Papers

Vehicular networks require timely visual information exchange to support safety-critical applications such as cooperative perception and hazard awareness, yet transmitting high-dimensional camera data over bandwidth-limited and dynamic wireless links remains challenging. In this paper, we propose an adaptive semantic communication architecture for vehicular multicast that adjusts the amount of visual information transmitted according to current channel conditions, available communication resources, and latency requirements. Specifically, the visual encoder uses residual quantization to represent each image at multiple bitrate and reconstruction-quality levels. At runtime, the system selects an appropriate level based on the communication conditions, enabling it to trade visual fidelity for lower transmission overhead when network resources are limited. Context-adaptive entropy coding further compresses the quantized representations using offline-learned statistics, without requiring retraining for different channel conditions. This design allows the visual representation to be learned offline while the communication strategy is adapted online. Experimental results demonstrate competitive rate-distortion performance at ultra-low bitrates, improved delivery reliability and deadline satisfaction across diverse vehicular scenarios, and strong downstream perception performance, achieving up to 0.88 mAP50 while dynamically adapting to changing communication conditions.

Quantum fidelity estimation is a fundamental task in quantum information and computing to benchmark the quality of quantum states, and hence of quantum processes, on noisy quantum hardware. Point estimates of fidelity by existing methods generally lack the rigorous uncertainty quantification required for reliable preparation and verification of these tasks. While Bayesian and bootstrap frameworks are widely used for uncertainty quantification, they are sensitive to model misspecification or lack formal coverage guarantees in non-asymptotic regimes. This paper introduces a hybrid "Bayesian-informed" conformal prediction-based framework to provide distribution-free, rigorous prediction intervals for quantum state fidelity estimation which can be used, with care, to approximate confidence intervals with respect to the quantum randomness of Born's rule. The framework requires a point estimator, and we consider both classical point estimators as well as data-driven neural net estimators. We evaluate the robustness of the methodology across a diverse range of experimental challenges, including finite-sample noise, tomographic incompleteness, physical model error, and out-of-distribution data. Our results demonstrate that conformalized estimators maintain statistical validity where traditional methods fail, offering a scalable and reliable approach for the verification of modern quantum systems. The best performing variant of our methodology is based on a class-conditional conformal prediction, as this most closely approximates the conditional coverage desired for a true confidence interval.

We prove that the analytic Besov space $B_{p,p}^{1/p}(\C_+^n)$ embeds continuously into Chang–Fefferman product BMO for every finite $n$ and $1\le p<\infty$. Consequently, every small Hankel operator in a finite Schatten class has a product BMO symbol. The proof uses smooth product wavelets and an estimate for dyadic rectangles. We also give a condition on Fejér means that yields a BMO symbol for a bounded Hankel operator on the polydisc.

Moving horizon estimation (MHE) is an estimation technique that formulates an optimization problem over a past horizon to find the states that require the minimum disturbances and noise to be feasible with the dynamics and measurements. For hybrid systems with both continuous and discrete states, this yields a mixed-integer program for the MHE, which can be difficult both to formulate and solve online under computational limitations. This paper shows how the hybrid zonotope representation for mixed-integer sets can be used to efficiently construct the feasible space for the program using reachability-based calculations for piecewise affine systems, without requiring conversion to a mixed logical dynamical system. A method for lifting the state space to explicitly estimate the dynamic mode is also presented. The proposed approach is evaluated in two numerical examples. Comparison against a standard mixed logical dynamical systems approach shows the proposed method can be solved orders of magnitude faster for one of the example problems.

In this work, we formulate decentralized continual learning within a multi-objective optimization framework. For a given inference task t (corresponding to a common minimizer shared by the cost functions of all agents), agents collecting data in a distributed and streamed manner are only allowed to perform local computations and to exchange information with neighboring agents over the underlying communication graph. As tasks evolve sequentially over time, agents must adapt to newly arriving tasks while retaining knowledge acquired from previously learned ones. This requirement leads to the wellknown stability plasticity dilemma, where stability refers to the ability to retain previous knowledge, while plasticity refers to the ability to learn and adapt to new tasks. To address the stability challenge, agents store subsets of samples from past tasks in local memory buffers. Then, through an appropriate multiobjective formulation, the stored information is incorporated into the learning process so that parameter updates account jointly for the current task and previously learned tasks. The proposed decentralized continual learning approach is analyzed in the mean square error sense under general assumptions on the individual cost functions and gradient noise processes. The analysis reveals that cooperation among agents improves the performance of continual learning. In particular, by exchanging information with neighboring agents, decentralized collaborative learning can exploit the diversity of locally observed data and memory buffers to improve the network average mean-square deviation (MSD) across tasks. Finally, simulations illustrate the theoretical findings and the effectiveness of the method in reducing forgetting and improving the average MSD across tasks.

We find the exact rate of equidistribution of several arithmetic point configurations in Wasserstein metric and $L^2$ discrepancy with respect to balls. Kronecker sequences in the torus and the Fibonacci lattice on the Euclidean unit sphere are shown to be more evenly distributed in Wasserstein metric than random points. Modular hyperbolas and modular parabolas in the torus behave like random points, although the constants in the asymptotics of the $L^2$ discrepancy with respect to balls differ from the random case. We also prove a sharp inequality between the quadratic Wasserstein metric and the $L^2$ discrepancy with respect to balls for an arbitrary probability measure on the torus or the sphere. In particular, we show that any point set that is optimally close to the uniform measure in $L^2$ discrepancy with respect to balls is also optimal in the quadratic Wasserstein metric.

We provide effective bounds on adjoint line bundles on $X$ for which the secant variety $\Sigma(X)$ satisfies property $N_{3,p}$. The given bounds only depend on $\operatorname{dim}(X)$ and $p$.

Molecular dynamics (MD) simulations model the motion of proteins between conformational states, but crossing free energy barriers and sampling multiple thermodynamic conditions remain computationally costly. We recently introduced MD-LLM-1, which showed that language models can generate conformational trajectories at lower cost, but required a separate model for each protein and did not explicitly model thermodynamics or kinetics. Here we introduce MD-LLM-2, a transferable language model that generates trajectories conditioned on sequence, temperature and molecular history. Because each step defines a normalized distribution over structural tokens, the model assigns an explicit likelihood to every generated or simulated trajectory. Trained across mdCATH domains, MD-LLM-2 reproduces the median radius of gyration of MD within 1 Angstrom in 10 of 12 unseen domains, predicts reduced Trp-cage compaction at higher temperature, and generates L99A T4 lysozyme trajectories that reach published transition-region backbone structures. In alanine dipeptide simulations, conditioning on a torsional scaling parameter $\lambda$ predicts basin populations at unseen couplings with a mean absolute error of 0.09 versus 0.35 for MBAR, and first-passage probabilities with an error of 0.08 versus 0.16 for a reversible Markov state model. Frame-isoentropic sampling further limits the accumulation of errors during autoregressive trajectory generation. Together, these results extend MD-LLM from protein-specific trajectory generation to transferable, physically conditioned modelling with explicit path likelihoods, and show that the framework can predict equilibrium populations for force-field parameters not seen during training, with an initial indication that first-passage kinetics can also be captured.

On-policy distillation (OPD) efficiently transfers capabilities from a stronger teacher to a student language model through dense token-level supervision on student-generated rollouts and has shown promise on complex tasks such as mathematical reasoning. However, in multi-turn agentic tasks, student decisions shape subsequent observations, causing early errors to accumulate across turns. The resulting trajectories can drift away from the teacher's rollout distribution, making the teacher's token-level supervision less reliable or even counterproductive for OPD training. To address this issue, we introduce STI-OPD, a stochastic teacher intervention framework for multi-turn agentic OPD. During multi-turn interaction, STI-OPD uses teacher intervention guided by teacher-student policy discrepancy to replace the student's proposed action with a teacher-generated one to maximize the acquisition of reliable supervision. We further develop a stochastic intervention strategy, addressing the limitations of previous threshold-based or fixed-schedule approaches, that estimates policy discrepancy using KL divergence and maps it to an intervention probability. By sampling whether to intervene from this probability, STI-OPD adaptively balances teacher control with student exploration. To learn from the resulting mixed-policy trajectories, we introduce an Importance-Weighted Reverse KL objective that corrects the token sampling mismatch between teacher-generated responses and the student policy to preserve the original OPD objective. Across tool-integrated reasoning and long-horizon interaction, STI-OPD outperforms the strongest prior OPD baseline on every evaluated benchmark and student size. Ablations further show that both discrepancy-guided intervention and importance weighting contribute to these gains.

The underwater sound speed distribution directly governs acoustic propagation paths, rendering it critically important for underwater acoustic communication and target localization. Conventional sound speed profile (SSP) prediction methods provide a good way to estimate the underwater sound speed distribution without on-site data measurement, thus breaking through the coverage area constraints of sonar observation equipment and making the model universal in most marine areas. However, underwater sound speed exhibits multi-scale variations, such as diurnal, quarterly, and intermittent fluctuations caused by ocean processes such as internal waves. This makes it difficult for the fixed structure models in existing methods to have good generalization ability for multi-scale sound speed distribution patterns. To tackle this problem, we proposed a lightweight hybrid basis-function empowered Kolmogorov-Arnold network (LHBF-KAN) model for multi-scale sound speed prediction. We aim to construct a multi-branch representation layer in which different basis functions respond to distinct temporal patterns, from slowly varying background trends to rapid fluctuations induced by dynamic ocean processes, allowing the model to naturally accommodate the inherently multi-scale evolution of sound speed at different depths. To prevent the multi-branch structure from increasing model size, a pruning strategy is further introduced to suppress branches with consistently low contribution during training, yielding a compact architecture, suitable for deployment on resource constrained underwater platforms.

Distributed satellites can deliver broadband connectivity directly to commercial handsets. In the formation of arrays (FoA) architecture, cooperating satellites synthesize a large aperture whoseextent depends on their number, arrangement, and spacing, with intersatellite distances ranging from tens of meters to hundreds of kilometers. For representative S-band geostationary and low-Earth-orbit configurations, the Fraunhofer distance may exceed the nadir link range at spacings on the order of a hundred meters. Therefore, accurate assessment of FoA performance across satellite populations and spacings requires spherical-wave modeling for users in the radiative near field, below the formation's Fraunhofer distance. Planar models of satellite positions, array orientations, and user locations must also be assessed against spherical geometries accounting for orbital and Earth curvature. This paper combines these models to quantify how simplifying assumptions affect throughput and outage probability. Numerical results show that multi-antenna precoding based on a local plane-wave approximation within each satellite array closely matches the spherical-wave reference. A global plane-wave approximation can instead cause severe losses, including full outage. In the investigated scenarios, formation curvature has little impact, whereas neglecting Earth curvature overestimates low-Earth-orbit throughput. These findings clarify when geometric and propagation approximations remain reliable and demonstrate that, for large distributed antenna apertures, space is much closer than one might think.

Motivated by recent applications in generative modeling and sampling, we introduce a framework for optimal measure transport where cost captures the notion of neural network complexity. In transport-based generative models, samples from a reference distribution (e.g. Gaussian) are mapped to samples of a target distribution along ordinary or stochastic differential equations. These are implemented as deep residual networks when discretized in time, where each hidden layer approximates the associated instantaneous velocity. Thus, given a pair of target and reference measures, a natural question is to search for the most efficient neural representation that implements this transport. Our starting point is the kinetic formulation of OT, due to Benamou and Brenier. We replace the average kinetic $L^2$ energy by the Barron energy \cite{bach2017breaking, ma2022barron}, a natural norm which measures the complexity of representing a given vector field with a neural hidden layer, and which captures the adaptive properties of feature learning. This defines a metric on the space of probability measures, complementing existing Wasserstein and Stein geometries. In this work we examine the properties of this metric in the context of generative modeling. As a first application, we quantify the suboptimality of diffusion generative modeling in the Barron geometry by establishing super-polynomial score approximation lower bounds for data generated by neural network pushforwards of the Gaussian. We then investigate the benefit of adaptivity as a way to study alternative generative models. In a companion paper \cite{companionpaper} we leverage the Barron transport geometry for sampling applications, extending the scope of Stein variational gradient methods via feature adaptation.

Ceramic materials are inorganic, predominantly nonmetallic solids whose performance is governed by the interplay among atomic bonding, crystal structure, processing, microstructure, and functional properties. Their ionic and covalent bonding provides high hardness, thermal and chemical stability, wear resistance, and diverse electrical behavior, but also limits plastic deformation and increases sensitivity to flaws, porosity, grain boundaries, and residual stresses. This review examines ceramics through the processing–microstructure–property–performance relationship, emphasizing the effects of crystal chemistry, defects, grain size, porosity, and phase stability on mechanical, thermal, electrical, and biological behavior. Conventional sintering, sol–gel processing, and additive manufacturing are discussed as key routes for controlling densification, porosity, geometry, and composition. Biomedical ceramics, including alumina, zirconia, calcium phosphates, hydroxyapatite, tricalcium phosphate, and bioactive glasses, are also reviewed. Emerging topics include nanoceramics, smart ceramics, composites, multimaterial manufacturing, defect engineering, immunomodulatory bioceramics, and sustainable processing. Major challenges remain in brittle fracture, processing heterogeneity, degradation control, scale-up, and the porosity–strength trade-off. Future advances will require integrating advanced manufacturing, multiscale characterization, predictive modeling, and data-driven design.

One-to-one matching without replacement is a classical approach to constructing comparable treated and control samples in the design of observational studies. It pairs each treated unit with a distinct control while minimizing a covariate distance objective. With continuous covariates, the matched pairs generally remain inexact, which contributes to bias in downstream analysis. Its key theoretical properties, such as the resulting imbalance between matched pairs and when it is negligible to support valid inference, remain unclear. In this paper, we analyze one-to-one matching based on $d$-dimensional, continuous covariates with a quadratic covariate-distance objective. First, we find that when $d\leq 3$, under standard conditions on the propensity score ensuring abundant control samples near each treated sample, the imbalance (difference between within-group averages) is root-$n$ negligible uniformly over the family of smooth functions with a common first- and second-order derivative bound. However, such balance is subject to a dimension restriction, as we construct examples in which the imbalance is root-$n$ non-negligible when $d=4$ and dominates root-$n$ rate when $d>4$. Second, we show that when $d\leq 3$, the matched design allows valid Wald-type and bootstrap inference for the average treatment effect on the treated, distributional treatment effects, and quantile treatment effects. Thus, the same outcome-blind matched design supports various downstream inferences without having to tailor the design to the targets. Finally, paired randomization inference based on the matched design is asymptotically valid in the super-population sense for $d\leq 3$ but can fail when $d=4$. We corroborate the theoretical results with numerical experiments.

We describe a general method for selecting an orthonormal basis of carrier waveforms that aligns the basis with delay / Doppler characteristics of a wireless channel. We show that our method enables low-complexity equalization for two channels of practical interest. The first is satellite communication and the second is communication from a ground station to an unmanned aerial vehicle (UAV). After Doppler compensation both scenarios are characterized by a first line of sight (LOS) path with zero delay and zero Doppler shift, and a second weaker path. We show that our method is robust to fractional delay and Doppler shifts. We consider orthonormal bases of carrier waveforms that are obtained from the pulsone basis of Zak-OTFS carrier waveforms by applying a generalization of the discrete affine Fourier transform (GDAFT). This family of waveforms includes AFDM and other modulations proposed for 6G. What distinguishes these bases is that the carrier waveforms are common eigenvectors of some maximal commutative subgroup S of a Heisenberg-Weyl group of discrete delay and Doppler shifts. We describe how to choose S to mitigate the damaging effects of interference between carriers. We represent the wireless channel by delay-Doppler taps and observe that a channel tap located within S multiplies every waveform by a complex phase. If all channel taps are located within S, then the channel multiplies every waveform by a complex phase, and a single tap equalizer supports reliable communication. This is the case for a linear time-invariant (LTI) channel, where S is the group of discrete time shifts and the carrier waveforms are discrete tones (OFDM). In general, we choose the subgroup S to maximize the diagonal component of the channel energy.

Large Language Models (LLMs) achieve strong performance across many domains, but their efficiency is limited by the quadratic cost of attention with respect to prompt length. Sparse attention reduces this cost by retaining only a small fraction of query-key interactions to approximate the full attention matrix. However, existing methods are trapped in a mathematically wrong view: they simply keep large scalar entries or high-mass regions of the attention matrix. This treats the attention matrix as a bag of values, ignoring that it is used as a structured matrix whose entries jointly determine the attention output through multiplication with value vectors. We argue that this is the core conceptual issue: sparse attention should be formulated as matrix approximation, not as blindly choosing the largest values from a bag of entries. Based on this view, we propose Matrix Approximation Sparse Attention (MASA). MASA replaces raw attention-mass ranking with a closed-form score that measures how much each sparse unit reduces matrix-product approximation error. As a theory-grounded plug-in correction, MASA can be added to existing sparse attention frameworks without changing their sparse kernels or budgets. Extensive experiments across multiple sparse attention methods, benchmarks, and LLM backbones show consistent accuracy gains, supporting both MASA and the matrix-approximation view of sparse attention.

Markov chain Monte Carlo (MCMC) methods are the standard tool for computing expectations under complex probability distributions. Control variates reduce the variance of the resulting estimates, but a good control variate requires solving the Poisson equation of the sampler, which rarely admits a closed-form solution. Exact solutions are available when the sampler's kernel has a known spectral decomposition on a simple reference density. In our work, we extend these solutions to general targets through a learned change of variables. A bijection, such as a normalizing flow, is trained so that the target becomes close to the reference in a latent space, and we show that Markov kernels and their Poisson solutions are transformed by any bijection. Running such samplers in the latent space then yields explicit control variates, and the estimator is consistent under mild tail conditions on the map and target. Importance sampling (IS) from the flow is the limiting case of the same construction and the control variates apply to it as well. Experiments on synthetic targets and real posteriors compare the procedure against state-of-the-art samplers and control variates.

This paper characterizes the spectral and Ambiguity Function (AF) properties of Frequency Modulated Orthogonal Frequency Division Multiplexing (FM-OFDM) waveforms employing Phase-Shift Keying (PSK). The mainlobe structure of the AF is well approximated by the Ellipse of Ambiguity (EOA) model. The EOA produces exact closed-form expressions that describe the AF mainlobe width in time-delay and Doppler as well as the degree of coupling between them. These expressions yield three fundamental insights into the spectral and AF shapes of FM-OFDM waveforms employing PSK: (1) these waveforms possess a fixed Root Mean Square (RMS) bandwidth for a given modulation index $h$, pulse-length $T$, and number of sub-carriers $L$, (2) they are roughly twice as spectrally efficient as Constant Envelope OFDM (CE-OFDM) waveforms with the same RMS bandwidth, and (3) for practical waveform design parameters will always possess a “Thumbtack-Like” AF shape. Finally, this paper demonstrates a waveform optimization technique that minimizes the FM-OFDM waveform's Auto-Correlation Function (ACF) sidelobes using only a subset of the sub-carrier symbols as sensing “pilot” symbols leaving the rest for communications. This pilot optimization technique is then demonstrated via two illustrative design examples.

We introduce Conversational Voice Aesthetic Model, a speech large language model for describing the voice aesthetics of real or synthetic speech responses in natural conversational contexts. Given a context and a response speech, CVAM describes salient moments that characterize the voice and predicts nine categorical attributes spanning gender, pitch, pacing, emotion, and delivery. The key challenge lies in perceptual fields such as emotion and delivery, which are inherently subjective and lack definitive ground truth. Therefore, we collect ~10 human annotations for each of 3k real and synthetic responses derived from the CANDOR corpus. CVAM is supervised finetuned on synthesized aesthetic descriptions and labels, then optimized with Group Relative Policy Optimization on human judgments. Experiments show that CVAM better agrees with human listeners than Gemini 3.1 Pro and open-source speech LLMs, and outperforms single-human-vs.-rest agreement. Together, we demonstrate the importance of grounding voice aesthetics in human perception and propose a principled framework for human alignment.

Complex Network (CN) classification requires high-level structural characterizations that are both scale-invariant and computationally efficient. Methods based on Life-Like Network Automata (LLNA) offer an interesting way to extract network descriptors by leveraging emergent temporal patterns without requiring provided features, but their efficacy is bottlenecked by a high-cost combinatorial optimization problem: the selection of the automaton transition rule. While current literature relies on exhaustive searches that are unfeasible for large-scale applications, this work reveals that the rule space is fundamentally structured by a property we term “jaggedness”, that quantifies the resemblance of a LLNA transition function with a sawtooth shape. We demonstrate that this metric acts as a theoretical proxy for chaoticity and sensitivity – properties essential for generating discriminative dynamic behaviors among network categories. Moreover, we introduce a heuristic search strategy that uses jaggedness to guide the rule selection. Experimental results show that our approach achieves classification accuracies within 5% of the global optimum while reducing computational overhead by 90% compared to exhaustive approach. Our findings provide a novel, efficient, framework for optimizing automata-based methods for pattern recognition.

We study the observational features of thin-disk accretion and emission spectra for static, spherically symmetric dyonic black holes in non-linear electrodynamics (NLED). In contrast to classical Maxwell theory, where electromagnetic duality assumes equal charges, the coupling parameters in NLED introduce a new gravitational potential and modify the geometry in the strong-field regime. We also study the kinematic characteristics of particles on circular orbits, such as their angular velocity, specific energy, and specific angular momentum. It is found that modifications of NLED lead to a shrinkage of the ISCO radius, resulting in a shift of the radiation spectrum thermal maximum towards smaller radii and, consequently, an increase in the local effective temperature in comparison with the standard Schwarzschild and Reissner-Nordström solutions. Additionally, we compute null-geodesic orbits to determine the optical edge of both the photon sphere and the black hole shadow. In order to assess the observational validity of the aforementioned alternatives, we carry out a $\chi^2$ goodness-of-fit test through the angular diameter constraints at the horizon scale collected by the Event Horizon Telescope (EHT) concerning Sagittarius A* ($\text{Sgr A}^*$). We prove that both these dyonic NLED and purely magnetic models have good statistical agreement with experimental data.

Self-supervised speech encoders contain linguistic and paralinguistic information in a shared, entangled representation space. We combine a TopK sparse autoencoder with route-specific supervision and cross-factor adversaries. Across frozen SPEAR and WavLM encoders, independent probes show factor-specific retention and suppression: linguistic information remains stronger in the linguistic route, while paralinguistic factors, including speaker identity, emotion, and prosody, are retained in the paralinguistic route and substantially reduced in the linguistic route. The route organisation learned on LibriSpeech persists on MSP-Podcast without representation-side retraining. Feature-space route interventions further transfer the swapped factor while largely preserving the information carried by the unchanged route. These results show consistent route-selective separation across encoders, corpora, independent probes, and representation-level interventions.

Large language models (LLMs) exhibit us-vs.-them bias: A behavioral asymmetry in which prompts framed around an ingroup (“we”/“us”) receive systematically more positive continuations than matched prompts framed around an outgroup (“they”/“them”). Using Edge Attribution Patching (EAP), we localize this behavior to directed circuits in GPT-2 Small, GPT-2 Large, Llama-2 7B, and Llama-3 8B. Across models, high-attribution edges are sparse and concentrated primarily in middle-to-late layers, while ingroup- and outgroup-related pathways are only partially overlapping and reorganize under fine-tuning. Behavioral comparisons and 30-token generations show that the measured asymmetry extends beyond next-token evaluation. Targeted patching of EAP-ranked edges reduces the bias score more than equal-cardinality random-edge controls, but also substantially degrades performance on CoLA, HellaSwag, and WikiText-2, suggesting that bias-relevant pathways are functionally entangled with broader language capabilities. Overall, our findings characterize us-vs.-them bias as a sparse, context-dependent, and functionally entangled computational phenomenon whose internal organization varies across the models examined.

We introduce multilevel Picard (MLP) approximations of McKean-Vlasov stochastic differential equations (SDEs) with jumps of finite or infinite activity. Under Lipschitz and integrability assumptions on the coefficients, we show that the MLP algorithm does not suffer from the curse of dimensionality when approximating the solution of the McKean-Vlasov SDE. The latter means that its computational cost grows at most polynomially in both the state-space dimension of the SDE and the reciprocal of the prescribed error tolerance. In two numerical experiments, we demonstrate the practical applicability of the MLP algorithm for two different McKean-Vlasov SDEs in dimensions up to 200.

Modeling heterogeneous materials remains a challenge for physics-informed neural networks such as the deep energy method (DEM). The DEM and its variants, here collectively referred to as the neural energy method (NEM), offer a differentiable variational framework. However, their conventional collocation-based implementation (C-NEM) often suffers from physically inadmissible displacement oscillations, integration errors, and high computational costs from automatic differentiation. This work introduces the mesh-based neural energy method (M-NEM), extending the NEM through a mesh-based discretization of the displacement field. By interpolating nodal displacements via shape functions, the M-NEM imposes a kinematic constraint that suppresses oscillations. Furthermore, the method replaces automatic differentiation with algebraic shape function derivatives for strain computation and employs high-order Gaussian quadrature for accurate energy integration. On a directly comparable benchmark problem, the M-NEM reduces stress errors by up to three orders of magnitude relative to the C-NEM while being one to two orders of magnitude faster. On two further benchmarks involving extreme stiffness contrasts, only the M-NEM converges. A comparative study of neural architectures reveals that radial basis function neural networks (RBFNNs) yield optimal performance within the M-NEM, resolving sharp gradients at material interfaces with higher accuracy than multi-layer perceptrons (MLPs) with random Fourier feature (RFF) mapping and faster convergence than Kolmogorov-Arnold networks (KANs).

In this paper, we investigate the quantum behaviour near the classical singularity of a black hole. We describe the black-hole interior by the Kantowski-Sachs metric, with a string propagating in this region. This approach is motivated by the fact that, near the classical singularity, spacetime curvature reaches Planck or string scales, necessitating a description in terms of string-theoretic degrees of freedom. The string dynamics is formulated via the Polyakov action, and the combined system is canonically quantized to derive the corresponding Wheeler-DeWitt equation. Although the equation is separable in the radial and azimuthal string sectors, the remaining geometric and string degrees of freedom are nontrivially coupled. To address this, we employ a perturbative approach and obtain the wave function up to first order. At the zeroth-order, the angular part is described by the general Heun function, while the geometric part is expressed in terms of the Bessel function. The first-order wave function is governed by a source term containing the zeroth-order solution, and we obtain its explicit expression in terms of the complementary function and the particular integral. We confirm regularity of the wave function at both zeroth and first order, at the singularity as well as at the horizon. Regularity at the horizon imposes a discretization condition on one eigenvalue, while another eigenvalue is quantized due to the azimuthal periodicity of the wave function. Importantly, both zeroth- and first-order solutions satisfy the DeWitt boundary condition, implying resolution of the black hole singularity within this quantum framework.

We establish nearly-matching converse bounds on the sample complexity of estimating the average mixing time of a Markov chain from a single stationary trajectory. Unlike the worst-case mixing time, which maximises the total-variation distance to stationarity over all initial states, the average mixing time averages this distance under the stationary distribution and can therefore be substantially smaller. Our converse bounds establish when estimation is impossible, and match the key dependencies in existing achievability bounds, up to logarithmic factors. Together, these bounds provide nearly-tight PAC guarantees for estimating the average mixing time.

Text-to-image diffusion models are increasingly distilled into few-step variants and being deployed to enable fast inference. However, their ability to generate harmful or undesired content poses significant safety risks. Data-driven unlearning methods suppress targeted generations by fine-tuning model weights using specialized unlearning objectives. Crucially, these objectives implicitly rely on multi-step denoising dynamics, an assumption that breaks down for few-step distilled (FSD) models, resulting in ineffective forgetting. Furthermore, performing unlearning on the non-distilled base model and subsequently re-distilling it to obtain an unlearned FSD model incurs substantial computational and time overhead, making it impractical in many settings. Hence, we address this limitation with a preference-driven unlearning framework that revisits Direct Preference Optimization (DPO) for diffusion models. We show that standard DPO and its unlearning derivatives, formulated around noise-prediction error, transfer poorly to FSD models due to their altered generation dynamics. To overcome this, we introduce a modified preference optimization formulation explicitly aligned with the few-step generation properties, enabling direct concept removal in FSD models while preserving few-step efficiency and maintaining strong retention of desirable (non-targeted) capabilities. We evaluate our framework primarily on identity and NSFW (nudity) removal tasks and also extend our method to object-level unlearning. Extensive experiments demonstrate consistent and effective forgetting, and strong retention performance, establishing our method as a practical and principled solution for unlearning in FSD models.

Analog/RF circuits remain the critical interface between digital computation and the physical world, and emerging standards from Wi-Fi 7 to 6G place stringent demands on them, yet analog/RF design remains one of the most labor-intensive steps in chip development. We present RFChipAgent, a first-of-its-kind multi-agent flow of large language model (LLM) agents for end-to-end analog/RF circuit design automation, in which AI agents collaboratively orchestrate the complete design flow under human supervision. RFChipAgent is built around four technical pillars. First, a multimodal retrieval-augmented generation (RAG) subsystem with private per-document FAISS indexing extracts design knowledge from existing engineering documentation. Second, a topology agent drives topology selection, and a schematic and testbench agent automates circuit and testbench assembly. Third, a closed-loop hybrid circuit-sizing engine combines Tree-structured Parzen Estimator (TPE) and CMA-ES optimization, evaluating every candidate in a simulator-in-the-loop framework. Fourth, a trust-scored simulation database accumulates verified performance data and builds an adaptive optimization model that informs subsequent trials. We validate RFChipAgent on a family of GF22FDSOI 60 GHz wideband mm-wave low-noise amplifier (LNA) topologies, demonstrating automated topology generation, specification-driven design-space exploration, and simulator-guided optimization. Experimental results show substantial reductions in design effort while maintaining signoff-quality verification. This work establishes a foundation for LLM-driven multi-agent electronic design automation (EDA) for analog/RF circuits.

Behavior cloning (BC) in non-Markovian environments is a challenging problem because policies have to reason over contextual information over long horizons. Existing policy architectures rely on recurrent or attention-based mechanisms to capture long-term dependencies. However, recurrent models suffer from hidden-state collapse and gradient instability under backpropagation through time, while attention-based models are fundamentally limited by context length. To address these issues, we propose Keyframe Mnemonics, a novel self-supervised method that $\textit{discovers}$ a set of information-critical observations ($\textit{mnemonics}$) by learning an objective from randomly sampled past observations and using it as a reward for keyframe selection. We then train a BC policy that conditions on the discovered keyframes to model the action distribution. Under certain task-structure assumptions, our formulation provides context retention guarantees over an infinite horizon, while maintaining a small set of decision-relevant keyframes in the policy's working memory. We evaluate our method on synthetic memory domains, where mnemonic-conditioned BC policies achieve $100$% success rates (SR) and generalize to horizons orders of magnitude beyond training without performance degradation. Additionally, we evaluate on memory-intensive robot manipulation benchmark, achieving a $13.9$% average absolute SR improvement over the strongest baseline across $23$ tasks and retaining $80$% SR at $20\times$ longer horizons on a real robot. Code and videos are available at https://keyframe-mnemonics.github.io.