Papers

In 2003, Héthelyi and Külshammer proved that if $G$ is a finite solvable group and $p$ is a prime such that $p^2$ divides $|G|$, then $k(G)\geq (49p+1)/60$, and they constructed an infinite family of groups for which this bound was claimed to be attained. We point out that the groups in this family are not Frobenius groups, so that their class numbers are considerably larger than stated, and that in fact the bound is never attained. We then determine the best possible bound of this shape: we show that $k(G)\geq (49p+7)/60$ for all primes $p$, which is sharp for $p=17$, and that $k(G)\geq (49p+451)/60$ for all primes $p>2719$, which is sharp for infinitely many primes $p$. Thus the slope $49/60$ found by Héthelyi and Külshammer is best possible, but the correct additive constant is $451/60$ rather than $1/60$.

We introduce MVGraph, a benchmark for evaluating large vision-language models (LVLMs) on multi-graph reasoning where the evidence required by a query is distributed across multiple interrelated visual graph views. Although such evidence commonly resides in source-specific graphs, temporal snapshots, or local observations, existing graph reasoning benchmarks remain confined to a single self-contained structure, assessing only graph perception and reasoning while leaving the alignment and composition of evidence across views underexplored. MVGraph comprises 8k instances spanning 8 graph-theoretic tasks, abstracted from two multi-graph scenarios (partial and temporal graph views). Each problem is programmatically constructed and verified to be unsolvable from a single view. Beyond end-to-end evaluation, we decompose multi-graph reasoning into four complementary capabilities—Perception, Alignment, Composition, and Reasoning—and design 29 diagnostic tasks with 64k instances to probe each one, along with golden intermediate representations for evaluating the intermediate process. Across 15 LVLMs, we reveal the difficulty of multi-graph reasoning and identify cross-view edge alignment and relation-level composition as prominent bottlenecks through stage-oriented diagnostics. Meanwhile, temporal constraints and increasing view counts expose further capability boundaries. Code and data are available at https://github.com/AAAndy-Zhu/MVGraph.

Matching repair after utility changes can reuse valid observations, but new evaluations must respect matching capacity and may return out of order. We study announced invalidations with bounded, possibly reward-dependent reporting delays and pending evaluations that do not occupy future matching capacity. Residualload repair (RLR) combines sound outcome certificates with batched matching schedules for unequal sample deficits. Its complete dyadic quota schedule admits a sharp issue-round bound with coefficient cb < 1.607 relative to the terminal residual endpoint load, together with separate delay and evidence-lifetime bounds. RLR-P monitors complete issue-order prefixes without changing the sampling plan before acceptance. With a deterministic pure oracle, a single-repair coupling from the same drained initial state guarantees no increase in certification time, issued observations, or time to a reusable checkpoint. We also derive an information-load lower bound. On fixed priority-star markets with unknown Bernoulli gaps, PrioritySearch attains the history-adjusted first-order constant for expected certification time as {\delta} {\sim} 0, under hypothesis-independent linear history scaling and sublogarithmic reporting delays. Paired simulations and measured-feedback replay quantify the trade-offs: in the replay, RLR-P has lower mean capped update-certification time than a monitored width-based baseline, at higher oracle CPU cost.

Video large language models (VLLMs) rely on long visual token sequences to understand complex temporal content, which makes visual token compression important for efficient inference. Existing training-free compression methods mainly reduce the number of tokens sent to the language model, but the compression process itself can still require many visual feature comparisons, especially for intra-frame token protection and inter-frame temporal token merging. This paper proposes a video codec-guided training-free token compression method for VLLMs that uses coding information already available in compressed video as a low-cost search prior. The method aligns reference-frame dependencies, motion vectors, and residuals with the visual token grid. Residual information forms compact candidate pools for token protection, while motion information is propagated along reference-frame chains to construct localized candidates for temporal token merging between sparsely sampled frames. Local visual feature similarity comparison is then used within these candidates to make the final compression decisions, without modifying the base VLLM. Experiments on three representative VLLMs and four video-understanding benchmarks show that the proposed method achieves performance comparable to the state-of-the-art training-free baseline FlashVID, and in some settings surpasses it, while substantially reducing the feature comparisons required by token protection and temporal matching. These results demonstrate that codec information can effectively improve the accuracy-complexity tradeoff of video token compression.

Diffusion-based TTS has demonstrated strong capability in emotional speech generation. However, existing emotion alignment methods primarily reinforce target emotional expressions while overlooking modeling of competing emotional modes, limiting fine-grained controllability. This issue becomes more pronounced under classifier-free guidance (CFG), which relies on contrasting conditional trajectories to shape generation. We propose Emotion Bidirectional Preference Optimization (Emo-BPO), a simple effective framework that jointly learns emotion-aligned and emotion-contrastive score functions from reordered same-text emotional pairs. Our method requires neither auxiliary reward models nor additional annotations, and can be seamlessly integrated into existing diffusion-based TTS systems to improve emotional controllability and expressiveness.

Embodied agents must translate multimodal observations and user requests into executable actions while adapting to product constraints, changing goals, and execution feedback. We present JoyInside-VLM-Agent, a ReAct-style multimodal agent developed through product-conditioned trajectory construction and staged policy learning for robotic platforms and smart hardware. A closed-loop sandbox generates multimodal interaction trajectories covering goal revisions and failure recovery, which are checked against execution outcomes and semantic criteria. Supervised fine-tuning and multi-teacher on-policy distillation precede reinforcement learning with DPER (Dual-Source Privileged On-Policy Self-Distillation with Token-Level Evidence Routing). DPER routes token-level evidence between a frozen privileged teacher and a privileged student sharing the rollout policy's parameters, modulating reward-derived token advantages while preserving their signs. Training rewards combine generative process evaluation, multi-judge rankings, and task-queue consistency. JoyInside-VLM-Agent achieves a BFCL v4 overall score of 77.44, exceeding the evaluated baselines; results on the other public benchmarks are mixed. On JoyInside-Devices and JoyInside-Robotics, the evaluated system, which includes domain-specific skill refinement, leads the baselines on all reported metrics. Two real-world quadruped case studies illustrate visually grounded search, replanning after execution failure, and explicit failure reporting.

We study a two-dimensional electron gas in the integer quantum Hall regime coupled to a single spatially modulated cavity mode in the static off-resonant limit. Retaining both paramagnetic and diamagnetic contributions on equal footing, we derive a gauge complete single-particle Hamiltonian in which virtual photon exchange generates a periodic kinetic renormalization and a diamagnetic scalar potential. Both terms transfer momentum by $2k_0$ and displace guiding centers by $\Delta X=2k_0\ell_B^2$, forming a finite-$k_0$ momentum ladder. Diagonalizing the strip Hamiltonian, we find that the ladder reconstructs the Landau-level band structure and redistributes, rather than multiplies, the associated chiral edge states. Occupied-subspace Chern numbers remain $C_\nu=\nu$ for $\nu=1,2,3$ throughout $0\le\lambda_{\mathrm{cav}}\le 0.5$, while the bulk gaps decrease without closing. Strip Kubo responses show cavity-induced displacements of the Hall-step energies; at finite width the plateau heights are noninteger and approach the integers as $L_x$ increases. The ladder is spectrally resolved at $k_0\ell_B=0.5$ and collapses at $k_0\ell_B=0.1$. These results isolate a spatially local, finite-$k_0$ momentum ladder as a clean-system mechanism by which a structured vacuum field reconstructs quantum Hall spectra and strip transport without changing the integer topology, complementary to cavity-mediated all-to-all hopping.

Let $b(n)$ denote the minimum number of perfect matchings in a simple brace of order $n$. De~Carvalho, Lucchesi and Murty (SIAM Journal on Discrete Mathematics, 27(2): (2013) 940-958) proved that $b(n)\ge(n-2)^2/8$ and conjectured that $b(n)=(n-2)^2/4$ for all sufficiently large even $n$. We prove this conjecture.

This paper introduces MathVis, a benchmark designed to evaluate LLMs' ability to visualize frontier mathematical problems and perform diagram-assisted reasoning. The benchmark consists of 512 tasks, each comprising a mathematical statement, a reference diagram, executable TikZ or SVG code, a Gold Intermediate Representation (IR), atomic rubrics, and error codes. Through rigorous evaluation, GPT-6-Astra, Claude Fable 5, and Gemini 3.1 Pro Preview achieve pass@1 scores of 31.25%, 26.56%, and 22.85%, respectively. We found that although the tasks require visualization, LLMs produce outputs dominated by formal languages, symbols, and graphics programs, rather than explicit diagram-mediated reasoning. Furthermore, while the solutions generated by LLMs may contain all the necessary elements, they are often visually confusing to humans. Ultimately, this benchmark aims to visualize mathematical problems and promote research on enabling LLMs to simplify their reasoning via visual diagrams.

We give an $O_{d,\varepsilon}(n+N^{d+\varepsilon})$-time algorithm for multidimensional subset sum on an explicitly listed multiset of $n$ vectors in $[-N,N]^d$, for every fixed $d$ and $\varepsilon>0$. This directly implies an $O_{d,\varepsilon}(n+N^{d+\varepsilon})$-time algorithm for feasibility test of integer programming. Prior to our work, the best-known algorithm has a running time of $O_{d}(n+N^{O(d^2)})$ [Eisenbrand, Weismantel'19]. Specifically, if $d=1$, our algorithm runs in $O_{\varepsilon}(n+N^{1+\varepsilon})$-time for the standard subset sum problem, which is near-linear in the largest input integer. Prior to our work, subset sum can be solved in time near-linear in the target $t$ [Bringmann'17], or near-linear in the mixed parameter $\sqrt{Nt}$ [Chen, Lian, Mao, Zhang'24]. It is a fundamental open problem whether the algorithm can be made near-linear in $N$, which is settled affirmatively in this paper up to an arbitrary small $N^{\varepsilon}$ term.

Image watermarking enables provenance tracing for photorealistic images generated by diffusion models. However, state-of-the-art (SOTA) removal attacks can suppress embedded signals with little perceptual degradation. This vulnerability limits the effectiveness of watermarks for intellectual property protection and misuse attribution. We propose WaveMark, a novel wavelet-domain watermarking method that embeds messages in a diffusion model's initial noise. To support robust recovery from perturbed carriers, WaveMark distributes keyed replicas of message bits across spatial positions, wavelet orientations, and scales. Each carrier groups coefficients from four latent channels and encodes a randomized bit through magnitude projection, providing an explicit decoding margin. We evaluate WaveMark with SD2.1 on SDP and MS-COCO Captions under 14 attacks. WaveMark achieves 100.0% bit accuracy (BA) without attacks, while maintaining image quality comparable to the evaluated baselines. Under SOTA MarkNull and MarkNull-A, it retains over 88% BA, outperforming all baselines.

The photonuclear response reflects nuclear structure and the dynamics of excitation and decay, with neutron-emission channels retaining information that can be obscured in inclusive dissociation yields. We calculate specified-side and mutual neutron-tagged Coulomb-dissociation cross sections in ultraperipheral $^{96}_{44}\mathrm{Ru}+{}^{96}_{44}\mathrm{Ru}$ and $^{96}_{40}\mathrm{Zr}+{}^{96}_{40}\mathrm{Zr}$ collisions at $\sqrt{s_{\mathrm{NN}}}=200~\mathrm{GeV}$ using an impact-parameter-dependent equivalent-photon framework with photonuclear inputs from TALYS calculations and ENDF evaluations. Across the two input sets, the predicted Ru/Zr ratios span $1.54$-$1.71$ for exact $1n$ and $2.49$-$3.09$ for $1n1n$, while inclusive $Xn$ (at least one neutron) and $XnXn$ ratios remain near unity at $0.96$-$0.99$ and $1.05$-$1.10$, respectively. The one-neutron ratios lie well above the corresponding flux-only $Z^2$ and $Z^4$ charge-scaling references, reflecting differences in the low-energy one-neutron response that are amplified by mutual tagging. This topology hierarchy identifies neutron-tagged isobar ratios as sensitive probes of photonuclear response, revealing response differences hidden in inclusive dissociation. These calculations also provide neutron-emission inputs for neutron-tagged vector-meson photoproduction in isobar collisions.

After centering and scaling, the length of the longest weakly increasing subsequence of a finite-state Markov random word converges to a Brownian last-passage functional with dependent components. We investigate when this functional, and more generally the limiting RSK Young-diagram shape, admits a Gaussian random-matrix representation. We introduce Hermitian Gaussian matrices with correlated diagonal entries and show that isotropy of the Brownian covariance on the trace-zero hyperplane yields such a representation. Within this natural class of Hermitian models with independent Gaussian off-diagonal entries, we prove a rigidity theorem showing that isotropy, together with equality of the off-diagonal variances, characterizes the conditional largest-eigenvalue representation. Explicit three-letter non-cyclic Markov chains demonstrate that this representation is not universal: the limiting Brownian functional may fail to have the law of the largest eigenvalue of any centered jointly Gaussian $3\times 3$ Hermitian matrix. Finally, we extend the random-matrix identification to chains with non-uniform stationary distributions and to countable state spaces.

We study quantum-assisted balanced rendezvous on the $d$-dimensional hypercube in a one-step two-agent quantum-walk framework, where the two agents move the same Hamming distance and meet at a common midpoint. The key structure is a projective $t$-sphere resolution, which governs exact finite-dimensional quantum attainment. Its scalar analogue recovers the corresponding classical characterization. We characterize finite-dimensional quantum attainment of the no-signalling benchmark, construct quantum strategies from projective sphere resolutions, and establish a rigidity theorem for optimal finite-dimensional strategies. A marked difference appears between nearest-neighbor and higher-cardinality updates: quantum advantage can occur in the former, whereas in the latter the geometry of the relevant Hamming spheres rules out exact finite-dimensional attainment of the no-signalling value. Together, these results connect quantum-walk dynamics, Hamming-sphere geometry, and quantum rendezvous within the quantum Bernoulli noises (QBN) framework.

AI agents increasingly select and pay service providers without human review. In emerging permissionless markets, however, adversaries can create inexpensive identities and fabricate feedback to inflate provider reputation, making reputation-based payment authorization vulnerable to Sybil attacks and exposing clients to unbounded financial loss. This paper presents AgentValve, a protocol for Sybil-resilient payment authorization in permissionless AI markets. AgentValve builds on a trust network that represents reputation as finite capacity in a directed graph and authorizes payments through trust paths with sufficient available capacity. A smart contract atomically reserves the capacity supporting each admitted payment, bounding honest agents' payment exposure by the capacity they extend into the adversarial region, and thus creating identities or interactions entirely within that region cannot increase this bound. To limit capacity depletion by malicious senders, AgentValve combines payment-backed capacity creation with bounded route length, preventing attackers from depleting honest capacity without incurring corresponding payment costs. AgentValve further decouples off-chain route discovery from on-chain verification and introduces a witness-commit mechanism that reduces route verification to linear work while requiring only constant persistent state per admitted payment. We implement a AgentValve prototype and evaluate it using six months of Ethereum data and synthetic workloads. Experimental results show that under attacks with up to 10,000 synthetic Sybil identities and with chosen attackers, the payment exposure and capacity depletion remain bounded. Regarding practicality, the witness-commit mechanism lowers admission cost by up to 40.8% compared with baselines, and admitting common payments costs approximately \$0.04-\$0.21.

A detection of helicity in a primordial gravitational-wave background (GWB) would provide compelling evidence for parity violation in the early universe and point toward physics beyond the standard picture of inflation. Since big bang cosmology is not time translation invariant, we identify that the so-called “regular” and often-neglected “irregular” solutions are independent degrees of freedom that can in principle carry different, even opposite, helicities. We note that this possibility complicates the interpretation of a measured net helicity. To determine the sensitivity of various GW detector configurations to helicity, we introduce a universal helicity efficiency coefficient that provides a unified geometric description of helicity sensitivity across gravitational-wave detectors which generalizes and improves previous estimators. We apply this helicity efficiency coefficient to estimate the sensitivity of a range of future GW experiments to helicity across twenty orders of magnitude in frequency assuming a fully helical background with an amplitude just below the current constraints.

Comparing distributions under severe sample imbalance requires effectively using abundant majority observations while retaining sensitivity to differences involving the smaller sample. This challenge is particularly relevant for complex, non-Euclidean data, such as graphs, whose structural characteristics call for flexible testing procedures. Classifier two-sample tests (C2STs) provide such flexibility, but existing procedures are primarily designed for balanced or comparably sized samples. In this paper, we study C2STs in a highly imbalanced regime, and show that severe sample imbalance may substantially degrade testing performance. Different from conventional imbalanced learning approaches that treat sample imbalance merely as a nuisance for classifier training, we turn it into a source of repeated testing evidence. Building on this insight, we propose an Enhanced Imbalance-Aware Deep Classifier Two-Sample Test (EIAD-C2ST), a classifier-agnostic framework designed for sample imbalance that accommodates diverse data modalities by tailoring classifiers to data structure. For computationally expensive deep classifiers, we further develop a scalable representation-amortized implementation strategy. Theoretically, we establish rigorous guarantees on asymptotic size and characterize conditions for power consistency, allowing the imbalance ratio to diverge. We demonstrate the empirical gains using simulations and an application to blockchain forensics. The results reveal that the majority-sample surplus, when properly leveraged, can be organized into useful statistical evidence, rather than an obstacle, for distributional comparisons with complex data.

Permutons can be thought of as "continuum limits" of permutations of diverging size, which encode information about the number of occurrences of any given finite subpattern. We construct a natural composition operation on permutons, analogous to composition of permutations, and explore its properties via a correspondence between permutons, Markov kernels, and Markov operators. We show that no extension of permutation composition to permutons can be (jointly) continuous with respect to the usual "weak" topology on permutons, but we construct a "strong" topology with respect to which composition is jointly continuous. Moreover, we characterize strong convergence of sequences of permutations of diverging size: a sequence of permutations converges strongly if and only if it converges weakly and its limit is the transpose of the graph of a measure-preserving function. The key insight behind these results is to apply functional analysis to certain operators associated to permutons; with this shift in perspective, our results have elegant and relatively "soft" proofs. As an application, we describe the permuton limit of a product of finitely many independent uniformly sampled separable permutations and give a formula for the expectation of this limit. We also show that in this case, as the number of compositions goes to infinity, the aforementioned expectation tends to the uniform permuton.

For a non-singular quadratic form $F$ in four variables, we study integer solutions to $F=0$ with an arbitrary weight attached to one of the variables. This allows us to investigate genuinely sparse subsets of the corresponding variety. Our main input is to obtain cancellation in sums of character sums over the moduli arising in the application of the DFI's delta method to the quadratic hypersurface. This cancellation relies crucially on the equidistribution of quadratic roots and the Weil bound for Kloosterman sums.

After the launch of Einstein Probe (EP), pulsars are observed to calibrate the timing system of the onboard Follow-up X-ray Telescope (FXT) by measuring the times of arrival (TOAs). FXT has two independently operating modules, namely FXTA and FXTB, each equipped with the Wolter-I optics and the pnCCD camera. For scientific observations, each pnCCD has three distinct readout modes that differ in frame cycles, the full frame mode (FF, 50 ms per frame), the partial windowed mode (PW, 2.2 ms per frame), and the timing mode (TM, 23.68 $\mu$s per row, 9.4352 ms per frame). Thus, 1RXS J170849.0–400910 with the spin period of 11 s is observed in FF, PSR B1509–58 (150 ms) in PW, and Crab pulsar (33 ms) in TM as well as PSR B1821–24 (3.05 ms) and PSR B1937+21 (1.56 ms). The TOAs of these pulsars measured by FXTA and FXTB are compared with the results of NICER, and for Crab pulsar with the Jodrell Bank Monthly Ephemeris (JBE). Results verify that the timing system of FXTA and FXTB in FF, PW, and TM modes are consistent with each other, and are in good alignment with NICER. The measured advance of the Crab pulsar's main peak relative to JBE is $357^{\pm14(stat)}_{\pm54(sys)} \mu$s in FXTA and $394^{\pm14(stat)}_{\pm67(sys)} \mu$s in FXTB. Based on measurements of PSR B1821–24 and PSR B1937+21, the preliminary absolute timing accuracy is estimated to be 6 $\mu$s for FXTA and 31 $\mu$s for FXTB in TM mode. Additionally, the systematic delay of FXTA timing results relative to FXTB is found to be $20^{\pm19(stat)}_{\pm21(sys)} \mu$s.

Vision-language models (VLMs) learn strong statistical regularities during training, which can make them fail to properly respond to visual evidence when input images violate those regularities. It is challenging to disambiguate these prior-induced errors from errors caused by the model missing the underlying visual capabilities. In this work, we use controlled visual in-context learning to encourage the model to focus on the visual evidence, and demonstrate that this alone is frequently sufficient to correct the errors – suggesting that the models in fact do possess the relevant visual capabilities. Specifically, we show that across five vision-centric tasks, demonstrations yield large gains on prior-conflicting counterfactual examples ($+27.2\%$ for Qwen3-VL 235B and $+15.1\%$ for Qwen3-VL 32B) while leaving accuracy on prior-aligned examples nearly unchanged. These findings generalize across five VLM families with gains from $+9.7\%$ to $+30.3\%$. We analyze visual representations and find that demonstrations indeed redirect attention toward grounding cues while reducing reliance on cues that support the learned prior. Finally, we find that in-context learning is limited when the underlying visual capability is weak or absent. Together, these results show that current VLMs possess visual grounding capabilities that standard evaluations may overlook, underscoring the need for controlled evaluation design in diagnosing and improving model capability.

Image deblurring is a fundamental task in computer vision, yet existing methods mainly specialize in isolated scenarios. Consequently, the deblurring performance of these models drops significantly across scenarios with different cameras and image contents. This motivates the development of a unified motion deblurring framework that can handle diverse blur patterns. To this end, we construct a multi-source dataset and develop a data pruning and quality control pipeline. Then, to restore blur images with various motion blur kernels across different scenarios, we propose a unified motion deblurring framework via Fourier Convolution Learning. Existing deblurring networks usually rely on pixel-level mappings and overlook the convolutional nature of blur. Thus, the network mostly fits the image content itself rather than learning the convolution process, making it difficult to handle multi-source blur images. Instead of relying on spatial mapping, we perform blur-adaptive global filter learning in Fourier space, which avoids the limited spatial support of kernel estimation. Extensive experiments demonstrate that our unified model effectively handles motion blurs across diverse sources and scenes, achieving competitive performance across both in-domain and OOD benchmarks. Code has been released at github.com/DeepMed-Lab-ECNU/Single-Image-Deblur.

Wider vector/SIMD lanes multiply compute throughput, but cache improvements remain challenging. We identify L1 data cache capacity as the most impactful parameter for performance and efficiency. L1 capacity is constrained by pipeline coupling and latency requirements; private L2 offers an order of magnitude more capacity but is inaccessible from software. This work proposes CacheFlex, an ISA and microarchitecture co-design that enables software-managed, direct access to private L2 SRAM by allowing runtime conversion of parts of L2 into a scratchpad memory (SPM). Through a lightweight ISA extension, software explicitly controls data placement and lifetime within the L2. CacheFlex integrates into an out-of-order pipeline with cross-domain memory consistency and OS context-switch support, with merely 2.02% area overhead relative to the L2 in a post-layout 12 nm implementation. We prototype CacheFlex based on the Armv8-A SVE ISA, model it in gem5, and evaluate it using optimized general matrix multiplication (GEMM) kernels with diverse model-derived shapes, FlashAttention-based fused attention, and full-layer workloads from LLaMA-3.2-1B and BERT-Base in the prefill phase. As the vector length (VL) scales from VL = 4 (512-bit) to VL = 16 (2048-bit), CacheFlex's kernel-level geometric-mean speedup and memory-subsystem energy reduction grow from 1.12x and 26% to 1.44x and 40%, respectively, bridging the widening gap between per-instruction data demand and memory performance. On full transformer layers combining CacheFlex with FlashAttention, the design delivers up to 1.78x speedup and 45% memory-subsystem energy savings (BERT-Base, sequence length T=4096, VL = 16; LLaMA-3.2-1B: 1.64x and 38%). CacheFlex is complementary to hardware prefetching, and its benefit grows as vector width and peak compute throughput increase for compute-intensive AI kernels.

Decoder hidden states from different layers of large language models (LLMs) often encode complementary information. However, existing speculative decoding methods typically rely on a small set of target-model layers chosen using fixed, position-based heuristics. Selecting an optimal subset of layers is inherently a combinatorial problem, making exhaustive evaluation infeasible even for moderately deep models. In this work, we present a principled framework for multi-layer hidden-state selection for speculative decoding based on two complementary criteria: informativeness, measured through matrix-entropy analysis, and diversity, quantified using centered kernel alignment (CKA). We investigate layer-wise Shannon entropy, aggregate entropy under hidden-state concatenation, and pairwise CKA dynamics across depth, revealing distinct geometric and informational compartments within decoder representations. Motivated by these findings, we propose entropy and CKA-based layer selection algorithms that favor hidden-state sets that are both highly informative and minimally redundant. As part of this framework, we introduce token-entropy filtering, which removes hidden states associated with low predictive-entropy tokens, thereby improving the quality of layer-selection statistics. In EAGLE3-style speculative decoding, our selected sets outperform fixed baseline choices, including the default $[2, N//2, N-3]$ rule, while providing a clearer explanation of why some defaults can remain competitive. Our results provide a practical recipe for multi-layer hidden-state selection for speculative decoding, insights into the geometry and information in LLM decoder states, and a foundation for extending similar analysis to related applications.

We study static indexes for exact subsequence matching over all equal-length windows of a time series. Under deterministic SETH, for every fixed $\beta\ge1$ and $\delta\in(0,1)$, we exclude $O(N^\beta)$ preprocessing together with $O(N^{1-\delta})$ worst-case query time on domains containing the reduction's polylogarithmic query lengths. The bounded-error counterpart assumes randomized SETH. The results cover specified warping, bottleneck, edit, subsequence, local-alignment, and complexity-adjusted scores. Their reductions share a data-independent query interface but require different arguments for all-window soundness. We give complete representative proofs for the distinct mechanisms and state the changes needed by related scores. For soft-DTW, integer scaling yields an exact Boolean-predicate reduction in Word-RAM; a model with exact transcendental primitives requires a separate assumption. For independent window-wise Z-normalization, balanced coordinate gadgets and shifted-window moment bounds yield exact lower bounds for squared-cost DTW and discrete Fréchet distance. We give finite-word comparisons and a specified length-dependent rounding rule preserving these gaps. Raw and normalized discrete Fréchet constructions also exclude feasible-solution approximation within any fixed factor below two. Finally, we prove conditional signal-attenuation bounds for normalized anchor constructions and a fast index under the all-window common-mean promise.

Conformal prediction provides finite-sample, distribution-free coverage guarantees that can support decision-making in specific settings. In multistage problems, earlier decisions determine the populations relevant to later calibration. When later scores are refit using earlier calibration results, reusing those cases for ranking need not preserve exchangeability with a surviving test case. We study sequential conformal calibration with a fresh fold at each stage: conditional on earlier folds, the selected fold scores and the surviving test score are exchangeable. This yields finite-sample coverage guarantees for every prefix of the decision sequence. For atomless survivor score distributions, we derive a universal Binomial-thinned Beta chain for the realized coverage process. Its law depends only on fold sizes and target levels, even under predictable refitting, and yields exact coverage slack, abstention probabilities, and calibration-conditional guarantees. We further characterize the tradeoff between freshness and data reuse. For fixed scores, strict-survivor reuse is exactly valid. For adaptive scores refit using past calibration data, reusing survivors can incur worst-case rank loss, while blocked designs provide an intermediate option between full reuse and stagewise fresh folds. As a case study, we apply the framework to serial multi-echelon inventory problem and propose a sequential conditional-quantile formulation. Each stock level is learned as a context-dependent quantile of cumulative demand among scenarios satisfying earlier no-backlog constraints. We connect these targets to common-shift stationarity and derive decision-level implications for the resulting calibrated policies. In a three-echelon simulation, fresh-fold refitting achieves 81.98% final-prefix coverage against an 81.82% target while reducing mean cost by 5.5% relative to the Bonferroni baseline.

Vision-language-action (VLA) models provide a unified framework for visual understanding, language grounding, and robot control, yet anticipating how the scene will evolve beyond the current observation can provide additional information for control. Action supervision alone does not explicitly encourage such anticipation, while future-image prediction entangles task-relevant motion with largely static appearance. To address these limitations, we introduce Evo-World, a lightweight VLA model that augments policy learning with future motion prediction through optical-flow supervision, thereby providing a task-relevant predictive signal focused on motion rather than appearance. We further design the training procedure to preserve these predictive representations during policy learning, regulating representation diversity while decoupling representation learning from action optimization. Across simulation benchmarks, Evo-World demonstrates strong performance, achieving a tier-averaged success rate of 91.1% on Meta-World MT50 , with a 13.0% relative improvement over the non-predictive baseline. On real-world AgileX robots, Evo-World outperforms the evaluated baselines across single-arm and bimanual manipulation tasks while using only 0.87B parameters and delivering lower GPU memory usage and higher inference efficiency. These results demonstrate that future motion prediction through optical-flow supervision provides an effective and lightweight approach to enhancing the predictive capabilities of VLA models.

A macroscopic method of the parton and hadron cascade model PACIAE combined with the coalescence model DCPC is employed to study the $\phi$-mesic nuclei in $pp$ collisions at $\sqrt{s}$ = 7 TeV for the first time in this work. Based on the final hadronic states of $pp$ collisions simulated by the PACIAE model, the $\phi$-mesic nuclei: $\mathrm{^3_{\phi} H}(\phi-pn)$, $\mathrm{^4_{\phi} H}(\phi-pnn)$, and $\mathrm{^4_{\phi} He}(\phi-ppn)$ are recombined by the DCPC model with constituents of protons, neutrons, and $\phi$ mesons. Their yields, transverse momentum spectra, and rapidity distributions are simulated separately. These theoretical predictions call for experimental confirmation.

Moving dilated arrays (MDAs) can increase the uniform degrees of freedom (uDOFs) while alleviating mutual coupling, but their performance is susceptible to unknown gain and phase errors (GPEs). To deal with this problem, we investigate self-calibration direction-of-arrival (DOA) estimation for MDAs with unknown GPEs. First, multi-position observations are phase aligned to construct an equivalent virtual array with an enlarged aperture. Next, the motion-induced relationships among the GPEs are exploited to establish explicit calibration constraints. By leveraging the orthogonality between the steering vectors and the noise subspace, the joint estimation of the DOAs and GPEs is formulated as a constrained optimization problem. To solve this problem, a two-stage alternating optimization (AO) algorithm is developed. In the first stage, the GPEs are estimated in closed form with the DOAs fixed. In the second stage, the estimated GPEs are used to calibrate the covariance matrix, after which the DOAs are refined using the multiple signal classification (MUSIC) algorithm. To obtain reliable initial estimates, a rotational invariance-like (RIL) initialization method is further developed by exploiting two translated virtual subarrays with identical GPEs. Furthermore, the Cramer-Rao bound (CRB) is derived to characterize the theoretical performance limit of the considered system. Simulation results demonstrate that the proposed method converges reliably and achieves accurate DOA estimation under different array apertures, numbers of snapshots, GPE levels, and numbers of sources.

Large language models have achieved remarkable advances in complex reasoning. However, scaling reasoning post-training with ever-larger corpora can substantially increase training cost without proportional performance gains. In this study, we therefore ask: how far can reasoning supervision be compressed without sacrificing capability? To this end, we propose an uncertainty-guided progressive contraction framework that concentrates supervision and optimization on the reasoning trajectories most valuable for learning. Specifically, rather than treating a teacher-generated chain-of-thought (CoT) as a single realized path, we construct uncertainty-profiled reasoning supervision by building Monte Carlo reasoning trees around intermediate reasoning states to expose process-level uncertainty. This uncertainty first contracts the original corpus into a compact teacher-informed pool. A second, learner-aware contraction then performs online routing during SFT, concentrating optimization according to the student's evolving learning state. Together, the two stages progressively contract both supervision and optimization, substantially reducing the student training budget. Experiments across diverse reasoning benchmarks and LLM families show that our method uses as little as 0.22% of the optimization budget of full-data SFT, over 450x less training exposure, while maintaining or improving reasoning performance. Notably, our framework generalizes well across heterogeneous student families, black-box teachers, and weak-to-strong transfer. This indicates that it is not only a way to accelerate training but can also enhance reasoning capability.