Papers

Transition-metal chalcophosphates (TMCs) are two-dimensional (2D) van der Waals materials supporting a broad range of electronic and magnetic properties. Among quaternary TMCs, AgVP$_2$Se$_6$ is a rare ferromagnet (FM) with a triangular V sublattice, in contrast to the antiferromagnetic (AFM) zigzag chains of the sulfide AgVP$_2$S$_6$. Prior Raman studies of AgVP$_2$Se$_6$ have been performed far above the Curie temperature ($T_C$), preventing studies of spin-phonon coupling. Here, we report polarization-resolved, temperature-dependent Raman and magneto-Raman spectroscopy of AgVP$_2$Se$_6$ single crystals grown by chemical vapor transport (CVT) and flux methods, across the FM transition, complemented by density functional theory (DFT) calculations of phonon, optical and magnetic properties. Cryogenic Raman spectra resolve up to thirty peaks, while angle-resolved measurements enable their symmetry assignment. Spectral differences between CVT- and flux-grown crystals are traced back to the presence of different interlayer stacking domains in these samples. Temperature- and field-dependent Raman spectra remain largely unchanged across $T_C$, suggesting weak spin-phonon coupling. However, pronounced spectral alterations near 100 K suggest a potential structural phase transition. Our DFT calculations further reconcile the large discrepancy between the transport activation gap ($\approx$ 0.325 eV) and optical absorption edge ($\approx$ 2.14 eV), attributing the former to a transition to the V-d upper Hubbard band that is optically dark but thermally accessible. We also suggest a theoretical explanation of the qualitative difference (reproduced by DFT calculations) between the magnetic properties of the sulfide and selenide. These results provide key information regarding the lattice dynamics of AgVP$_2$Se$_6$ and will guide future applications in spin-based electronics.

General Game Playing across arbitrary games from rules alone remains challenging due to differing algorithmic requirements across game classes and strict decision-time constraints. Rather than hand-designing search heuristics for specific domains, can we leverage Large Language Models (LLMs) to discover general game-playing algorithms? Because language models can propose and refactor structured code, they provide an expressive proposal engine for exploring the space of algorithmic designs. We introduce a multi-agent LLM meta-learning system to co-evolve game-agnostic procedural search mechanisms in C++ alongside domain heuristics synthesized directly from game rules. Controlling the compute budget, we benchmark the discovered mechanisms across more than 400 diverse environments, including OpenSpiel training and held-out games, procedural simulation engines, and games with deep neural policy-value representations trained via PPO. Evaluated via AlphaRank stationary distributions and Soft Condorcet Optimization (SCO) against 15 established MCTS baselines, the discovered search mechanisms consistently achieve top-tier ratings and pairwise ballot majorities over most baselines across independent evolutionary runs, generalizing to unseen human-designed and procedurally synthesized games and remaining competitive with baselines on frozen neural network representations.

For decades, statistical inference has largely been developed one problem at a time. Given a scientific target, such as a treatment effect or a regression function, statisticians design a problem-specific estimator together with a procedure for quantifying its uncertainty. This paper proposes a different paradigm. We focus on a classical problem in statistical inference, confidence interval construction, and develop TabCon, an amortized inference system built on a tabular foundation model that produces confidence intervals for new datasets through a simple forward pass. The key methodological ingredients of TabCon are a sparse mixture-of-experts architecture and reinforcement-learning-based post-training that calibrate the resulting confidence intervals to a desired coverage level. Across a wide range of benchmark datasets, TabCon attains near-nominal coverage while producing short confidence intervals. At inference time, it also offers considerably greater computational efficiency, running 50 times faster than the classical bootstrap procedure, even when the latter uses only 50 bootstrap samples.

As coding assistants become increasingly autonomous, developers run multiple sessions in parallel, shifting the challenge from code generation alone to coordinating and monitoring concurrent agent work. Through a formative study (N=14), we identified PILOT: five supervisory practices for Planning, Isolating, Logging, Observing, and Triaging parallel sessions. We present ParallelPilot, a design probe that instantiates PILOT through a planning interface, a run-logger, and an ambient dashboard alongside existing coding tools. In a counterbalanced within-subjects study (N=16), participants using ParallelPilot increased ticket throughput by 63% in short coding tasks and supervised an average of one more concurrent agent at peak, while their tracking effort and context switching dropped. ParallelPilot also clarified execution plans, task dependencies, and intervention cues, and 14 of 16 participants preferred it over their current setup. These gains were not accompanied by significant improvements in perceived control or perceived success in redirecting the agents. Our findings demonstrate the value of explicit supervision support and position PILOT as a scaffold for designing tools that help people supervise concurrent work within and beyond coding. We suggest that future coding assistants should pair high-level awareness with low-cost paths back to the implementation evidence developers need to judge and steer agent work.

Gaussian process stochastic differential equations (GP-SDEs) provide a flexible Bayesian model for unknown continuous-time state dynamics with uncertainty quantification, but learning and inference from noisy and irregular observations remain computationally challenging. To address this issue, we propose GP-SDE Matching, a simulation-free variational framework for Bayesian GP drift learning and continuous-time state smoothing. We analytically marginalize the sparse GP posterior to derive a tractable drift-matching objective that accounts for both the posterior mean and uncertainty of the unknown drift. To handle irregular observations, we further introduce an irregular-time-aware variational state posterior that incorporates the actual observation times during both encoding and continuous-time marginal querying. Experiments on the stochastic Lorenz–63 system demonstrate substantially improved drift recovery and state reconstruction under irregular observations, while five system identification benchmarks show robust forecasting under increasing observation sparsity and competitive performance against existing latent-SDE and state-space methods.

We study the family of functions $V_z:s \mapsto \zeta(s) \exp (zs)$ with numerical experiments. For selected sequences $z_n=x_nu$ on rays, our experiments suggest that suitable fixed points of $V_{z_n}$ approach nontrivial zeros of $\zeta$ in a nearly logarithmic pattern. We formulate this behavior as conjectures with explicit restrictions on the ray. We prove a conditional result identifying finite limits as zeros, and give sufficient hypotheses for the convergence of refinement diagnostics. Substantive AI assistance in the preparation of this draft is disclosed in Section 5.

Joint-Embedding Predictive Architectures (JEPAs) provide a framework for learning compact representations without directly reconstructing high-dimensional observations. However, in parameterized physical systems, learned representations can entangle geometry with operating conditions and task-specific physical responses, limiting their reuse across prediction tasks. We introduce D-JEPA (Design-recoverable JEPA), a geometry-centric JEPA that computes a compact representation from geometry alone and reuses it across operating conditions and physical response spaces through lightweight physics-specific decoders. An explicit design-recoverability objective encourages the geometry latent to preserve information about the underlying design variables, enabling the representation to support design analysis and optimization. We further identify a case-level collapse failure mode in which target representations become nearly invariant across distinct geometries despite low reconstruction error, and mitigate it using case-level variation constraints and auxiliary target reconstruction. Across four 3D aerodynamic, hydrodynamic, and structural benchmarks, D-JEPA maintains or improves full-field prediction accuracy while achieving near-perfect linear recoverability of design parameters. The frozen geometry representation can be reused at held-out operating conditions and transferred to a structural response task with fewer trainable parameters. Finally, the representation supports differentiable design optimization, with designs validated using high-fidelity CFD, preserving the predicted ranking of candidate designs. These results demonstrate that separating a reusable geometry representation from physics-specific prediction provides a practical representation for scientific surrogate modeling and design.

Grounding is a core capability of spatial vision-language models, yet most existing work focuses only on where a referred object is. Many 3D tasks also require knowing how it is oriented. Although existing 3D VLMs may predict oriented boxes, box pose does not explicitly capture object-centric orientation or symmetry-induced ambiguities. We introduce orientation grounding, a referring grounding task that predicts an object's 6D orientation and axial symmetry from a language or box query in single-view or multi-view scenes. To support this task, we construct ReferOri, with 331K multi-view and 387K single-view orientation-grounding queries obtained through scalable reconstruction, consistency checking, and human verification. We further present OG-VLM, which adapts a 3D VLM with structured box/orientation outputs, sign and symmetry tokens, and geometry-aware auxiliary losses. Across single-view and multi-view benchmarks, OG-VLM substantially outperforms orientation-aware VLM baselines and surpasses object-level orientation foundation models on scene-level referring benchmarks, showing that explicit orientation grounding is a distinct and learnable capability beyond localization. Downstream results validate its benefit for orientation-related spatial reasoning.

We prove that every finite loopless signed multigraph $\Sigma=(G,\sigma)$ satisfies $\chi'(\Sigma)\leq\Delta(G)+\mu(G)$, where $\chi'(\Sigma)$ is its chromatic index, and $\Delta(G)$ and $\mu(G)$ are the maximum degree and maximum multiplicity of $G$, respectively. This bound is sharp, even when both positive and negative edges are present, and generalizes both Vizing's theorem for ordinary multigraphs and Behr's theorem for signed simple graphs.

Let $p$ be an odd prime, $q=p^k$, and $r=p^s$ with $s\mid k$. We study $\mathbb{F}_r$-valued generalized Maiorana-McFarland functions $H(x,y,z)=P^{(z)}(x)+\operatorname{Tr}_s^k(yz)$ on $V_n\times\mathbb{F}_q\times\mathbb{F}_q$. The ingredients $P^{(z)}$ are vectorial dual-bent functions with weakly regular components, constant on the cosets of $\mathbb{F}_r^*$ in $\mathbb{F}_q^*$, and, for $z\ne 0$, of inversion type with respect to $t\mapsto t^{-1}$. Under a mild condition on $P^{(0)}$, we prove that the partition into the $\mathbb{F}_r$-valued level sets of $H$, refined according to the $\mathbb{F}_r$-lines of the relevant coordinates, is Fourier-reflexive. It therefore induces a translation association scheme with $\frac{q-1}{r-1}(r+1)+r$ classes (one fewer in a degenerate case), symmetric when the ingredients are even. For $s=1$ this recovers recent scalar constructions, while for $s=k$ it yields $(2q+1)$-class schemes from vectorial bent functions whose components may all be non-weakly regular. We also construct fusions along $\mathbb{F}_r$-subspaces, obtaining $(2r+1)$- and $(3r+2)$-class schemes and connections between different levels. Counterexamples show that the inversion, coset-constancy, subspace, and weak-regularity hypotheses cannot in general be omitted. To our knowledge, these are the first association schemes obtained from vectorial bent functions with non-weakly regular components.

Pretrained macro-placement policies can reduce repeated optimization across circuits, but deployment often exposes them to unfamiliar designs when the original training data are unavailable. Repeatedly fine-tuning a single serving model can overwrite earlier improvements, while simply saving checkpoints does not determine where they can be reliably reused. We introduce Continual Adaptation through the Reuse of Validated Expertise (CARVE), a framework that represents accumulated expertise as a frozen base policy, immutable specialists, and task-specific credentials obtained through local validation. For a new task, CARVE first checks existing specialists and trains a new specialist from the frozen base only when none qualifies. Under fixed task distributions and validation rules that control cumulative error, we establish expected-performance guarantees for repeated reuse. For bounded losses, we also derive matching worst-case bounds on the local samples needed for reliable reuse. In macro placement, a reuse-first follow-up reduces recorded training time by 58.5% (9.66 to 4.01 hours), while mean HPWL gain changes only from 8.41% to 7.86%. In a simulated receiving deployment, imported specialists are reused on six of seven new IBM circuits with no receiver-side training, achieving a 5.76% mean HPWL gain. Navigation studies provide complementary evidence on repair retention and repeated adaptation.

We report on the recent results in the theory of discrete integrable equations reduced modulo a prime number $p$ based on the previous results. This article mainly concerns the $q$-discrete analogues of the Painlevé equations. We first give a quick review of the idea of `almost good reduction', which is a property that most integrable systems over a finite field $F_p$ possess when reduced from those defined over the field of $p$-adic numbers $Q_p$. This idea has been introduced in our previous papers and the discrete and q-discrete Painlevé II equations have been proved to have `almost good reduction', which can be interpreted as an arithmetic analogue of the singularity confinement test. In this article we prove that this property holds for several other $q$-discrete Painlevé equations. The theory of Diophantine integrability is reviewed and its relation to the integrability detection by the algebraic entropy is discussed.

While action-conditioned video prediction provides an intuitive world model for robotics, purely data-driven predictors often suffer from compounding errors and physically implausible hallucinations in long-horizon rollouts, severely undermining downstream action planning. We propose VPTwin, a Real-Sim-Real video prediction framework that anchors real-world future prediction using real-synchronized simulation twins. For a target manipulation task, a VLM reconstructs an executable digital twin from a real demonstration episode. To accommodate the ill-posed estimation of unobserved physical properties, Isaac Sim simulates multiple forward dynamic rollouts across randomized physical configurations under candidate action trajectories. Using these rollouts as in-context references, VPTwin harmonizes both domains, using simulation dynamics to enforce physical plausibility while capturing unmodeled contact interactions from real video. Furthermore, we establish a predictive planning loop using VPTwin to visually verify VLM-proposed actions and guide reliable real-world execution. Evaluations show substantial reductions in physical hallucinations during video prediction and marked improvements in manipulation planning performance.

This paper investigates the fractional Laplacian equation in half-spaces, focusing on cases with nonlocal Neumann boundary conditions. We consider both single equations and systems, and establish two key principles: the decay at infinity principle and the narrow region principle. These foundational results, combined with the direct method of moving planes, allow us to derive symmetry and monotonicity properties for decaying solutions. To the best of our knowledge, these are the first results concerning the symmetry of solutions to fractional Laplacian equations with nonlocal Neumann conditions.

Multi-agent LLM systems are increasingly deployed for complex, long-horizon tasks or emerge as a natural consequence of agents interacting in the wild. Yet they give rise to significant safety and security risks: the flexible protocols that enable task generalization also expose novel threats, from cascading prompt injection to inter-agent collusion. Progress in defending against these threats has been slowed by a lack of shared empirical infrastructure, which forces bespoke environment development for every new defense and makes standardized comparison impossible. Existing evaluations address isolated threat models or single-agent settings, but none jointly vary attack, defense, and architecture across realistic multi-agent environments. To address this gap, we introduce ORBIT, a configurable evaluation framework for empirical multi-agent safety and security research, built on UK AISI's Inspect. ORBIT lets researchers configure communication topologies, memory, scheduling, and agent roles. It supports four threat types and four defense strategies, as well as non-adversarial failures, with a benchmark suite spanning five scenario families covering browser use, computer use, agentic coding, customer service, and cooperative allocation. Our central finding is a gap in defense transferability across threats: per-action defenses that cut a compromised agent's attack success by 60 points on multi-issue coding give no measurable protection against colluding agents, and none of the defenses we tested generalized over all attacks tested. We further demonstrate security-performance tradeoffs and interactions between architecture and defense effectiveness. We make ORBIT available open-source at https://github.com/wlanderson0/orbit.

Little is known about how to manually design agents capable of dexterous manipulation. Some design principles have been inferred from close examination of how animals manipulate objects, but these structures and behaviors have so far resisted biomimicry and may not be optimal for artificial machines. Here we evolve freeform robots to pick up, hold, rotate, and use diverse objects. Unlike other approaches to optimizing robot hands, we do not presuppose the presence, articulation, or geometry of any part of the body. Although familiar prehensile forms such as tails, beaks, paws and claws may emerge spontaneously under certain conditions–and while such conditions could be of interest to evolutionary biologists–de novo manipulator design can also reveal whole new solutions, overlooked or unknown structures which may be better suited for the task at hand. We use contrastive learning to create a highly searchable genetic embedding of design space, an autoregressive developmental model to decode designs, evolutionary strategies to find good designs, and reinforcement learning to train each evolved design. Winning designs were automatically converted into a manufacturable blueprint, printed, assembled and tested in the real world in a zero-shot manner. The results represent the state-of-the-art in evolutionary robotics in terms of performance, diversity and complexity.

Video models commonly use uniform grids even though visual complexity varies substantially across space and time. We introduce OctVideo, which approximates a video clip with an octree. This hierarchy recursively partitions a spatio-temporal volume into eight subvolumes, so that smooth regions remain coarse while detailed regions receive finer cells. Each leaf stores local RGB values and spatio-temporal gradients, supplemented by a lightweight learned residual. For reconstruction, a Conv1D VAE maps the serialized cells to a regular latent grid and selectively refines details during decoding. Our VAE achieves 36.12 dB PSNR with 38.2M parameters and 189.4 GFLOPs per clip on Kinetics-400 (K400). It also generalizes zero-shot to the high-resolution Densely Annotated VIdeo Segmentation (DAVIS) 2016 dataset with reconstruction quality comparable to the best evaluated models. On both datasets, it requires the fewest model FLOPs and achieves the fastest encoding and decoding among the evaluated models. OctVideo also supports video understanding, achieving competitive recognition performance with few input tokens when trained from scratch. By exploiting the redundancy already present in video signals and efficiently processing sparse structures, OctVideo provides an efficient representation for video.

The CVE record format defines a credits container that names who found or reported a vulnerability, with a typed role per entry. The OSV schema defines an equivalent field. GitHub, which assigns CVE identifiers for advisories in its ecosystems, collects this information from reporters, requires them to accept it, displays it on the advisory page, and serves it through its own REST API. It emits it into neither standardized format. Across 238 GitHub-assigned CVE records whose linked advisory publicly credits at least one party, zero carry a credits container, while all 238 carry metrics and problemTypes, two fields the CVE schema leaves optional exactly as it leaves credits. Across 302 advisories in the same pool we retrieved GitHub's own OSV export file, and zero carry a credits field. The omission is not a property of either format: the Erlang Ecosystem Foundation populates the CVE field on 18 of 18 records in the same pool using a freely available client for CVE Services. In a census of all 4,889 published CVE records in a two-week window, 46.9% carry credits, GitHub's rate is 0 of 570 without any advisory filter, and assigner behaviour is concentrated at the extremes without being exhausted by them: 16 assigners emit the field on no record and 13 on essentially every record, while 8 assigners covering 23% of the records sit in between. A request to close the gap has been open since January 2023; GitHub's stated reason for deferring it is quoted verbatim. We further show that the NVD API schema defines no credits field, so attribution that CNAs do emit does not reach the database most tooling consumes: of 43 credit-bearing records traced from advisory to CVE record to NVD, none retained it. We release the collection scripts and a frozen snapshot of every API response.

Classically, it is well-known that several fundamental cryptographic primitives, including one-way functions, pseudorandom number generators, commitments, and signatures, characterize the same cryptographic world, which is known as "Minicrypt". In this paper, we investigate to what extent this picture persists in the quantum-computation classical-communication (QCCC) setting, where parties may perform quantum local computation, but communicate through only classical messages. We demonstrate that the classical Minicrypt landscape breaks down in the QCCC model by oracle separations. We construct two oracle worlds where efficiently verifiable one-way puzzles (EV-OWPuzz) exist. By a known equivalence, QCCC one-time signatures also exist in both worlds. In the first, one-way functions do not exist, even if we allow quantum pseudodeterministic evaluation. In the second, QCCC bit commitments do not exist. Thus, the classical Minicrypt reductions from signatures to one-way functions and bit commitments have no fully black-box counterparts in the QCCC setting. Our proofs develop techniques for analyzing the random phase states, including a concentration theorem and an LOCC decoupling theorem. As a separate result, we establish quantum sum-binding for the NOVY protocol, settling the question of its post-quantum security. We also generalize it to a fully black-box construction of a QCCC commitment from EV-OWPuzz with nearly uniform puzzle distribution, complementing our oracle separation results.

Recent large-scale Vision-and-Language Navigation (VLN) models deliver strong accuracy but remain costly to deploy due to their large parameter counts and computational requirements. We tackle efficient VLN in two steps. First, we build a high-performing teacher that makes navigation evidence selection explicit and compressible. The teacher introduces a small set of learnable query slots to extract global and local action-sufficient navigable evidence from panoramic observations via a Navigable Query Generator, then progressively grounds these evidence tokens to the instruction with an Instruction-Query Aligner for policy prediction. Second, using this explicit query bottleneck as a distillation interface, we train a compact student by transferring both where to attend and what to do. We distill the teacher's global and local navigable queries with a navigation-aware token-adaptive objective, then further match action distributions during fine-tuning. Experiments on standard VLN benchmarks demonstrate that our student nearly matches the teacher's navigation performance while reducing the number of parameters by 93.65% compared to the teacher.

Rapid advances in humanoid robotics have motivated growing interest in the application of humanoids for healthcare and clinical tasks. However, it remains unclear how close contemporary humanoids are to meeting the kinematic demands of robot-assisted laparoscopic surgery. In this work, we address the question of optimal robot positioning through a quantitative analysis of workspace and robot setup configurations. We present a capability-map-based robot setup framework that optimizes humanoid base placement and tool mounting orientation to maximize bimanual humanoid reachability while accounting for tool-tip kinematics and remote-center-of-motion (RCM) constraints. We evaluate three humanoid platforms spanning different body dimensions and kinematic redundancy on workspace reachability for three representative general surgery procedures: cholecystectomy, inguinal hernia repair, and sleeve gastrectomy. The proposed joint optimization of base placement and tool mounting consistently outperforms base-only optimization and heuristic baselines. For cholecystectomy and inguinal hernia repair, which are characterized by relatively small and minimally overlapping workspaces, humanoid reachability approached 90%. For the larger, overlapping multi-port arm workspace of sleeve gastrectomy, humanoids yield substantially lower coverage. These results quantify the near-term promise of humanoids for selected laparoscopic procedures and clarify key limitations that must be addressed for broader deployment.

Generating responsive listener facial motion is an important task for embodied conversational AI. Two modeling challenges are central: accounting for the timing of speaker cues while maintaining continuity with the listener's ongoing motion, and capturing locally variable facial events alongside the overall motion trajectory. Listener responses may follow preceding cues with a temporal lag, while brief expressions and blinks introduce variation that is difficult to predict deterministically. These challenges motivate a framework that combines history-aware temporal alignment with stochastic expression refinement. We propose REALM (Reactive Embodied Audio-driven Listening Model), a coarse-to-fine framework for audio-driven reactive listening. A Reactive Gated Speaker-Listener Fusion module combines listener motion history with speaker audio through a delay-centered attention prior and adaptive gating. A coarse decoder predicts a base motion trajectory, which is augmented by audio-conditioned stochastic residuals in the expression subspace while retaining the coarse pose parameters. Evaluations on ViCo and L2L show improvements over the evaluated baselines across multiple motion-quality metrics. Additional analyses examine delay sensitivity, gate behavior, and blink dynamics. Finally, deployment on an Ameca humanoid robot and a perceptual user study demonstrate the applicability of the generated behavior to physical embodiment. Code: https://github.com/lipzh5/REALM Demo: https://youtu.be/Tf5mpd5S8VQ

Multipartite entanglement can endow a quantum network with capabilities unavailable classically, yet their evolution under progressively reduced physical and informational access remains largely unexplored. Here we realize the first eight-photon half-excitation Dicke state, with a fidelity of 0.922(11), and use it to implement two distinct network tasks: open-destination teleportation and quantum telecloning. An unknown state can be teleported from one agent to any of seven remote agents with fidelities of 0.926(7)-0.941(6), while seven approximate clones are distributed with a fidelity of 0.713(3), close to the optimal value of 5/7. The protocol remains above the classical limit under imperfect photon detection, transmission loss and missing information from participating agents, and outperforms the corresponding GHZ benchmarks. As fewer agents contribute, the teleportation fidelity falls through a stepwise hierarchy whose two extremes recover open-destination teleportation and optimal telecloning, connecting both tasks within a single operational framework. These results establish Dicke entanglement as a promising architecture for loss-resilient quantum networks, opening a route towards quantum technologies that retain useful functionality under realistic operating conditions.

Linear attention replaces the growing key–value (KV) cache of standard attention with a fixed-size recurrent state, substantially reducing memory growth with context length. This efficiency, however, changes how past information is stored: many tokens must share and repeatedly update the same memory. We study how this recurrent state functions as a memory system. Using an analytical decomposition together with controlled causal interventions in pretrained GLA and GDN models, we trace how recalled information is written, retained, and later accessed. We find that fact-specific information enters recurrent memory through concentrated, content-dependent writes and is later accessed through concentrated query-time read pathways. Multiple facts can remain selectively accessible within the same state, yet their internal representations exhibit cross-fact causal coupling rather than independent KV-like storage. As memory load increases, both recall and targeted editability degrade, whereas elapsed context alone has a substantially smaller effect within the tested regime. Causal interventions on subsequent writes further show that interference is shaped by their overlap with existing memory. Finally, in hybrid architectures that combine recurrent layers with full attention, the runtime memory directly supporting recall shifts predominantly to the full-attention KV state. Together, these results reveal how fixed-size recurrent memory supports selective recall despite shared storage, while exposing the interference and capacity limits that distinguish it from token-addressable KV memory.

This paper studies secure distributed linearly separable computation over a three-layer hierarchical network, where clustered users communicate with a central server through relays. The server aims to recover Kc linear combinations of K intermediate outcomes, where each intermediate outcome is a separable function of one dataset. We consider a more general setting with arbitrary heterogeneous data assignment across users, where ”arbitrary” means that the data assignment is given in advance (which can be in any form) and ”heterogeneous” means that the users may hold different numbers of datasets. Under this assignment, each user computes the intermediate outcomes of its assigned datasets and sends masked messages to its associated relay. The relays subsequently process and forward the received messages to the server. We impose two security constraints: (i) security against server, requiring the server to learn only the desired task function without gaining any additional information about users' inputs; and (ii) security against relays, ensuring each relay learns nothing about users' inputs. Moreover, the server or any relay may collude with a subset of users. For Kc=1, the underlying computation reduces to distributed gradient coding. We propose a secure scheme tolerating user dropouts and user collusion, achieving the optimal two-layer communication rates in one regime and order-optimal communication rates within a factor of 2 in the other regime. For Kc>1, we extend the proposed construction to multi-dimensional linearly separable tasks under the no-dropout setting.

For complex Hessian equations on compact Kähler manifolds, we give an alternative proof of the gradient estimate without using blow-up argument, and clarify its dependence on the right-hand side. In addition, using the similar approach, the case of Kähler manifolds with boundary is also investigated.

SLU encompasses a diverse set of tasks, including ISLR, CSLR, and SLT. Although these tasks share basic semantic and linguistic foundations, they are typically addressed with task-specific architectures and training pipelines, which hinders knowledge sharing and requires costly pretraining and finetuning for each task. In this paper, we focus on two aspects of SLU tasks: (1) training and inference pipelines are highly fragmented: most methods rely on pretraining on large-scale SL datasets followed by task- or dataset-specific finetuning, which leads to multiple specialized models rather than a single checkpoint. (2) current LLM-based methods may overlook the inherent modality discrepancy between sign and text tokens, simply concatenating them and processing both modalities with the same decoder layers. In this paper, we present OneSign, a unified framework that addresses multiple SLU tasks within a single model and a single checkpoint. OneSign reformulates ISLR, CSLR, and SLT under a single training paradigm. To accommodate the heterogeneous characteristics of sign and text representations, we introduce a Modality-Adaptive Mixture-of-Experts (MA-MoE) architecture, consisting of a shared expert and modality-specific experts for sign and text tokens. A modality router dynamically activates the corresponding experts, and their outputs are aggregated to form the final token representations. By enabling modality-dependent expert specialization while preserving a shared expert path, MA-MoE can effectively model the modality differences between continuous sign representations and discrete text tokens. Extensive experiments on multiple benchmarks demonstrate that OneSign achieves competitive or state-of-the-art performance on several benchmarks, highlighting its effectiveness as a unified SLU model. Datasets are available at : https://github.com/gswycf/OneSign.

The geometry of latent representations governs which components should interact and how information should propagate, making geometry-aware operator design a fundamental ingredient of structured deep representation learning. However, existing neural architectures typically rely on generic operator templates or geometry-specific constructions, creating a need for a unified framework that can derive admissible operators directly from fixed structural information while remaining adaptive to changing contexts. We introduce Geometry-Induced Operator Families (GIOF), a general framework that converts fixed geometry into a structured family of propagation operators and dynamically selects an appropriate member of this family according to the current context. GIOF first transforms geometry-derived interaction channels into reusable generator bases, then combines them through a context-dependent selector and adaptive propagation scale, and finally realizes the selected operator through stable continuous-time propagation and a bottleneck residual layer. We establish theoretical guarantees covering parameter compression, identifiability, stability, locality, compositional structure, and oversmoothing behavior, while controlled experiments validate these mechanisms and experiments on PEMS-BAY and METR-LA achieve the lowest mean MAE across all reported regional-outage settings, improving over the strongest retained baseline by 2.4%–8.8% at 30% missing sensors.

Traditional change detection (CD) identifies changes between bi-temporal remote sensing images, while semantic change detection (SCD) assigns predefined land-cover classes. However, mapping all changes may not meet a user's specific needs. Referring change detection (RCD) enables selective retrieval through category prompts. However, existing category-prompted RCD uses the queried category to specify the destination of a change and returns only a binary mask of the corresponding regions. Users may instead request a particular transition and paired semantic maps to understand what changed into what. Such requests require explicit source and target reasoning beyond target-class localization. To address these needs, we propose query-guided semantic change parsing (QSCP), which supports category names, synonyms, and intent-bearing sentences and returns a query-specific mask with paired temporal semantic maps. QSCP parses requests into intents and semantic slots, composes bidirectional visual evidence, and predicts both temporal states with a query-conditioned decoder. On SECOND, QSCP outperforms RCDNet on synonym, sentence, and transition queries and improves end-to-end semantic prediction over evaluated semantic baselines. WHU-CDC experiments further assess cross-dataset transfer and consistency across equivalent expressions without target-domain training. Code is available at https://github.com/qianyuancs/QSCP

Plug-and-Play (PnP) methods replace proximal operators with learned denoisers, which produce state-of-the-art reconstruction quality, but sacrifice the variational interpretation and convergence guarantees of proximal methods. Learned Proximal Networks (LPNs) address this problem by designing the denoiser architecture so that it is exactly the proximal operator of a regularizer. In this work, we clarify the theoretical foundations of LPNs and extend the framework to a broader class of activation functions. We then study two practical mechanisms for controlling the learned prior: (i) averaging the LPN with the identity, a common heuristic in PnP methods, and (ii) directly scaling the implicit regularizer induced by the proximal operator. In particular, we characterize the regularizer induced by averaging and develop a convergent method for evaluating the scaled proximal operator.