Papers

It is well established that students learn best through active engagement, particularly via interactive experiences tied to real-world concepts. Creating such experiences, however, typically requires labor-intensive design, costly development, and continuous teacher guidance to achieve measurably effective outcomes. Recent advances in generative UI open the door for a future of practice where the creation of tailored interactive experiences is automated. However, off-the-shelf models lack optimization for pedagogical precision and learning principles, often yielding unsatisfactory results for complex pedagogical constructs. To address these limitations, we present learning interactives, a structured framework leveraging the generative UI capabilities of Gemini to construct effective customized interactive simulations. We evaluate our approach through both an initial study with educators as well as a pedagogical rating of a varied set of simulations by expert teachers.

Layering is a key stage of the money laundering process in which assets are moved through intermediate entities to obscure their origin. We model this movement as a transaction graph, a labeled directed multigraph where nodes represent entities, such as individuals or organizations, and edges represent transactions between them. This work addresses the detection of layering patterns in transaction graphs. We define pass-through templates, a class of transaction graphs whose structure is indicative of a specific layering pattern in which entities receive funds and rapidly forward them. We formulate detecting instances of these templates within a larger transaction graph as a maximum-cardinality, maximum-weight matching problem. The resulting method uses Edmonds' blossom algorithm, which provably finds an optimal solution to this problem. Here we present a case study on publicly available Ethereum transaction data. We identify 283 pass-through template instances, chained through shared address nodes into a densely interconnected network that moves hundreds of millions of dollars in stablecoin value. We find that six addresses in the identified network are sanctioned by the U.S. Department of the Treasury for associations with criminal organizations, providing evidence of ties between the network and sanctioned criminal entities.

We investigate the electromagnetic form factors of the $\rho$ meson family within a holographic QCD framework based on Einstein-dilaton gravity with confining backgrounds. We obtain the elastic and transition form factors using a spectral decomposition of the three-point isospin current correlator and an independent approach based on the Kaluza-Klein expansion. Furthermore, we establish a holographic dictionary of the current matrix element. The elastic form factors are in agreement with available lattice QCD results, whereas the transition form factors, not yet determined within lattice QCD, are predictions of the model. For the elastic case, the electric form factor for the $\rho$ meson family exhibits a zero at $q^{2} = 6\, m_{\rho^{n}}^{2}$ and in particular for the ground state $q^{2} = 3.61\,\text{GeV}^{2}$, consistent with light-front and Dyson-Schwinger calculations. We also compute strong couplings between vector meson states and find some approximate selection rules. In the elastic case and low-$q^{2}$ regime, we calculate dimensionless electric radius, magnetic and quadrupole moments and compare with other approaches. In the high-$q^{2}$ regime, the form factors follow the expected scaling behavior, and the model predicts their asymptotic normalization. The results in the high-$q^{2}$ regime lead to superconvergence relations and establish a new sum rule involving masses, decay constants and couplings.

We prove existence and uniqueness of a strong initial trace for every bounded kinetic solution of a stochastic scalar conservation law, although no initial value is prescribed and no nondegeneracy condition is imposed on the flux. The core of the proof is pathwise. After fixing a realization, the rescaled stochastic terms and kinetic measure vanish in the blow-up limit, so Panov's compactness argument applies; degenerate flux intervals are handled by recursive dimension reduction. The stochastic setting creates several additional difficulties. The martingale identities must remain valid on one common full-probability set throughout the reductions, which requires a parameterized stochastic-Fubini construction. Moreover, the pathwise trace is not automatically measurable because its exceptional sets may depend on the realization. Deterministic time averages and right-continuity of the filtration yield a jointly measurable initial trace, with local strong convergence along essential times, both almost surely and in mean.

Reasoning and agentic workloads increasingly demand efficient long-context inference. Yet full-attention decoding reads the growing history at every step, although the benefit of global access varies across prediction positions. We find that, before global attention is computed for the current step, the decoding states available after local computation in frozen pretrained models already contain information predictive of its benefit over local attention. Building on this finding, we introduce On-Demand Attention (ODA), a local-first decoding method: after local computation, a lightweight recall head decides whether to recompute the current step with global attention. ODA trains only the recall head with modest data and compute budgets, leaving pretrained weights unchanged and retaining the complete historical KV cache so that information skipped at one step remains available for later access. Experiments across model scales and families, including hybrid attention backbones, show that ODA recovers most of the performance lost under local attention while substantially reducing the frequency of global attention. Controlled long-context measurements in vLLM further show that GPU-side conditional execution translates fewer global reads into practical decoding speedups over full attention. These findings show that pretrained decoding states can support both token prediction and decisions about accessing distant information, allowing models to allocate global computation as needed during decoding.

Principal component analysis (PCA) is a fundamental tool for learning low-dimensional structure from high-dimensional data. When data are collected from multiple sources, the underlying task distributions may exhibit unknown degrees of similarity, with some tasks potentially arising from arbitrary distributions. We propose new multi-task PCA procedures that exploit similarity structure across tasks to improve eigenspace estimation while remaining robust to outlier tasks. We establish non-asymptotic convergence rates and show that the proposed procedures attain minimax optimal rates in a range of regimes. One of the procedures builds on the matrix-depth notion of Chen, Gao, and Ren (2018) and can achieve the optimal dependence of the estimation error on the proportion of outlier tasks, addressing a key challenge in robust multi-task learning. Extensive simulations and real-data analyses demonstrate the effectiveness of the proposed methods.

Semantic cell annotation improves chunking interpretability for spreadsheets in LLM-driven RAG systems, aiding answer generation through enriched context rather than improved retrieval accuracy. We propose a novel framework of splitting any spreadsheet into interpretable chunks using cell role annotation. Our framework beats the state of the art, yet it faces a hard ceiling. Spreadsheets are fundamentally two-dimensional unstructured data with continuous relationships and infinite potential cell roles. Because classification models are restricted to finite, pre-defined classes, they cannot perfectly capture this structural nuance, even with human-level annotation. We show that addressing the spreadsheet-to-LLM bottleneck requires moving beyond discrete cell classification. Instead, the field must develop dimensionality-reduction techniques to directly flatten 2D unstructured spreadsheets into 1D unstructured text. Text chunks would be easier for downstream RAG to interpret and generate from.

Vision-based underwater target tracking is challenged by unreliable depth measurements and unknown target motion. This paper proposes a stereo visual-servoing framework for an autonomous underwater vehicle (AUV). For perception, the framework derives a stable 3D relative state from stereo images through target-specific depth extraction and Kalman filtering. It constructs a target-depth mask from color, disparity, and temporal cues to select reliable target pixels, and then filters the resulting depth measurement and detected image center separately. For control, the framework decouples yaw regulation from translational control, avoiding computationally expensive coupled multi-DOF optimization and enabling real-time translational MPC. The translational controller employs adaptive model-fusion predictive control, combining constant-velocity and zero-velocity target models to accommodate different target-motion patterns. It updates the model weights using historical prediction errors and computes translational commands subject to actuation, following-distance, and field-of-view constraints. Through simulations and real-world experiments, we validate the effectiveness of the proposed framework and show it has better performance than existing frameworks.

We study semiflexible active polymers confined within a soft, deformable droplet suspended in a fluid using dissipative particle dynamics (DPD) simulations. Extensile and contractile force dipoles along the polymer backbone generate distinct hydrodynamic flow fields that mediate effective interactions between polymer segments. Extensile activity promotes parallel alignment and lateral attraction, whereas contractile activity favors predominantly perpendicular organization, leading to qualitatively different collective behavior. The activity-generated flows couple strongly to the deformable interface, selectively enhancing low-order spherical-harmonic modes associated with long-wavelength droplet deformations. Activity also drives the interfacial relaxation away from passive capillary behavior, with extensile and contractile droplets exhibiting distinct mode-dependent dynamics. These differences in internal organization and interfacial fluctuations strongly influence droplet motility. Extensile activity produces increasingly persistent droplet motion with increasing polymer number, whereas contractile activity can sustain long-lived near-ballistic motion whose duration depends sensitively on polymer number and activity strength. Our results demonstrate how active hydrodynamics governs the interplay between internal structure, interfacial fluctuations, and emergent motility in confined active matter systems.

Blind quantum computation (BQC) allows low-resource clients to securely delegate computations to a quantum server, but server resource costs scale with the computation size, posing a bottleneck for implementations. By leveraging Pauli-based computation (PBC), we achieve BQC with a server whose size depends only on the non-Clifford gate count. Our protocol inherits fault tolerance and qubit virtualization from PBC and reveals that classical-client BQC is possible even in the absence of classical simulability. Finally, we present an entanglement-based dual protocol that performs a resource state computation with a dramatically reduced execution cost.

Mutually unbiased bases capture perfect complementarity between two quantum measurements. Extensions beyond pairwise unbiasedness have been proposed, but essentially no non-trivial higher-order constructions are known. We introduce $k$-fold unbiased measurements ($k$-UMs), extending the $k$-fold unbiased bases notion of [arXiv:1706.04446] from rank-one basis measurements to arbitrary-rank projective measurements, and show that this higher-rank setting supports a much richer theory. We develop the notions of algebraic and spectral $k$-UMs and prove that they coincide for rank-one measurements and triples of measurements (3-UMs). We establish strong no-go results for higher-order rank-one constructions and three-outcome 3-UMs, but obtain infinitely many higher-rank triples using Hadamard matrices and Clifford algebras. We then give these structures an exact operational interpretation in terms of measurement incompatibility. For 3-UMs with any number of outcomes, we determine their generalised incompatibility robustness exactly and construct an explicit joint measurement for their noisy versions at the compatibility threshold. Finally, we implement the symmetry reduction of the sum-of-squares hierarchy recently introduced in [New J. Phys. 28, 064509 (2026)] and give numerical evidence that the noise thresholds arising from the $k$-UM analysis may characterise the asymptotic behaviour of this hierarchy. In particular, with very high precision, we numerically show that our constructed four-outcome 3-UMs are among the most incompatible triples of four-outcome measurements.

Motivated by questions and results of Erdős, Sárközy and Sós (1989), and Khalfalah and Szemerédi (2006), we introduce an ergodic approach to additive problems concerning solutions of equations of the form \[ x+y=\lfloor\alpha(n)\rfloor,\quad x,y\in A,n\in\mathbb{N} \] where $\alpha(t)$ is a sufficiently regular function, such as a polynomial or a logarithmico-exponential function of polynomial growth (e.g. $\alpha(t)=t^{5/2}+t^2\log t$), and $A$ is either a given set of positive upper density, or a cell of a prescribed finite partition of $\mathbb{N}$. We give a complete description of the Hardy field functions of polynomial growth for which these partition and density problems are always solvable. The ergodic approach also applies to the more general problem of finding $x\in A_1,y\in A_2$, where $A_1,A_2$ are two given sets of positive density. This in turn allows us to treat equations of the form $kx+ly=\lfloor\alpha(n)\rfloor$, where $k,l\in\mathbb{Z}$. Some of our results also hold true when $A$ is a subset of the primes with positive relative upper density.

For a zero-one matrix $P$, let $\operatorname{Ex}(n,P)$ denote the maximum number of ones in an $n\times n$ zero-one matrix avoiding $P$. We prove that $$\operatorname{Ex}(n,P) \leq n^{1+O_P(1/\log\log n)}$$ for every acyclic $P$, settling the weak form of the Pach-Tardos conjecture.

The article arXiv:2410.21454 constructed a braided $\mathrm{W^*}$-tensor category of superselection sectors associated to a net of von Neumann algebras on a suitably geometric poset using localized and transportable endomorphisms. In this article, we construct an equivalent tensor product and braiding using the Connes fusion tensor product without localizing, using ideas from arXiv:1812.04470 for conformal nets. As an application, we prove that the category of superselection sectors associated to the 2D braided quantum spin system constructed from a unitary braided fusion category $\mathcal{B}$ in arXiv:2506.19969 is equivalent to $\mathsf{Hilb}(\mathcal{B})^{\rm op}$, the opposite of the unitary ind-completion of $\mathcal{B}$, as a braided $\mathrm{W^*}$-tensor category.

A longstanding conjecture attributed to Smith (1984) asserts that for every $k\ge2$, any two longest cycles in a $k$-connected graph share at least $k$ vertices. In this paper, we prove the first linear lower bound, showing that any two longest cycles in a $k$-connected graph share at least $k/600$ vertices. Departing from previous Turán-type extremal arguments, we develop a novel structural approach that also yields applications to related problems on longest cycles and paths.

Online image generation with Diffusion Transformers (DiTs) must meet latency service-level objectives (SLOs) while using GPU resources efficiently. Existing systems improve GPU utilization by batching multiple requests for joint execution. However, request-level batching offers limited control over batch size: batches may be too small to saturate GPU compute, while larger ones may violate latency SLOs. Globally coordinated scheduling introduces further delays by requiring independently progressing GPUs to synchronize before admitting new work. We present PixelFlow, a distributed DiT serving system that addresses these limitations through token-level workload management. Its key idea is to use image tokens (the units a DiT processes to generate an image) to divide and batch request workloads at a finer granularity. This allows each GPU to take on a portion of additional work under latency constraints. By distributing these portions across GPUs, PixelFlow accommodates more concurrent requests, improving GPU utilization while reducing queueing delays. To realize this flexibility, PixelFlow provides a runtime that splits requests into variable-sized partitions and batches them efficiently on each GPU. To reduce the resulting communication overhead, it optimizes token placement to limit cross-GPU data exchange while balancing GPU workloads. It further exploits similarity across denoising steps to overlap the remaining transfers with computation. An SLO-aware scheduler groups GPUs to share compute resources among requests with compatible latency requirements. Each group progresses independently, synchronizing with others only when their combined resources are needed to admit a new request. Evaluation with Stable Diffusion 3 and FLUX.1-dev on H100 GPUs shows that PixelFlow improves SLO attainment by up to 43% and achieves up to 2.8 times the goodput of state-of-the-art DiT serving systems.

Activation steering modifies LLM behavior at inference time, but identifying where and how strongly to steer remains manual. We introduce Deep Noir, a framework that uses Logit Lens convergence and causal head-level attribution to autonomously discover optimal steering parameters. Across three scales (1B x 3, 2-3B x 2, and 7-9B x 4), our engine achieves 16.7 percentage-point improvement on spam at 1B (standard deviation 4.7; 39 runs), with gains increasing to 21 to 42 percentage points at 7-9B across four architectures. On SST-2 sentiment, it achieves a 13.1 percentage-point improvement with zero code changes. Mechanistic grounding enables automated discovery of intervention points that generalize across tasks and architectures. On sentiment, RepE without head masking fails to improve over baseline, while Deep Noir improves all models (p less than 0.01). We further show that steering creates a predictable prompt-injection attack surface whose vulnerability increases monotonically with steering magnitude. This finding is relevant to agent systems deploying steered classifiers.

We present a quantum algorithm for simulating classical oscillator networks characterized by non-Markovian dissipation and time-varying material properties, extending recent speedups for undamped harmonic systems to viscoacoustic and viscoelastic media. We embed the history-dependent dynamics into a Markovian state space governed by a non-Hermitian operator by approximating memory kernels through a Prony series. We then use linear combination of Hamiltonian simulation to estimate the instantaneous kinetic and potential energy for a subset of oscillators at time $t$ within error $\epsilon$ using a number of queries to the oscillator system that scales as $\widetilde{\mathcal{O}}(\alpha_{\rm tot} t/\epsilon)$, where $\alpha_{\rm tot}$ is polynomial in the strength of the dissipation, spring constants, inverse masses, and sparsity of the connections in the network. We further show that this energy estimation task is in the worst-case classically hard (i.e., a corresponding decision problem is $\mathsf{BQP}$-complete), even in the presence of strong dissipation. For time-dependent materials, we show that changes in material properties appear as effective dissipation or growth in the energy representation. Additionally, we prove the infeasibility of exponential quantum advantages in locally coupled topologies through a novel form of Lieb-Robinson-like bounds that apply to differential equations. This allows our quantum algorithms to provide quartic speedups for locally coupled damped oscillator systems in three dimensions, raising the possibility of practical quantum speedups for realistically damped oscillator networks and approximated wave equations.

Youth increasingly use AI companions, and parents are the primary mediators of that use. How effective that mediation can be depends on whether parents are aware of how adolescents actually use these systems and what risks and benefits such use carries; nevertheless, prior work has only studied these demographic groups in isolation, and existing taxonomies attend almost entirely to risk. We analyze 1,628 Reddit posts about youth AI companion use from parenting and teenager communities (2023–2026); develop a codebook covering modes of use, risks, benefits, and parental mediation; and apply it at corpus scale with an LLM. The two communities yield divergent accounts. Teenagers most often discuss receipt of emotional support from AI companions (31% of teenager posts vs. 19% of parenting posts), whereas parents most often discuss teenage use of AI companions for romantic and sexual interaction (36% vs. 25%). Teenagers are not unaware of other risks, however; indeed, attachment and dependence is the risk they raise most (19%), close to the parental rate (16%). Teenagers also describe benefits that risk-centered taxonomies do not capture and parents rarely mention, most notably emotional support (27% vs. 5%). We argue these differences track what a given kind of use makes visible to someone outside the conversation. Chatting with a companion for hours every night leaves a trace beyond the chat itself; sexting with a character stands out when a parent reads the log; venting about a fight with a friend does neither, since it looks like any other conversation. The first surfaces as dependence, the second as sexual content, and the third as emotional support, which is the one parents most often miss. Parental guidance and system design should attend to use cases that reach parents by neither route, emotional support foremost among them.

Extended reality (XR) increasingly supports training and cognitive assessment, yet the age sensitivity of its interaction techniques is unclear. This study examined age, digital literacy, and interaction modality as correlates of psychomotor and cognitive-flexibility performance in immersive virtual reality (VR). Two hundred and two adults (19-90 years) completed a five-mode Fitts' law task (eye-gaze, head-gaze, controller ray-casting, virtual finger, and controller direct touch), the Trail Making Test in VR (TMT-VR), and a digital-literacy questionnaire. Age was associated with slower task times across modes, but controller direct touch carried the steepest relative age gradient yet remained among the fastest in absolute terms; technique altered relative age sensitivity without determining absolute efficiency. Higher digital literacy was associated with faster TMT-VR completion but not Fitts task times. A Fitts-derived speed score predicted TMT-VR performance beyond age and partly accounted for its age association, consistent with shared processing-speed variance; an exploratory full-battery extension confined the Fitts-score association to completion-time and error-adjusted-time indices and the digital-literacy association to error-adjusted-time indices, not wrong-target errors, mean selection distance, or relative Part B indices. Age-inclusive XR assessment should standardise interaction modality, evaluate rather than exclude mid-air direct selection, and interpret cognitive scores alongside digital literacy and psychomotor speed.

Christensen and Pedersen proved that every properly infinite $\mathrm{AW}^*$-algebra is monotone sequentially complete, and Saitô and Wright developed a transfinite form of their dilation argument. We revisit the transfinite construction using normality of $\mathrm{AW}^*$-algebras. Normality simplifies the limit stages by turning suprema into compressions of joins, so the construction only needs a supply of fresh orthogonal projections large enough to contain the supports of the summands at successor stages. We use this simplified proof to show that a $*$-homomorphism between $\mathrm{AW}^*$-algebras that preserves only the joins needed to encode such a sum preserves the sum itself. We also use it to deduce order-continuity facts about $\kappa$-join-preserving $*$-homomorphisms. We also show that a finite $\mathrm{AW}^*$-algebra has suprema for all bounded positive families whose supports have bounded total center-valued dimension.

We give an FPRAS for the permanent of an $n\times n$ $0/1$ matrix with running time $\widetilde O(n^3)$. Our algorithm extends to a strongly polynomial FPRAS for arbitrary nonnegative matrices with the same running-time bound (but in the unit-cost arithmetic model). Jerrum, Sinclair, and Vigoda (2004) gave the first FPRAS for the permanent of a nonnegative matrix. The running time was subsequently improved to $\widetilde{O}(n^7)$ by Bezáková, Štefankovič, Vazirani, and Vigoda (2008), and recently to $\widetilde{O}(n^6)$ by Chen, Vigoda, and Yang (2026). We introduce a multicommodity-flow bound inspired by electrical flows, replacing the usual path-length factor by routing energy. For the classical JSV chain with perfect-matching weights multiplied by $n^2$, we prove a relaxation-time bound of $O(n^3\log n)$ and obtain comparable bounds for estimating the stationary probabilities of having a specified pair of unmatched vertices. We use a separate chain on assignments to generate a warm start at any given temperature, avoiding the long initialization of the JSV chain. Finally, we replace the JSV chain with a new chain that uses only $n$ hole weights and speeds up hole-weight learning by a factor of $n$.

A theorem of Kollár, Miyaoka, and Mori states that on a rationally connected variety, any finite collection of points lies on a rational curve. Motivated by this, it is natural to ask what one can say about families of curves passing through many general points of an arbitrary smooth projective variety X. When X has nonnegative Kodaira dimension, we establish a sharp linear lower bound for the genus of such curves in terms of the number of points and the dimension of X, generalizing a theorem of Arapura and Archava. By contrast, the least possible gonality of a connecting family eventually stabilizes as the number of points grows. We characterize its limiting value in terms of varieties dominating X that are generically finite covers of rationally connected varieties. As an illustration, we study these invariants for hypersurfaces of large degree, determining in particular the joint asymptotic behavior of the minimal connecting genus as the number of points and the degree vary. Finally, we briefly consider higher-dimensional connecting subvarieties, proving linear bounds for their canonical volumes and computing asymptotic results for hypersurfaces.

Agent trajectories record what an agent does and what happens next. Yet standard supervised fine-tuning (SFT) applies loss only to agent-authored action tokens, using environment observations as context but not as prediction targets. We ask whether this convention provides the best initialization for subsequent reinforcement learning. We introduce ActObs, which also supervises the observation tokens already present in each trajectory. Although deployed agents never generate observations, learning to predict them encourages the policy to model action consequences without adding data, parameters, sequence tokens, or forward passes. The methods perform similarly after SFT but diverge after GRPO. On Qwen3-4B, GRPO from ActObs achieves higher pass@k at every evaluated sampling budget than its action-only counterpart on Terminal-Bench 2.0. On Qwen3-8B, it trades some pass@1 reliability for higher pass@k (+3.4 pp at pass@16) and solves more distinct tasks. The advantage extends to cross-domain code editing on aider-polyglot (+4.2 pp at pass@1 at 4B), whose tasks are unseen during SFT and RL. ActObs retains more entropy during RL while requiring less policy movement, leaving the final policy closer to its SFT initialization. Our analysis traces this difference to SFT: action and observation gradients rapidly become orthogonal, while action-only training leaves a large residual observation gradient and degrades environment prediction below the base model. Joint supervision prevents this one-sided specialization, preserving consequence prediction and preparing the policy for downstream exploration.

We construct an invertible map between the complete set of 3D Breit-frame pressure and shear force distributions and the constrained space of 2D infinite-momentum-frame pressure and shear force densities in coordinate space for spin-1 hadrons. The correspondence between the two sets of distributions in different frames is established by combining the geometric forward and inverse Abel transformations with recoil operators after separating the Wigner rotation induced mixing effects on the infinite-momentum-frame side. Unlike in the spin-1/2 case, these mixings complicate the coordinate space relations for spin-1 hadrons by introducing additional multipole structures, but the constraints among the form factors propagate into constraints on mechanical densities, so that these additional multipoles do not introduce new mechanical information.

As a fundamental task across computational statistics, scientific computing and machine learning, sampling from high-dimensional probability distributions has received increasing attention in recent years. Numerous sampling algorithms have been proposed, among which underdamped Langevin Monte Carlo (ULMC) methods based on underdamped Langevin dynamics (ULD) have emerged as a class of efficient ones. In this work, we introduce a “universal" predictor-corrector formulation that bridges Euler-type, UBU-type and randomized schemes through different choices of method parameters. Notably, the “universal" integrator induces two novel classes of low-cost integrators, termed low-cost randomized integrators (LC-RIs) and low-cost UBU integrators (LC-UBUIs), as well as their exponential-free variants based on polynomial and rational approximations. The resulting new UBU-type and randomized schemes require only one gradient evaluation and two Gaussians per iteration, considerably reducing the number of gradient evaluations or Gaussians per iteration required by existing counterparts. Further, a general framework of long-time error analysis is developed for general discretization schemes in a probability metric. Under certain smoothness and non-log-concavity conditions, we rely on the unified framework to establish non-asymptotic $\mathcal{W}_1$-error bounds of both old and new schemes, revealing convergence rates of order $\mathcal{O}(d^{\frac{1}{2}}h)$ for Euler-type schemes, order $\mathcal{O}(d h^2)$ for UBU-type ones and order $\mathcal{O}(d^{\frac{1}{2}}h^{\frac{3}{2}})$ for randomized ones. In the strongly convex setting, the same non-asymptotic error bounds can be recovered in $\mathcal{W}_2$-distance. Numerical experiments corroborate the theoretical findings.

This paper introduces and operationalizes summarization bias: a proposed systematic tendency of large language models (LLMs) to represent narrative meaning as an abstract summary label rather than as the reconstructable inferential structure that produces it. Within the Bulut Doctrine, narrative effect is theorized along a told-shown axis: in told mode, emotional and informational content is declared explicitly and requires little reader reconstruction; in shown mode, that content is suppressed at the surface and must be reconstructed from physical cues and indirection (Objective Projection). Shown mode is the higher-load condition the doctrine is designed to measure. The claim is that LLMs fail along this axis in a specific direction. Summarization bias is hypothesized to operate in two regimes: (i) a generative regime, in which a model asked to render an emotion through Objective Projection defaults to declaring it instead; and (ii) an evaluative regime, in which a model judging narrative quality rewards told-mode explicitness and under-detects shown-mode suppression. The evaluative regime is the more consequential, since LLMs increasingly serve as judges and reward models, and a directional bias toward told mode would impose a selection pressure degrading prose toward flat declaration. This report does not claim the bias is validated. It defines the construct, situates it against LLM-as-judge biases, rereads a completed independent reliability study as directional evidence consistent with it, and pre-registers a two-regime test with decision rules under which the construct would be abandoned.

Likelihood evaluation in Bayesian inverse problems often requires a forward-model solve. We study candidate screening using a likelihood-weighted prior moment matrix and two associated scores: a Christoffel ratio and a Nevai polynomial average. A finite pilot supplies likelihood information that is reused to rank further prior candidates. We connect finite-pilot matrix error, quantitative Legendre localization, and fixed-budget posterior-mass regret. Conditional likelihoods distinguish feature loss from polynomial and sampling errors, and a filtered Gaussian construction permits controlled feature selection and localization. In a nonlinear function-coefficient PDE, equal-budget comparisons separate methods using scalar likelihoods from surrogates using forward outputs. The Christoffel ratio outperforms the tested direct likelihood regressions, but forward-response surrogates capture more posterior mass at small retention budgets. Independent-pilot tests and reference resampling quantify two distinct sources of uncertainty. Controlled Gaussian experiments illustrate finite-filter truncation and the benefit of selecting relevant features. These results identify when moment geometry provides useful screening information, without asserting universal superiority over surrogate models or an exact posterior sampling method.

Considering triads in helical decomposition of three dimensional Navier-Stokes turbulence, three consecutive triads of the same shape and class, where the reference wave-number appears as the smallest, the middle and the largest wave-numbers respectively, constitutes an interesting object called the triad triplet that allows tracing the local transfer in wave-number space due to a given shape and class of triads. It is shown that, evolution equations for the triad triplet can be obtained from the equations of the three legs of a single triad that are put together via affine transformations involving scaling, rotation and reflection. Known power law solutions corresponding to constant flux of energy and helicity appear as exact solutions of a chain of triad triplets, with particular implications for the triadic phases. More interestingly, an exact, time dependent solution is available on an isolated triad triplet, that can be expressed using what appears to be straightforward generalization of Jacobi elliptic functions. These solutions, constitute novel exact nonlinear solutions of the inviscid limit of the Navier-Stokes equations.

World Action Models (WAMs) improve robot policy learning by incorporating future dynamics, yet explicitly generating future videos at inference introduces substantial computational overhead. Removing future generation improves efficiency, but leaves future dynamics only implicitly encoded in observation features, which can limit robustness under distribution shifts. We propose MoWAM, an efficient WAM that replaces future video generation with explicit future motion prediction. Instead of reconstructing the complete future scene, MoWAM models structured robot motion as a compact abstraction of the future, capturing how the robot is expected to evolve under the current scene and interaction constraints. A Mixture-of-Transformer architecture learns future visual dynamics during training while jointly predicting motion and action, allowing video generation to be removed entirely at inference while retaining an explicit representation of the future. The compact motion representation further enables efficient inference-time scaling by sampling multiple candidates of motion and action pairs and selecting among them with a motion-aware task-progress verifier. Experiments on LIBERO, LIBERO-Plus, and real-world manipulation tasks demonstrate that MoWAM achieves strong in-distribution performance, improved out-of-distribution robustness, and higher average real-world success than representative WAM baselines. In addition, performance improves as more candidates are explored, demonstrating that explicit future motion provides an effective and efficient basis for inference-time scaling.