arXiv:2605.18005v1 Announce Type: new
Abstract: Many real-world combinatorial problems involve uncertain parameters, which can be predicted given contextual features and historical data. These `predict-then-optimize' or `contextual optimization' problems have gained significant attention: end-to-end training methods can now minimize the downstream task cost rather than the predictive error. However, despite their effectiveness, these decision-focused learning (DFL) approaches often rely on repeated solving of the underlying combinatorial optimization problem during training, making them computationally expensive and difficult to scale. We reframe the learning problem as a cost-sensitive multi-output regression problem: multi-output due to the combinatorial problem having multiple uncertain parameters, and cost-sensitive due to the downstream task cost being the real target. Our technical contribution is the formalization of multiple loss function components that follow from this reframing: cost-insensitive normalization, decision-aware asymmetric penalization of over- and underpredictions, and instance-based costs that mimic the true downstream task-based loss locally. These components require zero or one solve per training data instance, while requiring no further solves during training. Experiments show that the combination of loss components achieves comparable downstream task quality to the state of the art, while being significantly more efficient, enabling scaling to problem sizes that have not been tackled before with DFL.
Science Journals
arXiv:2510.14699v2 Announce Type: replace
Abstract: Model checking for real-timed systems is a rich and diverse topic. Among the different logics considered, Metric Interval Temporal Logic (MITL) is a powerful and commonly used logic, which can succinctly encode many interesting timed properties especially when past and future modalities are used together. In this work, we develop a new approach for MITL model checking in the pointwise semantics, where our focus is on integrating past and maximizing determinism in the translated automata.
Towards this goal, we define synchronous networks of timed automata with shared variables and show that the past fragment of MITL can be translated in linear time to synchronous networks of deterministic timed automata. Moreover determinism can be preserved even when the logic is extended with future modalities at the top-level of the formula. We further extend this approach to the full MITL with past, translating it into networks of generalized timed automata (GTA) with future clocks (which extend timed automata and event clock automata). We present an SCC-based liveness algorithm to analyse GTA. We implement our translation in a prototype tool which handles both finite and infinite timed words and supports past modalities. Our experimental evaluation demonstrates that our approach significantly outperforms the state-of-the-art in MITL satisfiability checking in pointwise semantics on a benchmark suite of 72 formulas. Finally, we implement an end-to-end model checking algorithm for pointwise semantics and demonstrate its effectiveness on two well-known benchmarks.
arXiv:2510.15221v2 Announce Type: replace
Abstract: Affective computing has matured rapidly in laboratory settings, yet no prior dataset combines (i) months-to-years of duration, (ii) a naturalistic workplace context, (iii) a stable small-team social structure, and (iv) a fully passive sensing protocol that survives institutional review. We introduce WELD, the first dataset to satisfy all four. WELD comprises 733,780 per-frame seven-class facial-expression probability vectors from 49 employees of a Chinese software company over 30.1 months (Nov 2021 - May 2024) -- the longest naturalistic in-the-wild emotion corpus and the only multi-year corpus supporting both within-individual longitudinal and within-team relational analyses on the same subjects. Data are released under a four-tier access model with only aggregated probabilities publicly downloadable. We validate the corpus by replicating three established phenomena (+43.1% weekend valence boost; 13:00-trough diurnal cycle; Shanghai 2022 lockdown effect d=-0.40), and report four novel findings: (1) variance decomposition attributes 19.3% of daily-valence variance to between-person differences and 29.8% to month seasonality -- a quantitative ceiling for future predictive models; (2) Hidden Markov decomposition reveals six emotional regimes with asymmetric negative-state dwell times (16-18 d vs 3 d); (3) leave-one-person-out turnover prediction reaches AUC=0.79 yet a Cox concordance index of only 0.52, exposing a metric-trap when AUC is reported without survival-aware baselines; (4) the corpus reveals systematic over-prediction of "angry" by an off-the-shelf FER model on neutral Asian faces (0.194 vs ~0.05 Western priors), making WELD valuable for FER fairness audits. A complex-systems analysis of the corpus appears as a companion preprint (arXiv:2510.16046).
arXiv:2509.26597v4 Announce Type: replace
Abstract: Control Barrier Functions (CBFs) provide a powerful framework for ensuring safety in dynamical systems. However, their application typically relies on full state information, which is often violated in real-world due to the availability of partial state information. In this work, we propose a neural network-based framework for the co-design of a safety controller, observer, and CBF for partially observed continuous-time systems with input constraints. By formulating barrier conditions over an augmented state space, our approach ensures safety without requiring bounded estimation errors or handcrafted barrier functions. All components are jointly trained by formulating appropriate loss functions, and we introduce a validity condition to provide formal safety guarantees beyond the training data. Finally, we demonstrate the effectiveness of the proposed approach through several case studies.
arXiv:2605.17772v1 Announce Type: new
Abstract: Physical adversarial attacks often overfit single surrogate models and optimization objectives. While ensemble attacks can mitigate this, existing methods struggle with severe gradient conflicts within restricted physical texture spaces, significantly degrading cross-model transferability. To bridge this gap, this paper proposes a Joint Multi-Objective and Multi-Model Optimization Framework (JMOF) that leverages quantitative similarity analysis to select the optimal surrogate model ensemble. Within JMOF, a dual-level mechanism jointly suppresses prediction outputs and flattens intermediate feature distributions, balancing attack efficiency with deep generalization. Additionally, an Orthogonal Gradient Alignment (OGA) strategy resolves cross-model gradient conflicts, transforming mutually repulsive gradients into synergistic optimization directions. Extensive simulated and real-world experiments demonstrate that JMOF outperforms state-of-the-art baselines against diverse black-box detectors. Crucially, JMOF exhibits substantial cross-vision-task generalization, generating attacks capable of simultaneously deceiving object detection and semantic segmentation or monocular depth estimation models. This research advances the generalization limits of physical adversarial attacks, providing a robust framework for evaluating visual AI vulnerabilities in real-world deployments.
arXiv:2605.16337v1 Announce Type: cross
Abstract: Sub-diffusion in biological systems is conventionally treated as anomalous, requiring fractional derivatives, heavy-tailed waiting times, or fitted memory kernels. We argue that this anomaly is an artifact of an incomplete phase space. Standard frameworks model diffusing particles as points. Biological molecules are not points. They are three-dimensional deformable entities whose position, orientation, and internal structure are irreducible physical properties, not modeling conveniences appended to a point mass. Within the Extended Structural Dynamics (ESD) framework, each particle is a primitive structured entity with translational, orientational, and deformational degrees of freedom. When dynamics on this full phase space are projected onto the translational subspace alone, a memory kernel emerges from the projection without phenomenological postulate. The subdiffusion exponent is determined by the internal mode spectrum, independently measurable from B-factors, NMR order parameters, or molecular dynamics simulations, without fitting to transport data. Four falsifiable predictions follow: subdiffusion strength correlates with molecular flexibility; temperature drives crossover to normal diffusion at a characteristic energy scale set by internal mode frequencies; a non-zero rotation-translation cross-correlation spectrum encodes internal dynamics, identically zero in point-particle models; and memory timescales scale as the square of particle size. Quantitative consistency with experimental observations for proteins in crowded media is demonstrated using independently estimated structural parameters. What appears anomalous from the point-particle perspective is the expected behavior of structured matter projected onto an impoverished description. The anomaly is not in the physics. It is in the phase space.
arXiv:2605.17928v1 Announce Type: new
Abstract: Transfer Learning, a technique where a model/agent can use the knowledge/expertise that it gained from one task and exploit that to solve another closely-related task, is often used in tackling problems in deep learning. Through this project, we explore transfer learning in the purview of deep reinforcement learning. Specifically, we want to use transfer learning to achieve the fast lap times in OpenAI's Car racing environment by training the agent on one circuit, and racing it on other customized target environments by zero-shot transfer or by additional fine-tuning. In addition, we compare the performance of model-based and model-free approaches, and observe that model-based approaches dominate in performance and converge faster than model-free approaches in this environment. We observe that transfer learning in most setups not only boosts the performance on the target domain, but also shows high performance ability during learning.
arXiv:2601.02244v2 Announce Type: replace
Abstract: We derive a state-space characterization of all dynamic state-feedback controllers that make an equilibrium of a nonlinear input-affine continuous-time system locally exponentially stable. Specifically, any controller obtained as the sum of a linear state-feedback $u=Kx$, with $K$ stabilizing the linearized system, and the output of internal locally exponentially stable controller dynamics is itself locally exponentially stabilizing. Conversely, every dynamic state-feedback controller that locally exponentially stabilizes the equilibrium admits such a decomposition. The result can be viewed as a state-space nonlinear Youla-type parametrization specialized to local, rather than global, and exponential, rather than asymptotic, closed-loop stability. The residual locally exponentially stable controller dynamics can be implemented with stable recurrent neural networks and trained as neural ODEs to achieve high closed-loop performance in nonlinear control tasks.
arXiv:2605.17787v1 Announce Type: new
Abstract: It is widely believed that stochastic gradient descent (SGD) performs significantly worse than adaptive optimizers such as Adam in pre-training Large Language Models (LLMs). Yet the underlying reason for this gap remains unclear. In this work, we attribute a large part of the discrepancy to SGD's inability to sustain learning rates comparable to Adam's much larger effective learning rates. Through empirical and theoretical analysis of LLM pre-training dynamics, we identify that training is characterized by small gradient norms and large weight-to-gradient ratios, an effect that becomes more pronounced with larger batch sizes typical in pre-training, necessitating such large effective learning rates. However, we find that output-layer gradient magnitudes become highly uneven across token classes, and that large gradient spikes frequently occur during training. Together, these effects severely restrict the admissible learning rate of SGD. Guided by this understanding, we show that simple clipping mechanisms that stabilize SGD at large learning rates enable it to recover most of Adam's performance. In our large-scale experiments, the validation loss gap between large-learning-rate SGD and Adam shrinks from more than 50% to only about 3.5% when pre-training a 1B-parameter LLaMA model with a 1M-token batch size.
arXiv:2605.17791v1 Announce Type: new
Abstract: Wireless resource allocation in digital-twin-enabled unmanned aerial vehicle (UAV) swarms must be both network-feasible and certifiably safe for closed-loop control.
Existing packet-level or scalar-priority schedulers cannot meaningfully compare heterogeneous multi-hop actions that differ simultaneously in route, retransmission depth, blocklength, bidirectional delay, delivery probability, and TDMA slot cost.
This paper introduces a certificate-guided resource allocation framework for low-altitude multi-hop UAV swarms.
A digital twin maps predicted topology, channel, route, and controller-side state into a shared five-dimensional quality-of-service (QoS) certificate comprising uplink/downlink delay bounds, directional delivery guarantees, and a certified upper bound on the interval between successful bidirectional interactions.
A state-conditioned stochastic drift test then admits only certificates whose augmented Lyapunov drift is nonpositive under the current controller state.
Admitted actions are reduced to certified supply frontiers by removing dominated route-slot configurations, and the online scheduler maximizes Lyapunov-drift reduction under a shared TDMA slot budget via exact dynamic programming.
Closed-loop ns-3 simulations demonstrate that the proposed framework outperforms fixed-service, certificate-filtered fixed-priority, dynamic-transmission-count, and value-of-information baselines in both tracking accuracy and high-risk state suppression under identical communication budgets.
arXiv:2510.15712v3 Announce Type: replace
Abstract: How hard is it to find a local optimum? If we are given a graph and want to find a locally maximal cut--meaning that the number of edges in the cut can't be improved by moving a single vertex from one side to the other--then just iterating improving steps finds a local maximum in $ |E|$ steps. If, on the other hand, the edges are weighted, this problem becomes hard for the class PLS (Polynomial Local Search). We are interested in optimization problems with lexicographic costs. For Max-Cut this would mean that the edges $e_1,\dots, e_m$ have costs $c(e_i) = 2^i$. For such a cost function finding a global Max-Cut is easy. In contrast, we show that it is PLS-complete to find an assignment for a 4-CNF formula that is locally maximal (when the clauses have lexicographic weights); and also for a 3-CNF when we allow switching two variables at a time. We use these results to answer a question in Scheder and Tantow, who showed that finding a lexicographic local minimum of a string $s \in \{0,1\}^n$ under the action of a list of given permutations $\pi_1, \dots, \pi_k \in S_{n}$ is PLS-complete. They ask whether the problem stays PLS-complete when the $\pi_1,\dots,\pi_k$ commute, i.e., generate an Abelian subgroup $G$ of $S_n$. We show that it does, and in fact stays PLS-complete even (1) when every element in $G$ has order two or (2) when $G$ is cyclic. Additionally, we use it to further investigate the complexity of computing pure $\alpha$-Nash equilibria in congestion games. Using lexicographic 4-SAT, we obtain a simple proof of the PLS-completeness originally shown by Skopalik and V\"ocking that can be extended to exponential and polynomial delay functions with positive coefficients. The number of strategies per player and players per resource is bounded. However, the degree of the polynomials is not bounded by a constant.
arXiv:2411.10636v3 Announce Type: replace
Abstract: In this study, we investigate extrinsic gender bias in Bangla pretrained language models, a largely underexplored area in low-resource languages. To assess this bias, we construct four manually annotated, task-specific benchmark datasets for sentiment analysis, toxicity detection, hate speech detection, and sarcasm detection. Each dataset is augmented using nuanced gender perturbations, where we systematically swap gendered names and terms while preserving semantic content, enabling minimal-pair evaluation of gender-driven prediction shifts. We then propose RandSymKL, a randomized debiasing strategy integrated with symmetric KL divergence and cross-entropy loss to mitigate the bias across task-specific pretrained models. RandSymKL is a refined training approach to integrate these elements in a unified way for extrinsic gender bias mitigation focused on classification tasks. Our approach was evaluated against existing bias mitigation methods, with results showing that our technique not only effectively reduces bias but also maintains competitive accuracy compared to other baseline approaches. To promote further research, we have made both our implementation and datasets publicly available: https://github.com/sajib-kumar/Mitigating-Bangla-Extrinsic-Gender-Bias
arXiv:2605.18410v1 Announce Type: new
Abstract: Identifying which newly published scientific papers are likely to become highly cited is important for prioritizing research attention, supporting editorial decisions, and guiding the allocation of scientific resources, particularly under cold-start conditions where little direct evidence is available at publication time. In this work, we formulate impact prediction as a cohort-normalized top-P% classification task and compare graph-based and LLM-based approaches under a unified framework. We construct citation and textual-similarity graphs under temporal constraints and generate Node2Vec representations, either alone or combined with OpenAI text embeddings. The best supervised configuration combines directed citation graphs with textual embeddings, reaching approximately 0.84-0.85 AUC. We also evaluate a GPT-based GraphRAG setup, using GPT 5.5 and 5.4 Nano, in which graph neighborhoods are used as contextual evidence for prediction. Although the LLM-based approach achieves high performance, retrieved context does not consistently improve results; target-only prompts often perform as well as or better than GraphRAG prompts achieving the 0.87 mark. These findings indicate that structural and textual signals are complementary for supervised prediction, while retrieval augmentation must be carefully evaluated against simpler LLM baselines.
arXiv:2605.18229v1 Announce Type: new
Abstract: Sparse autoencoders (SAEs) are a core interpretability tool for large language models, and progress on SAE architectures depends on benchmarks that reliably distinguish better SAEs from worse ones. We audit the SAE quality metrics in SAEBench, the de-facto standard SAE evaluation suite, through three complementary lenses: reseed noise on a fixed SAE, ground-truth correlation on synthetic SAEs, and discriminability across training trajectories. We find that two of these metrics, Targeted Probe Perturbation (TPP) and Spurious Correlation Removal (SCR), fail multiple lenses at their canonical settings and should not be used to evaluate SAEs. The other metrics show higher reseed noise and lower discriminability than the field assumes. The sae-probes variant of $k$-sparse probing is the most reliable metric we tested, but even sae-probes struggles to separate variants of the same SAE architecture. Our results show the field needs better SAE benchmarks.
arXiv:2605.18572v1 Announce Type: new
Abstract: Persuasive dialogue generation plays a vital role in decision-making, negotiation, counseling, and behavior change, yet it remains a challenging problem. In complex persuasion where the persuadee's internal states are not expressed clearly, the persuader must interpret responses, infer the persuadee's latent mental states (e.g., beliefs and desires), and translate them into targeted, strategy-consistent actions; however, current approaches often produce generic or weakly grounded responses even when such cues are identified. Moreover, although large language models (LLMs) can generate persuasive content, their performance varies substantially across domains due to uneven knowledge coverage and limited reasoning generalization. To address these challenges, we propose MA$^{2}$P, a meta-cognitive autonomous intelligent agent framework for complex persuasion. Specifically, we develop an autonomous multi-agent architecture that coordinates perception management, mental-state inference, strategy execution, memory maintenance, and performance evaluation. To mitigate cross-domain performance variation, we further design a meta-cognitive configurator that selects an appropriate meta-strategy from a structured knowledge base at the outset, thereby guiding subsequent reasoning and planning. Experimental results show that our approach achieves a higher persuasion success rate than baselines.
Gravity, Fine-Structure Constant and Natural Units -- some Thoughts based on Dimensional Analysis --
arXiv:2605.18637v1 Announce Type: new
Abstract: Here we discuss direct links of the number of fundamental dimensions to the fundamental natural constants using simple arguments of dimensional analysis \corr{based on Maxwell's dimensions length (L), time (T) and mass (M) as well as the constants $G$, $c$, $\hbar$ and $e$}. We find that the \corr{form} of the fine-structure constant is a direct consequence of this connection. Additionally, our approach emphasises that gravity is a quite distinct area of physics which is not yet successfully quantised, i.e. not yet combined with quantum mechanics. We also discuss different unit systems based on dimensional analysis and natural constants.
arXiv:2404.15187v2 Announce Type: replace
Abstract: As machine learning (ML)-based decision support tools proliferate in clinical practice, understanding how clinicians integrate personalized ML predictions alongside randomized controlled trial (RCT) evidence is critical. We designed a web-based clinical decision support system (CDSS) presenting survival and adverse event data from a simulated RCT and ML model across 12 synthetic multiple myeloma scenarios. In a within- subjects study with 32 physicians, we evaluated how clinicians synthesize competing evidence sources to make treatment decisions. When ML and RCT outputs were concordant, physicians reported greater confidence than with RCT data alone. When results were discordant, most physicians shifted toward the ML-supported treatment, often before reviewing any information about model training or validation, suggesting a tendency toward automation bias rather than algorithm avoidance. Despite reporting higher perceived reliability after viewing model quality disclosures, physicians were largely unable to describe the validation procedures they had reviewed. Taken together, these findings reveal that clinicians may over-rely on ML recommendations even when equipped with tools designed to support critical appraisal. We discuss implications for CDSS design, clinician training, and the institutional safeguards needed before ML-based systems are deployed in high-stakes oncology settings.
arXiv:2502.10665v2 Announce Type: replace
Abstract: In this paper, we propose a novel dual-based Lawson's method, termed {b-d-Lawson}, designed for addressing the rational minimax approximation under specific interpolation conditions. The {b-d-Lawson} approach incorporates two pivotal components that have been recently gained prominence in the realm of the rational approximations: the barycentric representation of the rational function and the dual framework for tackling minimax approximation challenges. The employment of barycentric formulae enables a streamlined parameterization of the rational function, ensuring natural satisfaction of interpolation conditions while mitigating numerical instability typically associated with Vandermonde basis matrices when monomial bases are utilized. This enhances both the accuracy and computational stability of the method. To address the bi-level min-max structure, the dual framework effectively transforms the challenge into a max-min dual problem, thereby facilitating the efficient application of Lawson's iteration. The integration of this dual perspective is crucial for optimizing the approximation process. We will discuss several applications of interpolation-constrained rational minimax approximation and illustrate numerical results to evaluate the performance of the {b-d-Lawson} method.
arXiv:2504.14820v2 Announce Type: replace
Abstract: For peg-in-hole tasks, humans rely on binocular visual perception to locate the peg above the hole surface and then proceed with insertion. This paper draws insights from this behavior to enable agents to learn efficient assembly strategies through visual reinforcement learning. Hence, we propose a Separate Primitive Policy (S2P) to learn how to derive location and insertion actions simultaneously. S2P is compatible with model-free reinforcement learning algorithms. Ten insertion tasks featuring different polygons are developed as benchmarks for evaluations. Simulation experiments show that S2P can boost the sample efficiency and success rate even with force constraints. Real-world experiments are also performed to verify the feasibility of S2P. Ablations are finally given to discuss the generalizability of S2P and some factors that affect its performance.
arXiv:2509.24143v2 Announce Type: replace
Abstract: In this paper, we propose a new modeling approach and a fast algorithm for 3D motion planning, applicable for fixed-wing unmanned aerial vehicles. The goal is to construct the shortest path connecting given initial and final configurations subject to motion constraints. Our work differs from existing literature in two ways. First, we consider full vehicle orientation using a body-attached frame, which includes roll, pitch, and yaw angles. However, existing work uses only pitch and/or heading angle, which is insufficient to uniquely determine orientation. Second, we use two control inputs to represent bounded pitch and yaw rates, reflecting control by two separate actuators. In contrast, most previous methods rely on a single input, such as path curvature, which is insufficient for accurately modeling the vehicle's kinematics in 3D. We use a rotation minimizing frame to describe the vehicle's configuration and its evolution, and construct paths by concatenating optimal Dubins paths on spherical, cylindrical, or planar surfaces. Numerical simulations show our approach generates feasible paths within 10 seconds on average and yields shorter paths than existing methods in most cases.
arXiv:2605.17808v1 Announce Type: new
Abstract: We develop a unified theoretical framework for data-free one-step sampling from unnormalized target distributions based on Wasserstein gradient flows. For a broad class of standard f-divergence objectives, we show that the induced velocity field admits the universal form $\mathbf{V}(x)=w(r(x))\,\beta(x)$, where $\beta(x)=\nabla \log (p(x)/q(x))$ is shared across objectives and $w$ is determined solely by the choice of divergence. This decomposition shows that standard f-divergence drifts share the same asymptotic target distribution $p$ and differ primarily in how they redistribute transient repair effort across under-covered regions. To formalize this distinction, we derive a one-step regional-response theory for a soft under-coverage functional and obtain a compression--elasticity identity that links divergence choice to the geometry of mass transport into under-covered regions. We further extend the framework beyond the f-divergence family to the Log-Variance (LV) divergence, analyze how the reference distribution alters the resulting drift structure, and motivate a practical LV-inspired surrogate for data-free training. Based on this theory, we instantiate the framework with a KDE-based implementation and describe a complementary normalizing-flow route, enabling one-step inference after training. Experiments on multimodal Gaussian-mixture benchmarks are consistent with the theoretical predictions and demonstrate effective one-step sampling on these targets.
arXiv:2605.18472v1 Announce Type: cross
Abstract: Generative models can produce nonsensical text, unrealistic images, and unstable materials faster than simulation or human review can absorb; without per-sample confidence, trust erodes. Existing fixes run $k$ ensembles or stochastic trajectories at $k\times$ compute, measuring variability between models, not model confidence. We propose Flow Matching with Confidence (FMwC). FMwC injects input-dependent multiplicative noise at selected layers, propagates its variance through the network in closed form, and integrates it along the ODE trajectory, yielding a per-sample confidence score at standard sampling cost. The score supports multiple uses: filtering improves image quality and thermodynamic stability of crystals; editing rewinds trajectories to the points where the model commits and redirects them; and adaptive stepping concentrates ODE compute where the flow is ambiguous. We find that the confidence score correlates with the magnitude of the divergence of the learned velocity field, which gives us a window to understand the generative process, opening up surgical forms of guidance that target the moments that matter, new sampling algorithms and interpretability of generative models.
arXiv:2605.18335v1 Announce Type: new
Abstract: Let $S\subseteq F_2^u$ have size $n=2^\ell$, and let $h:F_2^u\to F_2^\ell$ be a uniformly random linear map. For $y\in F_2^\ell$, write $Load_h(y):=|h^{-1}(y)\cap S|$, and let $M(S,h):=\max_{y\in F_2^\ell} Load_h(y)$ be the maximum load. Jaber, Kumar and Zuckerman (STOC 2025) proved that the expected maximum load of $h$ on $S$ is at most $16\log n/\log\log n$, matching the fully independent keys-into-bins scale up to constants. Their proof also gives the tail estimate \[
\Pr\left[
M(S,h)\ge R\frac{\log n}{\log\log n}
\right]
\le O\left(\frac{1}{R^{2}}\right). \] We record a base optimization in their exponential-potential method showing that binary linear hashing nearly matches fully independent hashing also at the level of the second-order maximum-load scale. For every $R>1$ satisfying $R\ell^{1-1/R}\ge D\ln\ell$, where $D$ is an absolute constant, we prove \[
\Pr\left[
M(S,h)\ge R\frac{\log n}{\log\log n}
\right]
\le
O\left(
\frac{(\log\log n)^2}{R^2(\log n)^{2-2/R}}
\right). \] Integrating this tail yields \[
E[M(S,h)]
\le
\left(
1+
(1+o(1))
\frac{\log\log\log n}{\log\log n}
\right)
\frac{\log n}{\log\log n}. \] Thus binary linear hashing matches fully independent hashing in the leading term and matches the dominant second-order correction up to a $1+o(1)$ factor.
We also prove, by an independent self-contained argument, a sharp tail bound for one prescribed bucket: for fixed $y\in F_2^\ell$, \[
\Pr[ Load_h(y)>2^a-2]\le \gamma^{-1}2^{-a^2}, \] where $ \gamma=\prod_{j\ge1}(1-2^{-j}) $. A subspace construction shows that this is asymptotically tight even in the leading constant as $ a\to\infty $. However, this controls only a fixed bucket; a direct union bound over all buckets loses a factor $ 2^\ell $.
arXiv:2605.18562v1 Announce Type: cross
Abstract: Accurate estimates of item difficulty are essential for valid assessment and effective adaptive learning. However, for newly created tasks, response data are typically unavailable. Pretesting and expert judgement can be costly and slow, while machine learning methods often require large labelled training datasets. Recent work suggests that large language models (LLMs) may help. However, there is limited evidence on the elicitation procedures and prompt configurations used to emulate experts for difficulty estimation. This study addresses this gap by evaluating three off-the-shelf LLMs as difficulty raters for newly created items without access to response data. Using an item bank from an online learning system, the study examined 6 domains of primary-school mathematics, with empirical difficulty estimates treated as empirical reference. The study used a full factorial design crossing three factors: judgement format (absolute vs pairwise), decision type (hard decisions vs token-probability-based estimates), and prompting strategy (zero-shot vs few-shot). LLM-derived difficulty estimates were compared with empirical difficulties using Spearman rank correlations. Across domains, LLM-based estimates exhibited moderate to strong positive correlations with empirical item difficulties. For simpler arithmetic tasks, some configurations approached the upper end of the accuracy range reported for human experts in previous research. Pairwise comparison consistently outperformed absolute judgement in the absence of additional refinements. However, when token-level probabilities were incorporated and examples of items with known empirical difficulty were provided, the absolute judgement configuration likewise demonstrated moderate-to-high alignment. The study positions LLMs as a promising tool for initial item calibration and offers insights into effective workflow configuration.
arXiv:2605.18638v1 Announce Type: cross
Abstract: A quantitative understanding of the processes that trigger light-induced demagnetization on ultrashort timescales is crucial for achieving an ultrafast, radiation-controlled magnetic response in materials. This milestone is essential for developing next-generation magnetic storage devices and ultrafast magnetic switches. In this theoretical study, we investigated demagnetization triggered in a single magnetic domain by light pulses ranging from a few to a few tens of femtoseconds in duration, with photon energies spanning the optical and X-ray regimes, under strongly non-equilibrium conditions. We predicted a loss of magnetization in the sub-100-fs range in all cases, primarily due to the excitation of the electronic system and the subsequent redistribution of electrons within the magneto-sensitive band. The considered timescales were too short for phonon-mediated processes or inter-site Heisenberg exchange processes to contribute significantly. These findings pave the way for highly accurate, radiation-driven magnetization control in magnetic materials at sub-100-femtosecond timescales with potential practical applications.