Papers

An agent that drives an LLM sends the model the same conversation again and again, and each turn adds only a little text at the end. Inference engines reuse the KV cache of the shared prefix, so only the new tokens pass through the model. However, tokenization has no such shortcut. The CPU front end of the serving engine converts every request back into token IDs from its first character, which lengthens the time to first token (TTFT) and consumes CPU on every turn. We present Delta Tokenizer, a CPU tokenization front end that tokenizes only the delta between a request and the previous request of the same session. It retains the earlier token sequence, encodes again only the appended text and the short tail whose tokens the append could affect, and joins the two only at a position the tokenizer's splitting rules themselves cannot move, which keeps the result exact. For long requests with no state to reuse, it cuts the text where practical tokenizers already keep neighboring pieces independent, encodes the pieces on several cores at once, and concatenates the outputs into the reference encoding, exactly. A shared CPU pool schedules these chunks together with the short incremental updates, so an update runs between two chunks rather than behind an entire long job. The incremental path shortens the tokenization of a session turn by roughly 40x relative to the Hugging Face reference tokenizer, and on 16 cores the chunk-parallel path encodes a four-million-character request 8.2x faster than a serial encode and 1.6-2.1x faster than LoPT. Inside SGLang, Delta Tokenizer reduces the median TTFT through the chat interface by 59% at 100K tokens and brings the P99 TTFT of agent sessions down 9.5x under load and 23x when long requests tie up the front end. Every output we checked matches the reference, among them 41.8 billion documents encoded by its fast encoder.

Judicious partition problems ask for vertex partitions of graphs or hypergraphs that optimize several quantities simultaneously. In this paper, we investigate judicious partitions of graphs and hypergraphs in which each class meets many edges and establish the following results. (1) Every hypergraph with nonnegative edge weights and all edges of size at most $2$ has a bipartition in which each vertex class meets edges of total weight at least $(w_1-\Delta_1)/2+2w_2/3$, where $w_i$ is the total weight of the edges of size $i$, and $\Delta_1$ is the maximum weight of an edge of size $1$. (2) Every hypergraph with all edges of size at most $3$ has a bipartition in which each vertex class meets at least $m_1/2+3m_2/4+7m_3/8+o(m_1+m_2+m_3)$ edges, where $m_i$ is the number of edges of size $i$. (3) For any integer $k\ge4$, every graph with $m\ge2(k-1)(k-2)$ edges has a partition into $k$ classes, each meeting at least $2m/(2k-1)$ edges. Both the coefficient of $m$ and the edge threshold are best possible. (4) For all sufficiently large $m$, every $4$-uniform hypergraph with $m$ edges has a partition into four classes, each meeting at least $4m/7$ edges. The first three statements are conjectures of Bollobás and Scott, and the last is a conjecture of Bollobás and Thomason on 4-uniform hypergraphs. All of the above results are best possible.

Recent work lets LLM agents evolve their own harness, up to the team itself. Yet in human groups, the same abilities achieve different outcomes under different social conditions. Borrowing the notion of scaffolding from developmental psychology, we investigate whether the social scaffolding of a self-evolving multi-agent system (MAS), namely its team composition and structure of interdependence (e.g., collaboration, conformity, or competition), shapes how the team evolves. We present AGORA (Agents Growing through Organization and Relational Arrangements), a framework that varies the two axes independently across three evolution mechanisms. Across web search, codebase understanding, and document QA, we find that (1) evolution alone rarely helps, while the right scaffolding surpasses a strong agent evolved alone by up to 25 points; (2) it does so by moving authority to the most capable member while the others step back; and (3) this member, having grown within the team, outperforms the same model alone. Designing a self-evolving MAS thus requires designing its social scaffolding, which shapes not only how its agents learn, but who gets to lead.

Continuum robots enable dexterous access to confined spaces in applications such as minimally invasive surgery and industrial inspection. However, their actuation systems are often custom-designed for specific robot architectures and tasks, limiting reuse across publications, institutions, and applications. This paper presents a unified actuation platform that decouples actuation hardware and software from continuum robot design. The platform provides modular actuation across continuum robot classes, scales to a large number of degrees of freedom (DOFs), and integrates with conventional serial manipulators for hybrid architectures. We validate the platform on an open-sourced surgical robotic system and experimentally characterize the actuation modules, achieving sub-millimeter translational accuracy and less than $5^\circ$ rotational error over ranges of $30$~mm and $180^\circ$, respectively. We further demonstrate the platform in two surgical use cases: teleoperation of a continuum camera in a constrained environment and bimanual manipulation using $2.53$~mm concentric-tube-robot-based forceps alongside a conventional wristed instrument. All hardware designs and ROS-based software are open-sourced to facilitate reuse and further research in continuum and surgical robotics.

Non-periodic functions on closed intervals are extended into sufficiently smooth periodic functions through a continuous Hermite interpolation framework with necessary and sufficient endpoint conditions, using smooth blend-to-zero operators and short extrapolation recurrences. A matrix-free method is introduced for generating these smooth periodic extensions on the fly directly from function values at equidistant points. No precomputed continuation operator or auxiliary basis construction is required. The resulting extensions can then be used for FFT-based differentiation of non-periodic functions. Numerical tests are provided to show the effectiveness of the method, including for the highly accurate solution of a 1D linear advection equation.

In Theory-of-Mind (ToM) reasoning, large language models may correctly infer the agent's mental state but fail to use that inference when predicting or judging the agent's subsequent actions. In this work, we investigate whether explicitly connecting perception, belief, and action with rules improves ToM reasoning. We generate concise if–then rules that express relations between perception to action and use Group Relative Policy Optimization (GRPO) to train Qwen2.5 and Llama3 models across four ToM benchmarks. GRPO with rule generation outperforms prompting, supervised fine-tuning, and think reasoning. Moreover, rules generated by larger models ($\geq$3B) provide transferable knowledge that improves downstream performance of GPT-4o-mini. These findings suggest that explicit rules help models bridge the reasoning gap in ToM and support knowledge transfer across models.

Video world models aim to simulate complex environments with realistic appearance and dynamics. Maintaining consistency over long interactions requires tracking past actions and understanding how those actions affect the environment. Video world models can only generate partial observations of the entire world at a time. Remembering past observations alone may not be sufficient in every scenario, as they may no longer reflect the world after a sequence of actions. We introduce a paradigm that decouples a persistent, updatable abstract state from the visual state. The abstract state keeps track of the entities' changes as the world evolves, and is used to condition the visual state, which represents the current view. We propose StateCraft, a novel architecture that pairs a language model with a video diffusion model to evolve the dynamic world. We evaluate our approach on generative interfaces, which pose a substantial challenge because a single action may change parts of the state that are not currently visible. To support training and evaluation, we develop a data collection pipeline that produces informative, densely annotated trajectories at scale without human or agent supervision, together with a benchmark measuring generation quality, memory, and controllability. On this benchmark, our approach improves surpasses the state-of-the-art baselines. We demonstrate that StateCraft maintains high self-consistency and strong generation quality over long trajectories. Because the abstract state is explicit, it can be edited directly, and generation follows edits to states never observed in the data. Finally, a proof-of-concept 3D experiment, in which actions change the illumination of an unobserved room, shows that the paradigm can also be applied to spatial environments. Project page: https://insait-institute.github.io/StateCraft/.

Cumulative energy fields in irreversible evolution depend on the loading path, even when terminal states and global work agree. We derive a posteriori bounds for these fields in scalar gradient damage with a prescribed driving density. A perturbation estimate for the incremental obstacle map yields a continuous loading history, which is enclosed by nondecreasing residual supersolutions. A primitive identity transfers this enclosure to the cumulative field. An exact endpoint-rule defect and outward arithmetic certify the output delivered by the numerical method. The analysis separates spatial, loading, and algebraic errors and gives sufficient conditions for certificate decay. Computable realizations use splines and verified supersolutions in one dimension and on two-dimensional rectangles. The production bounds cover the independently enclosed errors of all 417 saved histories from 28 adaptive calculations and all 25 fixed-parameter controls. In a narrow-localization case, the verified relative error decreases from approximately 158.78% to below 2.125% at a 5% certified target. Source-oriented marking reduces accumulated matrix–vector work by 35.9% and 51.9% in two comparisons. A mechanically generated two-dimensional benchmark shows how auxiliary supersolutions sharpen constant barriers and enable acceptance of both loading orders.

Universal conductance fluctuations are conventionally organized by symmetry class, but crystalline anisotropy introduces additional structure in spin transport. Here we demonstrate orientation-dependent universal spin-transport fluctuations in disordered two-dimensional $d$-wave altermagnets without spin-orbit coupling. Rotating the altermagnetic orientation changes both longitudinal spin-conductance and transverse spin-Hall conductance fluctuations, while each conserved-spin sector remains in class AI. Altermagnetic orientation controls both the fluctuation amplitudes and the development of disorder-insensitive plateaus. These plateaus become flatter and less sensitive to the altermagnetic strength over the studied parameter ranges as the orientation approaches $45^\circ$, with representative fluctuation amplitudes of approximately $0.60e/(4\pi)$ for the longitudinal spin conductance and $0.40\,e/(4\pi)$ for the spin-Hall conductance. The longitudinal fluctuation amplitude correlates strongly with anisotropy of the clean-band Fermi-velocity tensor. Spin-sector covariances explain how the conserved channels combine into total fluctuations. Our results extend anisotropy-sensitive universal-fluctuation physics to conserved-spin altermagnetic transport and establish crystalline orientation as a control parameter within a fixed symmetry class.

Speculative decoding's effectiveness is governed by two quantities: the acceptance rate of drafted tokens and the cost of producing them. We show the two objectives can be co-optimized with algorithm-system co-design, and present JetSpec++, which retains a strong learned draft model while hiding its cost almost entirely. JetSpec++ combines three components: intra-block self refinement, which trains the draft model to iteratively correct its own parallel predictions within a block of tokens; inter-block foresight drafting, which begins the next block before the current one is verified; and pipelined drafting and verification, which overlaps the two stages so drafting's marginal wall-clock cost approaches zero. In comparison with state-of-the-art speculative decoding methods, JetSpec++ attains a wall-clock speedup of up to $7.45\times$ over autoregressive (AR) decoding and $1.54\times$ over DSpark, with up to 1,361 tokens per second for a single request on GB200, and an average acceptance length of 8.94 across seven benchmarks, while preserving the target model's output distribution. Our code and models are available at https://github.com/hao-ai-lab/JetSpec.

We study operator systems arising from Peter-Weyl and Dirac spectral truncations of $\mathrm{SU}(2)$ in the sense of Connes-Van Suijlekom. We determine operator system invariants for these systems, including the $C^*$-envelope and uniform bounds on the propagation number. For Peter-Weyl truncations, we find $\mathrm{prop} \leq 2$ for all connected compact Lie groups, generalizing known results for the torus. We also carry out an analysis of the spectral localizer by Loring and Schulz-Baldes on $\mathrm{SU}(2)$. In this analysis, we find numerical evidence that an index map for operator systems previously proposed by Van Suijlekom only captures the right information in a suitable interval of the parameter $\kappa$, instead of the limit $\kappa \downarrow 0$.

Multi-zone HVAC control is a shared-resource problem: zones on a floor share one fan and cooling coil, so each zone's demand affects its neighbours and the building's peak power. One controller per zone scales well and isolates faults, but each controller then observes only its own zone, not the shared air loop. In this work, we present a decentralised controller that assigns each zone an independent active-inference agent, which plans by minimising expected free energy and learns its zone dynamics online. The agents exchange no messages, so none depends on peers or a coordinator; each accounts for the unobserved coupling through a latent disturbance and a congestion signal derived from the metered power of the other floors. Fifteen agents are evaluated in EnergyPlus on a Sinergym office building against three rule-based controllers and three MADDPG fleets, one given the same floor meters. On five noisy weather years unseen during training, the fleet attains the lowest mean building peak (88.3 kW, 3 to 17 % below the baselines) and staggers the floor peaks better than any baseline, with a coincidence factor (building peak over the sum of the floor peaks) of 0.929 versus 0.936 to 0.994. Compared with a reactive rule at similar comfort (0.912 versus 0.916), it lowers the sum of monthly peaks, on which demand charges are billed, by 33 kW (4 %) in every year, at the cost of about 10 % more energy. It costs 9% less per year than the proactive rule (at lower comfort) and 1% less than the MADDPG fleet given the same floor meters, in every test year. The whole fleet runs on a single low-cost Raspberry Pi 5, closing the observation-to-action loop over MQTT in 442 ms at p95, far below the 15-minute control step.

Self-distillation in agentic reinforcement learning has produced a growing number of methods. However, existing evaluations often reuse published baseline scores under differing experimental conditions, provide few direct comparisons among contemporaneous methods, and give limited attention to training stability and computational cost. These limitations obscure the source of reported gains and the practical strengths and weaknesses of competing methods. Costly agent training further motivates a common basis for comparison. To address these gaps, we compare ten representative methods against GRPO on ALFWorld, ScienceWorld, Search-QA, and WebShop across three model sizes. Our study comprises 132 training runs totaling 12,124.4 recorded H800 GPU-hours, with repeated evaluations over eight rollout seeds for the pretrained backbones and all eleven trained methods. Beyond final task performance, we examine training progress, stability, and measured computational cost. Our evaluation yields three key findings. First, gains over GRPO remain limited in scope, with no method consistently outperforming it across settings. Second, strong final performance can mask unstable training. Third, additional training cost does not consistently translate into better performance. We establish this benchmark to support fair, comprehensive comparison and guide future research toward reliable and cost-effective improvements in agent training. Project page: https://aim-uofa.github.io/Self-Distillation-AgentRL/

We prove the sharp volume bound $\mathrm{vol}(\mathcal{F})\ge 1/6$ for complex foliated surfaces of general type with positive geometric genus. We also study the equality case and apply the bound to the algebraic integrability and finiteness of small volumes on irregular surfaces.

We obtain a uniform lower bound for the drift of random walks on hyperbolic spaces in terms of joint minimal displacement. Our main theorem applies to weakly acylindrical actions on Gromov-hyperbolic spaces and is quantitative in all relevant constants. For discrete isometry groups of Hadamard manifolds with pinched negative curvature, the required assumptions are automatically satisfied by the Margulis lemma. This yields uniform gaps at zero in drift spectra for pinched negatively curved Hadamard manifolds, hyperbolic groups, and mapping class groups acting on curve graphs.

Generating LiDAR point clouds from multi-view camera images is a valuable task with applications in controllable data synthesis, cross-modal simulation and various perception tasks. However, most existing methods are not specifically designed for this task, and the quality of their generated LiDAR remains limited. Moreover, these methods typically focus only on semantic cues in images or generate LiDAR from a monocular camera image. In this work, we introduce LiFi (LiDAR From images), a dedicated framework for generating visually and geometrically aligned LiDAR scenes from multi-view camera images. LiFi guides the latent diffusion process through two complementary branches: geometry and semantics. The geometry branch constructs scene features from images through a reverse sampling algorithm and an uncertainty-aware geometric encoder combined with DepthAnything3, whereas the semantic branch provides high-level semantic representations via a cross-view interaction module. We further introduce a dual-branch balanced classifier-free guidance (CFG) strategy, which enhances the model's conditional generation capability while preserving the independent learning and collaborative controllability of the two branches. Extensive experiments demonstrate that LiFi outperforms state-of-the-art methods in generating high-fidelity LiDAR scenes. The code will be publicly available at: https://github.com/szzhou88/LiFi.

Crash Moment Localization aims to localize the major physical impact that interrupts controlled flight in an onboard first-person-view (FPV) video recorded by a drone, thereby providing a temporal reference for retrospective crash analysis in aerial robotics. However, existing crash-video datasets predominantly target surveillance or dash-camera footage, and their annotation schemes and task formulations are not designed for temporal localization of the major physical impact in UAV onboard FPV videos. To address this gap, we present FPV-CRASH, a dataset and fixed-protocol reference evaluation for offline Crash Moment Localization in drone FPV videos. FPV-CRASH contains 1,052 drone FPV clips (526 Crash and 526 Normal); each Crash clip has a single-frame reference annotation for the Crash Moment, and every clip is paired with four English captions automatically generated from sampled frames and the known Crash/Normal label. Normal clips carry no timestamp target and provide training-time background supervision. The captions support an auxiliary Text-to-Video Retrieval task, whereas localization inference remains video-only. We further provide a heatmap-based reference model that estimates a continuous Crash Moment timestamp from sparsely sampled frames. Under the fixed, non-source-disjoint clip-level protocol, the reference model reduces MAE from 1.12 s for the strongest fixed timing-prior baseline to 0.56 s (a 50% relative reduction) and achieves a median absolute error (MedAE) of 0.33 s; the fraction of clips localized within 0.5 s rises from 37.14% to 65.71%. The release includes annotations, available source video identifiers and URLs, clipping metadata, fixed split lists, and preprocessing code so that the reportable portion can be reconstructed without redistributing source footage. At submission time, all source-compilation URLs remained accessible.

We consider a discrete memoryless state-dependent channel with noiseless feedback, where the transmitter uses randomized encoding to jointly perform message transmission, identification, and state sensing. In this setting, the transmitter sends a conventional transmission message and an identification message while estimating the unknown channel state sequence under an average distortion constraint. We establish a single-letter characterization of the randomized identification-transmission-sensing capacity-distortion region. The result reveals a single-letter separation structure: the communication rates are determined by the averaged channel, subject to the sensing-induced constraint on admissible input distributions. Specifically, the transmission rate is characterized by mutual information, while the identification rate is characterized by output entropy under the same distortion constraint. The achievability proof combines constant-composition transmission coding, output partitioning, and combinatorial identification coding, while the converse follows from an averaged-channel reduction, distortion lower bounds, and feedback-identification converse arguments.

Reinforcement learning (RL) holds the promise of learning a policy that can outperform what is shown in the data. However, in practice, such systems suffer from instability and hyperparameter sensitivity. In contrast, supervised learning provides a stable and scalable training objective, but is fundamentally limited by the quality of the demonstrated behavior. In this paper, we ask whether we can perform policy optimization with something as simple and stable as supervised learning but as performant as RL. Unfortunately, naively training the policy with supervised learning and conditioning on future rewards or advantages typically underperform dedicated RL methods. We introduce a new policy extraction method, Advantage Guidance, that retains the simple supervised learning structure with advantage conditioning while outperforming prior RL methods through effective conditional training and contrastive diffusion guidance during sampling. We show that Advantage Guidance can significantly improve a model's ability to respond to conditional advantage signals, and the contrastive guidance during sampling can use the learned advantage-conditioned policy to target the KL-regularized optimal policy. Empirically, we find that Advantage Guidance significantly outperforms prior state-of-the-art RL methods on 26 long-horizon, sparse reward tasks across datasets with varying degrees of optimality.

Population health stratification frameworks, such as the Italian DM77, organize patients by clinical need and care pathways but offer limited guidance on which care changes to prioritize under constrained resources. We present PROMETHEUS (Proactive Resource Optimization through Multi-treatment Effect-based Targeting in Healthcare Environments Using Stratification), a framework that formulates population health stratification as a multi-treatment causal ranking problem. Its objective is to order eligible patient-treatment opportunities by expected incremental benefit rather than obtain perfectly calibrated individual treatment-effect estimates. Each clinically admissible care intensification is compared with maintaining the patient's current pathway. Treatments are learned jointly to produce a globally comparable ranking across patients and care profiles, within domains sharing a reference condition, outcome, follow-up horizon, and benefit scale. This separates clinical need, treatment benefit, and resource-constrained allocation. PROMETHEUS combines doubly robust causal signals with a Siamese neural ranking model and contrastive representation pretraining. The shared representation captures similarities across care transitions, supporting prioritization under capacity constraints. Synthetic experiments and semi-synthetic experiments using real administrative covariates from ASL Benevento evaluate ranking quality, allocation value, robustness, and failure modes. The results support the framework's ability to recover generated benefit orderings and prioritize care opportunities in the evaluated settings. PROMETHEUS provides a preclinical approach to actionable stratification; validation with observed treatment-outcome data is required before clinical use.

We introduce SNACK, a string representation for probabilistic graph generation that enables sequence models to generate and model graphs with discrete node and edge features. SNACK linearizes graphs by encoding the nonzero entries of the lower-triangular adjacency matrix, establishing a bijective correspondence between valid sequences and ordered adjacency matrices. This design enables invalid logit masking to enforce structural constraints–such as chemical valence and ordering rules–guaranteeing 100% valid generated sequences. SNACK also enables principled string-based GFlowNet training by explicitly accounting for node-ordering symmetries. Across standard graph-generation tasks and molecular distribution-learning benchmarks, SNACK achieves competitive sample quality, while substantially improving the throughput of GFlowNet training relative to graph-based generation. Probing analyses further show that models trained on SNACK encode meaningful local and global graph structure despite receiving only sequential supervision. These results position SNACK as a practical framework for probabilistic graph generation with deep sequence models.

Laboratory experiments involve more than following predefined protocols; they require adaptive decision-making as the experimental state changes. Existing scientific benchmarks rarely assess such evidence-based decisions in laboratory settings. Here we present LabOPBench, a multimodal benchmark of 756 expert-authored, independently reviewed questions in organic synthesis and materials science. Each item pairs laboratory evidence with procedural context and an open-ended judgment, evaluated using a question-specific scoring rubric. Eight multimodal models obtain overall normalized scores of 28.8-45.8%, leaving substantial room for improvement. On a controlled 100-question subset, the strongest models outperform undergraduate participants on average but remain below the average performance of PhD participants. Expert analysis of responses from the three leading models identifies Evidence Misreading and Evidence-Decision Conflict as the dominant error patterns. These results reveal that current models still struggle to turn multimodal perception into reliable laboratory decision-making.

Coherent noise poses a fundamentally greater challenge to quantum error correction than independent s- tochastic Pauli errors, because unitary errors preserve interference between error paths, can accumulate over multiple quantum error correction rounds, and leave the encoded logical channel with a residual coherent com- ponent. If the parameters of such coherent noise can be accurately determined, this knowledge can be exploited to inject correlated priors into the decoding graph, and to perform maximum-likelihood decoding under poly- nomially tractable structures, significantly improving the accuracy of syndrome-based decoding. In this work, we introduce one protocol to determine the model and parameters of coherent noise, and reduce the complexity of the experiment from 16nto O(16), which is of great significance for correcting coherent noise in quantum error correction.

Computational compressive imaging, such as single-pixel imaging and lensless imaging, is a promising imaging technique, enabling the reconstruction of objects from under-sampled measurements through compressed sensing algorithms or deep learning methods. However, the demand for electronic computational resources grows rapidly when recovering high-resolution and multi-dimensional images and training neural networks with numerous parameters, which has become a bottleneck for the widespread adoption of this technique. Here, we propose a physics-driven reconstruction framework that formulates imaging inverse problems as Ising models and directly recovers target objects through the self-evolution of non-von Neumann Ising machines toward the ground state of the Hamiltonian. We employ a simulated-annealing-based Ising solver to demonstrate this proof-of-concept by reconstructing objects in both single-pixel imaging and a lensless diffuser camera at sampling rates ranging from 1% to 25%. By further incorporating a foreground-sparsity constraint and a smoothness constraint, the reconstruction quality of our method is comparable to or even better than that of mainstream algorithms. This approach has the potential to substantially reduce the electronic computational burden of inverse reconstruction, paving the way for real-time, low-power computational imaging.

Autoregressive models have proven effective for triangular mesh generation by transforming it into predicting the next face, converting the non-differentiable connectivity prediction into a sequence of token predictions. However, generating quad-only meshes remains challenging because quad faces impose stricter topological constraints than triangles. The model must not only serialize quad faces into a valid token sequence, but also support unambiguous connectivity reconstruction during de-serialization. To address this, we propose Q-MAGIC, a novel autoregressive model for quad mesh generation. We first introduce a tailored serialization scheme for quad meshes, which requires at least two new vertices for the next face and is less flexible than triangles due to strict wiring constraints. To meet these requirements and reduce serialization length, we propose a singularity-aware serialization that prioritizes wiring from singular points, leading to more coherent traversals. Additionally, we propose a circular relative offset tokenization that encodes geometry mainly via local relative offsets. Built upon this representation, an autoregressive Transformer learns the underlying distribution of quad meshes via next-token prediction, enabling effective quad mesh generation. Extensive experiments demonstrate that Q-MAGIC produces more compact sequences while consistently improving geometric fidelity and mesh quality compared to state-of-the-art methods.

We study free-material optimization for nonlinear bond-based nonlocal diffusion and its localization as the interaction horizon $\delta$ vanishes. Bond conductivities are subject to pointwise bounds and a global material budget constraint. After normalization, the asymptotic behavior of these problems is governed by the fraction $\theta_\delta$ of potentially active bonds that can be assigned the maximal conductivity. We identify three distinct limiting regimes. If $\theta_\delta\to0$, the normalized optimal values converge to those of the classical vanishing-material optimal design problem, equivalently formulated as a Lipschitz-constrained state problem or a measure-valued flux problem. For $\theta_\delta\to\theta\in(0,1)$, we obtain a directional local free-material problem governed by the upper tail of the directional $p$-strain over position-direction space. Thus the state variable localizes, while the limiting constitutive law retains an internal directional variable inherited from the bonds. If $\theta_\delta\to\theta\geq1$, the limit is the isotropic local $p$-Dirichlet problem. A convex minimax argument eliminates the normalized conductivity variable exactly, after which the analysis combines convex duality, nonlocal compactness, and $\Gamma$-convergence for convex integrands. We prove a unified $\Gamma$-convergence result for the reduced state energies whenever $\theta_\delta\to\theta\in[0,+\infty)$, yielding convergence of normalized optimal values and compactness and identification of optimal states throughout the full parameter range. At the vanishing-material endpoint, we additionally recover optimal measure-valued local fluxes from optimal nonlocal two-point fluxes.

More than 50 years ago, Golomb and Welch conjectured that no tilings of $\mathbb{Z}^n$ by Lee balls of radius $r$ exist for $n \geq 3$ and $r \geq 2$. This conjecture remains open even under the additional assumption that the tiling is a lattice tiling. In general, there are two known effective approaches to the lattice case which are based on symmetric polynomials and on the arithmetic of group-ring equations, respectively. In this paper, we develop both approaches. First, we determine all coefficients of the Q-polynomials associated with Lee balls; previously, only leading coefficients and certain special cases were known. Second, for arbitrary radii, we give necessary and sufficient conditions for the existence of lattice tilings by Lee balls in terms of group-ring equations, extending earlier results for radii $r=2$ and $3$. We then derive new necessary conditions for such tilings. For every radius $3\le r\le 50$, we prove that the set of dimensions for which no lattice tiling exists has positive density in \(\mathbb{Z}^+\). We also give an algorithm that combines the available necessary conditions and apply it to all pairs $(n,r)$ for which the corresponding Lee ball of radius $r$ and dimension $n$ has size less than $2^{30}$. Among these $1{,}358$ pairs, the combined method excludes $1{,}356$, leaving only $(n,r)=(35,3)$ and $(805,3)$.

Zero-shot text-to-speech (TTS) typically conditions on a short speech prompt, which conveys timbre but provides only limited evidence of a speaker's prosodic patterns. We formulate Long-Prompt Zero-Shot TTS, a task that uses long speech prompts at inference time to reproduce speaker-specific prosody without target-speaker fine-tuning. We introduce LP-TTS-Bench, a bilingual benchmark of 37 speakers with 63.95 prompt hours and 2,728 held-out test utterances. Beyond intelligibility and timbre similarity, LP-TTS-Bench evaluates timing, prominence, intonation, and model-based prosody metrics, enabling multidimensional evaluation of prosody reproduction. As a reference system, we develop LPTTS, whose hierarchical Long-Prompt Encoder compresses long speech prompts into a fixed number of continuous prosody vectors. Experiments show improvements in several prosodic dimensions over a short-prompt baseline, with overall gains as prompt duration increases up to approximately 10 minutes and saturation at longer durations.

Score-based generative models driven by $\alpha$-stable Lévy processes have been proposed as an alternative to Brownian diffusion models, with empirical evidence suggesting improved sampling and better modeling of heavy-tailed data. Yet theoretical guarantees for these models remain limited. We develop a non-asymptotic convergence analysis for scale-preserving $\alpha$-stable generative dynamics, covering both compactly supported and power-law targets. In p-Wasserstein distance, we quantify the effects of early stopping, initialization, score approximation, and time discretization, and show exponential decay of the initialization error. A comparison with Brownian dynamics reveals that global Wasserstein convergence alone does not fundamentally distinguish the two models: both initialization errors decay exponentially with the forward horizon on the common class of heavy-tailed targets. A sharp separation emerges instead in the tails. At any positive generation time, stable dynamics produces power-law tails with index $\alpha$, whereas Brownian dynamics remains light-tailed. For a target with tail index $\nu$, asymptotically correct extreme-quantile scaling is possible precisely when $\alpha$=$\nu$. These results identify tail-index matching as a principled mechanism behind the ability of stable generative models to capture extreme events.

This work introduces a Process Additive Neural Network (PANN) framework to disentangle compensating biases in atmospheric models, where errors in different physical processes can offset each other and obscure their origins. Using a single-column model, each PANN branch represents the tendency error associated with a separate physical process, and the summed branch outputs approximate the total error relative to a reference tendency. Once trained successfully, the branch outputs are expected to provide process-level error attributions and, when averaged, estimates of process-level bias. Initial experiments focus on cloud-related processes in OpenIFS SCM case studies, where cloud and convection tendencies are strongly coupled and compensation is difficult to diagnose using standard approaches. The aim is not to replace human interpretation of physical processes, but to extend it to regimes where model complexity, process interaction, and compensating errors make direct diagnosis difficult. By providing a physically structured form of machine-learning interpretability, PANN can help connect complex model behaviour with process-level explanations. This work supports both improved understanding of compensating errors and the development of more physically consistent weather and climate models.