Papers

The electron-positron heavy-flavor factories — BaBar, Belle, Belle~II, and BESIII — continue to deliver a broad and sensitive physics program. I report selected highlights presented at ICHEP 2026, covering neutral- and charged-current $B$ processes, tests of lepton-flavor universality in $b\to c\ell\nu$ transitions, precision measurement of Cabibbo–Kobayashi–Maskawa matrix elements, and hadron spectroscopy.

The surfaces of airless bodies evolve through processes such as (micro)meteoroid impacts and thermal fatigue, which modify physical properties such as grain size, porosity, and mineral texture. These properties provide clues to surface evolution and are necessary for interpreting telescopic observations. Near-Sun asteroids (NSAs), which reach heliocentric distances of $\lesssim$0.2 au, are notable targets, as their surfaces are likely modified by intense solar radiation. However, experimental studies of how radiative heating modifies the physical properties of carbonaceous asteroid surfaces remain scarce compared with studies of thermally induced compositional and spectral changes. We investigate these modifications experimentally. Near-Sun conditions at heliocentric distances $0.09<r<0.19$ au are simulated using the Space and High-Irradiance Near-Sun Simulator. CM-type carbonaceous chondrite simulants are irradiated under vacuum. Brightness is monitored in situ with a video camera during heating, and morphological changes are examined using a stage microscope and a scanning electron microscope (SEM). The irradiated samples show initial darkening followed by brightening, consolidation, and morphological modifications from sub-micrometer to millimeter scales. The observed brightness modifications are more consistent with changes in the absorption properties of the sample than with variations in surface roughness. SEM imaging of the heated samples shows structures similar to those formed by sintering, which are completely absent in unheated samples. These results suggest that sintering is a likely candidate for the mechanism responsible for the observed consolidation and morphological changes. This work provides experimental evidence to help constrain the surface evolution of NSAs in general, and supports sintering as a possible mechanism proposed for (3200) Phaethon in particular.

Recent coding large language models (LLMs) can synthesize dynamic 4D worlds from natural language, but the resulting content remains a visual artifact. It lacks physical semantics such as the collision geometry, mass, friction, inertia, and joint structure, required to enable it to simulate the physical world, and its dynamics are scripted to look plausible rather than designed to execute. What is needed is an executable world: one that a physics engine can load and step, resolving contact physically. We present Code2Worlds-2, an extension of Code2Worlds that turns 4D world generation into an embodied world simulation. We keep the original dual-stream generation pipeline intact and append two modules. First, a SimReady Scene Compiler that turns a generated visual scene into a simulator-compatible representation: it assigns collision meshes via convex decomposition, estimates physical attributes with a vision-language model, infers a lightweight support graph, instantiates the engine's contact, friction, and dynamics constraints, and applies a gravity settling pass, before exporting the scene as MuJoCo MJCF. Second, a Simulator-in-the-Loop 4D Refiner that implements an automated agent harness-a compile, simulate, critique and refine loop-that converts visual dynamics into executable rigid and articulated dynamics and evolves the physical settings rather than only the code, replacing the purely visual motion critic with a simulator critic that inspects penetration depth, collision pairs, stability, contact forces, joint limits, and robot reachability. We further propose SimCode4D, a state-based benchmark with five task templates for evaluating embodied simulation. Experiments on SimCode4D and across natural, indoor, industrial, urban, and service scenes show that Code2Worlds-2 produces physically plausible, simulator-compatible, and robot-interactable scenes.

Let $k=\overline{\mathbb{F}}_p$ and let $f\in k[X]$ be a polynomial of degree at least $2$ such that $f-f(0)$ is non-additive. For $\alpha,\beta$ in an algebraically closed extension $L$ of $k$, we prove that there are infinitely many $\lambda\in L$ for which both points are preperiodic under $f(X)+\lambda$ if and only if $\alpha,\beta\in k$ or $f(\beta)-f(\alpha)\in E_f$. Here $E_f=\{c\in G_f:(f-f(0))^n(c)\in G_f\text{ for every }n\ge0\}$, where $G_f=\{c\in k : f(X+c)-f(X)\in k\}$. We also provide a necessary and sufficient criterion for the corresponding colliding orbits set to be infinite.

We give an explicit local description of ray class refinements in cyclotomic Iwasawa theory. For distinct primes $p\geq5$ and $\ell$, and even $2\leq k\leq p-3$, we prove that the $\omega^{1-k}$-component of the $p$-primary ray class group of $\mathbb{Q}(\zeta_p)$, with squarefree modulus supported above $\ell$, is nonzero if and only if $p\mid\ell(1-\ell^k)B_k$. In the cyclotomic tower, we determine the local modules and their correction modulo the diagonal global Tate module, obtaining an explicit determinant formula. Their Frobenius Euler factors, combined with the Mazur–Wiles theorem, yield a ray class form of the Iwasawa main conjecture for nonexceptional odd characters. We also obtain exact class number valuation comparisons at every layer, including those before stabilization, recover Finat's formula for $\ell=2$, and deduce refined $\mu$-vanishing from Ferrero–Washington. The cyclotomic character explains the Wieferich exception, while existing Eisenstein congruence theorems connect the divisibility criteria with prime-level Ramanujan-style congruences.

We study the number of uniform quantum examples needed to exactly learn a Boolean function with at most $k$ nonzero Fourier coefficients. We give a learner with near-optimal $\widetilde{O}(k)$ sample complexity independent of the input length $n$. The learner uses only separate measurements of individual examples. This improves the previous $O(k^{3/2}\log^2 k)$ upper bound (Arunachalam, Chakraborty, Lee, Paraashar, and de Wolf, 2021). The main ingredient is a candidate set formed by symmetric differences of subsets from independent groups of Fourier samples. A multilinear majority polynomial combines unbiased random approximations into an accurate witness whose Fourier support lies in this set. Granularity then forces the set to contain the entire Fourier support, including subsets never directly sampled. For comparison, we derive the tight classical sample complexity $\Theta(nk)$ by combining known sparse-recovery and lower-bound results.

We review the promise of upcoming gravitational-wave (GW) observations in addressing some of the important open questions in astrophysics and cosmology. A decade after the first direct detection of GWs, the field is entering a transformative phase driven by progressive detector upgrades and the anticipated advent of space-based and next-generation ground-based observatories. These instruments will not only push the distance horizon of GW observations to cosmological redshifts, but will dramatically extend the accessible frequency band, opening entirely new source classes that lie beyond the reach of current detectors. The source landscape is rich enough that surprises are likely. This review surveys our current understanding across this landscape and offers some perspective on the discoveries that upcoming GW observations are poised to deliver.

By equipping the category $\mathcal{M}$ of modules over a finite dimensional algebra with the action of a finite tensor category $\mathcal{C}$, we introduce a subcategory $\mathcal{PM}$ satisfying numerous remarkable properties: it is generating and cogenerating, functorially finite, closed under Auslander–Reiten translations (i.e. precluster tilting), and it computes the finitistic dimension. Through a functor category perspective, $\mathcal{PM}$ is identified with the $\mathcal{C}$-module functors that are projective, and we also prove a $\mathcal{C}$-equivariant version of the Auslander(–Solberg) correspondence. As examples, we show that $\mathcal{PM}$ contains only finitely many indecomposable modules for some tensor product algebras. For some family of 1-Iwanaga–Gorenstein algebras introduced by Geiss–Leclerc–Schröer, we show that $\mathcal{PM}$ is exactly the subcategory of $\tau$-locally free modules.

The growing demand for edge computing, content delivery, and AI services is driving the interconnection of edge data centers (DCs) with distribution networks. Before interconnection, utilities evaluate how much DC capacity can be accommodated without violating feeder current and voltage limits. Fixed peak load representations can overlook service dependent demand patterns, cooling related facility demand, and delay tolerant computing tasks. This paper develops a hosting capacity (HC) assessment model for edge DCs with shiftable workload scheduling. Three representative types are considered: mobile edge computing (MEC), content delivery network (CDN), and AI DCs. Facility demand is modeled by combining fixed base demand, service driven demand, prescribed cooling-overhead coefficient, and a shiftable workload component. Workload execution is optimized under arrival causality, maximum delay, daily energy balance constraints, and the resulting active and reactive loads are embedded in a distribution power flow model. Compared with the baseline without load shifting, the maximum bus level HC gain on the IEEE 33-bus system reaches 4.46% for MEC DCs and 9.89% for AI DCs, while CDN case shows negligible gain under the assumed cache management windows.

Knowledge distillation (KD) frameworks place teacher and student on the same GPUs, so per-GPU memory limits the teachers that fit. DisaggKD separates them across nodes: teacher replicas stream hidden states to the student, a KD loss over row windows and vocabulary shards equals the full-vocabulary loss in exact arithmetic without forming the full-vocabulary logits, and a prefetch ring paces producer and trainer. Closed-form memory and traffic models locate the memory limits of each layout. On the Qwen3.5-35B-A3B to 9B pair, the disaggregated layout matches the LM loss of the colocated run with the same loss and is faster than that run; our fused loss also lets a colocated run train on as few nodes at faster speed, while the split is memory efficient when the student spans several nodes. On the larger pairs, colocated runs with a fused loss still run OOM where the split trains, because teacher weights and student states fill the budget.

An enterprise agent that answers under a written policy must choose an action before it says anything: answer, ask for a missing fact, ask for confirmation, call one or several tools, escalate, or refuse. Holding one 27B Korean enterprise model fixed, we vary whether the decision is a generated JSON object or a single constrained token, and whether the model may reason first. On 2800 in-distribution items we did not detect an accuracy difference between the two deployed paths (93.46% vs 94.14%), while they differ about tenfold in restart stability (3.00% of actions flip vs 0.29%); they also differ in reasoning, so this is an operational comparison. On a sealed benchmark of 300 items whose labels come from a hidden executable policy, reasoning is worth +17.3 points [+12.3, +23.0] on exact action. With reasoning off, the format difference was 0.0 points [-4.3, +4.0], a failure to detect an advantage for either interface, not equivalence; with reasoning on it is unresolved. Against a token-matched random control, boundary-targeted supervision moves the two covered boundaries by +17.5 and +20.0 points and leaves a held-out boundary unchanged. In a 3-seed training x reasoning factorial, the sealed-rendering interaction is -4.9 [-8.1, -1.7], consistent with partial substitution. All supervision was Korean. On independently rendered English versions, the model is 0.82 points lower [-2.68, +0.93] with reasoning on, the same order as re-rendering in Korean; the reasoning-off gain from targeted supervision is not stable in either language, so we do not claim transfer. The original text stays private as the confirmatory set. An open-model re-rendering made after these results reproduced the reasoning effect and the English verdict; the interaction kept its sign but did not replicate under item-clustered intervals. We release the model and that re-rendering with gold labels.

Low-altitude platforms are evolving from connected sensing nodes into autonomous agents capable of bounded task interpretation, skill invocation, and local decision making. Increasing the intelligence of individual unmanned aerial vehicles (UAVs), however, does not resolve the organization problem that arises when mission workflows depend on capabilities distributed across multiple platforms and provider feasibility changes with network, resource, and mobility conditions. We propose low-altitude agentic networking as a task-level networking paradigm and develop a reference architecture that separates workflow logic from executor identity. Within a validated domain-specific workflow space, each ready operation is translated into a capability requirement and dynamically bound to an agent that remains feasible under current conditions. Task contracts and structured evidence govern workflow execution, while routine provider and link changes are handled through workflow-preserving local adaptation before high-level repair is invoked. A trace-calibrated discrete-event case study identifies a bounded operating region: conventional organization remains effective for simple workflows under stable conditions, whereas agentic networking becomes beneficial when workflow dependencies are tightly coupled, capability feasibility changes during execution, and viable local recovery paths remain available.

Bias scores in language-model evaluations often conflate what a model prefers with whether it answers at all. We identify this confound in BBQ, whose ambiguous score factorizes into answerability and signed preference. Across 11 categories, 28,}824 items, and five models, contrastive steering lowers the signed ambiguous score in 11/11 categories but lowers the signed disambiguated preference score in only 8/11. Across 99 configurations, the answerability channel exceeds half of the observed score change in 17% and accounts for the entire change in 11%. In a six-category disambiguated evaluation, 20.8% of 1,500 items flip to the unknown option, where abstention is incorrect; StereoSet shows no analogous answer-rate shift. The effect reflects selection and near-orthogonality between the contrastive and preference-gradient directions. We introduce Gradient-Constrained Direction Design (GCD), an option-gradient construction with a first-order unknown-logit constraint. Under a matched Qwen-7B protocol, GCD reduces answer-rate distortion 14-fold and yields a 4-fold larger preference change, while ablations show similar gains for alternative and unconstrained option-gradient directions; nulling the unknown gradient alone is not responsible for the gain. We recommend reporting answerability alongside published scores.

Spatial understanding is essential for embodied agents navigating and interacting with the physical world. As observations arrive incrementally, agents must reason in a streaming manner. Yet streaming understanding must also be closed-loop: task-relevant evidence may require both recalling past observations and actively acquiring new views. Existing streaming approaches largely emphasize processing incoming observations, leaving task-driven active exploration underexplored. We introduce MemAct, a framework for streaming spatial understanding with memory and action. A shared vision–language model incrementally writes structured historical memory, retrieves records and past frames on demand, and acquires additional evidence through movement and turning. Retrieved evidence and action observations inform subsequent decisions, enabling the agent to continue exploring or answer within a unified reasoning loop. We develop the MemAct suite, a data generation pipeline and collection across real and simulated environments, with approximately 1M training examples for spatial reasoning, memory writing, retrieval, and exploration. Its MemAct-bench comprises 20,000 main QA pairs evaluating current-observation understanding, historical evidence use, and active exploration, plus 2,000 separate Timing questions. MemAct combines supervised fine-tuning for memory and interaction with counterfactual action optimization using cumulative evidence gains, action costs, and terminal answer quality to improve exploration and stopping decisions. Experiments show that MemAct outperforms existing spatial understanding and streaming baselines and approaches frontier multimodal models on MemAct-bench while retaining streaming inference efficiency.

Aesthetic image cropping improves composition by balancing subjects, context, and image boundaries. Large vision-language models bring semantic knowledge to this task, but their scale limits lightweight photography assistance. We propose FrameLite, a compact cropping model built on Qwen3.5-0.8B. Our approach is motivated by the observation that a small model can generate better crops than its first answer suggests. We develop three-stage training to turn this potential into stronger direct predictions. Spatial and composition training establishes localization and framing preferences. Quality-Guided Online Supervision (QOS) then learns the highest-quality complete answers among the current policy's generated candidates. Greedy-Referenced Optimization (GRO) further refines the policy using positive and negative quality differences relative to its current greedy answer. Both online stages use annotation-derived feedback, while inference returns one coordinate answer without search or an external scorer. Experiments show that FrameLite outperforms the compared large-VLM croppers across public benchmarks with a substantially smaller backbone. Controlled studies confirm that selecting high-quality training answers improves the final model beyond online sampling alone. We will release our code and model weights at https://github.com/JianzeLi-114/FrameLite .

World Action Models (WAMs) use generative visual representations to condition robot actions, yet how these representations organize action-relevant information remains poorly understood. We identify persistent high-norm spatial outliers in WAM representations and find that their action relevance persists even after normalization and K/V projection attenuate their extreme magnitude. Motivated by this observation, we introduce RegisterWAM, which adds learnable non-spatial registers to the world model and uses them directly for action conditioning. Registers alone do not fully eliminate spatial outliers; pairing them with observation flow-matching (FM) loss supervision suppresses spatial outliers while concentrating high-norm responses in registers. Beyond this reorganization, observation FM loss supervision also improves action learning without registers, motivating an additional noised-observation FM objective that learns current-scene recovery from corrupted inputs. The resulting model achieves 81.64% success on LIBERO-Plus without additional embodied pretraining data or foundation models, reaches 93.0% average success on RoboTwin 2.0, and improves real-world manipulation performance.

Since scaling laws were introduced for modern LLMs (Kaplan et al., 2020), several works have extended them to account for quantization, tracking the emerging low-precision data types supported on AI accelerators. We develop a more accurate scaling law for quantized pretraining with mixed precision across the forward and backward passes, grounded in optimization theory and validated empirically. Our formulation separates the effects of quantization on model capacity and on optimization efficiency, and explicitly models the persistent optimization error from forward and backward quantization identified through convergence analysis. To select the regimes for fitting and evaluating our law, we first decompose existing 4-bit training recipes into their forward and backward components, isolating those that most affect loss. Our Qwen3 experiments under selected 4-bit regimes, together with published Llama-style experiments, show that our law predicts loss with up to $11\times$ lower MSE than existing laws as model size and token count scale. Finally, we extend our law to layer-wise mixed precision and identify the optimal quantized-pretraining recipe, i.e., model size, training tokens, and per-layer forward/backward precision, under a hardware-aware compute budget. Unlike prior precision scaling laws, our law predicts that the optimal precision increases with the compute budget.

The Safety-Aware Denoiser (SAD) is a recent, training-free, safety-guidance framework for text diffusion models. During inference, SAD steers text samples toward safe regions of the token probability space. In this paper, we propose $\mathit{SADDER}$ (Safety-Aware Denoising with Directional Embedding-based Revision), which improves the safety and quality trade-offs of SAD by exploiting a safety-guidance signal in the embedding (or activation) space for each token position, then updating the token positions using the SAD update rule multiplied by the guidance signal. This multiplication acts as a gating mechanism: tokens with a high unsafe signal are more likely to be modified during inference following the SAD update rule. However, such an update does not automatically preserve the conditional mean, i.e., the denoiser of a fixed target distribution. We therefore theoretically derive new position-wise target distributions for which the modified denoiser is exact. Furthermore, we derive conditions under which the position-wise target distributions match a global target distribution. We test our $\mathit{SADDER}$ method on popular Masked Diffusion Language Models (MDLMs) and Uniform-State Diffusion Models (USDMs) across unsafe continuation and jailbreak settings, and show that $\mathit{SADDER}$ achieves a better balance between safety, generation quality, and inference cost than existing methods.

Partial multi-label learning (PML) aims to train a classifier on datasets whose instances are over-annotated with not only relevant labels but also irrelevant labels, which is common when datasets are collected from crowd-sourcing platform. Existing works primarily approach it from a curriculum learning perspective, leveraging the memorization effect to disambiguate noisy labels and produce robust predictions. However, these methods are based on non-adaptive weighting functions and lack theoretical guidance for optimal weighting. To overcome these issues, a calibrated disambiguation model named PML-CD is proposed. We first formulate the optimal weighting function for curriculum-based disambiguation, which is equivalent to the calibration of the model's predicted confidences, thus providing guidance for curriculum designing. To obtain the optimal weighting function from PML dataset during the training, a transferable calibrator is designed, which takes the histogram of positive samples' confidences as input, and outputs the optimal curriculum weighting for training. Prototype alignment regularization is also proposed to promote the model's performance. Experiments conducted on Pascal VOC, MS-COCO, NUS-WIDE and CUB have verified that our method outperforms existing state-of-the-art PML methods.

We explore properties of the Berezin range $B(C_\phi)$ of a composition operator $C_\phi$ on the Hardy space $H^2$, including constraints on its location in the complex plane $\mathbb{C}$, topological properties, shape, symmetry, and convexity. For example, we show that $B(C_\phi) \subseteq \{z\in \mathbb{C}: \Re(z) > 0 \ \text{and}\ |z| \le 1 + |\phi(0)|\}$, that $B(C_\phi)$ is closed if and only if $C_\phi$ is the identity operator, and that $B(C_\phi)$ containa all its boundary points except for $0$ if $C_\phi$ is compact. Addressing questions raised by Cowen and Felder, we show that $C_\phi$ can be a (nondegenerate) disk and characterize when $B(C_\phi)$ is convex if $\phi$ is linear.

Work on debugging LLM agents treats the "first mistake" marked by a human or LLM judge as ground truth for where a trajectory failed. We ask whether such labels point at causes or symptoms, and make the distinction executable: we restart the agent from reconstructed intermediate states of a failed trajectory and estimate its prefix value V(h_t), the probability of success from each step, with a certified point of no return (PNR) for a failure. On 150 SWE-bench Verified tasks with two frozen open-weight agents, we build such curves for 47 and 60 failed trajectories and probe every step labeled by four frontier judges under the Traverse rubric. We find that the labels do not mark what a controller needs. Judges of different lineages agree on the exact step in only 21/57 cases, and the newest judges flag mistakes in 8/10 and 10/10 successful runs. For 66% of the labels, the agent's success probability does not drop at the labeled step; only 7/188 answers name the decisive step. Restarting at the measured restart point raises expected success from 0.44 to 0.57 offline, and real restarts confirm the advantage, whereas restarting at a judge's label does not (-0.08 to -0.03). We release our code, curves, and labels.

When used as function approximators, quantum circuits often lack interpretability and face a fundamental trade-off between expressivity and trainability. We propose a problem-informed framework for financial return generation that uses relational structure and symmetry-inspired parameter sharing to guide the construction of quantum circuits with few trainable parameters and empirically testable operator roles. We evaluate three quantum generator architectures, referred to as ZZ, directed ZZ-CRX, and structured time evolution, within a hybrid Wasserstein quantum generative adversarial network trained to generate 16-step Bitcoin return windows. Across circuits with one to four layers and one to eight trainable coefficients, these generators recover meaningful marginal and temporal distributional features, while single-layer configurations remain competitive with deeper variants. Across matched depths, independently trained ZZ-CRX configurations exhibit a predominantly downward shift in median leverage relative to ZZ, consistent with the intended directional role of the controlled-rotation construction. The small number of coefficients also enables direct landscape analysis, revealing competing parameter preferences between marginal and temporal objectives and helping to explain the difficulty of finding parameter settings that perform well on both. These results provide an initial demonstration that structural assumptions can guide the design of compact quantum generators and link circuit architecture to observable statistical behaviour, motivating more systematic and parameter-efficient approaches to quantum circuit construction.

A complete mapping of a finite group $G$ is a permutation $\theta$ of $G$ such that $x\mapsto x\theta(x)$ is also a permutation of $G$. Complete mappings have applications in cryptography, particularly in the design of round functions for cryptographic systems. The study of their parity has led to the question of which finite groups admit complete mappings of both parities. A useful approach to this question is to construct complete mappings stabilizing suitable subgroups, in particular Sylow $2$-subgroups. We show that, for every $n\geq2$, every prime power $q$, and every $Z\leq Z(\mathrm{SL}_n(q))$, the group $\mathrm{SL}_n(q)/Z$ admits a complete mapping stabilizing a Sylow $2$-subgroup if and only if $(n,q)\neq(2,2)$.

In outdoor environments, varying terrain and contact conditions can cause identical action commands to produce different motion outcomes for quadruped robots. Predicting these outcomes is essential for reliable navigation and informed path selection. Existing video world models can generate visually plausible futures, yet often struggle to capture robot dynamics and terrain interactions, leading to overly optimistic predictions of action outcomes. We present DR-WM, a physically consistent world model that incorporates robot-terrain contact dynamics to predict the consequences of quadruped actions. Starting from an initial RGB image, our method reconstructs scene geometry and integrates dense, dimensionless priors over terrain contact properties, calibrated using real-world action-response data. The resulting terrain model supports the simulation of physics with spatially varying contact properties such as friction. Given the initial state of the robot and candidate action sequences, we simulate its future motion and use the resulting camera trajectories and rendered geometry to guide the training of a video world model. The generated future observations are then used to update the terrain reconstruction, enabling iterative model rollouts without additional real-world images. Extensive experiments demonstrate that DR-WM substantially outperforms geometry-only baselines and baselines with uniform physical parameters on key physical metrics characterizing action outcomes, while achieving the best performance among the evaluated baselines. These physically grounded predictions support more informed action selection: across 90 challenging scenarios, an 8B vision-language model augmented with DR-WM outperforms an unassisted 32B vision-language model on five of six evaluation metrics.

We study the stability of a thin shell of ordinary matter that separates a flat interior from a Schwarzschild exterior, which is the simplest model of a subluminal warp drive. The matter content of the shell is fixed by the junction conditions and satisfies all the standard energy conditions except very close to the horizon. For a shell made of causal matter we find an exact radius below which it cannot be stable under radial perturbations. We then place a black hole inside the shell and show that this radius grows with the black hole mass, so that the flat interior is the most favourable case. Since such shells are known to be unstable to non-radial perturbations, our result marks the boundary of the region in which any stabilising mechanism would have to operate.

We study static, spherically symmetric black holes surrounded by dark matter halos in the presence of a positive cosmological constant. Assuming vanishing radial pressure, we derive the constraints imposed by the null, weak, strong, and dominant energy conditions on the halo matter. The halo is confined to a finite radial interval separated from both horizons, and the total mass is bounded above by the Nariai value. We construct a Hernquist-type profile and study black hole images, showing that a positive cosmological constant can substantially change the images. We also compute scalar quasinormal modes of the Hernquist-type spacetime. When the dark matter mass is sufficiently small, the relative difference of a selected mode is approximately linear in the compactness of the matter halo, i.e., the ratio of mass parameter $M_{\text{DM}}$ and scale parameter $a$, with a coefficient that depends on the cosmological constant.

Filtering search is one of the crucial applications of approximate nearest neighbor search (ANNS). In filtering search, label information is used in conjunction with unstructured vector data. ANNS provides efficient similarity search in large-scale datasets, however, the memory footprint of storing both vector data and their associated label becomes a significant cost factor as dataset sizes grow. To address this problem of increasing DRAM usage, we propose AiSAQ-in-Filtering, with a novel quantization method called LiPQ (Label-inclusive Product Quantization). LiPQ combines unstructured data and structured labels into a single representation, leading no growth of encoded data. Our proposal increased recall@1 of single-label searches by up to 55% and fewer disk I/Os compared with existing methods. This also retains the main advantages of AiSAQ, which can reduce DRAM footprint by up to 1/78 and index switching time comparing with existing methods. This proposal can also be applied to sparse-dense hybrid search beyond label filtering such as semantic and keyword search of documents.

We study a broad class of stochastic transport problems under controlled McKean-Vlasov dynamics, allowing control of both drift and volatility, with weak terminal constraints. In contrast to the classical Schrödinger problem, the reference dynamics depend on the evolving law of the process, leading to nonlinear optimization problems on path space, while the terminal constraint is formulated through weak optimal transport, permitting a flexible treatment of distributional targets. This framework encompasses several problems of current interest, including the mean field Schrödinger problem, martingale optimal transport, and Schrödinger-Bass bridges. We establish three main results. First, we prove the existence of optimal controls under general coercivity, continuity, and convexity assumptions. Second, we derive a convex dual representation that extends weak Kantorovich duality and stochastic optimal transport duality to controlled McKean-Vlasov dynamics. Finally, for the mean field Schrödinger problem, we prove convergence, at the level of value functions, of the associated finite-particle Schrödinger bridge problems to the mean field limit, thereby identifying the nonlinear problem as the exact infinite-particle limit of finite-particle Schrödinger bridges. As a byproduct, we establish the existence of an optimal mean field Schrödinger potential, providing a variational foundation for duality in nonlinear stochastic transport.

For video generation in dynamic world modeling, observed static and dynamic content should be efficiently reused to provide conditions for repeated generation at different times and viewpoints. We introduce 4LC, a 4D latent cache with composite visual representations and a flexible spatiotemporal access interface. As a latent cache, 4LC directly reuses visual representations of static and dynamic content to provide generation conditions, avoiding per-request RGB rendering and re-encoding. As a composite cache, 4LC binds visual representations from multiple visual encoders (e.g., VAE, DINO, V-JEPA, VGGT) to shared geometry and motion, allowing the composite representations to describe the dynamic world with rich information. Besides, we design a flexible spatiotemporal interface, which directly reads the cache at independently specified times and viewpoints and combines readouts across observations, providing a common conditioning format for diverse downstream tasks. Building on 4LC, we develop 4LC-Video to address multiple video generation tasks through different configurations of source observations, spatiotemporal requests, and historical reuse, including camera control, temporal control, novel-view synthesis, scene revisits, and long-term generation. Our experiments show more efficient condition acquisition, effective spatiotemporal controllability, and scene consistency across tasks using a single 4LC-Video model without task-specific fine-tuning.

In spin-$3/2$ targets, octupole polarization can reveal quark and gluon correlations beyond those probed by vector polarization and quadrupole alignment. Here, we construct the complete leading-twist gluon transverse-momentum-dependent distribution basis, with 32 independent coefficients for each specified Wilson-line and color structure. Fourteen of these describe octupole dependence in gluon number, helicity, and linear polarization. In heavy-quark-pair leptoproduction at small, nonzero pair imbalance, comparing target states with opposite octupoles and identical lower moments isolates the octupole contribution. Beam-helicity reversal and joint angular projections in target orientation and pair-imbalance azimuth can then separate all fourteen gluon octupole responses at leading-power Born order. We also derive the incoming-target quark responses in semi-inclusive deep-inelastic scattering and Drell-Yan production. Time-reversal relations between distributions remain valid under symmetry-preserving renormalization and evolution, while predictions across processes require factorization formulas connecting those distributions to scattering observables. Finally, we connect this framework to polarized $^{7}$Li through its collinear limits and nuclear spin-orbital correlations.