Papers

Given a compact complex surface with a nonflat Ricci-flat Kähler metric, we show that its holomorphic tangent bundle admits an RC-positive Hermitian metric. The proof relies on a characterization of RC-positivity through the anti-self-dual part of the Weyl operator, the Weitzenböck formula on the four dimensional Einstein manifold, and a conformal perturbation on the Ricci-flat metric. As a consequence, we prove that RC-positivity is not preserved after taking tensor, exterior, or symmetric power. Moreover, we show that RC-positivity is a strictly weaker notion than uniform RC-positivity, and that RC-positivity of holomorphic tangent bundle does not necessarily imply rational connectedness of the base manifold.

Curriculum learning has found broad application across numerous domains. Nevertheless, its effectiveness is intrinsically curtailed by catastrophic forgetting, driven by the shifts in model parameter distributions between curriculum tasks. In this paper, we investigate the phenomenon of catastrophic forgetting in this training paradigm, building on the established efficacy of curriculum learning. Our theoretical analyses of parameter update dynamics demonstrate that catastrophic forgetting in curriculum learning stems from the divergence of task optima, which is generally essential to the faster convergence of curriculum learning; therefore, forgetting cannot be completely eliminated. Based on this finding, we augment the training process and propose IV-EWC, which incorporates Elastic Weight Consolidation (EWC) into the curriculum learning objective to curb catastrophic forgetting in mathematical reasoning, a prototypical curriculum learning scenario. IV-EWC employs the influence function to construct a representative validation set from the curriculum's training data, which is used to drive dynamic regularization during training. We further present an extended theoretical analysis to show that EWC-based regularization methods mitigate catastrophic forgetting in curriculum learning, thereby providing theoretical support for IV-EWC. Empirical evaluations on three backbone models and three benchmarks indicate that curriculum learning exhibits catastrophic forgetting. IV-EWC alleviates this issue, reducing forgetting by 162% on average relative to vanilla curriculum learning and yielding positive backward transfer, as evidenced by improved performance on easier tasks after subsequent training on challenging tasks.

This paper proposes an adaptive model reduction approach based on nonlinear participation factors (NPFs) which determines the most effective selection of unimportant generators in a power system to be linearized to accelerate time-domain simulation for the entire system. The method enables a dynamic transition between the full-order model, and a hybrid reduced model. It uses modal energies to rank system modes under contingencies, and computes NPFs for highly energized modes based on Normal Form theory. To accelerate the computation of NPFs and make it achievable online, a tensor contraction technique is introduced. The proposed approach is tested on a 48-machine, 140-bus NPCC system using both partitioned and unpartitioned strategies. It demonstrates significant simulation speedup while preserving better accuracy than a linear participation factor-based method if the nonlinear behaviors of the system cannot be ignored, especially when a near-resonance condition is presented.

Reinforcement learning (RL) enables generalist robot policies to improve through trial-and-error interaction, yet its effectiveness is fundamentally constrained by sparse task rewards. Existing general-purpose reward models typically alleviate this issue by learning task progress from expert demonstrations, but introduce a distribution mismatch with the mixed-quality rollouts encountered during policy optimization, making their estimates unreliable on suboptimal and failed behaviors from which the policy must learn. In this work, we introduce a demonstration-free reward learning paradigm where dense reward feedback can be learned directly from sparse task outcomes and policy experience. We theoretically show that terminal task outcomes implicitly define dense success-probability feedback at intermediate timesteps, which can be recursively learned through bootstrapping. Based on this insight, we introduce eVTA$_0$, which learns success probabilities from mixed-quality policy rollouts through temporal-difference-style bootstrapping, without expert demonstrations or intermediate annotations. We further introduce RL with Evolving Rewards (RLER), a closed-loop framework that adapts eVTA$_0$ using newly collected rollouts as the policy evolves. Experiments show that eVTA$_0$ provides more informative rewards than state-of-the-art reward models and achieves the best average policy performance across all LIBERO task suites under the same RL training budget, improving success rates by 5.4%-13.8% over the initial policy. In real-world manipulation, RLER further improves overall success rates by 20%-26%, with 35%-36% gains under out-of-distribution conditions. These results demonstrate the effectiveness of demonstration-free reward learning and adapting rewards as the policy evolves. Project webpage: https://duowuyms.github.io/evta0.

Context-aware dynamic trees allocate the speculative decoding budget according to draft path probabilities, adapting their depth and branching to the current context. Under stochastic decoding, however, we find that this structural advantage does not always compensate for the acceptance gains of random sampling paired with advanced verification, and such dynamic trees can fall behind sampled chains in some settings. These trees grow their topology from the candidates themselves, so the tokens submitted for verification are typically the deterministic high-score tokens selected during construction. This coupling is not inherent: once the topology is fixed, its nodes can be repopulated by sampling, allowing dynamic trees to retain their structural advantage while also benefiting from random sampling and advanced verification. Diffusion-based drafters make this practical, as their parallel outputs or lightweight conditional corrections allow candidates to be regenerated cheaply after the complete topology is known. We introduce Tsubame, a two-pass tree speculative decoding framework for diffusion-based drafters. The first pass plans and freezes a context-aware topology using draft path scores; the second replays the fixed topology, sampling the tokens that populate its nodes to form the candidate tree for verification. We prove that Tsubame is lossless under compatible sampling and verification strategies. Experiments across three diffusion-based drafters, six datasets, and multiple candidate budgets show that Tsubame improves acceptance length and throughput over deterministic trees, including settings where it reverses their disadvantage against sampled chains.

We prove log-concavity for the determinant-weighted external semi-activity polynomials of all real flat arrangements, strengthening their known trapezoidality. In fact, we establish a quadratic coefficient inequality that, in rank at least two, implies power concavity with an explicit rank-dependent exponent. The proof uses a new mixed-volume representation of the coefficients and the Alexandrov–Fenchel inequality. A more general formula gives a factorization and log-concavity for related mixed-volume sequences. As applications, we establish the conjectured log-concavity for spanning-tree polynomials of Eulerian digraphs, extend it to positive circulation weights, and strengthen the coefficient inequalities for Alexander polynomials of special alternating links.

Word-level forced alignment estimates when each transcript word occurs in an audio recording. It underpins text-based media editing, subtitling, speech-data curation, and phonetic analysis. Existing evaluations understate the difficulty of forced alignment by relying on short, clean speech, perfect transcripts, and metrics that obscure consequential alignment errors. In contrast, real-world media and data-processing pipelines operate on long and diverse recordings. Additionally, forced aligners often operate on error-prone automatic speech recognition (ASR) output. We address these gaps with improved evaluation metrics, a scoring protocol for real ASR transcripts, and AlignBench, a benchmark spanning diverse speaker, acoustic, and text conditions. We further introduce FuseAlign, a transformer-based aligner trained on large-scale pseudo-labeled speech with online label correction. FuseAlign performs joint contextualization of audio and text for the localization of coarse words. The model then refines boundaries at millisecond resolution and detects missing transcript words in the audio without lexicon-based or Viterbi decoding. On AlignBench, FuseAlign substantially outperforms all baselines and remains robust under real ASR transcripts. Ablations show that convolutional upsampling and EMA-snapshot label correction matter more than model properties such as parameter count.

Learning mappings between probability distributions arises naturally when inputs and outputs are represented by populations of samples rather than individual observations. We develop an approximation-theoretic framework for distribution-to-distribution learning and extend it to mappings between stochastic processes. For continuous operators on $W_2$-compact families of finite-dimensional probability laws, we establish uniform neural approximation in the 2-Wasserstein metric using finite law statistics, a simplex-valued neural map, and a shared atomic output support that guarantees valid probability measures. We further extend this principle to probability laws on separable Hilbert spaces through finite-rank orthogonal projections. These results establish the representational feasibility of learning transformations between probability laws rather than deterministic vectors or functions. To demonstrate practical relevance, we study two problems naturally defined at the distribution level: prediction of first-passage-time distributions for an Ornstein–Uhlenbeck process and nonlinear response-path laws of a Duffing oscillator. Because the theory is model-agnostic and broader than any single practical architecture, the experiments use task-adapted neural models rather than reproducing the theoretical construction exactly. In both problems, the proposed models outperform a fixed-feature MLP baseline and distribution-space kernel regression. These experiments complement the theory by demonstrating the practical learnability of distribution-to-distribution transformations in random systems.

The combination of ultra-wide bandwidth and large-scale multiple-input multiple-output arrays with frequency-independent phase shifters induces beam squint, causing frequency and distance dependent array gain variations across subcarriers and degrading integrated sensing and communications performance. Transceiver beamforming and group index modulation (GIM) can alleviate the impact of beam squint on communication and sensing performance. However, their designs are coupled in the frequency domain, as beamforming shapes the subcarrier responses on which GIM grouping and activation depend. To address this coupling, we propose a joint transceiver beamforming and GIM design that maximizes a weighted combination of normalized worst-case communication and sensing distances. An alternating optimization algorithm jointly refines the transceiver beamformers and GIM configuration. Simulation results show that the proposed joint design reduces bit error rate in the high signal-to-noise ratio region and achieves a more favorable communication-sensing trade-off, while maintaining an average sensing AUC comparable to that of the considered GIM based benchmark schemes.

Many indoor environments in which robots operate, such as warehouses, offices, and hospitals, already have cameras installed. They observe parts of the building that the robot cannot see from where it stands, yet navigation policies, including recent vision-language-action (VLA) models, do not use them. We propose InfraVLA, an end-to-end method that adapts a pretrained navigation VLA to such static infrastructure views: a closed-circuit television (CCTV) encoder turns each external view into tokens of the input sequence. Because the views matter only at rare decision points, fine-tuning alone did not make the policy use them in our experiments; we therefore train in two stages, on demonstrations with upsampled counterfactual data and then on recovery data. We evaluate on two simulated warehouse tasks, finding an object named in the instruction and rerouting around blocked aisles, where the deciding information is often visible only to the infrastructure cameras. Tested in distribution, InfraVLA reached a success rate of 100% on both, against 34.0% and 73.6% for a baseline without CCTV input. On out-of-distribution test sets it reached 88.2% and 88.9%. On a real quadruped fine-tuned with under 10 minutes of demonstrations, the policy reached 83.3% against 29.2% for the on-board-only baseline.

Browser-use agents require seamless alignment between structured web metadata and visual information, while preserving relevant context across long interactions. Existing interfaces often rely on either screenshot-level action prediction or static Set-of-Marks overlays, leaving the model to resolve dense DOM-pixel alignment before every operation. We introduce Probe to Act (P2A), an active probing framework for the browser-agent loop that moves this alignment into decision time. P2A addresses an asymmetric bridge between symbolic DOM hypotheses and screenshot layout by rendering on-demand symbolic DOM structure back into pixels. Before committing a state-changing browser operation, the agent can issue lightweight probes to translate DOM handles into pixel evidence, map screen regions back to DOM candidates, register visual-only targets, and commit verified notes. These interleaved processes naturally produce evidence-based memory: only probed, acted-on, or explicitly committed observations are kept across steps, preserving only decision-critical evidence in long-horizon contexts. P2A can be used as a prompting strategy for proprietary models under the standard DOM+SoM interface, and can be distilled into open-weight models through cold-start synthesis and self-bootstrapped SFT. Across three browser-use benchmarks, P2A shows clear gains on task success rate for both proprietary and fine-tuned models; on VisualWebArena, for example, it improves Gemini-3-Pro from 54.1% to 61.2% and Qwen3-VL-8B from 24.6% to 32.9%, while matching the costly full-observation history ($\sim$3$\times$) at only $\sim$1.2$\times$ the peak retained input context of action-only history.

Connectionist temporal classification (CTC) naturally supports offline and streaming speech recognition with utterance-level supervision, but conventional implementations materialize frame-by-vocabulary activations in memory, making CTC training with native LLM vocabularies prohibitively memory-intensive. A key observation is that every valid CTC alignment uses only target tokens and blank, and their union across a batch typically forms a small subset of the full vocabulary. We introduce Pruned CTC, which restricts alignment computation to this subset while retaining full-vocabulary normalization. We prove that this vocabulary reduction is exactly equivalent to full-vocabulary CTC in loss and gradients. Head-and-loss activation memory no longer scales linearly with vocabulary size. We further apply finite-beam alignment pruning. Building on Pruned CTC, we develop LLM-CTC, which adapts pretrained LLMs for non-autoregressive ASR while retaining causal attention and native vocabularies, and extend it to bounded-history streaming, avoiding chunk-level speech–text alignments. Experiments show that, with Zipformer-M encoder and 180K vocabulary, Pruned CTC reduces full-step memory by 5.1$\times$ with only 17% step-time overhead. Across three corpora, it matches standard CTC accuracy. On GigaSpeech, across six Qwen3 model sizes from 0.6B to 32B, LLM-CTC remains within 7% relative WER of LLM-CE with 7 to 10$\times$ faster recognition; when fine-tuning Qwen3-ASR for bounded-history streaming, LLM-CTC remains within 3% relative WER of matched offline models on the test set. Together, these results establish Pruned CTC as a scalable sequence objective for native-vocabulary LLM ASR across offline and streaming settings.

In an earlier paper, M. Talagrand made a number of daring conjectures. An AI model provided a very beautiful proof of one of them which we explain here.

We give a short, self-contained proof of Bernstein's theorem: every entire minimal graph in $R^3$ is a plane. The only global tool is the Omori-Yau maximum principle, which holds on entire minimal graphs with their induced metric. We apply it exactly once to a single explicit function $F$ built from the surface's angle function and principal curvatures. A pointwise differential inequality for $F$, combined with the Omori-Yau principle, forces it to attain its minimum value everywhere, which yields the planarity of the surface and hence Bernstein's theorem. As a by-product of our approach, we show that the same method, with a different function and with some extra work, also proves in a simple and self-contained way the generalization of Bernstein's theorem given by Osserman that a complete minimal surface in $R^3$ whose normals omit a neighbourhood of some direction must be a plane.

Real-world tasks often require large language models (LLMs) to learn from complex task-specific context rather than pretrained parametric knowledge. This capability remains a weakness of LLMs, while human annotation for such task contexts is expensive and difficult to scale. Public high-quality documents are an abundant alternative, but much of the public web has already been consumed during pretraining: training on such documents naively would reward memorization rather than context learning. In this work, we attempt to make use of high-quality public documents with small perturbations and empirically find that LLMs can successfully generate context-dependent reasoning traces and answers, which are then used to train a student model. Specifically, we construct a synthesis pipeline that (i) rewrites source documents to reduce memorization risk, (ii) generates questions and rubrics that require reasoning over the document, (iii) answers the questions with the document as context, and (iv) admits only samples that genuinely depend on the document. Without any human annotators, our pipeline generates about 10k samples from 3.5k documents, and the resulting student model substantially improves the performance on CL-bench. SFT raises a Qwen3.6-35B-A3B student from 13.7% to 22.8%, and a subsequent rubric-reward RL stage reaches 24.6%, on CL-bench comparable with a frontier model of over a trillion parameters, Qwen3.8-2.4T (23.9%). We also observe a broad transfer of improvements to long-context understanding, instruction following, and reasoning, while code generation and knowledge remain mostly flat. We hope this work provides a reproducible and scalable way to improve the ability of LLMs to learn from context, and to facilitate further research on context-grounded reasoning.

Several businesses apply maintenance, repair, and overhaul (MRO) principles to the life-cycle of their existing products. In cases like casted gas turbine component Product Lifecycle Management (PLM), repairing components in frequent intervals can extend the lifetime expectation of the product, provide higher cost efficiency compared to newly produced components, and even improve the part design during the repair cycle. Another aspect of repair concerns sustainability, as products often contain rare materials. The emissions produced by the repair process are usually smaller than mining materials and casting new components. To optimize the repair process further, we propose the Smart Expert System (SES), which assists engineering experts with machine learning-based decision support throughout the repair process. We elaborate on its IT architecture and present machine learning models employed for representative MRO use cases. The SES is evaluated using actual industry data from a leading gas turbine company and demonstrably fulfills formulated requirements concerning the suitability of the overall decision support and the stability of the enclosing IT architecture.

Molecular multimodal models support diverse understanding and generation tasks but may introduce safety vulnerabilities when handling hazardous molecules. In this work, We reveal substantial jailbreak vulnerabilities under both text-only and graph-conditioned settings. Our analysis further shows that safety robustness must hold across input modalities while balancing safety, over-refusal, and utility. To address these challenges, we construct SafeMolBench, a molecular multimodal safety-alignment benchmark with 3702 samples covering 618 unique hazardous molecules and safe molecular tasks, organized into hazardous-harmful, hazardous-allowed, and utility-replay subsets to support unified training and evaluation of safety, over-refusal, and utility. Based on SafeMolBench, we propose SafeMol, a parameter-efficient safety alignment framework that jointly optimizes lightweight modules across text-only and graph-conditioned inputs, uses MMD for distribution-level representation alignment to reduce modality-induced discrepancies, and explicitly models molecular hazardousness and harmful operational intent. Experiments on SafeMolBench show that SafeMol reduces attack success by several tens of percentage points while largely maintaining low over-refusal and preserving molecular-task utility.

Existing large language model (LLM) unlearning has focused primarily on removing specific knowledge, such as harmful facts, private data, or copyrighted content. However, as LLMs are increasingly deployed as autonomous agents, a fundamental yet overlooked problem emerges: beyond suppressing what an agent knows, an agent should not reproduce undesired behaviors through its action trajectories. In this work, we introduce trajectory-level unlearning, a new problem formulation that targets the removal of specific action trajectories in long-horizon agentic tasks, rather than factual knowledge. We identify two fundamental challenges that distinguish trajectory unlearning from knowledge unlearning: (1) our unlearning target is what the agent does, not what it says; and (2) trajectories are sequentially dependent action sequences that cannot be decomposed into isolated prompt-response pairs without losing inter-step structure. To address these challenges, we propose Group-injected Relative Policy Optimization (GiRPO), which injects forget trajectories into the policy rollout group with penalized rewards and isolates the normalization statistics, yielding a stable and bounded unlearning signal that does not corrupt gradient updates for normal task trajectories. We construct trajectory unlearning benchmarks from two application scenarios, household tasks (ALFWorld) and online shopping (WebShop), and design three complementary metrics for evaluating forgetting quality and model utility. Experiments on ALFWorld and WebShop demonstrate that GiRPO effectively unlearns target trajectories while preserving task success rates, outperforming existing knowledge-unlearning baselines on both forgetting quality and task utility.

We introduce RareTrap, a framework for estimating the probability of severe behaviors in black box large language models (LLMs). A key challenge for probability estimation is defining a tractable distribution over the input space. To accomplish that, RareTrap uses a surrogate LLM and constructs a geometry-aware mapping from a lower-dimensional latent reference space into its token-embedding space to induce an explicit and reproducible distribution over input prompts. A response-level performance function is utilized on the response to quantify behavior severity. This enables sequential rare event simulation that concentrates evaluations on progressively more severe behaviors while preserving probability under the induced prompt distribution, which would otherwise be prohibitive to measure. Across 10 open-weight and two frontier models (GPT-5.4 and Claude Sonnet 4.6), we find that RareTrap successfully induces severe resource consumption behaviors and computes their probability with as few as 200 evaluations. RareTrap provides model developers a principled approach for evaluating language models under a common distribution, and prioritizing alignment effort to improve safety and mitigate risks.

In this paper, we propose a hierarchical multi-agent reinforcement learning framework for coordinating robot teams in warehouse environments under communication loss. We partition the robot team into groups, with centralized coordination within each group and distributed coordination across groups. Each group uses a recurrent predictor to estimate unavailable interaction information due to communication loss. A higher-level policy then generates a compact coordination reference that conditions the local control policy within each group. A predictive safety filter evaluates and modifies the proposed controls when they violate safety constraints. Simulation results show improved task completion under communication loss, reduced communication growth as the team size increases, and safe operation in the tested scenarios.

We introduce the $m$-ary recursive tree, a tree structure that starts with a single node. At each step of the growth process, a random node, called the recruiter, is selected, and $m$ new nodes are attached to this recruiter. The main objective is an asymptotic analysis of distances in this structure. We first derive the distribution of the depth of nodes in such a tree as a convolution of independent (though not identically distributed) Bernoulli random variables. This representation yields normal and Poisson approximations with quantified errors for the depth. We also investigate the height of these trees, that is, the longest root-to-leaf distance, via a coupling to a weighted random recursive tree with suitably chosen weights. The coupling transfers the results on a strong law and tightness from the weighted recursive tree to the $m$-ary recursive tree. Furthermore, we establish a bivariate limit law for the Wiener index, that is, the sum of all pairwise distances, and the internal path length, that is, the sum of the depths of all nodes, using the contraction method. As a novel technical feature of our approach, we employ weighted norms instead of Euclidean norms within the contraction method.

Complex systems are routinely measured and represented through pairwise networks, even when the underlying interactions involve more than two units at once. Recovering this latent hypergraph structure from pairwise measurements is a fundamental inverse problem, but as the space of candidate hyperedges grows exponentially with system size, scalable hypergraph reconstruction at arbitrary interaction orders is out of reach for existing methods. Here we cast hypergraph reconstruction as a local signal-to-noise discrimination problem and use this locality to build a fast algorithm that reconstructs hypergraphs up to any interaction order. Across diverse synthetic and real-world systems our method achieves a high recovery accuracy of latent hypergraph structure while reconstructing hypergraphs up to orders of magnitude more quickly than current approaches. Our approach also yields an information-theoretic detectability boundary that sharply predicts which latent hyperedges are recoverable from pairwise measurements.

Guard models are the last line of defense between a language model and a harmful output, yet their training objective is surprisingly narrow. Existing guards learn to predict a single verdict token from a conversational context, concentrating supervision on a single target. The consequences are structural: models latch onto shortcut features, are overconfident, and remain sensitive to where safety evidence appears in the sequence rather than its role in the full context. We propose a different framing. Rather than predicting a label from text, our LLaDA-Guard asks which label better explains the text: scoring the prompt or response under each label hypothesis and classifying based on their difference. This shifts supervision to every token in the moderated region, forcing the model to account for full content rather than its most discriminative fragments. We instantiate this idea with a masked diffusion language model, fine-tuning LLaDA-8B-Instruct with a class-conditional reconstruction objective using LoRA and requiring no architectural changes beyond the base model. LLaDA-Guard leads on average rank against discriminative baselines trained on stronger backbones across seven held-out safety benchmarks, while exhibiting substantially better confidence calibration (ECE 0.0875 vs. 0.1384 for Qwen3Guard), less over-defense on benign prompts with unsafe-looking cues, and less prompt leakage when moderating responses. Its generative nature further enables token-level risk localization as a natural byproduct, yielding a pipeline for rewriting unsafe prompts into safe equivalents without additional training and achieving a 60.7% average conversion-to-safe rate.

For every integer $\nu\geq 2$, we construct a $(\nu+1)$-dimensional, locally compact, geodesically complete CAT(0) space of asymptotic rank $\nu$ which does not satisfy a linear isoperimetric inequality for integral $\nu$-cycles. Its filling function is bounded below by $c v\log v$ for all sufficiently large $v$.

Let $X$ be a fixed complex K3 surface and let $0\ne\alpha\in\overline{Kah_X}$ be a $(1,1)$-class on the boundary of the Kähler cone with $\alpha^2=0$. We build a novel connection between two seemingly unrelated, intensively studied problems: the rigidity of a closed positive current in the class $\alpha$ and the collapse geometry of a sequence of Ricci-flat Kähler metrics in the Kähler class $\alpha+t\kappa$ as $t\to 0^+$. More precisely, we prove that $\alpha$ contains a unique closed positive $(1,1)$-current if and only if the Ricci-flat metrics in class $\alpha+t\kappa$ collapse to a point in the Gromov–Hausdorff sense. Then we exhibit the first example of a nonrigid irrational nef class $\alpha$ on a Kummer surface, which answers a question of Filip–Tosatti and Sibony–Soldatenkov–Verbitsky. We also construct many new examples of rigid nef classes on hyperkähler manifolds, which extend the work of Filip–Tosatti and Sibony–Soldatenkov–Verbitsky.

Predicting the full spin Hall conductivity tensor of a magnetic crystal is difficult because crystallographic and magnetic symmetries do not constrain all parts of the response in the same way. Here, we separate the spin Hall conductivity of altermagnets into time-reversal-even and time-reversal-odd channels and combine symmetry analysis with first-principles calculations for six representative compounds spanning distinct crystallographic classes. The even channel follows crystallographic selection rules consistent with its Berry-curvature Fermi-sea origin. The odd channel is set by magnetic symmetry and can be reshaped by antiunitary operations whose spatial parts originate from screw or glide symmetries. Momentum-resolved analysis further links the even response to spin-orbit-driven avoided crossings and the odd response to anisotropic near-Fermi-level spin-current response textures. By converting crystallographic and magnetic symmetry operations into linear constraints on the full 27-component SHC tensor, this framework provides a computational prescreening route for identifying symmetry-allowed spin Hall channels before dense first-principles transport calculations. Extending the same analysis to 62 spin-split collinear antiferromagnets yields a magnetic-point-group tensor atlas, identifying design limits such as the complete 13/14tensor partition in CuF2 and the one-parameter time-odd tensor compression in MnSe.

Differentiable optimization brings the structural guarantees of mathematical optimization to network pipelines, allowing them to be trained end-to-end. However, its application remains challenging for nonconvex constrained problems, as existing differentiable solvers often suffer from limited modeling expressiveness due to their reliance on specialized problem structures, while also incurring substantial computation time and memory overhead in both the forward and backward passes. To address these challenges, we propose lapanda, a matrix-free differentiable solver for nonconvex optimization with general constraints. It reformulates the problem to a sequence of augmented Lagrangian subproblems, each handled by a first-order inner solver through a proximal averaged quasi-Newton algorithm with adaptive linesearch, thus enabling efficient forward optimization. We establish local well-posedness of the solution map and convergence of the outer iterations, and further derive a sensitivity alignment between the original problem and the final subproblem in the backward pass, demonstrating that the subproblem sensitivity, which can be computed efficiently in a matrix-free manner, provides a principled approximation to the exact optimizer sensitivity. We evaluate lapanda on nonconvex constrained Rosenbrock benchmarks, imitation learning with several representative constrained optimal control problems, and embedded robotic obstacle-avoidance tasks. Compared with state-of-the-art differentiable solvers, lapanda delivers substantial reductions in computation time and memory footprint while maintaining reliable constraint satisfaction and learning performance.

Smoothing empirical data can fill gaps between observations, while noise in the surrounding space can move mass away from the manifold supporting the data. We derive Wasserstein error bounds for ambient Gaussian smoothing and for smoothing through an encoder–decoder representation. For a compact connected smooth manifold without boundary and a smooth positive target density, established heat-flow and entropy estimates imply that sufficiently small intrinsic heat smoothing improves the squared intrinsic Wasserstein error. Coupling this estimate with ambient noise yields a bound whose quadratic term includes ambient dimension and a curvature correction. Our main latent bound tracks reconstruction error, tangential distortion, and the decoder's response to orthogonal latent noise. Its quadratic surrogate gives bandwidth rules and explicit conditions under which the latent upper-bound surrogate is smaller than the ambient one. These surrogate comparisons do not assert an ordering of the exact Wasserstein errors. Synthetic experiments examine the predicted scaling and latent geometry on spheres and a product of spheres.

Prompt injection is a leading security risk for LLMs and LLM-based applications such as agents. State-of-the-art red-teaming methods for prompt injection leverage reinforcement learning (RL) to train an attacker LLM to generate effective injected prompts. However, when targeting frontier LLMs such as GPT-6-Luna, a major challenge is the cold-start problem: every attack attempt by the attacker LLM fails and thus receives zero reward, providing no signal for learning. In this work, we propose a curriculum learning-based method to address the cold-start problem. In particular, we propose to train the attacker LLM against a sequence of increasingly robust target LLMs, with each stage warm-starting from the attacker LLM obtained in the previous one. However, simply training against a weak target (e.g., GPT-4o-mini) may not sufficiently prepare the attacker LLM to obtain useful learning signals against a frontier LLM (e.g., GPT-5.6-Terra). Instead, we find that the design of the curriculum is critical: after each stage, the attacker LLM needs to partially succeed against the next target LLM such that it can learn from successful attempts to attack the new target. Our extensive evaluation shows that our method can effectively red-team frontier LLMs, achieving an attack success rate (ASR@10) of 93.8% and 45.0% against GPT-5.6-Luna and GPT-5.6-Terra on AgentDyn, whereas state-of-the-art RL methods such as RL-Hammer and PISmith achieve 0% ASR under the same setting. Moreover, we find that the attacker LLM transfers across targets, e.g., an attacker LLM trained to defeat one strong LLM (GPT-5.6-Terra) also succeeds against six other frontier LLMs (e.g., GPT-6-Luna) it was never trained on. Our code is available at https://github.com/albert-y1n/PIForge.

Despite recent progress in agentic multi-shot video generation, producing coherent and consistent long-form stories remains challenging. Existing agentic pipelines typically rely on textual shot plans or previously generated pixels, yet lack an explicit mechanism for propagating the consequences of story events and maintaining the video world state across shots. As a result, missing visual details may be reconstructed inaccurately, while visual drift may propagate across subsequent shots, undermining both narrative coherence and visual consistency. To address these challenges, we propose StoryEngine, a state-grounded agentic framework for video storytelling. StoryEngine establishes a separation between authoritative semantic plans and unreliable visual observations. Specifically, StoryEngine maintains a structured representation of entity placement and story-relevant states, and propagates event-induced changes to define the intended start and end states of each shot. To visually realize these states, StoryEngine constructs canonical references for recurring entities and environments, and compiles state and visual constraints into executable render plans. Meanwhile, to realize these states correctly, a bounded evaluation-guided repair loop further corrects local state inconsistencies. Together, these mechanisms preserve causal story progression and prevent local visual errors from propagating across shots. To comprehensively evaluate long-form storytelling, we construct a benchmark across diverse scenarios and visual styles, with metrics assessing storytelling quality, narrative coherence, and visual consistency. Experimental results demonstrate that StoryEngine consistently outperforms state-of-the-art methods across all evaluation dimensions, validating its effectiveness for coherent and consistent video storytelling.