Papers

Three-dimensional (3D) atomic-structure analysis is of central importance in (scanning) transmission electron microscopy (STEM). STEM techniques to reconstruct 3D structure include tilt-series or defocus-series annular dark-field, best suited to heavier atomic species, and dynamical-scattering-model inversion applied to single-defocus four-dimensional (4D) STEM data, requiring computationally expensive post-experiment analysis. In this study, we propose a 3D-structure linear inversion (3D LINV) STEM algorithm, which enables a fast and direct reconstruction of 3D structures from a single-defocus 4D-STEM dataset. This method is based on solving linear equations relating the measured 4D-STEM data and the unknown 3D specimen potential under the thick weak phase object approximation. We show the capabilities of 3D LINV STEM through systematic 4D-STEM simulations across various observation parameters such as specimen thickness, partial coherence, and shot noise, and through an experimental demonstration of 3D structure reconstruction of a stacked freestanding membrane with atomic-scale lateral resolution and nanometre-scale depth resolution.

Continuous-aperture arrays (CAPAs) provide a new electromagnetic transmission paradigm by directly controlling the source-current distribution over a continuous radiating aperture. This paper studies CAPA-enabled integrated sensing and communication (ISAC) with spatially extended sensing targets, for which the electromagnetic response over each target region is characterized by an aperture-to-region operator. Unlike point-target models, the resulting illumination operator may have infinite rank, precluding a priori finite-dimensional reduction of the transmit design. We formulate the joint communication and target-illumination beamforming problem in the continuous electromagnetic domain and develop an operator semidefinite relaxation (SDR). A key structural result is that the optimal transmit covariance operators remain finite rank even when the aggregate illumination operator has infinite rank. We further establish the tightness of the operator SDR and provide a constructive rank-one recovery of the information beamformers. Since the finite electromagnetic subspace supporting the optimum is generally unknown, we develop a dual-slack-driven adaptive mode-enrichment method that discovers the required modes from the full-space optimality conditions. The dual-slack violation simultaneously identifies missing modes and yields a computable certificate of the remaining full-space optimality gap. Global convergence of the enrichment sequence to the full-space optimum is established. Numerical results validate the finite-rank optimal structure and show that the proposed method approaches the full-space optimum with substantially fewer electromagnetic modes than truncated-SVD and spatial-Fourier representations.

Topology optimization has found significant utility in additive manufacturing, but the resulting geometries are often difficult to realize using subtractive methods. The complex, curved surfaces of optimized designs typically require time-consuming point milling operations. In contrast, geometries composed of developable surfaces are well suited to flank milling, enabling substantial improvements in machining efficiency and surface quality. However, globally minimizing Gaussian curvature leads to overly simplistic designs. We address this challenge with a novel method that represents geometry using three implicit neural fields, optimized to produce machinable components. The resulting designs consist of regions of developable surfaces separated by seamlines where curvature is concentrated. Seamlines are efficiently computed as intersections of the implicit fields, while the geometry emerges through their product. By constraining surfaces to align with the cutter's normal or tangential direction, our approach further accommodates practical constraints of 3-axis machining. We demonstrate concurrent optimization of topology and Gaussian curvature, enabling control over seamline feature scale. Compared to methods that enforce subtractive machinability without considering milling efficiency, our approach consistently reduces machining time while maintaining competitive structural performance.

Ultra-reliable and low-latency communication (URLLC) is essential for mission-critical cellular Internet of Things (IoT) applications requiring reliable short-packet transmission and efficient radio-resource allocation. However, finite-blocklength (FBL)-aware beamforming becomes computationally demanding as the numbers of users and antennas increase. Existing successive convex approximation (SCA) methods typically rely on general-purpose convex solvers without exploiting the structure of the resulting beamforming problem. This paper develops a structure-exploiting consensus alternating direction method of multipliers (ADMM) framework for low-complexity FBL-aware beamforming in downlink multi-user multiple-input single-output (MU-MISO) cellular IoT networks. The FBL sum rate is maximized subject to transmit-power and per-user minimum-rate constraints. Each SCA iteration yields a convex quadratically constrained quadratic program (QCQP), reformulated into an equivalent consensus problem. For an M-antenna base station serving N IoT nodes, the global update exploits Kronecker structure to replace an MN-by-MN factorization with a shared M-by-M factorization, while rank-one channel matrices enable low-complexity local projections. CVX-SCA serves as a general-purpose benchmark, whereas standard ADMM-SCA isolates the gains from structural exploitation. Numerical results demonstrate close agreement with CVX-SCA in objective value, feasibility, and convergence. Under user scaling, the proposed method achieves more than 4-fold end-to-end speedup over CVX-SCA and approximately 6-fold per-iteration speedup over standard ADMM-SCA, demonstrating its computational efficiency for cellular IoT resource allocation.

Misclassification is a critical problem in many machine learning applications. Since even the classifier models with high accuracy (e.g., > 95%) still introduce some misclassification error, it may not be possible to rely on the output of a classifier. In this paper, we introduce trustable learning, which prompts the learning model to yield only the true output, thus avoiding misclassifications. Whenever the model cannot decide the output accurately, the learning model should indicate that there could be a misclassification error if it is forced to classify, and hence, it should reject to make a decision or defer it to a human expert. Therefore, we develop a methodology for trustable learning and apply it to artificial neural networks and show that it is possible to develop a classifier with 0% misclassification error. We propose a novel neural network architecture named WisdomNet that could provide zero prediction error by introducing an additional neuron named as conjugate neuron that would indicate whether the network is able to classify the data correctly or not. The WisdomNet architecture can be applied to any previously built model, and we have evaluated WisdomNet with several network architectures such as multilayer perceptron, convolutional neural network, and deep network on different data sets. The results show that the WisdomNet is able to reduce the classification error rate to 0%, while labeling the data is difficult to classify as `reject' at a low percentage of within around 10%.

Large language models (LLMs) offer a new approach to wearable-sensor-based human activity recognition. Retrieval-augmented generation (RAG) further introduces similar motion examples and discriminative sensor knowledge, enabling decisions grounded in observations relevant to the current query. More evidence, however, does not necessarily mean better-organized evidence. When online prompts and LLM agents primarily orchestrate inference, decisions about which activities to compare and when to invoke discriminative knowledge remain concentrated at inference time. As the activity vocabulary grows, the model must repeatedly process more candidates and associated knowledge, whereas pruning candidates too early risks excluding the true activity. We propose confusion-hierarchy evidence-aware reasoning (CHEAR), which moves part of this knowledge organization offline. CHEAR constructs and validates an activity hierarchy from recurrent cross-subject retrieval errors and builds corresponding activity-pair knowledge. At inference time, the hierarchy orders candidate comparisons; the LLM retains candidates progressively, and local discriminative knowledge is accessed only for the remaining activities. Across eight datasets, CHEAR achieves 86.79% mean cross-subject accuracy, a 75.91% candidate reduction rate, and 96.44% true-activity retention. Per-sample token use is 85.15% lower on average than in a variant without the hierarchical structure. Mean accuracy across eight cross-dataset transfer directions is 88.81%. These results show that organizing candidates and discriminative knowledge around observed activity confusions reduces online LLM input while maintaining recognition performance.

Recently, AutoRegressive Visual Generation (ARVG) models have emerged as a competitive paradigm for high-quality image synthesis. However, their substantial computational and memory demands make them difficult to deploy on resource-constrained edge devices. Post-Training Quantization (PTQ) provides a promising solution to reduce the computational and memory costs of ARVG models, yet existing methods often suffer from substantial image quality degradation under low-bit quantization. In this paper, we propose a training-free PTQ framework for ARVG, consisting of Tail-Aware Bounded-init Grid Refinement (T-BGR) and Coarse-to-Fine Activation Precision Scheduling (CAPS). T-BGR introduces a tail-aware reconstruction objective for weight quantizer calibration, assigning greater importance to distribution-tail coefficients and preserving fine-grained information without introducing additional parameters or high-precision branches. CAPS performs coarse-to-fine activation precision scheduling by jointly considering the importance and computational cost of different generation stages, enabling efficient mixed-precision allocation under a given bit budget. Extensive experiments on multiple ARVG backbones demonstrate that our framework consistently improves robustness under aggressive low-bit quantization. Notably, on Infinity, our framework achieves near full-precision image generation quality at an effective W4A5.6 activation precision, while existing methods at W4A6 still exhibit noticeable quality degradation or inconsistent performance. Code is available at https://github.com/lxm-lc/HGA-Quant.

This paper examines the use of recurrent neural networks and their extensions for forecasting autoregressive causal-noncausal processes, characterized by local explosive patterns such as bubbles and spikes. We study the recurrent neural networks (RNN), long short-term memory networks (LSTM), gated recurrent unit (GRU), bidirectional LSTM, and also a simple feed-forward network (FNN) to reveal the difficulty of forecasting extreme values depending on the type of network and the length of the training set. We show that FNN outperforms other networks in predicting extreme values of a univariate noncausal time series during a bubble. We also examine the improvements of point predictions of extreme values resulting from pooling and a modified loss function.

This study investigates the chemical evolution history and radial migration in the Milky Way utilizing high-precision age measurements based on large-scale stellar spectroscopic surveys. Recent observational data have revealed a distinct break in the age-metallicity relation of stars in the solar neighborhood, suggesting that stellar populations of the Milky Way can be divided into two evolutionary sequences. Based on galactic chemical evolution models, we confirm that this break in the age-metallicity relation can be explained by a recent major gas accretion event, which diluted the metallicity in the disk and triggered a starburst, leading to the formation of an independent age-metallicity sequence. To assess the impact of stellar radial migration, we incorporate a simplified treatment of this process into our multi-zone chemical evolution model. Radial migration is modeled as a probabilistic diffusion process, characterized by a Gaussian distribution. By fitting the model-predicted metallicity distribution functions (MDFs) of mono-age stellar populations to observations, we infer a migration strength of $\sigma = 2.15^{+0.100}_{-0.103}\,{\rm kpc}$ for stars with ages between 2 and 6 Gyr located at 9.5-11.5 kpc, corresponding to an average radial displacement of 1.92 kpc over 10 Gyr. This result is lower than previous estimates of stellar radial migration, suggesting that the role of radial migration in shaping the chemical structure of the Milky Way is less important than previously estimated.

Evaluating robot manipulation policies through repeated physical trials is costly. We study whether an action-conditioned world model can serve as a closed-loop test environment whose policy success rates track those on real robots. Beyond realistic video, the model must return the camera views and proprioceptive state needed for the policy's next action and preserve failed-action outcomes to avoid overestimating policy capability. We introduce ProWorld, a world model that jointly predicts multi-view video and robot state, then feeds both back to a frozen policy for repeated interaction. ProWorld comprises a shared transformer for joint video-state flow prediction and Shared-Time View Encoding to distinguish cameras while preserving temporal synchronization. To reduce interaction hallucinations that turn missed grasps into successful lifts, we augment training with failed interactions collected in high-fidelity simulation, reducing inflated success rates in the generated environment. ProWorld achieves the highest overall TriWorldBench score among the compared methods. Across three policies and four local manipulation tasks, it attains a Pearson correlation of 0.95 and a Spearman correlation of 0.94 between generated and real success rates. These results support joint visual-proprioceptive feedback and failure-aware training as a basis for world-model-based policy evaluation.

In this short note, we point out that the recent lower bounds for off-diagonal Ramsey numbers $r(s,t)$ with fixed $s\ge 5$, together with the recent proof of the Ajtai–Erdős–Komlós–Szemerédi independence conjecture, imply \[ r(4,t)=\frac{t^3}{(\log t)^{2+o(1)}}. \] This note is solely for informal circulation and will not be submitted for publication.

LLMs increasingly support sensor-based human activity recognition (HAR) by linking motion signals with activity semantics and physical knowledge. Retrieval-augmented generation (RAG) grounds decisions in sensor examples and domain features, enabling training-free target-user inference with less dependence on raw numerical arrays. However, existing LLM/RAG-based HAR typically searches single-level activity spaces using static population knowledge. Consequently, they compare many unrelated candidates using the same static population evidence and overlook personalized motion patterns. We propose OntoAR-HAR, an ontology-guided agentic RAG framework combining static population and personalized knowledge. Its tree-structured activity ontology decomposes classification into local decisions among semantically related activities. The static store supplies node-constrained examples, while offline-discovered executable signal features provide numerical evidence for local distinctions. During inference, the personalized store collects selected user observations, which the LLM integrates with static knowledge and signal features while traversing the ontology to an activity label. Cross-subject and heterogeneous-sensing experiments show complementary gains from hierarchical retrieval and personalized memory across multiple LLM backbones, achieving state-of-the-art performance. By explicitly modeling hierarchical relations across activity granularities, OntoAR-HAR also addresses the long-overlooked semantic inclusion problem and avoids treating related labels as independent categories.

Recently, OpenAI announced a uniform $7/8$ zero-free half-plane for finite-order Hecke $L$-functions over $\mathbb{Q}(\sqrt{-3})$, together with its transfer to Dirichlet $L$-functions. Assuming the analytic inputs of that work, we improve the boundary from $7/8=0.875$ to $8748867/10000000=0.8748867$ for the same families. The improvement combines a relaxed direct estimate with an amplified first moment of the reflected numerator, obtained from the existing fourth-moment estimate. A two-stage parameter argument yields the stated boundary without strengthening the inverse-moment estimate.

We present Co-DSL, a framework in which users and LLMs co-design reusable spatial concepts for layout generation. In the first stage, our system allows users to create a library of personalized operations. To add a concept, a user provides a description, which the LLM converts into an initial implementation. The user can then observe the concept's execution behavior over example scenarios and provide lightweight feedback to the LLM, which revises the concept's implementation logic. In the second stage, given a library, an LLM can author a layout program that meets a new layout request from a user. Executing a layout program instantiates a concept-graph, a declarative composition of library concepts. In this way, we require the LLM only to specify which concepts should hold, while we use a solver to search for a layout that satisfies them. Across five spatial layout domains, we find that Co-DSL libraries let LLMs capture layout patterns that are challenging for prior fixed-operation systems, and demonstrate that our concept-graph representation is needed for LLMs to reliably compose concepts together. We further find that Co-DSL lets LLMs author generative layout programs that expose high-level parametric controls users can manipulate to explore a distribution of related layouts without re-prompting.

Sharing of information in multiagent systems allow for improved coordination. Delays in communication can cause asymmetries in information, causing classical results to fail. We study the decentralized LQG problem with delayed information. In general, the optimal policies are not linear and are difficult to calculate. Restricting to linear policies, we analytically calculate the gradient descent for gains from private information. This naturally lends itself to a gradient descent algorithm which we apply to examples to show policy improvements.

Let $\Lambda_m$ be the Barnes-Wall lattice of dimension $2^m$, normalized to have minimum squared norm $d_m:=2^{m-1}$. We determine its complete norm spectrum strictly between $d_m$ and $2d_m$, proving that, for every integer $m\ge1$, $\{\|x\|^2:x\in\Lambda_m,\ d_m<\|x\|^2<2d_m\}=\{2d_m-2^j:j\in\mathbb Z,\ \lceil m/2\rceil\le j\le m-2\}$. In particular, the norm spectrum in this interval is nonempty for $m\ge4$. The proof uses a Gaussian-integer model in which lattice automorphisms arising from Clifford unitaries transform a vector into a pair of coordinate subvectors in a lower-dimensional lattice. Divisibility of the differences of their squared norms and a matrix Parseval identity provide the arithmetic and averaging constraints needed for induction on $m$. Every listed norm is realized explicitly by a sum of two minimal vectors of the lattice.

Category-level 6D pose and shape estimation requires recovering an object's pose and geometry from partial observations without an exact instance model. We present ASM-6D, which couples generative complete-geometry prediction with explicit category-level pose-shape inference through shared correspondences. Given an RGB-D image, ASM-6D generates alternative complete 3D correspondence hypotheses whose point identities are shared with a category-level Active Shape Model (ASM), including occluded points. Each hypothesis is fitted directly for rotation, translation, metric scale, and instance shape without a separate correspondence-assignment stage. We analytically eliminate translation and shape coefficients, reducing fitting to a nine-variable scaled-rotation optimization problem that enables efficient batched evaluation of multiple hypotheses in real time. ASM-6D achieves state-of-the-art performance on ROPE and HouseCat6D benchmarks. Ablations demonstrate the importance of generative correspondence prediction and active shape variation. The representation also supports shape completion, shape-dependent pose ambiguity, tracking, and robotic grasping at 6-38 Hz, depending on the inference budget.

The accuracy of detecting protein crystals for fluorescence microscopy images is very critical for high throughput and automated systems. Although the trace fluorescent labeling method could highlight protein crystals, reflection and emission from the fluorescence dye is not always due to crystal regions. Therefore, the analysis of the peak wavelength in the emission spectra of a fluorophore may not always yield effective results. In this paper, we show that using the subordinate color intensity corresponding to longer wavelengths than the peak wavelength of the emission spectra could improve the accuracy of protein crystal detection. Hence, we have built a segmentation method based on the percentile intensity of the subordinate color for trace fluorescently labeled (TFL'd) protein crystallization trial images. Compared to using the dominant color channel, our segmentation method on subordinate color channel was able to reduce the misclassification rate of likely-leads or crystals as non-crystals by the percentage of from 9.71% to 2.02% depending on the classifier. Similarly, the accuracy of classifiers were increased by the percentage of from 1.77% to 5.53%. Our method reached around 94% accuracy while keeping misclassification of likely-leads and crystals as non-crystals below 1%. Moreover, to evaluate the generalizability of our method, we have conducted new wet lab experiments on two proteins, Concanavalin A (Con A) and Ab inorganic pyrophosphate (AbIPPase), and the misclassification rate was below 1%. Our experiments show that using the subordinate channel may be more helpful for TFL'd protein trial image classification.

Multi-hop retrieval-augmented generation (RAG) requires finding documents whose evidence is useful in combination. Query relevance and graph connectivity help locate related content, but neither directly measures the additional information one document contributes given another. We introduce SG$^2$RAG, a framework that represents this complementarity through semantic gain. Offline, a large language model assesses the relevant and nonredundant information contributed by one chunk given another within neighborhoods proposed by semantic similarity. These ordered assessments are aggregated into symmetric edge weights to construct a reusable Semantic Gain Graph. Online, controlled Personalized PageRank starts from query-relevant seeds and ranks complementary evidence beyond the initial retrieval set. Experiments on MuSiQue, 2Wiki, and HotpotQA with two language model backbones show that SG$^2$RAG achieves the best average EM, F1, and Recall@10 among the evaluated single-retrieval methods. Under identical candidate support and propagation, semantic gain improves average F1 and Recall@10 over similarity weighting by 4.08 and 4.31 points. Analyses of supporting documents and improvements in three iterative retrieval frameworks further support its effectiveness as a reusable retrieval component.

Drug discovery requires efficient exploration of an astronomically large chemical space. Molecular graph diffusion models offer a promising approach to this task, but many require graph size to be fixed before generation. Although atom-level insertion and deletion can enable flexible-size generation, jointly modeling molecular size, atom types, and bonds while maintaining chemical validity remains challenging. We introduce FragFlex, a flexible-length discrete diffusion model that performs node insertion and deletion at the fragment level. During denoising, FragFlex jointly learns the size, fragment identities, and inter-fragment connectivity of the fragment graph. A neural attachment-site predictor and valence-aware assembler then convert the generated fragment graph into an atom-level molecule. In large-scale experiments generating 10 million molecules, FragFlex achieves near-perfect chemical validity while maintaining high uniqueness, demonstrating a strong balance between the two.

In off-policy evaluation, merging decision-time histories that matter differently for a specified policy value or comparison can make that evaluation unidentified, even with observed actions and outcomes and known behavior and target policies. We characterize which distinctions must be preserved: identification holds if and only if the action-specific evaluation weights are constant within each released record, and the coarsest exact release groups histories by these weights. For normalized outcomes, the largest sharp width induced by the release equals a behavior-weighted within-record radius of these weights. The same radius becomes a release-design objective when each record may be refined into at most $m$ categories. The optimum has an exact $m$-center characterization. When behavior does not vary within a released record, we give a finite-data repair algorithm whose maximum evaluation-weight radius is at most twice the finite-data optimum. For a fixed action-outcome distribution within a released record, a distinct sharp-identification problem remains. Under the same condition, the action-specific outcome distributions are identified, and optimizing over their couplings gives the sharp interval. We construct an AIPW envelope containing this sharp interval; it matches the interval for all such outcome distributions exactly when the extreme within-record action-coefficient vectors take at most two values in each action coordinate. In 24 KuaiRec tasks, the repair algorithm yields a 93% median reduction in mean pairwise sharp width at $m=64$ relative to the unrepaired release.

Large Language Models (LLMs) have made substantial progress in multilingual question answering, yet their ability to understand low-resource sociolinguistic contexts remains under-explored. We study North Korea as a unique testbed where decades of division have produced distinct differences from South Korea in vocabulary, orthography, norms, and ideological discourse. We introduce LENS (Language and sociocultural Evaluation for North Korean Society), a human-validated benchmark of 1,765 questions evaluating LLMs across three dimensions: linguistic robustness, sociocultural perspective alignment, and domain-specific knowledge. Evaluating diverse recent LLMs, we find a modest performance drop on North Korean language inputs, a larger gap in sociocultural perspective alignment, and severe limitations on domain-specific knowledge. Qualitative analysis reveals that models often conflate formal institutions with lived realities, project liberal-democratic assumptions, or rely on coarse stereotypes. Our results demonstrate that linguistic similarity alone does not guarantee sociocultural or domain-specific understanding, highlighting the critical need for grounded evaluation resources for underrepresented cultural and political contexts.

Verifier-guided inference-time scaling uses additional computation to score intermediate states and steer generation toward better outputs. However, imperfect intermediate verifiers can distort sampling, and repeated refinement alone does not ensure recovery of the desired reward-tilted distribution. We introduce Continuous-State Verifier-Guided Backtracking (CS-VGB), an inference-time scaling method for sampling from reward-tilted distributions with continuous generative models through repeated denoising and renoising. With correctly paired denoising and renoising transitions, the stationary distribution of CS-VGB at the clean checkpoint equals the desired reward-tilted target, even when intermediate verifiers are inaccurate. Under stated regularity conditions, CS-VGB converges exponentially to the target despite verifier error, and the expected number of updates needed to reach a clean sample grows only linearly with the number of checkpoints. In analytically tractable settings, we empirically demonstrate that CS-VGB recovers the desired reward-tilted distribution despite verifier error, whereas the compared verifier-based sampling methods fail to recover the target under the same verifier errors. We also instantiate the framework with diffusion models and one-step stochastic posterior maps. Across prompt-guided ImageNet generation, facial-attribute generation on CelebA, and multi-robot planning, recurrent CS-VGB search improves reward and task success as inference budgets grow, with image-generation rewards continuing beyond the observed plateaus of denoising-only baselines.

Depth estimation and Gaussian reconstruction share a need for multi-scale feature processing, yet use different prediction interfaces and training objectives. Whether a decoder's internal computation can be optimized once and reused across these systems remains a structural design question. Search over primitive configurations alone leaves the organization of transformations fixed. To address this gap, we propose GeoBridge, an evolutionary framework for transferable decoder topologies. First, GeoBridge makes stage-internal topology searchable through residual, sequential, and parallel composition of configurable primitives. Shape-preserving composition retains the stage interfaces of a fixed multi-scale scaffold. Second, a functional-tree encoding supports stage-aware crossover and hierarchical mutation, while a gradient sensitivity-alignment proxy evaluates candidates without training. Multi-objective evolution balances this proxy with computation and parameter cost. Third, selected topologies are instantiated and trained in target systems with task-specific prediction interfaces. A single source search takes approximately 12 GPU hours. GeoBridgeNet-A3 achieves the best depth accuracy among four adapted decoder baselines under a common encoder and training protocol on NYU Depth V2 and KITTI. The same topology reaches 27.11 dB PSNR in Gaussian novel-view synthesis on RealEstate10K, and its refined representations support open-vocabulary segmentation on LERF. These results support decoder topology as a reusable design object across the evaluated geometric vision systems. Code and pretrained weights are available at https://github.com/EMI-Group/GeoBridge-NAS.

In this paper, we determine the structure of the cut locus for a class of complete warped product manifolds $M=(R^1\times S^1,dt^2+m(t)^2d\theta^2)$, where the warping function $m(t)$ is positive and even, under the assumption that there exists a positive number $t_1$ such that the Gaussian curvature is nonpositive on the domain $t^{-1}\left((t_1,\infty) \right)$ and is decreasing along the subarc $t^{-1}([0,t_1])\cap\theta^{-1}(0)$ of the upper half meridian.

In this paper, we extend Lusztig's description of quotients of Coxeter varieties by unipotent radicals of parabolic subgroups, to quotients of certain open neighbourhoods in the smooth compactification of Coxeter varieties. These quotients are products of an affine space with a Coxeter variety for an associated Levi quotient, and this result holds uniformly for any connected reductive group over a finite field. As an application, we prove a conjecture of Wang computing the invariants, under the action of unipotent subgroups, of the cohomology of the Deligne-Lusztig coverings of Coxeter varieties. We also prove that derived Alvis-Curtis duality sends the compactly supported cohomology of these coverings to their ordinary cohomology.

Large language models are typically evaluated in terms of the correctness of their output. However, output correctness alone does not confirm whether the latent knowledge supporting an answer has stable internal representations. We therefore propose latent state stability (LSS) and knowledge topology stability (KTS) to investigate the stability of individual knowledge states and their relational structure, respectively. Specifically, we first separately average the model's internal representations of the same knowledge under each elicitation condition. Using the mean representation under the baseline condition as a reference, we remove shared shifts to obtain corrected representations. We then formulate LSS as the distance between each corrected representation and its reference representation, normalized against the typical distance between knowledge items of the same type. We formulate KTS as the cross-condition consistency of the ordered pairwise representation distances among knowledge items of the same type. Next, we construct EpiStableBench, which comprises 4,411 items spanning factual knowledge and mathematical reasoning, with 76,766 controlled queries. Across 16 LLMs from four families, representation stability varies substantially even among items answered correctly under the base condition. Within models, higher stability generally corresponds to higher accuracy under held-out elicitation conditions; across models, stability does not consistently increase with model size or overall accuracy. Meanwhile, we present LatentDPO to learn a knowledge-editing policy that accounts for the stability of latent knowledge. Experimental results show that integrating LatentDPO with multiple existing editing methods consistently improves editing success and generalization across different expressions.

Let $X$ be a product-quotient surface, which is by definition a minimal resolution of $(C_1\times C_2)/G$, where $C_i$ are smooth curves of genus $\geq 2$ and $G$ is a finite group. When $G$ acts freely, we show that every product Bridgeland stability condition on $C_1\times C_2$ induces a tilt stability condition on $X$, and that, if $p_g(X)=q(X)=0$, every tilt stability condition on $X$ arises this way. When $(C_1\times C_2)/G$ has only $A_1$-singularities, we use induction \cite{MMS} and derived McKay correspondence \cite{BKR} to produce non-geometric stability conditions $\sigma_X$ on $X$, which satisfy the full support property and lie in the closure of the geometric chamber. Whether $\sigma_X$ also lies in the closure of the $\widetilde{\mathrm{GL}}^+(2,\mathbb{R})$-orbit of the tilt stability conditions depends on a single inequality, $\omega_X^2 \ge n/8$, where $n$ is the number of $A_1$-singularities. When it fails, the geometric chamber is strictly larger than this orbit.

We study stable solutions of the Lane–Emden equation $$-\Delta u=|u|^{p-1}u$$ on graphs with polynomial volume growth. Due to the lack of a chain rule in the discrete setting, we establish suitable algebraic inequalities which serve as substitutes for the usual differential identities. Combining these inequalities with the stability condition and cutoff arguments, we obtain nonexistence results for stable solutions in a range of exponents analogous to the Joseph–Lundgren range. As an application, we derive a lower bound for the Sobolev best constant in the discrete setting.

Training humanoid robots to learn human behaviors requires expensive data collection, and human-robot interaction data can be even more difficult and costly to collect. Training a specialized reaction model for each humanoid embodiment can also be time-consuming and resource-intensive. Human-to-humanoid motion retargeting provides a more scalable alternative, allowing human-human reaction data to serve as a common motion representation for different humanoid embodiments. However, due to morphological and kinematic differences between humans and humanoid robots, a reaction preferred in human motion space may not be the most suitable one for execution on a particular robot embodiment. In this work, we propose an inference-time reaction search framework that leverages stochastic sampling from a generative reaction model and jointly considers reaction quality and humanoid embodiment feasibility. Given the observed interaction, our framework generates multiple plausible reaction candidates. Each candidate is retargeted to the target humanoid and evaluated using complementary interaction and embodiment-specific feasibility criteria, allowing candidate selection under the physical constraints of the target embodiment. Since the reaction generator remains frozen, the framework can adapt to different humanoid embodiments at inference time without retraining. Experimental results demonstrate that the proposed framework maintains overall human reaction quality while improving the feasibility of retargeted humanoid reactions across different embodiments. The proposed pipeline improves humanoid retargeting feasibility by 1.61%. Moreover, human-space and G1 best-candidate selections disagree in 78.98% of samples, demonstrating substantial embodiment dependence. Code will be released.