Papers

We study universal unequal error protection of a single special message over discrete memoryless channels. We construct a sequence of codes with a decoding rule that does not depend on the channel transition law. We derive an achievable error exponent for the special message while ensuring reliable decoding of the ordinary messages. The resulting exponent strictly improves on the natural equal-error-protection random-coding baseline and remains positive as the rate approaches capacity. For symmetric channels, it converges to the optimal red-alert exponent at capacity.

Haptic shared control in surgical robotics combines human-side and robot-side forces at a shared end effector while preserving operator involvement. However, the effects of geometric safety choices on task execution and force coordination remain unclear. We model the interaction as a two-agent cooperative Markov game under centralized training and decentralized execution, comparing learned human control with a task-tuned fixed-impedance baseline. This model-free multi-agent reinforcement learning framework supports joint policy adaptation without requiring a complete analytical interaction model. It compares MADDPG and rMAPPO with an epigraph-constrained approach under common geometric task definitions. In simulation, rMAPPO generally achieved the highest return and tracking performance, whereas the epigraph approach produced more conservative motions and lower geometric exposure, including no observed collision or dangerous-region exposure after geometry transfer. With real operator input, fixed-impedance-trained policies were faster and successful in all recorded trials. Policies trained with a learned partner exhibited greater command opposition, while the fixed epigraph condition produced the most aligned commands. This work provides a benchmark for studying human-control representation and constraint-handling trade-offs in haptic shared control.

Suppose that each of $n$ players rolls a different die and the players are ordered by their rolls. Can the dice use disjoint labels such that ties are impossible, while all $n!$ orders remain equally likely? We give two general constructions of such dice and solve some related problems.

We study the undetected-error exponent of discrete memoryless channels with erasure decoding. Assuming that the undetected-error and erasure probabilities vanish, we derive an upper bound on the undetected-error exponent at positive rates. The bound uses Somekh-Baruch's genie-aided argument where an auxiliary output provides the decoder with a list of codewords. It recovers Telatar's tight rate-zero converse and is at least as tight as the straight-line bound. A numerical example shows that the improvement over the straight-line bound can be strict.

We derive a quantitative central limit theorem under sublinear expectations from a spatial endpoint regularity estimate for the one-dimensional \(G\)-heat equation. For bounded Lipschitz initial data, the second spatial derivative and the time derivative of its solution are Lipschitz in space and \(1/2\)-Hölder in time away from the initial time. In particular, \([u_{xx}(t,\cdot)]_{\mathrm{Lip}}\le C_G\Lip(\phi)/t\). Combining this estimate with the nonlinear Stein identity introduced in Song \cite{Song2020} and a replacement argument yields a bound of order \((1+\log n)/\sqrt n\) for bounded Lipschitz tests when the third absolute moment is finite and the lower variance is positive. The final replacement step is estimated directly, avoiding the nonintegrable singularity at time zero.

Formal modeling and verification of autonomous driving systems remain challenging due to the vast operational space and the complexity of the control logic. We propose a hybrid verification approach that combines formal model verification and runtime monitoring for the trajectory-following control node of Autoware, an open-source autonomous driving platform. We formalize the controller as a hybrid system in differential dynamic logic (dL), and introduce an abstract model that captures the essential control dynamics. We then prove safety and liveness properties of the model using the KeYmaera X proof assistant. Complementarily, we monitor the constraints that assure the compatibility between the model and the Autoware implementation across numerical simulation runs using the Autoware toolchain, quantifying to what extent the implementation's behavior is subsumed by the verified model. The experimental results confirmed that (i) monitoring provides a sound evaluation of target following with accuracy bounds, and (ii) the Autoware implementation reaches the target with an accuracy of approximately 0.2-0.4 (m) in position and 0.8 (m/s) in velocity.

Mixture-of-experts (MoE) models activate only a few experts per token, but when their expert weights are offloaded to host memory, host-to-device (H2D) expert transfers enter the critical path of decoding. Speculative decoding verifies several draft tokens in one forward pass, yet in an MoE model each verified token activates its own experts, so a larger draft tree transfers more experts. Because of this H2D cost, speculative decoding commits several tokens per verification cycle yet is sometimes even slower than autoregressive decoding. Based on this observation, we propose SpecFit, which chooses the verified draft subtree to maximize predicted throughput rather than acceptance length. SpecFit estimates the expected number of committed tokens from draft path probabilities and predicts cycle time from the node count and the per-layer union of the experts the subtree activates; this union is a monotone submodular coverage function, so each node pays only for the experts it adds. An exact search over ancestor-closed subtrees returns the subtree with the highest predicted throughput; run after each draft level, the same search also decides when to stop drafting, and the unmodified target verifies the result. On CNN/DailyMail summarization and a GSM8K subset with Qwen3-30B-A3B, SpecFit decodes 21.6% and 7.0% faster than EAGLE-3 with the same expert cache and 1.97x and 1.72x as fast as vanilla EAGLE-3. Code is available at https://github.com/Chlience/SpecFit.

Let $h\geq2$ be an integer and let $\mathbb{N}_0=W_1\cup\cdots\cup W_h$ be a partition into infinite sets. For $W\subseteq\mathbb{N}_0$, let $A(W)$ denote the set of all finite nonempty sums of distinct powers $2^w$ with $w\in W$. We give a necessary and sufficient condition for $A=A(W_1)\cup\cdots\cup A(W_h)$ to be a strongly minimal asymptotic basis of order $h$. This provides a complete answer to a problem posed by Nathanson in 1988.

Before an agent acts, it must decide whether action is warranted. A single accuracy cannot distinguish failure to recognize a warranted action from reluctance to act. Signal-detection theory separates sensitivity from criterion, but criteria estimated from authored binary labels depend on each benchmark's example mix. We introduce FlipAct, a diagnostic of tool use in physical states. A rule over annotated tool properties computes each answer and a graded evidence score, fixing the Yes/No boundary at zero across models. Questions form 2-by-2 quads that hold required knowledge fixed while the state flips. The slope of the fitted Yes-rate curve measures sensitivity; its crossing at one half measures criterion. Across 44 open models, sensitivity rises with size within a family, and its ranking agrees with three of four external when-to-act benchmarks. Models respond to evidence sign rather than magnitude, accepting actions that leave the state no better about as often as helpful ones. When Yes means act, most models are conservative across rephrasings; in some, this partly reflects a preference for No. Criterion is not determined by size. Activation steering shifts criterion with weights fixed; distillation from a model's own steered copy puts the shift into its weights without a significant sensitivity change. The distilled shift transfers to six external benchmarks, including two without Yes/No answers, while criterion-free AUC is preserved on the five benchmarks where it is available. Accuracy improves where models start conservative and declines or remains within error where they start permissive. Project page: https://sixundong.com/projects/flipact

Multimodal remote sensing image generation emerges as a promising paradigm for recovering complete and complementary observations from heterogeneous and partially observed remote sensing data. However, existing methods predominantly depend on sensor-specific fine-tuning of natural image generation models, limiting unified multimodal generation capacity due to the absence of shared representations and robust conditioning mechanisms. To address these challenges, we propose OmniRSI, a unified multimodal remote sensing image generation model. Specifically, we develop a remote sensing-specific variational autoencoder that captures multimodal priors and promotes a locally smooth latent space for unified representation and robust reconstruction across diverse observed data. Building upon that, we fully adapt Stable Diffusion 3.5 with a ControlNet branch to support unified multimodal generation and translation conditioned on textual and visual cues. Besides, we devise a training-free cyclic latent alignment mechanism that iteratively enriches incomplete visual conditions with generated multimodal information, progressively improving guidance reliability while preserving observed measurements. We also construct RSI-MM, a large-scale dataset comprising 11.5M multi-resolution images with text annotations and partially paired data for training and evaluation. Extensive experiments verify that OmniRSI achieves superior performance in multimodal reconstruction, generation and translation.

In this paper, we focus on decoding optimal Reed-Solomon codes of dimension two for insdel errors up to the half-Singleton bound. We present a decoding algorithm for the general insertion-and-deletion scenario with a time complexity smaller than brute-force decoding. Our algorithm corrects insdel errors up to the half-Singleton bound, which exceeds the scope of existing methods. Additionally, for the special cases of insertion-only and deletion-only insdel error patterns, we present two different algorithms with a time complexity smaller than our general algorithm.

Large reasoning models generate reasoning trajectories token by token. At a given prefix, multiple next-token candidates may be plausible, yet shape subsequent reasoning and differ in their chances of leading to the correct answer. Whether these differences are reflected in internal representations remains unclear. To study this question, we define relative long-horizon candidate value to quantify within-prefix differences and construct the Reasoning Candidate-Token Value (RCTV) dataset, pairing mathematical reasoning prefixes with plausible next-token candidates and their empirical long-horizon candidate values. Using RCTV, we examine hidden states, multilayer perceptron outputs, and attention outputs at candidate positions with sparse linear probes. Experimental results provide evidence that relative long-horizon candidate value is linearly decodable from these representations at multiple layers. Candidate-value probes can also outperform probability- and embedding-based baselines. Furthermore, a controlled online intervention experiment shows that using the decoded signals to guide token selection during generation can improve the chances of eventual success. Our findings provide evidence that internal representations encode information about relative long-horizon candidate value, offering insights into how local candidate-level representations relate to long-horizon reasoning outcomes.

We formulate the finite-time response problem for a radially accelerated Unruh–DeWitt detector coupled to a real massless scalar field outside a static, spherically symmetric, horizonless compact star. The stellar exterior is described by the Schwarzschild geometry, while unresolved field–surface interactions are represented by a local Robin condition at the stellar radius. After reducing the Klein–Gordon equation to a half-line Schrödinger problem, we identify a sufficiently stable branch of the Robin family from positivity of the radial operator, construct delta-normalized continuum modes, and define the static ground state with respect to Schwarzschild time. We derive a mode-amplitude representation of the smoothly switched detector response that avoids a direct numerical treatment of the coincidence singularity of the Wightman distribution. We obtain a radially aligned trajectory of constant signed proper acceleration in terms of the rapidity measured by static observers. The resulting formulation separates the effects of compactness, surface condition, closest approach, detector gap, and interaction duration. We also state the flat-space, Dirichlet, static-detector, low-frequency, large-distance, and long-interaction limits required to validate a numerical implementation. The framework provides a controlled extension of detector studies with static reflective compact objects to finite-time moving probes.

We introduce upper and lower discrete intermediate dimensions for unbounded subsets of Euclidean space and extend them to metric spaces. The definitions restrict the covering radii within a scale-dependent range of dyadic shells and take a supremum over an auxiliary parameter. The resulting dimensions are monotone in the parameter and recover the Barlow–Taylor discrete Hausdorff dimension at zero. We prove continuity at every positive parameter, with a sharp quantitative bound, and give an example with a jump at zero. At the upper endpoint, the upper dimension equals upper mass dimension for uniformly discrete Euclidean sets; the analogous lower mass identity fails. We establish a mass distribution principle and prove quasi-isometric invariance under a uniform coarse packing condition. For spaces with uniform polynomial volume growth, we construct clustered subsets attaining the continuity bound. Independent thinning truncates these spectra at the resulting mass dimension, almost surely for all parameters simultaneously. Applications include the discrete Heisenberg group with its word metric and the ranges of simple symmetric random walks.

Enterprise agents need retrieval evaluation sets that expose domain-specific failures and guide developers towards efficient deployment tradeoffs. Neither expert-human-authored sets nor current synthetic generation methods provide a methodology for achieving the necessary coverage, reliability, efficiency, and discriminability required for such decision-making. Simultaneously, the field does not have an assessment framework for determining when an evaluation set has satisfied these properties. We introduce an evaluation set assessment framework for these criteria and CoverSynth – a generator specifically designed to satisfy these criteria without incurring the high cost of human expert labeling. Starting from an unannotated corpus, CoverSynth targets coverage across retrieval demands and system capabilities. Deterministic checks locate evidence quotes in their sources, while model-based checks assess semantic validity to guarantee reliable ground truth. Across five public enterprise-style corpora, our method provides informative variation in difficulty, revealing unseen failure modes such as an inability of agents to handle underspecified or ambiguous requests. On the RepLiQA corpus, 91% of human-generated queries can be answered by all members on a panel of 12 retrieval systems, compared to only 12% of CoverSynth-generated queries. Finally, in a repeated TechQA/RepLiQA study, 12 of 12 within-harness model contrasts have positive nominal 95% intervals on generated sets, compared with 4 of 12 on human sets. CoverSynth makes coverage and evidence quality explicit construction objectives, producing corpus-grounded evaluations that reveal retrieval headroom and differences between agent configurations.

Formal verification of distributed protocols is still dominated by inductive-invariant proofs, whose central challenge is discovering strengthening assertions that rule out unreachable states. This burden is often misaligned with how protocol designers reason: they explain correctness by following representative executions, causal histories, and phase-structured interactions among nodes. This paper introduces scenario proofs, a verification methodology that makes such execution-oriented reasoning formal. A scenario is a structured expression describing representative protocol executions, enriched with ghost variables. Rather than enumerate all possible interleavings, a scenario describes canonical executions and uses a sound semi-commutation relation to account for reorderings that preserve feasibility and final states. Verification then factors into two main obligations. Coverage shows that every feasible protocol execution is equivalent, up to semi-commutation, to one described by the scenario; this obligation is independent of the safety property and serves as a reusable behavioral characterization of the protocol. Correctness proves the desired safety property only over the representative executions, using Hoare-style weakest-precondition reasoning along the scenario structure. We formalize the scenario language, its layered semantics, and proof rules for coverage and correctness. Through case studies of ring leader election, two-phase commit, a decentralized lock, two variants of multi-signature payment, and single-decree Paxos, we show how scenario proofs capture the causal and phase-based arguments used informally by protocol designers. These examples illustrate that scenario proofs can replace monolithic invariant discovery with structured reasoning over representative executions, while retaining a rigorous connection to all feasible protocol behaviors.

An end-to-end success rate alone cannot distinguish failure to learn an action from failure to apply it as task state changes. We study this distinction in deterministic tool workflows that provide the current artifact state and candidate action recipes. Using 1.7B, 8B, and 27B Qwen models, we compare supervised learning across workflow horizons and cross the state representation used for training with the one used at evaluation. Horizon-matched supervision yields high completion, but an H4-trained 1.7B model transfers poorly to longer workflows under full-state observations. In an H16 crossover, compact-trained 1.7B adapters complete 50/50 held-out tasks in compact view and 0/50 in full view for each of three paired training seeds; full-trained outcomes vary across seeds. A separate 8B adapter pair shows a similar asymmetry. The view dependence also appears in paired-choice tasks where both candidate calls are executable and the correct choice depends on table contents; here, the compact mask does not consult the target action. An explicit relevance cue improves full-view execution but does not close the gap for the tested checkpoint. In a separate 27B ScienceWorld study, compact-state training improves local accuracy under both views, indicating that the transfer pattern depends on the task and observation construction. Together, these experiments identify representation-sensitive transfer as a bottleneck in the controlled workflows, without isolating content reduction from other changes to the observation.

Let $N$ be a 3-dimensional integral homology sphere. We prove the existence of a sequence of 4-dimensional topologically negatively curved manifolds $M_k$, $k=1,2,\dots$, satisfying the following: (1) all aspherical manifolds $M_k$ have the same universal cover $U_N$ depending only on $N$; (2) all fundamental groups $\pi_1(M_k)$ are hyperbolic and share the same Gromov boundary $X_N$ depending only on $N$; (3) the groups $\pi_1(M_k)$ represent infinitely many distinct quasi-isometry classes. The last conclusion, which represents the new feature, shows that negatively curved geometries in dimension 4 exhibit substantially richer structure than those in dimension 3.

We study radial bound states of \[ \Delta u-\abs{u}^{q-1}u+\abs{u}^{p-1}u=0 \quad\text{in }\R^n, \qquad n\ge3,\qquad 1<q<p<\frac{n+2}{n-2}. \] For every integer $k\ge1$, we prove that there is exactly one radial bound state with $k$ simple zeros and $u(0)>0$. Its absolute maximum is attained at the origin. This confirms the zero-mass, Sobolev-subcritical case of Tang's double-power uniqueness conjecture. The proof adapts Tang's phase-transition analysis and combines it with a finite-level separation argument inspired by Cortázar–García-Huidobro–Yarur. Three main difficulties arise in the zero-mass double-power setting: the sign changes of key comparison quantities in the low-amplitude region, the possible failure of pointwise positivity of an auxiliary quantity when $n=3$ and $p+q<3$, and the absence of exponential decay at infinity. We overcome these difficulties by introducing bridge functionals to propagate the required sign information through low amplitudes, establishing a weighted integral positivity estimate in the exceptional three-dimensional range, and combining a radial-flux tail estimate with finite-level inverse-branch comparison. We also establish the strict ordering of the bound-state shooting heights and show that the shooting variation along the \(k\)-node state has exactly \(k+1\) simple zeros.

The AI-RAN paradigm makes the next-generation cellular network more versatile by co-locating AI and RAN workloads on the same commodity hardware. While the GPU is a promising platform for AI-RAN realization, a generic concurrent AI application interferes with the latency-sensitive RAN on GPU compute resources. In this paper, we propose Eunoia, a dynamic real-time AI-RAN GPU scheduler that is transparent to both AI applications and the RAN workload and operates at the granularity level of the RAN slot. We deploy Eunoia onto NVIDIA Aerial AI-RAN and evaluate Eunoia on both an over-the-air 5G private network and an emulated multi-cell network. We demonstrate that in a 27-cell AI-RAN, Eunoia keeps the RAN uplink P99 latency under 3 ms while delivering higher AI performance than other RAN-safe static partitioning methods.

Crowdsourced disaster imagery provides timely, ground-level observations when conventional disaster mapping is delayed or incomplete, yet its geographic value depends on where observations are produced, how they are interpreted, and whether they can be reliably located as actionable Geospatial Intelligence (GEOINT). Using more than a decade of PhotoMappers, a crowdsourced disaster-mapping initiative, this study examines the changing geography of disaster information and asks how emerging GeoAI models compare with human geographic interpretation. We combine longitudinal spatial analysis with cross-view geolocalization using street view imagery (SVI) and remote sensing imagery (RSI), and evaluate vision-language models (VLMs) reasoning through 30 indicators spanning geographic cues and reasoning evidence. The results reveal a geographically and temporally uneven archive shaped by changing disaster types, Community Lifelines, and operational priorities. Integrating VGI, SVI, and RSI with Sinkhorn re-ranking achieves 40.90% R@1, 61.10% R@5, and 69.45% R@10, while yearly R@1 varies markedly from 25.00% to 65.07%. Geographic reasoning is similarly uneven: Qwen3.6-27B achieves an overall agreement of 67% compared with 51% for InternVL3-8B, with both models showing greater difficulty with localized and place-specific evidence than broad spatial configurations. We argue that the value of GeoAI lies less in replacing volunteered geographic interpretation than in complementing it, scaling candidate retrieval while retaining human judgment for ambiguous and consequential cases. This provides a pathway toward more human-centered and responsible GeoAI for disaster mapping. All data and code are openly available at https://github.com/bobleegogogo/PhotoMappers-VLM.

Wyner's common information $J(p)$ and the common entropy $G(p)$ of a pair of random variables $(X,Y)$ with finite ranges and joint distribution $p$ are both defined by an optimization over the auxiliary random variables $W$ that make $X$ and $Y$ conditionally independent: $J(p)$ is the infimum of the mutual information $I(X,Y;W)$, and $G(p)$ is the infimum of the entropy $H(W)$. We prove that both quantities are NP-hard to compute. For Wyner's common information, deciding whether $J(p)$ is strictly smaller than a given integer $r$ is NP-hard, and the problem is NP-complete on tables that are uniform on their support and have the same number of positive entries in every row. The reduction is from Maximum Edge Biclique and rests on an exact criterion, in terms of rectangles in the support of $p$, for improving on the auxiliary $W=X$; every yes-instance satisfies $J(p)<r-1/(4N^2)$ and every no-instance satisfies $J(p)=r$, where $N$ is the number of positive entries of $p$. For the common entropy, deciding whether $G(p)\le r$ for a rational number $r$ is NP-hard, even for tables with at most four nonzero entries in each row, all taking one of two values. The reduction is from exact cover by $3$-sets and rests on a majorization property of the masses of the nonnegative rank-one decompositions of $p$, combined with a quantitative form of the Schur concavity of entropy. In both cases the separation between yes- and no-instances is inverse-polynomial in the size of $p$, so that approximating $J(p)$ or $G(p)$ within a suitable inverse-polynomial additive error is also NP-hard. The two mechanisms are genuinely different: we exhibit a table on which a large rectangle in the support lowers $J$ below the threshold of our first reduction while leaving $G$ on it.

VLMs provide promising solutions to embodied reward design. Most current methods that train VLMs as reward regressors not only require extensive annotations but are also primarily designed for finetuning pretrained policies, and perform less well in the more challenging from-scratch RL setting. This issue stems from a fundamental mismatch: regressing precise rewards is misaligned with what VLMs naturally excel at. We posit that it is more aligned with VLMs' inherent multi-modal VQA capabilities for the models to function as success detectors, and propose VLM success reward via Exploration-Augmented Key-Observation Gating (VLMeg) to well harness VLM for embodied reward design. As the core of VLMeg, the proposed exploration-augmented key-observation gating first determines whether the current RL episode is judgment-worthy based on its similarity to a generated success trajectory. Then, the key observation with the lowest confusion from the judgment-worthy episode will be selected for VLM evaluation as episodic reward. This gating mechanism not only avoids redundant calls but also enables higher detection accuracy of VLM. Considering the sparsity of judgment-worthy episodes, the advanced exploration incentives based on the generated trajectory are introduced, enabling more efficient exploration toward judgment-worthy trajectories for more VLM reward triggers and thus gaining higher RL efficiency. Extensive experiments in MetaWorld demonstrate VLMeg achieves state-of-the-art from-scratch RL, outperforming advanced VLM-based baselines on 12 challenging reward-free tasks. Furthermore, VLMeg also enables effective RL without any ground-truth reward in 3 challenging real-world experiments. Code will be open after acceptance at https://github.com/Raina915/VLMeg.

Photonic matrix multipliers can accelerate neural-network inference, but their practical utility depends on how optical weight elements respond to source noise, thermal variation, and calibration error. This paper compares Mach-Zehnder modulator (MZM) and microring-resonator (MRR) implementations under laser relative-intensity noise (RIN), column-wise thermal/phase drift, and their joint action. Two CIFAR-10 classifiers - a compact four-layer CNN and ResNet-8 - are mapped to matched photonic multiply-accumulate chains using common source-distribution, detection, numerical, and calibration assumptions. Both architectures reproduce the same zero-perturbation baseline for each workload: 79.5% classification accuracy for the Small CNN and 70.0% for ResNet-8. Robustness is then evaluated using separate RIN-only and drift-only sweeps and a full two-dimensional RIN-drift grid, with dimensionless RMS perturbation levels extending from 0.5% to 20%. The analysis reports classification accuracy, class normalized confusion matrices, rolling-accuracy traces, one-dimensional robustness curves, and multidimensional response surfaces. Device equations and parameter definitions follow the models implemented in the QPI Labs Photonic Inference Simulator, with shared laser fluctuations propagated as correlated multiplicative noise and slow drift represented as a per-output-column perturbation of calibrated weights. All numerical results are generated from recorded experiment configurations and random seeds. The study provides a controlled system-level framework for comparing interferometric and resonant photonic weight elements while limiting conclusions to the implemented device models, perturbation ranges, calibration policy, and neural-network workloads.

Stochastic gradient descent (SGD) and randomized block coordinate descent (RBCD) belong to two fundamentally different classes of stochastic iterative regularization methods, and are promising and popular for solving large-scale inverse problems, due to their excellent scalability with respect to data size and signal size, respectively. In this work, we propose a doubly stochastic block gradient descent (DSBGD) method with early stopping, by integrating the updating strategies of both SGD and RBCD, for solving linear inverse problems in infinite-dimensional Hilbert spaces. At each iteration, the method randomly selects one data pair to obtain a stochastic gradient estimate, and then uses it to update one randomly selected block coordinate. We prove the regularizing property of DSBGD under a priori stopping rules and then derive its convergence rates with the additional source condition and a condition on the forward operator. To the best of our knowledge, these are the first convergence rate results of randomized coordinate descent-type iterative methods for inverse problems from the perspective of regularization theory. We also prove that the DSBGD iteration can be stopped by the classical discrepancy principle in finitely many steps with high probability, and that the mean squared error decreases monotonically before stopping. Several numerical experiments are provided to complement the theoretical analysis.

Large language models (LLMs) demonstrate strong generalization across a broad range of reasoning and generation tasks, but their large parameter counts impose substantial memory and computation costs, hindering deployment in practical resource-constrained settings. One-shot low-rank compression is a promising solution since it reduces model size and inference cost effectively. However, existing SVD-based methods primarily target multiple-choice benchmarks and often fail to preserve performance on generation tasks. Moreover, their rank allocation strategies are typically heuristic. We propose GA-SVD, a generation-aware low-rank compression framework for LLMs. First, we introduce Generation-Aware Weight Whitening (GAWW), which leverages gradients from on-policy knowledge distillation to construct whitening transformations aligned with generative behavior. Second, we develop an evolutionary global rank allocation method that searches for effective layer-wise rank allocation under a given global compression ratio. Across extensive experiments on Mistral-7B, Qwen3 series, and Llama-3.3 models, evaluated on both multiple-choice and generative benchmarks, GA-SVD consistently outperforms existing SVD-based baselines and achieves state-of-the-art (SoTA) results. We further demonstrate scalability by applying our method to models with up to 70B parameters.

In this paper, we propose and analyse a novel explicit fourth-order symmetric low-regularity trigonometric integrator for the semilinear Klein-Gordon equation with non-smooth solution in the $d$-dimensional space, where $d=1,2,3$. The integrator is constructed based on the full use of Duhamel's formula, the employment of a twisted function tailored for trigonometric integrals and the symmetrization procedure of trigonometric integrators. Robust error analysis is conducted, demonstrating that the proposed scheme achieves fourth-order accuracy in the energy space under a weak regularity requirement in $H^{2+\max(\mu,1)}(\mathbb{T}^d)\times H^{1+\max(\mu,1)}(\mathbb{T}^d)$ with $\mu> \frac{d}{2}$. A numerical experiment shows that the proposed low-regularity integrator is much more accurate than some well-known exponential integrators for approximating the Klein-Gordon equation with non-smooth solutions.

Genomic language models generate long nucleotide continuations from short prefixes, exposing a direct route for studying training-sequence extraction through the generation interface. We present an output-only black-box attack on Evo 2 that selects convergent groups of repeated generations without gradients, token likelihoods, or training-corpus access during candidate selection. Recovered content is then scored by an evaluator combining aligned length, nucleotide identity, match multiplicity, and sequence complexity. Across 304 runs on Evo 2 7B with bacteriophage and plasmid prefixes, the attack yields 888 candidate clusters, of which 85 match training segments of at least 500 bp, giving a cluster-level attack success rate of 9.57%. Final filtering retains 22 uniquely matched extraction events at the 500-bp threshold and 15 at 1,000 bp, covering 14 and 7 distinct training-sequence regions, respectively. Within-category source-homology screening retains 11 of the 22 events at a 99% exclusion threshold and four at 98%, with the latter mapping to two reference regions. The results establish convergence among repeated nucleotide generations as a practical output-only signal for recovering long training-sequence segments and characterize how recovery depends on prefix length, cluster size, perplexity, early stopping, and sequence domains.

Let $\mathcal B=(B_g)_{g\in G}$ be a saturated Fell bundle over a countable discrete group, equipped with a spectral triple. We give explicit sufficient conditions for lifting this triple to the reduced cross-sectional C\Star-algebra $C_r^*(\mathcal B)$. Using finite projective realizations of the homogeneous Morita equivalence $B_e$-bimodules, we transport the base Dirac operator to the individual fibres and assemble the resulting operators into a fibrewise Dirac operator. We introduce a spectral-regularity condition ensuring bounded commutators and give a sufficient criterion in terms of uniform derivative bounds on smooth factor-system data. Combining the fibrewise operator with a length operator associated with a proper translation-bounded matrix-valued length function yields the lifted spectral triple. When $B_e$ is separable, the lifted triple, with a suitable grading, represents the Kasparov product of the vertical class with the class of the unit-fibre triple. We also establish a summability criterion and sufficient conditions for stability under central cocycle twisting. A range of examples illustrates the scope of the construction, including twisted crossed products, free compact Abelian actions, and Fell bundles with nonfree homogeneous fibres.

Structured pruning is typically formulated as identifying which model dimensions to remove, often within the model's original representation. However, the effect of coordinate deletion fundamentally depends on the basis in which pruning is performed. This raises a more fundamental question: how should the basis be chosen specifically for coordinate deletion? We introduce WUSPruner, a transform-based framework for structured pruning of large language models. We formulate basis selection as a local linear reconstruction problem that directly minimizes the reconstruction loss induced by pruning. Inspired by the second-moment transformation in WUSH, we consider a WUS transform constructed jointly from activation and weight statistics. We show that under positive-definite second moments, WUS transform minimizes the local reconstruction loss over all invertible changes of basis. In the resulting basis, the activation and weight second moments are simultaneously diagonalized and balanced, causing the deletion error to decompose into independent spectral contributions and yielding a principled criterion for coordinate selection. Guided by this result, we develop a scalable pruning method based on blockwise WUS transformations and compact input projections. Experiments on Llama and Qwen models from 8B to 72B parameters show consistent improvements over structured pruning baselines across language modeling, knowledge, commonsense reasoning, mathematics, and code generation benchmarks, while also delivering practical reductions in inference latency and memory usage.