steering rather than missing low-level skills; finetuning with only one demonstration per task improves OOD success from $0.4\%$ to $54.7\%$. For semantically dependent tasks, effective coverage must capture relational structure rather than only factor diversity. These findings suggest that efficient robot data collection should prioritize dependency coverage in instruction space over exhaustive task expansion. Additional results, code, and dataset are available on the \href{https://yixiaowang7.github.io/Diagnosing_Compositional_Generalization_Robot_Page/}{project website}.

cs.RO↗

arXiv2026

Exact minimum measurement dependence for faithful local deterministic models of multipartite GHZ-Mermin correlations

A local deterministic model can reproduce Bell-inequality violations only if the hidden state depends on the measurement settings. Hall found the minimum such dependence for the singlet state [Phys. Rev. Lett. 105, 250404 (2010)] and posed the corresponding problem for the Mermin state [Phys. Rev. A 84, 022102 (2011)]. This paper solves it, for the $n$-party GHZ-Mermin scenario at every $n \geq 3$, with the marginals reproduced as well as the correlators. The minimum measurement-dependence fraction is $F_{\min}(n) = R/[2(R+1)]$, with $R = 2^{\lfloor (n-1)/2 \rfloor}$ the Mermin violation ratio: $1/3, 2/5, 4/9, 8/17, \ldots$, always below $1/2$. The lower bound follows from Mermin's inequality by a general overlap bound; the upper bound is an explicit model, uniform on the hidden-variable classes that violate the fewest constraints, with closed-form counts; a reduction theorem shows that for Mermin scenarios the marginals impose no additional dependence. The Mermin values are also certified by integer-arithmetic enumeration through $n = 22$. Every minimal contradiction of size $k$ among stabilizer constraints has correlator-only minimum $1/(k-1)$. With the marginals included the minimum is the same on every core of the $C_5$ ring cluster, on the size-4 and size-5 cores of $C_4$ and on every four-core of $C_6$, but larger on the size-6 and size-7 cores of $C_4$ and on 112 of the 1,920 five-cores of $C_6$, with exact certificates on both sides in every case.

quant-ph↗

arXiv2026

Sharp bounds for non-adaptive randomized approximation of high-dimensional vectors

We study the complexity of approximating the finite-dimensional vector space embedding $\ell_p^m \hookrightarrow \ell_q^m$ for $2 \leq p < q \leq \infty$ based on non-adaptive randomized algorithms that use up to $n$ arbitrary linear functionals as information on a problem instance $x \in \mathbb{R}^m$, where $n \ll m$. We prove lower bounds on the non-adaptive randomized approximation error with a joint dependence on $(n,m)$ matching previously known upper bounds.

math.NA↗

arXiv2026

A Structural Matrix Autoregression Framework for International Spillovers

Understanding how macroeconomic shocks propagate across countries requires structural models that can jointly identify country-specific shocks and their international transmission. Yet extending structural vector autoregressions (SVARs) to large multi-country systems is challenging due to rapidly increasing dimensionality, computational costs, and the proliferation of identifying restrictions. This paper develops a Bayesian Structural Matrix Autoregression (BSMAR) framework that exploits the natural matrix structure of international macroeconomic data. By separating dependence across economic variables from dependence across countries, the framework provides a parsimonious representation that substantially reduces the dimensionality of large structural systems. We develop a Bayesian sampling algorithm for posterior inference that accommodates zero, sign, and ranking (magnitude) restrictions, allowing established SVAR identification schemes to be combined with a novel approach to identifying contemporaneous international spillovers. Applying the model to quarterly data for 15 economies, we find substantial heterogeneity in international shock transmission, with demand shocks playing a more prominent role than supply shocks in generating cross-country spillovers.

econ.EM↗

arXiv2026

Rethinking Agentic Kernel Generation for Emerging Accelerators

Emerging accelerators often lack mature compiler backends, motivating neural agents that generate and repair kernels from architectural documentation and simulator feedback. This approach repeatedly reconstructs workload-invariant machine semantics, including instruction behavior, legality constraints, synchronization rules, and memory protocols, for every workload. We argue that these semantics should be compiled once into a persistent symbolic artifact, while neural reasoning should focus on workload-dependent mapping decisions. We present Zomboss, a compiler-mediated agentic framework for kernel generation that places neural search within a verified compiler boundary. Zomboss compiles machine semantics and legality constraints into a reusable mapping interface, then uses a neural agent to optimize workload-dependent decisions within the validated mapping space. Across 20 Gemmini and 36 PLENA workload instances, Zomboss returns a correct verified kernel on all 56 instances. Relative to the compiler default, Zomboss achieves geometric-mean speedups of 3.34x on Gemmini and 1.10x on PLENA. Additional comparisons against KernelCraft reduce tokens per verified kernel by 26.3% on 20 Gemmini instances and 98.2% on 18 composite PLENA instances. These results show that partial mapping specification and symbolic completion turn kernel generation into verified design-space exploration. The shared interface supports competitive conventional and neural search, while improving kernel quality and token efficiency within the same agentic harness. Zomboss thus separates reusable machine realization from the policies that explore workload-dependent mappings.

cs.AR↗

arXiv2026

Multilevel limits of spiked random matrix corners processes

We consider the largest eigenvalues of submatrices of the classical Gaussian random matrices with a finite rank spike in the critical BBP regime. We show that they converge to a multilevel interlacing particle system whose lowest level is the Airy$_β$ point process. Our construction and scaling limits extend in a natural way to non-classical $β>0$.

math.PR↗

arXiv2026

Optimality of Gaussian Entanglement of Formation

We prove that the entanglement of formation of every two-mode Gaussian state coincides with its Gaussian restriction, solving a longstanding open problem in continuous variable quantum information theory. The key result is a sharp affine relation between entanglement and a generalized Einstein--Podolsky--Rosen observable, valid for arbitrary pure two-mode states, including non-Gaussian ones. We further prove that the entanglement of formation is additive on arbitrary tensor products of two-mode Gaussian states, and hence coincides with the entanglement cost, settling the latter for all two-mode Gaussian states. As a consequence, we obtain in closed form the entanglement cost of thermal-loss, thermal-amplifier and additive-noise bosonic channels. Our results, which also extend to bisymmetric multimode states, establish that no two-mode state is less entangled than the Gaussian state with the same covariance matrix, yielding measurable lower bounds on both the entanglement of formation and the entanglement cost of arbitrary non-Gaussian states.

quant-ph↗

arXiv2026

Optimal Unambiguous DNFs and Alon-Saks-Seymour

We construct unambiguous DNFs having width $O(n)$ but $0$-certificate complexity $Ω(n^2)$. By utilizing the special structure of these DNFs, we prove a lifting theorem with a constant-sized gadget that lifts the DNF to a communication problem, while losslessly translating the separation in certificate complexity to a separation in communication complexity. This leads to an optimal refutation of the Alon-Saks-Seymour conjecture, as well as an optimal communication lower bound for the Clique versus Independent Set problem, improving the previous results of Balodis, Ben-David, Göös, Jain and Kothari (FOCS 2021, SICOMP 2023) by several doubly logarithmic factors. As further applications of our construction to query complexity and learning theory, we exhibit: (a) a family of Boolean functions that has an optimal quartic separation between certificate complexity and approximate degree, and (b) a sample compression lower bound of $Ω(\sqrt{\log c})$ for multiclass concept classes over $c$ labels.

cs.CC↗

arXiv2026

Don't Regenerate, Debug: A Domain-Specific Agent for Repairing Near-Miss Accelerator Kernels

Kernel generation for hardware accelerators such as GPUs and NPUs has become a proving ground for large language models (LLMs), and state-of-the-art systems raise correctness through pipelines that couple LLMs with agentic reinforcement learning and evolutionary search. Such pipelines generate, compile, and execute large numbers of candidate kernels, discarding most of them and forgoing the opportunity to distill failures into reusable knowledge. Many discarded candidates are near-miss operators that compile and run but fail numerical validation; each embodies genuine domain knowledge and a nontrivial investment in LLM inference, cross-compilation, and hardware execution. We argue for a paradigm shift: rather than regenerate, debug. Debugging is far more constrained than generating from scratch: the search space is small and feedback is dense. We present a domain-specific debug agent that addresses three core challenges in autonomous repair: mitigating knowledge scarcity through retrieved patterns and diagnostic instrumentation, ensuring integrity through anti-cheat detection and full-coverage evaluation, and controlling cost via convergence guards and bounded iteration. Debugging serves two complementary roles: it extends the capability frontier by recovering operators that repeated regeneration fails to produce, and it lowers cost per deliverable operator. Debug Pass@1 achieves 66.7% versus Regenerate Avg Pass@1's 25.9% and Regenerate Pass@3's 40.7%, while consuming 92.8% fewer tokens per success than three-trial regeneration. Component ablations show that the knowledge base drives recovery, while integrity gates reject 12.5-33.3% of the successes the workflow itself accepted.

cs.SE↗