Papers

The article contains exact results for the behavior of the Casimir force of Ising chain of $N$ atoms containing an impurity atom. The force is considered as a function of $N$ and on both the temperature $T$ and the external magnetic field $h$. The interactions between nearest neighbors within the chain are supposed to be of a ferromagnetic short-ranged type $J>0$. The impurity atom interacts with constants $J_{ia}$ with its nearest neighbors, where $J_{ia}$ can be both of ferromagnetic type, i.e., $J_{ia}>0$, as well as of antiferromagnetic type, i.e., $J_{ia}<0$. It turns out that the Casimir force can be both attractive or repulsive, depending on the sign and the magnitude of the ratio $J_{ia}/J$.

Data assimilation combines model forecasts with noisy, incomplete observations to estimate the evolving state of a dynamical system. Existing methods face two compounding challenges: high-dimensional nonlinear dynamics make repeated forward simulation computationally expensive, while sparse observations provide limited direct information about the full state. To address these challenges, we propose the Latent-Dynamics Ensemble Flow Filter (LD-EnFF), a sequential Bayesian filtering framework that performs both forecast propagation and filtering updates in a compact latent space. LD-EnFF combines a latent dynamics surrogate for ensemble propagation with a variational autoencoder (VAE)-based observation model that evaluates a state-dependent observation likelihood in latent space. At each assimilation step, an ensemble filtering update based on flow matching uses the forecast ensemble and this likelihood to generate posterior samples, jointly updating latent states and uncertain parameters. This design avoids repeated full-state simulation during forecasting and full-field reconstruction during likelihood evaluation. LD-EnFF substantially outperforms a broad range of data assimilation algorithms on benchmarks spanning Kolmogorov flow, tsunami propagation, and atmospheric modeling, all featuring complex dynamics and sparse, noisy observations.

Information and infectious diseases spread through social networks, but the spreading probabilities driving them are hard to estimate without per-node activation times. Applications seldom supply these, and inference must instead proceed through indirect and noisy proxies for the terminal infection states. We study this inverse problem on a fixed, known graph under the Hidden Independent Cascade (HIC) model, with one spreading probability per node rather than a single global rate, so the number of unknowns scales with the number of nodes. Seed sets and observation parameters are known, while activation times and terminal infection states are latent, and the observed-data likelihood requires marginalizing over every spreading outcome. We propose a simulation-based amortized estimator that recovers the full node-level parameter vector without reconstructing individual latent cascades. Repeated seed-conditioned symptom observations are summarized as Symptom-Aware Cascade Features (SACF), which combine empirical symptom statistics with neighborhood and structural information. SACF are mapped to parameters by SAGE-HC, a permutation-equivariant gated graph neural network whose learned gates attenuate neighborhood messages corrupted by false positives and false negatives, and training on simulated HIC realizations yields a reusable inverse map. As a benchmark under the same hidden observations, we extend the Dynamic Message Passing learning framework to the HIC emission model. On synthetic and empirical graphs the two methods separate by topology. DMP is highly accurate on trees, whereas SAGE-HC is substantially better on heterogeneous, loopy graphs under noisy terminal symptoms.

The stress in a flowing complex fluid such as a solution of polymers, surfactants and/or colloidal particles is a fundamental dynamic property of the material. It reflects the evolution of the fluid microstructure under deformation and determines the motion of the fluid. While spatially resolved measurements of flow (via velocimetry) and microstructure (e.g.~via scattering) can be made, neither of these individually can uniquely determine the stress. In particular, due to the degenerate nature of the relationship between the stress tensor and the net force exerted by the microstructure on the fluid, the stress tensor is hidden from direct observation. We show that integrating velocity and microstructure measurements with principles of continuum mechanics can break this degeneracy, unveiling the stress tensor. The approach has two stages. In the first, velocity information is used along with the momentum and mass conservation equations to infer the force density exerted by the microstructure on the fluid using a data assimilation framework. In the second, the equation relating force density to stress is solved. This equation has a nontrivial nullspace, introducing a homogeneous solution whose structure must be found to uniquely determine the stress. We do so by using microstructural data and a general model between microstructure and stress, the parameters of which are determined, along with the nullspace solution, by solving a least-squares problem. The approach is illustrated using synthetic velocity and microstructural data from simulation of a flowing polymer solution, demonstrating its validity and robustness.

Let $Q$ be a Gorenstein local ring, let $I$ be a proper ideal of $Q$, and set $R=Q/I$. We investigate when finite injective dimension of the conormal module $I/I^2$ forces $I$ to be generated by a regular sequence. We prove this implication for every ideal in the linkage class of a complete intersection. When $Q$ is regular, we also establish it under several numerical conditions in terms of the number of generators of $I$ and the type of $R$. For normal domain quotients, we show that finite injective dimension of $I/I^2$ forces $(\mathrm{ht}(I)+1)[\omega_R]=0$ in $\operatorname{Cl}(R)$, yielding the desired conclusion when the divisor class group is torsionfree. In the graded setting, we further prove the implication for all monomial ideals in polynomial rings. We also obtain a converse to Kunz's description of the first Koszul homology of an almost complete intersection.

In autonomous mobility duopolies, platforms compete for riders based on vehicle proximity. A critical operational challenge—faced by an incumbent proactively defending against a market entrant—is how to dispatch fleets to minimize demand poached by a reactive competitor. We model this competition as a zero-sum robotaxi assignment game, focusing on computing optimal deterministic Stackelberg strategies for the leader. We formulate this problem as an exact single-level integer linear program and use its relaxation to design a polynomial-time approximation algorithm achieving an additive error from the optimum. We argue that this is not far from best possible by proving that deciding whether a strictly positive payoff is achievable is NP-complete, and that approximating the optimal payoff within an additive error scaling linearly with the number of riders is NP-hard. We also provide an exact polynomial-time dynamic programming algorithm for computing the optimal Stackelberg payoff when riders and vehicles are on the Euclidean line. Finally, we complement our theoretical findings with an empirical evaluation using real-world ride-hailing data. The experiments demonstrate that our LP-based algorithm significantly outperforms its worst-case guarantee in practice, while lightweight heuristics achieve highly competitive payoffs with negligible computational overhead, offering practical solutions for large-scale deployments.

Non-monotonic steady state response curves can readily arise from an incoherent feedforward loop (IFFL), which has also been conjectured to be a necessary mechanism. In a previous work, we showed this conjecture to be false for systems where the control parameter directly influences only one state variable. Here, we extend this result to arbitrary systems. We show that a stable non-monotonic response requires either an IFFL or a combination of positive and negative feedback loops. Finally, we apply our theoretical findings to three network-structured biological contexts: signaling pathways, gene regulation, and ecological consumer-resource models. For the first two contexts, we identify necessary motifs for non-monotonic responses, while for consumer-resource models, we provide an alternative proof of the Competitive Exclusion Principle.

Clinical MRI routinely acquires multiple contrast-weighted images of the same anatomy for complementary tissue characterization. However, current accelerated MRI methods typically reconstruct each contrast independently, without fully exploiting shared anatomical information. This work aims to learn anatomical representations invariant to contrast-dependent appearance for reconstruction of accelerated multi-contrast MRI. We propose MAX (MAnifold eXpansion), a subject-specific framework that learns anatomical representations from a single fully sampled reference contrast. To address the under-constrained separation of shared anatomy and contrast-dependent components from a single image, MAX expands the multi-contrast manifold using anatomy-preserving intensity augmentations. A disentangled implicit neural representation models augmented samples using shared spatial coordinates for anatomy and spatially invariant coordinates for contrast appearance. The learned anatomical representation is then fixed, with the contrast representation adapted to the undersampled target data, followed by unrolled refinement. Theoretical analyses further provide insight into the disentangled representation learning and explain how the learned anatomical representation improves the target contrast reconstruction. At R = 8 for brain MRI and R = 6 for knee MRI, MAX achieves the highest mean PSNR and SSIM across all tasks, improving PSNR by more than 1 dB over the strongest baseline for both brain contrasts. MAX more faithfully recovers subtle anatomical and pathological structures and remains robust to inter-contrast motion, structural heterogeneity between reference and target contrasts, and measurement noise. Therefore, MAX provides a general strategy for leveraging high-quality reference scans in accelerated MRI and has the potential to be extended to other reference-assisted MRI inverse problems.

We give approximation algorithms for $\max\{F(x):x\in\K\}$, where $\K$ is a nonempty compact down-closed convex subset of the unit cube and $F$ is a nonnegative diminishing-returns (DR) submodular polynomial: every entry of its Hessian is nonpositive on the cube. Starting from quadratic or cubic coefficients, we decompose the objective exactly into nonnegative rooted atoms and affine terms. Concave upper bounds for these components give a tractable roof. We then decrease the coordinates of a roof optimizer using maps that work for all components at once, recovering a fraction of the roof value while preserving feasibility. For quadratics, we also retain the concave diagonal residual exactly. Under the stated assumptions on optimization access, these constructions give deterministic polynomial-time factors of $1/2$ for quadratics and $8/17$ for cubics, up to any prescribed additive error. The cubic result includes positive cubic coefficients and repeated variables. The factor $8/17$ also holds for two larger classes: supplied compatible rooted certificates of literal degree at most twelve, and sums of nonnegative submodular local functions of arity at most four. At arbitrary finite literal degree, a common scalar map attains the optimal single-map factor $2\sqrt3-3$. Global monotonicity and concave-cardinality structure give stronger guarantees for multilinear local-function sums, with no recovery beyond the identity map. Standard matroid rounding transfers the multilinear guarantees without loss. We also prove online preservation for directed-hypergraph cuts and, separately, a Unique-Games inapproximability bound of approximately $0.82843$ for explicit quadratic input under a cardinality upper bound.

Dense embedding models are core to modern text retrieval, enabling systems ranging from web search to retrieval-augmented generation (RAG). Yet, retrievers are usually deployed within opaque systems, exposing only ranked results, cited sources, or generated answers. This opacity prevents users from verifying which retrievers providers serve and may create a false sense of robustness against retrieval attacks. We show that attackers can infer retrievers' identity only through queries. We introduce TellTail, a fingerprinting attack for identifying retrievers behind black-box systems across a spectrum of access levels. Despite sharing many properties, retrievers can be steered to emit distinct results. When retrieved passages are exposed, TellTail compares retrieval overlap to deduce the underlying model. When only the final generated response is exposed, TellTail optimizes model-specific queries that induce a chosen retrieval behavior on the target retriever but transfer poorly to others. Interestingly, the poor transferability that limits attacks elsewhere is exactly what makes them useful for fingerprinting. We evaluate TellTail using 53 retrievers under three increasingly restrictive settings. TellTail perfectly identifies the deployed retriever from full retrieval rankings; in 94.3% of attempts with unordered top-3 results; and in 92.5% of cases from language-model-generated answers alone. Furthermore, fingerprinting succeeds against a popular RAG system (OpenWebUI). Overall, TellTail shows that retrieval-based systems leak the identity of their embedding model—exposing intellectual property and enabling reconnaissance ahead of model-specific attacks such as corpus poisoning.

The Izhikevich model is a computationally efficient neuron model that can exhibit a wide range of firing patterns observed in the brain. However, it is a discontinuous dynamical system, which means the methods for applying weakly coupled oscillator theory developed for continuous dynamical systems cannot be applied. Therefore, the collective behaviour of coupled Izhikevich model has not been fully studied. To our knowledge, we carry out the first computation of the phase model for an Izhikevich neuronal model with chemical synapses. Using the phase model we study the existence and stability of phase-locking states and how these vary with parameters. Moreover, we find an interesting connection between the stability of anti-phase states of the phase model and the bifurcation behaviour of the uncoupled Izhikevich model itself. The accuracy of the prediction of the phase model is supported by simulations of two weakly coupled Izhikevich neurons.

Extreme values of a physical system are rare by definition, yet they can govern some of its most consequential and anomalous behavior. Their sparsity makes them particularly costly to identify in large data sets. Quantum computation offers a potential way to reduce this cost. The challenge is that quantum amplitudes cannot simply be read, copied, compared, or marked using conventional search oracles. Here we introduce an algorithm for searching amplitude-encoded quantum signals that exploits their underlying structure. Through a nonlinear amplitude transformation, the algorithm identifies and certifies a global extremum while exponentially reducing the effective search space for structured signals. We establish a polylogarithmic query complexity in the data size $N$, together with global completeness, efficient classical verification, and a measurable criterion for quantifying exploitable structure. We demonstrate the framework using computational turbulence data. Applied to line cuts of velocity gradients from a $1024^3$ simulation containing more than one billion grid points, the algorithm consistently isolates the extreme tail and reduces the median search space to $O(\log N)$. The clustered structure characteristic of turbulence further accelerates the search. These results establish a direct connection between physical structure and quantum advantage in extreme-value search. For accessibility, the main text emphasizes the central ideas and results, while the theoretical derivations are provided in the Appendices.

We introduce and study multi-indexed Schatten spaces which lift the commutative $\ell_{q_1}\![\ell_{q_2}\![\ell_{q_3}\![\dots]]]$ -spaces to the quantum toolbox. They extend Pisier's operator-valued Schatten norms and the recently introduced two-indexed Schatten quasi-norms. For every ordered tuple $\mathcal{Q}=(q_1,\dots,q_n)$ of non-zero indices we define a quasi-norm (for positive indices) or an anti-norm (for negative indices) on operators on an $n$-fold tensor product of Hilbert spaces. We do this for indices of the same sign satisfying the mutual compatibility condition $|\frac{1}{q_i}-\frac{1}{q_j}|\leq1$. Beyond establishing desirable properties of these quasi- and anti-norms via factorization formulas that combine operator space and matrix-analytic techniques, we lift several central tools and results of the seminal [Devetak, Junge, King, Ruskai, CMP 2006] to the multi-indexed and quasi-normed setting. These include a general non-commutative Minkowski inequality relating swapped systems and two identity-removal equalities. As a consequence, complete hypercontractivity and complete reverse hypercontractivity tensorize for all compatible indices, including negative ones. Concerning quantum information theory we prove that the completely bounded minimal and the maximal output conditional entropies are additive under tensor products of quantum channels for all $\alpha\geq\frac12$. This extends the case $\alpha>1$ of [Fawzi, Kochanowski, Rouzé, Van Himbeeck, CMP 2026] and the unconditional results of [Devetak, Junge, King, Ruskai, CMP 2006]. Beyond tensor products, we establish chain rules for $\tilde H^\uparrow_\alpha$, $\alpha\in[\frac12,1)$, for compositions of possibly signaling channels, extending upon the smooth max-entropy chain rule used in device-independent entanglement certification to the whole interval $\alpha\in[1/2,1)$.

Powered neck exoskeletons are developed to restore head-neck motions for those with neck muscle weakness. Current methods using hand-held input devices to control these robotic systems are unintuitive or non-viable for these populations. Alternatively, the eyes coordinate with the head to accomplish many daily tasks. Therefore, movements of the eyes can be a useful signal to control the neck exoskeletons without needing to use the hands. However, previous control models lack biobehavioral basis as well as means to personalize the control behavior, causing unnatural head-neck movements. This paper presents a novel eye-tracking controller design leveraging the vestibulo-ocular reflex to emulate natural eyehead coordination. Personalization tools were also designed, consisting of sliders to allow users to adjust the parameters of this controller. Here, we present the technical design and validation of this system in human users. Compared to the previous eye-tracking model, the new controller provides natural head motions personalized to the user through more natural velocity profiles and a 24 percent average increase of accurate motion intent detection. This system provides a powerful platform for studying eye-tracking controllers in the context of personalization and preference, and ultimately restoring the lost head-neck mobility in patient populations.

Generative artificial intelligence has become increasingly incorporated into digital media and more generally into production workflows with which the public frequently interacts. Current provenance standards and disclosure methods frequently rely on binary categorizations, differentiating only between entirely human-authored and AI-generated content, or depend on technical watermarking that lacks user-facing clarity. However, there are very different risks and outcomes depending on the different uses of AI in the creation and consumption of end products. Therefore, we propose the Reported Engagement with AI Level (REAL) Rating framework which addresses these concerns by introducing a six-tier scale (Levels 0-5) that discloses the extent of AI involvement in both product creation and user experience. This paper details the structural methodology of the REAL Rating system and the specifics of its application across text, image, audio, video, and software products.

Sparse Autoencoders (SAEs) began as an unsupervised tool for decomposing neural representations into sparse, interpretable features, and are increasingly used not only for passive analysis but also for active interventions such as unlearning, bias mitigation, and concept editing. A central challenge for these editing and steering methods is reliably matching features to target concepts; most current approaches address this by computing post-hoc scores over an already-trained, frozen dictionary. We instead introduce ClasSAE, a novel method that both automatically assigns classes to features and guides the encoder toward class-separable representations during training. Specifically, we apply a differentiable top-$k$ operator to a trainable feature–class affinity matrix with per-feature budgets, coupling the features selected for each sample to the classes they are trained to represent. Because gradients flow through the selection of active features rather than only through their magnitudes, the encoder and the affinity matrix co-adapt rather than being fit in separate stages. The result is a dictionary that is both class-separable and class-annotated, with no need for post-hoc probing. We propose three variants for enforcing sparsity within this framework, which achieve comparable overall performance with slightly different trade-offs. Using CLIP ViT-L/14 embeddings on ImageNet, we show that the learned affinity matrix agrees closely with an independently estimated post-hoc feature-class matrix computed on held-out data. The model also supports direct class prediction from the encoder and affinity matrix alone, without a separately fitted classifier, and its more class-aligned encoder yields improved separation in Targeted Probe Perturbation evaluations. https://github.com/St0pien/ClasSAE.

Graph based cyber attack detection studies employ various graph construction and representation strategies across different cybersecurity application domains. This diversity motivates a quantitative examination of how representation strategies are distributed across these application domains. This study presents a quantitative analysis of 37 original studies published between 2019 and 2026. Each study was coded according to publication year, application domain, graph representation type, feature extraction strategy, learning paradigm, algorithm, and dataset. Frequency analysis, cross tabulation, and statistical association tests were applied. Automated representation learning was the most frequently employed strategy, accounting for 73.0% of the studies, while handcrafted representation strategies accounted for 27.0%. The Fisher Freeman Halton exact test revealed a statistically significant association between application domain and representation strategy (exact p = 0.008; Cramer's V = 0.540). The findings indicate that automated representation learning predominates within the analyzed corpus and that the distribution of representation strategies differs across cybersecurity application domains.

A growing number of countries are adopting policies to reduce greenhouse-gas emissions, a process expected to reshape production systems and labour markets by altering relative prices and changing production and demand patterns across sectors. We develop an agent-based monetary input–output network model to analyse the medium-term effects of climate policies on production networks and sectoral labour allocation. The model features heterogeneous industries and households, incorporates greenhouse-gas emissions accounting, and is calibrated to a multi-regional input–output database covering the world economy. We simulate two alternative climate-policy scenarios over 2026–2035: one based on countries' nationally determined contributions and another targeting larger reductions in global emissions. The results reveal significant economy-wide reallocation: fossil-energy sectors contract, low-carbon energy sectors expand, and their positions within production networks change asymmetrically. Fossil energy loses relevance as a direct supplier and exerts less forward influence, while its remaining production becomes more dependent on intermediate inputs and upstream suppliers; low-carbon energy primarily strengthens its role as a supplier. Carbon pricing also generates sectoral labour gaps that, under mobility frictions, imply greater potential transitional unemployment. Because the model allows only limited technological change and adjustment within existing production links, the simulations provide a counterfactual assessment of how existing production structures respond to a relatively rapid climate transition, revealing the adjustment pressures that emerge when policy ambitions advance faster than the productive system's capacity to adapt.

Localizing behavior to individual components of a language model is a central goal of mechanistic interpretability. However, scoring components one at a time misses context-dependent effects: a primary component can inhibit the activation of a backup, leading to issues with ranking components. Actual causality studies the structure of such interactions via witnesses: variables that provide contextual information to resolve interaction terms. However, estimation with witnesses typically requires combinatorial enumeration and is infeasible in practice. We introduce the witness-integrated set effect (WISE), a family of causal estimands that build on the witness mechanism while taking expectations over sets of causes and witnesses to remain computationally feasible. Building on this approach, we introduce JuntaLearner, a gradient-based circuit discovery method that learns to rank components by their causal impact across varying-sized sets of components and witnesses. Alongside faithfulness metrics, we introduce measures of necessity and task specificity, and the circuit recognition score (CRS) to summarize each metric across circuit sizes while emphasizing effects achieved by small circuits. Across tasks and models of increasing size, JuntaLearner achieves higher mean CRS compared to attribution baselines on all metrics. Since its cost does not grow with the number of candidate components, JuntaLearner scales to large models while accounting for set-level interactions and avoiding first-order approximations.

We present an analysis of active interrogation in space with the goal to verify the absence of nuclear weapons hidden in a large constellation of satellites. We propose a 16 MeV photon beam generated by advanced laser wakefield accelerators and the detection of fission neutrons using segmented organic scintillators. We use Starlink as a real-world example for the constellation and solve the inspector routing problem against this set of 7,852 satellites over a 5-year mission period. We perform detailed simulation of the nuclear and orbit physics: signal generation and detection with GEANT4 against an orbit-resolved neutron and gamma background, routes flown with Orekit including the effects from the Earth's oblateness, and detection decided by a likelihood ratio test. We identify different encounter types and fleet designs based on a range of inspector platforms. The radiation dose to target satellites from the beam can be kept to about 1% or less of the 5-year space environment dose. We find that a small number of inspection platforms, 20-70 depending on the accelerator assumptions, can serve inspections to the full constellation with a detection probability of 90% against a single deployed warhead. A 10% random sample of the whole fleet can be inspected by 2-20 platforms providing a 37% detection probability against 5 deployed warheads.

We study Balbuzanov and Kotowski's (2019) exclusion core for object allocation problems with complex endowments. We focus on mixed-ownership object allocation problems in which each object is either individually owned by one agent or publicly owned by all agents. Given a priority order over agents, an endowment structure, an initial allocation, and agents' preferences, we construct serial top trading cycles (STTC) graphs and define the associated STTC algorithm. The algorithm is the central tool for our analysis of exclusion-core-stable allocations. First, we show that, among domains defined by restrictions on endowment structures, the mixed-ownership domain is the largest on which the STTC algorithms characterize the exclusion core. Second, we provide a simple test for exclusion core stability: an allocation is exclusion core stable if and only if it is a fixed point of the STTC algorithm initialized at that allocation, independently of the priority order. Third, we show that the exclusion core is a von Neumann–Morgenstern (1944) stable set with respect to exclusion-domination. Finally, we study a dynamic exclusion-blocking process and show that, from any allocation, there exists a self-contained exclusion-blocking path to the exclusion core.

We introduce the first learned articulated body simulator based on a selective state space model (SSM), called PhysMamba. PhysMamba predicts next-frame full-body state from position, rotation, and joint-action history, without velocity inputs. We compare four architectures under partial- and full-observation inputs and three training protocols. The from-scratch rollout training protocol gives Mamba2 strong short- and mid-horizon accuracy under partial observation (s10 = 43 mm, 2/50 diverged), while the two-stage teacher-based rollout protocol stabilizes GRU but fails for Mamba2. With CUDA graph compilation, Mamba2 reaches 0.107 ms per frame (9,334 FPS) on an H100 GPU, within 1.1$\times$ of GRU's un-compiled throughput, adding under 1% latency to a 30 Hz HMR pipeline and enabling integration as a differentiable physics module for video-based mesh recovery.

Micro aerial vehicles (MAVs) enable rapid indoor 3D reconstruction for inspection and time-critical situational awareness, but must operate under strict flight-time budgets and safety constraints that require explicit return-to-home (RTH) feasibility with a conservative margin. We present a topology-first active reconstruction framework that decouples high-fidelity rendering from navigation. A dense 3D Gaussian Splatting (3DGS) map is optimized as the reconstruction target, while a lightweight Truncated Signed Distance Field (TSDF)/occupancy scaffold supports conservative collision checking and online construction of a sparse 3D Voronoi skeleton roadmap. Since directly extracting roadmaps from TSDF geometry can be unstable under noisy and incomplete online fusion, we validate nodes and edges using carved free-space consistency and dense visibility checks, which suppress behind-wall phantom structure and stabilize planning. Viewpoints are selected on the roadmap using a flight-time-budget-aware objective and a lightweight receding-horizon lookahead to improve non-myopic exploration behavior. We evaluate on photorealistic indoor simulation benchmarks (ReplicaCAD, Gibson, and HM3D), reporting reconstruction coverage/error, RTH success, and computational cost. Results demonstrate improved or competitive performance relative to recent GS-based baselines under identical flight-time budgets.

Language-model systems can separate contextual computation, persistent storage, and exact execution instead of updating all capabilities through one shared parameter system. We investigate FEM-ASM, a finite-element-method-inspired organization in which independently constructed document states and deterministic executable skills contribute typed proposals to a shared language-model state. An explicit residual operator reconciles proposals attached to common interface nodes. We evaluate this organization through controlled experiments and negative results rather than claiming a physical finite-element formulation of language. An attention-free Multi-Mesh prototype learns causal language modeling but does not establish competitive general capability. A versioned store contains 52,809 reconstructive memory elements near a 1.7-billion-floating-value budget; reconstruction is incomplete, with approximately 75% token accuracy. Support-aware lexical indices make these elements addressable under provenance-controlled query construction. For executable arithmetic, positional result observations substantially improve neural rendering relative to a repeated global result vector, and output substitutions change the model's preferred answer. A bounded attachment demonstration further measures the effect of making selected evidence available, without establishing the utility of loading an entire multi-billion-value store. The results support a separation of storage, execution, and neural coordination, while identifying unresolved limitations in question-only retrieval, unrestricted answer generation, and end-to-end efficiency.

Reinforcement learning with verifiable rewards improves reasoning, while the allocation of learning signal shapes which solutions remain accessible under repeated sampling. Group-relative objectives assign equal advantages to equally rewarded responses, making aggregate credit proportional to sampled mode frequency. We introduce Exploration-Preserving Policy Optimization (ExPPO), a lightweight advantage-shaping rule that redistributes credit using prompt-relative, length-normalized response surprisal and prompt pass rate. ExPPO combines bounded shaping with shared normalization to preserve verifier polarity and approximately maintain each prompt group's total absolute sequence-advantage mass. Our analysis characterizes response-level credit allocation alongside sampled mode updates, deriving local conditions for gains in entropy and correct-mode discovery. Experiments show improved in-domain and out-of-domain reasoning coverage, higher aggregate response accuracy, and strong coverage at large sampling budgets. A controlled multi-answer evaluation further demonstrates increased correct-mode yield and gains in diversity among verified-correct responses. Code is available at https://github.com/jinhangzhan/ExPPO

Zero-sum Markov games arise in a wide variety of sequential decision-making problems such as adversarial learning and planning against modeled uncertainties. However, prior work on finite-sample guarantees on the learned state-action value function ($Q$-function) for zero-sum Markov games is largely restricted to finite-action settings, or to continuous-action games in which agents have linear dynamics and quadratic rewards (i.e. linear-quadratic, or LQ, games). A central challenge in extending such guarantees to more general continuous-action zero-sum Markov games is that the associated Bellman operator involves a minimax problem that need not admit a tractable saddle-point solution. To this end, we first introduce a class of neural network function approximators for the $Q$-function that is convex-concave in the players' actions, which guarantees that this minimax problem admits a pure-strategy saddle point. We then study an online variant of fitted $Q$-iteration employing this function class and establish, to the best of our knowledge, the first finite-sample guarantees for non-LQ zero-sum Markov games with continuous states and actions. Our code can be found at https://github.com/CLeARoboticsLab/QCanPlayThatGame.

Vision-language-action models (VLAs) inherit strong semantic grounding from pretrained vision-language backbones but are typically optimized for predicting actions rather than future observations. They can see and act, but they do not imagine the future before acting. World action models (WAMs) built on video diffusion backbones can imagine but treat language as frozen conditioning on a continuous latent space. Unified models bring these modalities into one architecture, but they either decode autoregressively, one token at a time, or keep video continuous with an auxiliary action head. In this work, we present SUAVE, a Single vocabulary Unified Action-Video modEl in which a masked diffusion transformer generates video and actions conditioned on language, with all three modalities represented as discrete tokens in a shared sequence. Choosing which tokens to mask at inference turns the same network into a world model, a robot policy, or a video-action model. For action-free co-training, the action positions of unlabeled video are filled with mask tokens and excluded from the loss. Simulation and real-world experiments demonstrate two findings. First, a single SUAVE model predicts long-horizon video and acts as a policy, competitive with dedicated world models and specialized action policies on static and dynamic manipulation tasks. On a real robot, our model generates subgoal images and an action chunk spanning one second of motion in 1,030 ms on an RTX 5090 GPU, sustaining closed-loop control at 2.5 actions per second. Second, pretraining on robot video and co-training on human video substantially improves policy performance and zero-shot robustness to distribution shift. Together, these results show that masked diffusion is a practical and versatile foundation for unified video-action modeling.

Executable Agent Skills combine natural-language instructions and scripts into reusable packages for LLM agents, and revising them requires fixing errors without breaking correct behavior. Existing benchmarks do not systematically distinguish documentation repair, script repair, and preservation when evaluating skill self-evolution. We introduce SkillScriptBench, a 350-task benchmark designed to evaluate these capabilities separately. From a survey of over 35,000 GitHub-hosted Skill roots, we select 100 packages and construct 150 repair tasks. Each task pairs a package containing injected script faults with a maintenance request and executable checks of the required behavior. A complementary controlled track contains 200 tasks from 50 packages, each evaluated under the same maintenance request in four states: clean, documentation faults, script faults, and faults in both. Across four LLMs, methods that edit both documentation and scripts can repair script faults but do not consistently outperform Markdown-only revision on documentation repair or preservation. We therefore introduce AST-Guided Skill Revision, which uses abstract syntax trees and calling relationships to link maintenance requirements to relevant code locations. It restricts script edits to these locations and updates the documentation to match the revised scripts. Averaged across models, this revision stage yields absolute gains in repair success of 21.9% for Raw Package and 27.7% for CoEvoSkills on faulty packages. Absolute gains in the proportion of tasks solved in all three runs reach 20.8% and 31.5%, respectively, indicating more consistent repair success across repeated runs.

We present VolS-GS, a relightable Gaussian splatting framework that reconstructs objects from one-light-at-a-time (OLAT) captures and renders them under novel lighting and viewpoints. Relightable Gaussian Splatting methods typically model appearance independently at each primitive, which makes non-local effects difficult to represent. This limitation is particularly apparent for subsurface scattering, where light entering the object at one location can emerge at another. Rather than modeling this effect solely with a neural network or a local kernel at each primitive, we use the spatial support of the Gaussian scene as the domain of a differentiable finite-volume transport solver, so that light can propagate through the object's interior. A small network predicts scattering and absorption coefficients for each Gaussian, and the solve redistributes incident light through the resulting field. The coefficients are fit to images rather than measured, so the solve supplies a transport-shaped path for aggregating per-primitive appearance, not a measurement of the material. To keep the learned shadow and specular terms from taking over the other components, our shadow term is predicted from visibility together with the transmittances and the scattering the solve produces, and a regularizer suppresses specular highlights in regions the shadow term predicts to be unlit. Experiments on three OLAT benchmarks show that VolS-GS consistently improves relighting quality on held-out lights and views.

Limited training data diversity constrains generative modeling of 3D human bodies: conservative models remain close to observed examples, whereas exploratory models often violate basic body proportions. We introduce a verifier-guided augmentation framework that uses global and mode-local PCA to generate inexpensive candidates, screens them using correspondence-derived skeletal proportions and body-part geometry, and retrains a diffusion model on accepted candidates. Elastic registration provides both the modal structure used by distributed PCA and the dense anatomical correspondence needed for scalable screening without per-candidate body-model fitting. A blinded human study supports the verifier as a conservative gatekeeper, favoring verifier-accepted over rejected outputs. We evaluate full-pool verifier acceptance separately from the coverage and departure of accepted samples and combine them through EAUC. On 4,498 registered DFAUST surfaces, distributed-PCA augmentation achieves 86.32% acceptance, the highest CP-AUC (0.871), and the highest EAUC (0.752), improving EAUC by 32% over real-only and self-augmented diffusion. These results show that mode-local, verifier-guided proposals broaden diffusion generation while maintaining high agreement with calibrated body measurements.