arXiv:2605.15794v1 Announce Type: new
Abstract: We present ForMaT (Format-Preserving Multilingual Translation), a parallel corpus of 3,956 PDFs across 15 language pairs that preserves original layout metadata proposed for multimodal machine translation. To ensure structural diversity in the dataset, we employ K-Medoids sampling over 45 geometric features, capturing complex elements like nested tables and formulas to focus only on visually diverse PDF documents. Our evaluation reveals that current MT systems struggle with spatial grounding and geometric synchronization, often losing the link between text and its visual context. ForMaT provides a benchmark for developing layout-aware translation models that integrate visual and textual context for high-fidelity document reconstruction.
Science Journals
arXiv:2605.15883v1 Announce Type: cross
Abstract: Precise control of magnetic domain formation at the nanoscale remains constrained by stochastic defect-mediated and unstable pinning, limiting scalability and reproducibility in spintronic architectures. Here we demonstrate that spatially engineered anisotropy gradients provide a deterministic alternative. Using focused Ga+-ion irradiation, we pattern magnetic energy landscapes containing nanoscale "anisotropy wells" that confine magnetic domain walls and enable bidirectional sequential switching without reliance on difficult-to-control material disorder. An analytical framework describing domain-wall energetics in graded anisotropy profiles yields predictive design rules for depinning and stability, which are supported by micromagnetic simulations and experiments. We realize programmable multi-domain configurations in continuous ferromagnetic films and demonstrate robust, reproducible switching of 750 nm regions, while first results for 100 nm are shown, approaching the theoretical limit set by the domain-wall width. By replacing unstable pinning with engineered energy landscapes, this anisotropy landscape establishes a scalable materials strategy for deterministic magnetic-state programming and opens a pathway toward dense, energy-efficient spintronic and reconfigurable magnetic nanodevices.
arXiv:2605.16070v1 Announce Type: cross
Abstract: Antibody-based therapeutics-including antibody-drug conjugates (ADCs), bispecific antibodies, and novel formats-are reshaping oncology, yet key determinants of efficacy, safety, and manufacturability frequently emerge after conjugation and formulation. We argue that computational biophysics provides an underexploited framework to address this gap by connecting molecular interactions to biological outcomes. We highlight how molecular dynamics, coarse-grained simulations, and free energy calculations reveal how conjugation site, linker chemistry, and drug-antibody ratio reshape conformational landscapes. We emphasize structural coupling between antibody, linker, and payload, with implications for antigen binding, internalization, and developability. We propose that integrating physics-based modeling into development pipelines-alongside experimental validation-can reduce empirical iteration and de-risk translation. As force fields, and hybrid physics-machine-learning methods improve, this field is poised to become a central driver of next-generation ADC design.
arXiv:2512.01089v2 Announce Type: replace
Abstract: Automated Scientific Discovery (ASD) systems can help automatically generate and run code-based experiments, but their capabilities are limited by the code they can reliably generate from parametric knowledge alone. As a result, current systems either mutate a small number of manually-crafted experiment examples, or operate solely from parametric knowledge, limiting quality and reach. We introduce CodeDistiller, a system that automatically distills large collections of scientific Github repositories into a vetted library of working domain-specific code examples, allowing ASD agents to expand their capabilities without manual effort. Using a combination of automatic and domain-expert evaluation on 250 materials science repositories, we find the best model is capable of producing functional examples for 74% of repositories, while our downstream evaluation shows an ASD agent augmented with a CodeDistiller generated library produces more accurate, complete, and scientifically sound experiments than an agent with only general materials-science code examples. We also evaluate LLM-as-a-judge ratings against domain-expert ratings in an A/B testing paradigm, finding moderate agreement and suggesting that inexpensive proxy metrics may be feasible for evaluating scientific discovery systems at scale.
arXiv:2605.14324v2 Announce Type: replace-cross
Abstract: We analyze convergence rates of norm-minimization-based outer approximation algorithms for convex vector optimization when the scalarization uses an $\ell_p$ norm with $p \in (1,\infty)$. While the Euclidean case ($p=2$) achieves the optimal rate $O(k^{2/(1-q)})$, the behavior under general $\ell_p$ norms has remained open. A direct approach via the modulus of smoothness yields only the weaker exponent $\min(p,2)$, which degrades for $1 < p < 2$. We prove that the Hausdorff approximation error satisfies $\delta_H(P_k, A) = O(k^{2/(1-q)})$ for \emph{every} $p \in (1,\infty)$, where $q$ is the number of objectives and $k$ is the iteration count. The proof introduces a Euclidean intermediary technique that exploits the ambient inner product structure of $\R^q$ to obtain a quadratic bound on the hyperplane distance, bypassing the $\ell_p$ smoothness limitation; norm equivalence then converts this to any $\ell_p$ metric at the cost of only a dimension-dependent constant, not a loss of exponent. Numerical experiments confirm the $p$-independent rate predicted by the theory.
arXiv:2605.16112v1 Announce Type: new
Abstract: Transformer-based architectures have become the dominant paradigm for Continuous-Time Dynamic Graph (CTDG) learning, yet their performance remains limited on temporally shifted datasets. In this work, we identify attention dispersion as a shared failure mode of dynamic graph Transformers under temporal distribution shift. Through controlled ablation contrasting structurally and temporally distinguished historical neighbors against random ones, we show that prediction depends on a class of critical nodes that carry consistently more predictive signal than arbitrary neighbors. However, existing Transformers fail to focus on these nodes even when they are present in the input, as temporal shift weakens attention contrast and produces overly dispersed attention distributions. This diagnosis suggests a simple and transferable fix: replace standard attention with differential attention, which suppresses common-mode attention and amplifies distinctive token-level signals. When added to three representative CTDG Transformer baselines, differential attention consistently improves performance, with gains concentrated on high-shift datasets. Attention-level measurements further confirm the mechanism, showing reduced attention entropy and increased attention mass on critical nodes. Building on these findings, we introduce DiffDyG, a reference implementation combining differential attention with standard input encodings. Across 9 benchmarks and three negative sampling protocols, DiffDyG achieves SOTA performance, with especially large gains on the most shifted datasets.
arXiv:2605.15800v1 Announce Type: cross
Abstract: The Alliance for Open Media (AOMedia) has developed the AV2 video coding standard to supersede AV1, aiming for substantial compression efficiency gains across diverse media applications. This paper details the quality and performance evaluation methodology defined in the AV2 Common Test Conditions (CTC), which introduces new evaluation methods and content, including convex-hull-based adaptive streaming (AS) configuration, user-generated content (UGC), and extended chroma formats. We present the coding gains of the AV2 (v13.0) against the AV1 baseline. Experimental results show that AV2 achieves significant Bj{\o}ntegaard-Delta Rate (BD-rate) reductions of 29.81\% and 33.79\% for PSNR-YUV and VMAF, respectively, under random access configuration, validating the efficiency of AV2 for next-generation streaming applications.
arXiv:2605.15688v1 Announce Type: cross
Abstract: Concept Activation Vectors (CAVs) are a fundamental tool for concept-based explainability in deep learning, yet their practical utility is limited by statistical instability. We analyze the stochastic nature of CAVs and the Testing with CAVs (TCAV) method, deriving the distributions of major CAV classes including PatternCAV, FastCAV, and ridge regression-based CAVs. We then identify a fundamental flaw in the standard TCAV score: its reliance on a discontinuous indicator function induces non-decaying variance in critical regimes. To address this, we introduce $\alpha$-TCAV, a generalized framework that replaces the indicator with a parameterized smooth function, yielding a unified probabilistic formulation that subsumes both TCAV and Multi-TCAV. We characterize the induced distributions of sensitivity scores and different TCAV variants, showing that established state-of-the-art choices lack theoretical justification. We provide principled guidance on tuning the parameter in $\alpha$-TCAV -- either to imitate Multi-TCAV at substantially lower computational cost, or to obtain a calibrated Bayes-optimal probabilistic measure of a concept's influence. Finally, our analysis yields practical recommendations that challenge established routines: most notably, allocating the full sampling budget to a single CAV rather than splitting it across several.
arXiv:2605.15707v1 Announce Type: cross
Abstract: Whole-heart multi-compartment CT segmentation is clinically important, but standard CNNs do not explicitly enforce anatomical plausibility. Based on statistics derived from the training data, we evaluate whether lightweight explicit shape priors, implemented as shape-aware losses and spatial label distribution heatmap-guided U-Net variants, improve 3D cardiac segmentation on MM-WHS CT and WHS++. Across all experiments, a standard 3D U-Net surprisingly remained a very strong baseline, with handcrafted priors yielding at best marginal and inconsistent changes and often degrading performance. These results suggest that the baseline already captures substantial implicit anatomical regularities and that future gains will likely require more expressive learned priors rather than simple handcrafted anatomical shape constraints.
arXiv:2605.15793v1 Announce Type: new
Abstract: Pre-training neural operators on diverse partial differential equation (PDE) datasets has emerged as a promising direction for building general-purpose surrogate models in scientific machine learning. However, the inherent complexity and structural diversity of PDE solution operators make multi-PDE pre-training fundamentally challenging. Existing methods mainly address this by increasing model capacity, while leaving the target solution operators unchanged. Inspired by classical numerical analysis, we instead propose to transform complex and diverse solution operators into simpler, better-aligned forms that are easier to model jointly. Since the optimal transformation varies across PDE types, it must be adaptive and input-dependent, allowing a single neural operator to approximate an entire family of operators. We instantiate this idea as AOT-POT (adaptive operator-transformation for pre-training operator transformer), which expands hidden representations into multiple parallel streams, adaptively aggregates and redistributes them before and after each sub-layer, and mixes streams through Sinkhorn-projected doubly stochastic matrices for stable training. These mechanisms together reshape diverse solution operators into a unified form that can be effectively modeled by a single architecture. Empirically, AOT-POT achieves state-of-the-art performance on 12 PDE benchmarks with only 3\% additional parameters, reducing relative L2 error by up to 77.6\% (40.9\% on average). Fine-tuning AOT-POT further reduces L2 error by up to 92\% on in-domain PDEs and 89\% on out-of-domain PDEs (unseen types during pre-training), demonstrating that adaptive operator transformation is an effective and complementary direction for advancing PDE foundation models beyond simply scaling model capacity.
arXiv:2605.16249v1 Announce Type: cross
Abstract: Entanglement and interference are among the most fundamental properties of quantum mechanics. In this work, we investigate the role and power of interference in the context of detecting entanglement. We do so from a computational complexity lens by proving that unentanglement gives no additional power to stoquastic Merlin-Arthur verification. For every polynomial number of provers $k=k(n)$, \[
\text{StoqMa}(k)=\text{StoqMa} . \] Conceptually, the proof separates the role of entanglement from the role of interference: once destructive interference is ruled out by stoquasticity, the product-state constraint can be absorbed into a polynomially larger one-witness stoquastic verification.
The main analytic ingredient is a positive, value-based de Finetti theorem for separately symmetric extensions. If $M$ is an entrywise nonnegative positive semidefinite contraction on $A_1\otimes\cdots\otimes A_k$, then the nonnegative product value of $M$ is approximated to additive error $\epsilon$ by the largest eigenvalue of \[
\Pi_R^{<k}
(M_{A_{1,1}\cdots A_{k-1,1}A_k}\otimes I)
\Pi_R^{<k},
\qquad
R=O\!\left(\frac{k^2\sum_i\log\dim A_i}{\epsilon^3}\right), \] where $\Pi_R^{<k}$ is the operator on $A_1^{\otimes R} \otimes \cdots \otimes A_{k-1}^{\otimes R} \otimes A_k$ projecting to the subspace $\mathrm{Sym}^R(A_1) \otimes \cdots \otimes \mathrm{Sym}^{R}(A_{k-1}) \otimes A_k$.
The spectral relaxation is then realized as an actual one-witness stoquastic verifier. After replacing the uniform permutation averages in the symmetric projectors by inverse-polynomially close dyadic inverse-invariant averages. Consequently, \[
\text{StoqMa}(k)=\text{StoqMa}\subseteq\text{AM}\cap\text{PP}\subseteq\text{PSPACE} . \] The positive de Finetti theorem is isolated as a standalone technique and may be useful in other nonnegative tensor-optimization and stoquastic-verification settings.
arXiv:2605.15792v1 Announce Type: new
Abstract: The long-standing goal of multimodal AI is to build unified models in which visual understanding and visual generation mutually enhance one another. Despite recent works such as BAGEL, BLIP3o achieves remarkable progress; In practice, however, this unification remains one-directional: understanding routinely guides generation, yet how and why generation can support understanding is rarely investigated. We revisit this asymmetry and propose Generation-to-Understanding (G2U) synergy, where visual generation becomes an explicit intermediate reasoning step. Our framework enables a model to perform controlled generative acts, such as detail enhancement, context expansion or structural visualisation, to produce self-generated visual thoughts, which are then fed back into the model to refine perception without retraining or external tools. Through a comprehensive evaluation on twelve benchmarks, this reversed information flow consistently improves multimodal understanding. We show that generative fidelity bounds perceptual gain and that distinct families of edit prompts govern transfer efficiency. We further analyse whether models can decide what to imagine. While they can produce plausible edits, these self-generated visual thoughts lack stable task alignment, revealing that current large multimodal models fall short of true self-reflection. This work exposes a missing mechanism in unified cognition and suggests that imagination is not the end of understanding but its beginning.
arXiv:2605.15865v1 Announce Type: new
Abstract: Large Language Models (LLMs) have shown increasing potential in automating model-driven software engineering tasks, particularly in generating models conforming to Domain Specific Languages (DSLs) from natural language. While most existing approaches rely on large proprietary models, their high cost and limited deployability hinder broader adoption.
In this paper, we evaluate whether open-source LLMs of varying sizes (0.5B to 32B parameters) can generate DSL-conformant models using only few-shot prompting, without any fine-tuning. Our evaluation focuses on key model-driven engineering (MDE) requirements, including syntactic validity, semantic completeness, and inter-model reference consistency.
We extend our prior work by moving from generating user interface models (referred to as "UI models" in this paper) over fixed, predefined data schemas ("data models") to generating both the UI and data models entirely from scratch. This shift serves two purposes: first, it highlights the LLM's ability to infer domain-specific relationships and maintain consistency across multiple interconnected models; second, it allows us to generalize earlier findings by testing DSL generation across models of different natures and structural roles. Our structured evaluation combines automatic parsing and expert feedback across 39 LLMs, revealing that several compact models (e.g., \texttt{gemma3:12b}, \texttt{mistral:7b-instruct}) approach or match the quality of much larger models.
These findings demonstrate the feasibility of using smaller, open-source LLMs for grammar-conformant DSL generation in MDE workflows, offering a cost-effective and deployable alternative to closed LLMs.
arXiv:2605.15808v1 Announce Type: cross
Abstract: Integrated sensing and communication (ISAC) relies on monostatic sensing (MS) and bistatic positioning (BP) to enable comprehensive environmental awareness and user localization. However, existing frameworks predominantly assume static geometries and optimize these modalities independently, neglecting user mobility and sequential information sharing. In this paper, we propose a velocity-aware sequential beamforming framework that dynamically couples MS and BP in time. We derive the Cramer-Rao bounds (CRBs) in the position domain to formulate a non-convex resource allocation problem. Instead of relying on static weighted-sum tradeoffs, we introduce a sequential Bayesian optimization strategy where MS is executed first to construct a reliable structural prior on the UE and passive targets (PTs). This covariance prior is subsequently passed to the UE to regularize the BP estimation stage. We demonstrate that optimizing a single shared beamformer globally across both phases yields superior synergistic gains compared to a two-stage greedy approach. Simulation results validate that the shared sequential design efficiently balances limited symbol resources, achieving centimeter-level positioning accuracy for both the UE and PTs, robust velocity estimation, and a significantly reduced computational runtime.
arXiv:2605.15642v1 Announce Type: cross
Abstract: Nuclear-powered submarines are difficult to track with conventional methods in congested waterways. We revisit antineutrino-based detection as a barrier concept, analogous to a neutrino-enabled SOSUS-style fence in strategic straits. Using analytic scaling relations and numerical estimates, we show that detectability depends primarily on closest approach, detector depth, and deployed mass. For representative assumptions, a 20\,kt detector in the Strait of Gibraltar reaches a local benchmark score $Z_A\simeq2.54$ for an assumed 100\,MW thermal-power sensitivity-study case in a conservative worst-case transit (with Poisson operating point $(P_\mathrm{FA},P_\mathrm{det})\simeq(5.5\times10^{-3},0.51)$ at threshold $k=2$), while a three-detector line raises the mapped score to $Z_A\simeq4.66$. For broad ocean passages such as GIUK, required detector counts are substantially larger; in the baseline maximum passing distance $\mathrm{PDD}_{\max}=5$\,km geometry, about 80 detectors yield only $Z_A\sim1.6$. The paper outlines detector technology choices, statistical assumptions, and deployment constraints for a first-generation feasibility assessment.
arXiv:2605.15656v1 Announce Type: cross
Abstract: Under the trend of multi-waveform coexistence in 6G IoT, intelligent receivers must first identify physical-layer waveform types before performing correct demodulation and resource scheduling. However, existing signal identification research largely focuses on symbol-level modulation classification. Research directly targeting physical-layer waveform types (e.g., OFDM, OTFS, LoRa) is not only extremely scarce but also heavily reliant on deep neural networks and complex time-frequency transforms, making deployment on resource-constrained terminals difficult. Symbol modulation classification methods themselves cannot circumvent the prerequisite of ``waveform identification first.''
To address this dual gap, we propose an ultra-lightweight waveform classification framework based on time-frequency multidimensional features with a cooperative Z-test tree (ZTree). The framework employs low-complexity time-domain feature extraction, and the classification backend adopts a ZTree optimized by Z-statistical testing, which uses hypothesis testing confidence to automatically control decision tree splitting and size, ensuring efficient execution on resource-limited processors. Tested on ten 6G candidate waveforms including OFDM, OTFS, DSSS, LoRa, and NB-IoT, the method achieves 99.5\% average accuracy under AWGN and 87.4\% under TDL-C multipath channels, with main confusion between OTFS and LoRa. Implemented in C on an x86 platform, single inference latency is under 4~ms. To the best of our knowledge, this is the first work achieving real-time recognition of ten IoT waveform types. Future work will target deployment acceleration on embedded MCUs. Code and dataset are open-sourced at: https://github.com/Einstein-sworder/IoT-wave.
arXiv:2605.15579v1 Announce Type: cross
Abstract: To fit diverse display and bandwidth constraints, high-frame-rate videos are temporally downscaled to low-frame-rate (LFR) and later upscaled, requiring joint optimization for effective frame-rate rescaling. However, existing methods typically link the two operations via training objectives, without fully exploiting their reciprocal nature, which may cause high-frequency information loss. Moreover, they overlook the impact of lossy codecs on LFR videos, limiting real-world applicability. In this work, we propose an end-to-end framework for compression-aware frame-rate rescaling, named TVRN. To regularize high-frequency information lost during frame-rate downscaling, TVRN adopts an invertible architecture that combines a Multi-Input Multi-Output Temporal Wavelet Transform with a high-frequency reconstruction module. To enable end-to-end training through non-differentiable lossy codecs, we design a surrogate network that approximates their gradients. Finally, to improve robustness under various compression levels, we extend TVRN to an asymmetric architecture by incorporating compression-aware features learned via a learning-to-rank strategy. Extensive experiments show that TVRN outperforms existing methods in reconstruction quality under industrial video compression settings. Source code is publicly available at https://github.com/fengxinmin/TVRN_public.
arXiv:2602.22918v3 Announce Type: replace
Abstract: Vision-language models (VLMs) can read text from images, but where does this optical character recognition (OCR) information enter the language processing stream? We investigate the OCR routing mechanism across three architecture families (Qwen3-VL, Phi-4, InternVL3.5) using causal interventions. By computing activation differences between original images and text-inpainted versions, we identify architecture-specific OCR bottlenecks whose dominant location depends on the vision-language integration strategy: DeepStack models (Qwen) show peak sensitivity at mid-depth (about 50%) for scene text, while single-stage projection models (Phi-4, InternVL) peak at early layers (6-25%), though the exact layer of maximum effect varies across datasets. The OCR signal is remarkably low-dimensional: PC1 captures up to 72.9% of variance. Crucially, principal component analysis (PCA) directions learned on one dataset transfer to others, demonstrating shared text-processing pathways. Surprisingly, in models with modular OCR circuits (notably Qwen3-VL-4B), OCR removal can improve counting performance (up to +6.9 percentage points), suggesting OCR interferes with other visual processing in sufficiently modular architectures.
arXiv:2605.16101v1 Announce Type: cross
Abstract: Measurement is an important scientific activity. In most of science, including classical physics, is may be understood as a way of finding out about the physical world and representing the results numerically. No-go theorems show that measurement of quantum observables is not like that: the recorded outcome is typically created rather than revealed in a quantum measurement, in which case there is no objective fact about the observable's prior value. Other no-go theorems show that unitary quantum theory can generally neither explain nor even represent a unique recorded outcome, thereby threatening that outcome's objectivity. Methodological norms inherent in quantum physical practice nevertheless institute the objectivity, not only of unique recorded outcomes of quantum measurements, but also of non-quantum features of the world that physicists and other scientists take their models to represent.
arXiv:2605.16109v1 Announce Type: new
Abstract: The increasing environmental impact of the telecom industry has heightened the need for sustainable telecommunications networks. With skyrocketing data traffic and 5G gaining a foothold, telecom operators are under pressure to sustain digital growth while meeting their environmental responsibilities. In this paper, we discuss two fundamental drivers of sustainability in the telecom sector, namely, the design of environmentally friendly networks and the implementation of circular economy (CE) principles. Energy efficiency is pursued through dynamic network sleep modes, AI-based traffic management, and the utilization of renewable energy sources in base stations and data centers. Concurrently, circular economy practices, including device second-hand sales, e-waste treatment, and equipment lifespan extension, are becoming increasingly popular to address resource demand and mitigate carbon footprint. Case histories from the world's largest operators demonstrate some of the reductions in power consumption and operational emissions, as well as the associated savings and public image benefits. Although these solutions are promising, the paper also highlights several limitations, including technology constraints, policy shortcomings, and the need for cross-sector partnerships. We conclude with research implications in the form of a sustainable perspective that integrates the green adoption of technology, circular supply chains, and the role of regulation in driving long-term environmental and economic sustainability in the telecom industry.
arXiv:2507.08752v3 Announce Type: replace
Abstract: We investigate the propagation of initial value perturbations along the solution of a linear ordinary differential equation \( y'(t) = Ay(t) \). This propagation is analyzed using the relative error rather than the absolute error. Our focus is on the long-term behavior of this relative error, which differs significantly from that of the absolute error. The present paper is a practical sequel to the theoretical papers \cite{M1,M2} on the long-time behavior of the relative error: it includes applicative examples and important issues not addressed in \cite{M1,M2}. In addition, the present paper shows that understanding the long-term behavior provides insights into the growth of the relative error over all times, not just at large times. Therefore, it represents a crucial and fundamental aspect of the conditioning of linear ordinary differential equations, with applications in, for example, non-normal dynamics.
arXiv:2605.11485v2 Announce Type: replace
Abstract: Imitation learning powered by generative models has proven effective for modeling complex single-agent behaviors. However, teaching multi-agent systems, like multiple arms or vehicles, to coordinate through imitation learning is hindered by a fundamental data bottleneck: as the joint state-action space grows exponentially with the number of agents, collecting a sufficient amount of coordinated multi-agent demonstrations becomes extremely costly. In this work, we ask: how can we leverage single-agent demonstration data to learn multi-agent policies? We present Coordinated Diffusion (CoDi), a framework that couples independently trained single-agent diffusion policies through a user-defined multi-agent cost function, without requiring any coordinated demonstrations. We derive a new diffusion-based sampling scheme wherein the diffusion score function decomposes into independent, single-agent pre-trained base policies plus a cost-driven guidance term that coordinates these base policies into cohesive multi-agent behavior. We show that this guidance term can be estimated in a gradient-free manner, making CoDi applicable to black-box, non-differentiable cost functions without additional training. Theoretically and empirically, we analyze the conditions under which this composition can faithfully approximate a target multi-agent behavior. We find a complementary role for demonstration data versus the cost function: single-agent demonstrations must cover the support of the desired multi-agent behavior, while the cost function must promote desired behavior from this product of single-agent policies. Our results in simulation and hardware experiments of a two-arm manipulation task show that CoDi discovers robust coordinated behavior from single-agent data, is more data-efficient than multi-agent baselines, and highlights the importance of joint guidance, base policy support, and cost design.
arXiv:2507.08762v3 Announce Type: replace
Abstract: We are interested in the relative
conditioning of the problem $y_0\mapsto \mathrm{e}^{tA}y_0$, i.e., the
relative conditioning of the action of the matrix exponential $\mathrm{e}%
^{tA}$ on a vector with respect to perturbations of this vector. The present paper is a qualitative study of the long-time behavior of this
conditioning. In other words, we are interested in studying the propagation to the solution $y(t)$ of perturbations of the initial value for a linear ordinary differential equation $y^\prime(t)=Ay(t)$, by measuring these perturbations with relative errors. We introduce three condition numbers: the first considers a specific initial value and a specific direction of perturbation; the second considers a specific initial value and the worst case by varying the direction of perturbation; and the third considers the worst case by varying both the initial value
and the direction of perturbation. The long-time behaviors of
these three condition numbers are studied.
arXiv:2507.01679v3 Announce Type: replace
Abstract: Existing LLMs-post-training techniques are broadly categorized into supervised fine-tuning (SFT) and reinforcement fine-tuning (RFT). Each paradigm presents a distinct trade-off: (1) SFT excels at mimicking demonstration data, but can lead to problematic generalization as a form of behavior cloning. (2) Conversely, RFT can significantly enhance a model's performance but is prone to learning unexpected behaviors, and its performance is sensitive to the initial policy. In this paper, we propose a unified view of these methods and introduce Prefix-RFT, a hybrid approach that synergizes learning from both demonstration and exploration. Using mathematical reasoning problems as a test bed, we empirically demonstrate that Prefix-RFT is simple yet effective. Not only does it surpass the performance of standalone SFT and RFT, but it also outperforms parallel mixed-policy RFT methods. Our analysis highlights the complementary nature of SFT and RFT, validating that Prefix-RFT effectively harmonizes them. Further ablation studies confirm the method's robustness to variations in the quality and quantity of demonstration data.
arXiv:2605.15438v1 Announce Type: cross
Abstract: The fluidic pinball presents a significant benchmark for nonlinear flow control, managing the complex interactions of three cylinder wakes. This study addresses the stabilization of the fluidic pinball to its unstable steady-state solution using a model-based nonlinear feedback strategy. We propose a framework that combines interpolatory model order reduction (IMOR) with the quadratic-quadratic regulator (QQR), a feedback control methodology that is specifically suited to the quadratic nonlinearity of the Navier-Stokes equations. A finite element model (FEM) of the problem coupled with IMOR is used to produce a reduced-order model (ROM) that accurately represents the input-output dynamics of the actuated wake. The performance of the QQR control is evaluated against the traditional linear feedback control for two different Reynolds numbers, $Re_D = 30$ and $Re_D = 50$. At $Re_D = 30$, the QQR controller is able to stabilize the wake and reaches the desired performance criteria 40.1\% faster than using a linear feedback controller. More significantly, at $Re_D = 50$, the QQR controller successfully stabilizes the wake, whereas the linear controller fails to overcome the nonlinearity of the flow. The QQR control effectively suppresses vortex shedding, resulting in the elimination of lift oscillations and a reduction in the drag coefficient. These results demonstrate that the IMOR-QQR framework provides an effective model-based control strategy that can manage nonlinear hydrodynamic instabilities in such complex wake flows.