Papers

We study the voter model with opinion graph, a generalization of the standard (pull) voter model that adds a notion of bounded confidence. In this process, we consider a finite set $A$ of $n$ agents. Each agent $u \in A$ has an opinion $x_u \in O$, where we model opinions as vertices in an undirected opinion graph $G = (O,E)$ with $|O|=q$. In each step, an agent $u$ interacts with another agent $v \in A$. In contrast to classical voting, $u$ adopts the opinion $x_v$ if and only if $x_v$ and $x_u$ are neighbors in $G$. The process is stable once all remaining opinions are an independent set in $G$. We analyze two variants of the process: the ordinary EdgeVOG process, which samples a pair of interacting agents uniformly at random from all possible pairs, and the productive EdgeVOG process, which samples only pairs with neighboring opinions in $G$. We show the following: - For every opinion graph and every initial configuration, ordinary EdgeVOG stabilizes within $O(n^2\log n)$ steps in expectation and with high probability. The expectation bound is asymptotically tight. For the productive EdgeVOG process, the expected stabilization time is exactly the initial number of compatible agent pairs, while $O(n^2\log n)$ steps suffice with high probability. - An opinion $i$ with initial support $s_i$ survives with probability at least $p_i:=s_i/(s_i+\sum_{j\in N(i)}s_j)$. Further, let $\mu = \sum_{i \in O} p_i$, then we show the probability that less than $(1-\delta)\mu$ opinions survive is at most $\exp(-\delta^2\mu/(2(\Delta^2+1)))$ for every $0\leq\delta\leq1$. -If $G$ has maximum degree $\Delta$ and every opinion initially has support at most $\hat{s}$, then no opinion ever acquires more than $\tilde{O}(\min\{n,\Delta^6\hat{s}\})$ agents with high probability. This yields near-linear stabilization bounds for productive EdgeVOG for a large class of configurations.

This paper delves into the intricate aspects of Reconfigurable Intelligent Surfaces (RIS) in the antenna design. It investigates the properties of the array factor of RIS, highlighting the significance of phase shifts in establishing of the reflect path. Additionally, the paper investigates spatial positions requiring identical phase shifts, nullification of the array factor, the count of total maxima, second maximum determination (amplitude of the second lobe), and the calculation of the 3dB bandwidth. They are very useful for RIS-assisted radio communication systems.

Resampling is the standard remedy against weight degeneracy in particle filters, yet its effect on the spectrum of the particle second-moment matrix is poorly understood. We study a single resampling step for a d-dimensional ensemble of N particles with d/N -> c. For any unbiased scheme, the resampled empirical second-moment matrix dominates its pre-resampling counterpart in conditional convex order, while the conditional mean is preserved; the excess second spectral moment equals the Frobenius energy of the resampling perturbation. For multinomial resampling, the empirical count law converges to the mixed-Poisson law determined by the limiting weight law. For residual resampling, the count law is determined by the joint limit of floor-fraction pairs: we classify all residual limits of weight sequences converging to delta_1 in law as a one-parameter family between the deterministic identity and the full multinomial count law. Each count law feeds a common covariance-side spectral map, yielding exact consequences: a closed-form zero-eigenvalue mass, a rank-and-spectral-gap transition with a universal lower edge benchmark, computable regular edges, unbounded right support, and scheme-specific second-moment costs. The effective sample size determines one bulk statistic but cannot determine the limiting spectrum. Pre-registered numerical experiments confirm the theory at every level.

Spatial reasoning agents can inspect tool outputs and repair errors, but reusing these lessons requires preserving both the computation and the conditions that make it valid. We introduce EvoSpatial, a framework that learns from execution experience by updating a library of linked skills and tools. Skills describe procedures, geometric assumptions, and verification steps; tools implement the operations those procedures require. When solving a task, the agent retrieves relevant skills and synthesizes reusable computational functions if existing tools are insufficient. After each task, execution feedback and evidence checks guide skill revision and tool consolidation, without ground-truth answers or benchmark scores. Across 20 benchmarks, EvoSpatial averages 63.9, 4.0 percentage points above the average reported by SpatialClaw. The evolved library also improves held-out and cross-benchmark performance when updates are disabled, and trajectories generated with evolved skills improve supervised fine-tuning, even without external skills at evaluation. Keeping checked procedures on record, together with the tools that support them, lets an agent carry spatial reasoning experience from one task to the next.

The latent variable proximal point (LVPP) method solves optimization problems in function spaces with pointwise constraints by a sequence of smooth subproblems whose iterates are strictly feasible. We apply it to linear-quadratic elliptic optimal control problems. Control and observation are distributed but may be restricted to subdomains. We prove that the LVPP subproblems are well posed in appropriate function spaces, that the iteration converges for every sequence of proximity parameters with divergent sum, and that it delivers the Lagrange multiplier of the constraint as a by-product. We interpret the Newton step for the LVPP subproblem as a linear-quadratic optimal control problem with a spatially varying control cost, and we show that Newton's method converges locally quadratically. The Newton systems are solved by the minimal residual method with a block-diagonal preconditioner. We prove that the spectrum of the Newton operator with respect to the inner product defined by the preconditioner is bounded independently of the proximity parameter, the iterate, the mesh and the observation and control domains. The results are combined into a complete algorithm, and tested in numerical experiments.

We study the recovery of the hidden vertex correspondence between two correlated dense random geometric graphs. Each graph is generated from $n$ latent unit vectors in $\mathbb R^d$; the vectors $u_i^A$ and $u_i^B$ of corresponding vertices satisfy $\langle u_i^A,u_i^B\rangle=\rho$, and the vertex labels of the second graph are permuted by an unknown permutation $\pi$. For every fixed correlation $\rho\in(0,1]$ and every edge density bounded away from zero and one, we give a randomized polynomial time algorithm that recovers $\pi$ exactly with probability tending to one whenever $d\ge(\log n)^L$, where $L$ depends only on the correlation and the density bounds. The algorithm assigns to each vertex a signature formed by counting decorated paths with a constant number of seeds. The number of such seeded templates grows exponentially with the path length, with an arbitrarily large constant base, so the resulting statistics amplify an arbitrarily small constant correlation. We control the dependencies created by the latent geometry in two ways: when $d$ is larger than $n/(\log n)^{L_0}$ for a suitable constant $L_0$, by comparing local moments with those of correlated Erdős–Rényi graphs; for smaller $d$, by spectral estimation of the latent geometry combined with a harmonic correction. We also provide low-degree evidence for a tradeoff between the correlation and the computational cost.

Bayesian inference for latent point process intensities often relies on per-dataset sampling or optimization, making repeated inference computationally expensive. We propose a neural-network-based amortized variational framework that learns a reusable inference rule mapping a variable number of replicated point patterns to a distribution over their shared latent intensity. Trained from event times using the point process likelihood, the model learns an amortized inference rule without ground-truth intensity supervision. At test time, it performs inference of the latent distribution in a forward pass. On synthetic data, additional realizations improve intensity recovery and yield narrower credible intervals with broadly stable coverage. Our method is tested on bicycle-sharing data and achieves the highest mean held-out log likelihood among the evaluated methods while requiring substantially less inference time than the Log-Gaussian Cox Process baseline.

Accurate modelling of soft tactile sensors remains difficult because finite element methods (FEM) are computa- tionally expensive, while real-time simulators often lack fidelity for hyperelastic deformation. Large physical datasets are also impractical to collect because repeated testing can damage fragile sensors. We present a data-efficient framework that combines limited real-world validation, high-fidelity FEM, and graph neural networks (GNNs) for accurate real-time prediction of two-dimensional tactile deformation in a planar soft tactile structure. The key idea is to decouple validation from training: 82 camera-tracked contact configurations are used only to tune and validate an ANSYS FEM model, which then generates 768 synthetic contact scenarios for GNN training. We evaluate both forward prediction from marker deformation to contact localisation and inverse inference from contact configuration to marker deformation. The validated FEM achieves sub-0.5 mm error in more than 90% of validation cases, while the learned GNN surrogate reaches a mean absolute error of 0.32 mm with millisecond-scale inference, compared with minute-scale FEM simulation. Models trained entirely on synthetic FEM data retain sub-millimetre accuracy on real measurements from the 2D tactile structure, demonstrating strong sim-to-real transfer within the tested planar setting. We further integrate the learned model into a real-time visualisation pipeline, enabling rapid deformation prediction for virtual prototyping and simulator-based design exploration without extensive physical testing.

Vision-language models (VLMs) like CLIP have shown great success in image tasks, however, applying CLIP to open-vocabulary video recognition poses challenges. Due to the limited text information, directly fine-tuning CLIP on video recognition datasets may lead to overfitting and hinder its generalizability. A prevalent method is to enrich text information by generating prompts using Large Language Models (LLMs). However, limited efforts have been made to explore how to generate higher-quality prompts that can contribute to classify unseen categories, and how to further enhance vision-text alignment based on these prompts. In this paper, we propose P2CLIP (Prompt-guided CLIP), which aims to bridge this gap by exploring the impact of prompts across three aspects: category, video, and frame. At the category level, we argue that LLM-generated prompts under simple instructions may suffer from semantic overgeneralization, which can blur the category boundaries and hinder the performance of the model. To address this issue, we design Generic-Discriminative Prompt using LLMs to obtain discriminative category embeddings with rich semantic information. At the video and frame levels, we first use VLM and LLM to generate frame and video descriptions for enhancing vision-text alignment. Then we propose a Knowledge-Guided Temporal Aggregation mechanism, which leverages the expert knowledge derived from LLMs to guide the temporal modeling of videos and encourage a better construction of the joint visual-textual feature space. Extensive experiments across various benchmarks, including zero-shot and few-shot settings, demonstrate the effectiveness of our method.

There is growing interest in applying Parameter-Efficient Fine-Tuning (PEFT) to Continual Learning, as it enables faster training, mitigates catastrophic forgetting, and facilitates better adaptation to new tasks. Prior approaches have explored a range of strategies, including extending new LoRA branches for each incoming task, training under orthogonal loss objectives across all task-specific LoRA modules, and employing gating mechanisms to integrate new and existing LoRA modules. However, these methods incur memory costs that grow linearly with the number of tasks, limiting their scalability. More recent approaches investigate training a single LoRA by leveraging asymmetries in its parameterization; however, they often suffer from insufficient representational alignment across the LoRA parameter space. To address these limitations, we propose Stiefel Optimization and Aligned Rotation (SOAR), a two-stage framework for continual LoRA learning. First, we constrain the A matrix to lie on the Stiefel manifold, thereby reducing coordinate misalignment to the space of orthogonal rotation matrices. Second, we introduce an Orthogonal Procrustes alignment procedure for the B matrix to estimate the optimal rotation, coupled with a per-rank retention merging strategy that quantifies directional agreement between representations of new and previously learned tasks. We conduct extensive experiments across multiple models and benchmarks, demonstrating that SOAR achieves strong continual learning performance without incurring additional memory overhead.

An LLM agent using tools can fail silently. It stops before the task is done, raises no error, and answers fluently. Two kinds of monitor address this, one deciding whether a run failed and the other naming the step where failure became unavoidable. Much of the reported performance on both tasks comes from regularities that need no model. Failing runs are longer, and the step labelled decisive is usually the last. A rule that always names the last step is correct $67\%$ to $96\%$ of the time here, without reading the run at all. That ceiling reflects how the labels were written, not how agents break. On failures whose decisive step replay can confirm, it falls to near chance. Reporting gain over that rule therefore changes what a score means. Under that correction, methods tested here gain nothing on give-up failures, while several published systems keep a clear advantage on other splits. For detection, the agent's internal states beat transcript length and text similarity on the agent benchmark, and hold up where the text baseline does not. Precision stays low when failures are rare, so such a monitor should rank runs for review, not replace it.

Information-theoretic and geometric compression have been widely studied as possible explanations for generalization. Yet their temporal dynamics in recurrent networks remain largely unexplored. Using discretized LSTMs, whose finite embedding space enables direct estimates of information quantities, we observe pronounced compression across the final timesteps of many datasets. We explain this effect through three competing mechanisms: (i) class separability permits stronger compression at the final timestep; (ii) shared recurrent dynamics propagate this pressure across timesteps with similar activation states, making its extent depend on temporal stationarity; and (iii) limited representational capacity opposes prolonged compression because it restricts information available for subsequent computation. We systematically test these mechanisms through controlled synthetic interventions and real-world sequence tasks. Our results identify class separability, temporal stationarity, and network capacity as key determinants of temporal compression, and suggest that compression acts as a regularizer-potentially beneficial when excess capacity is available, but harmful to generalization when it consumes memory needed for the task.

Wireless propagation modeling is foundational to the evaluation and design of modern communication systems. To achieve accurate wireless propagation prediction, recent learning-based approaches leverage scene geometry and materials, demonstrating promising generalization across transceiver locations and unseen scenes. However, these approaches remain largely confined to a fixed configuration of array size, receiver orientation, and transmit beam. In this work, we introduce RFWeave, a learned wireless propagation model designed to generalize across scenes, transceiver locations, and transceiver configurations. To accommodate varying array structures, RFWeave incorporates variable-length transceiver tokens that represent antenna elements individually. Furthermore, to capture the geometry between transmit and receive antenna elements, RFWeave aggregates their pairwise spatial relations into propagation tokens. A configuration-conditioned decoder predicts the spatial spectrum and received power. RFWeave is trained on a large-scale simulated dataset spanning 10,000 indoor scenes and more than 5 million channel records under diverse transceiver configurations. Extensive evaluations show that RFWeave achieves state-of-the-art performance across all evaluated generalization settings, improving spatial spectrum structural similarity (SSIM) by up to 15.7% and reducing received power mean absolute error (MAE) by up to 35.4% over the strongest baselines on unseen scenes. Additional experiments on measured DICHASUS data and in beam management further demonstrate RFWeave's broader applicability to real-world channels and downstream wireless tasks.

Decision APIs that return a probability for each option are routinely used as if those probabilities were properties of the options themselves. That reading is valid only if the model satisfies independence of irrelevant alternatives (IIA): adding an option that is neither the right answer nor its strongest rival should leave the odds between those two unchanged. We test this in a pre-registered study of jev-1.13.0, a hosted decision model, using 299,463 calls on intent classification (BANKING77, CLINC150) and topic classification (AG News). Every added option moves the log-odds between the gold label and the strongest wrong label: the root-mean-square systematic shift is 0.20-0.52 nats, 1.2 to 3 times the run-to-run variation, even when the added option takes at most 0.1% of the probability mass. The shifts are directional. An option similar to the wrong answer draws probability from it (+0.10 nats toward the gold label). A paraphrase of the wrong answer produces an intermediate pattern: the gold label's probability is almost conserved, but the paraphrase receives only about a third of the wrong answer's share rather than the half that strict substitution implies. The distortion grows steadily with the logarithm of the number of options, reaching about 1 nat at 255 options, and off-domain padding pushes the odds against the gold label. In contrast, questions packed into one call do not interact (bias < 0.001). Scoring each option with an independent yes/no question removes the option-set dependence but picks the right answer 8.7 points less often. Jev sits between two local baselines, an option-independent scorer and a prompt readout. Its probabilities are best read as relative to the option list they were computed over.

Flow matching models are typically trained to transport a Gaussian source to the data distribution, with source and target samples paired independently. We replace the source with a fitted Gaussian mixture and couple each data point to a mixture component through an entropic optimal transport problem. We show that the resulting transport reduces to the standard Gaussian-source problem up to a guidance-like correction, which enables the reuse of a pretrained velocity field. This correction is a closed-form function of the fitted mixture plus a term that we learn with a small correction network. We test our model on published checkpoints for CIFAR-10 and CelebA-HQ. It improves FID at every step count, and on CelebA-HQ it reaches the quality of the baseline with about half the steps. The closed-form term alone, with no training, already delivers most of this improvement; the small correction network accounts for the rest.

Counting is a simple task on which transformers can nevertheless fail at long sequence lengths. We study the cost of counting in a single attention layer, up to a maximum length $L$, focusing on how softmax attention and layer normalization shape the representation from which the count is recovered. We mainly focus on regression read-out but also consider classification read-out. For regression, we show unnormalized linear attention counts exactly at parameter norms independent of $L$. For softmax attention, regression cannot count exactly with finite parameters; it recovers the count after rounding, but only when the vector parameter norms grow with $L$. We measure this cost by $B_{\min}$, the smallest bound that can be placed on every trainable vector to ensure exact counting after rounding, and derive tight rates. At fixed model dimension, $B_{\min}$ grows as $L$ without normalization, as $L^{3/2}$ under bare post-normalization, and as $L^{3/4}$ with learned post-normalization. The last rate is unexpected: post-normalization discards the magnitude that carries the count and might be expected to make counting harder, yet with a learnable gain it counts at a smaller norm than softmax without normalization. Bare pre-normalization is different: it bounds the attention scores, so beyond a finite length no parameter norm suffices. A classification read-out keeps every norm bounded under every placement, but a dense head stores one output vector per count and costs more in storage. Experiments on the post-normalized model reproduce this split between the two read-outs. Together, our theoretical and empirical findings characterize how self-attention, layer-normalization placement, and read-out choice shape the representation geometry and parameter cost of counting in the minimal single-head architecture studied here.

We introduce IND-Eval, a public benchmark that organizes industrial time series across domains into source-specific forecasting tasks. Relative to established benchmarks such as GIFT-Eval, it emphasizes finer sampling resolutions and a greater prevalence of multivariate forecasting. Evaluating Chronos-2, TiRex-2, and TimesFM-3, we find that TimesFM-3 achieves the lowest source-balanced aggregate nMASE and nCRPS and leads seven of nine sources under each metric; source-specific exceptions reinforce the need for domain-representative evaluation for model selection. These findings also motivate improving domain alignment during pretraining, where real industrial data are often too scarce to close domain-specific gaps directly; we therefore investigate whether a domain's statistical structure can guide simulator design. In a case study on two offshore well-monitoring regimes, we improve a general simulator's coverage using an oscillator-augmented simulation pipeline. This lowers forecasting error in the target domain but reduces performance on the subset of GIFT-Eval with natively univariate targets. A 50/50 mixture of the general and augmented simulation recipes achieves the lowest error among the three training recipes for all four event-metric pairs in the case study while recovering most of the lost GIFT-Eval performance. Together, these results illustrate how domain-representative evaluation can guide model selection and the composition of simulated data while revealing a trade-off between specialization and generality.

Industrial software applications often require engineers to tune the software deployment platform. Configuration tuning identifies valuable configurations that minimize costs while ensuring the application performance. However, finding these configurations is difficult. The number of tunable configuration parameters in industrial applications is large, and engineers cannot assess different configurations in production because users may experience performance degradation. This work targets Kubernetes: A system for automating the deployment, scaling, and management of containerized applications. This paper proposes a domain-knowledge-driven solution for finding configurations of industrial applications in a practical time. The solution relies on a catalog of constraints encountered by domain experts in similar applications. Depending on the problem under analysis, engineers can customize the optimization problem by selecting the relevant constraints from the catalog for the application at hand. We rely on two alternative solvers to find an optimal configuration: The first is based on heuristics, while the second reuses existing optimization-based solutions. We implemented our solution within an industrial tool from a software company specializing in performance engineering and optimization. We compare our solution to a baseline, considering a set of predefined configuration values provided by engineers. Our results confirm the effectiveness of our solution: Compared to the baseline, the heuristic-based and optimization-based solutions provide significant average savings of 11591 USD/mo and 15874 USD/mo per Kubernetes, respectively, accounting for 24.03% and 32.90% of the costs, in practical time (0.71 seconds per extraction for the heuristic-based and 45.54 seconds per extraction for the optimization-based solution).

The sums of the absolute values of higher-order cumulants are classical contrast functions for independent component analysis (ICA) and lead naturally to robust approximate diagonalization of higher-order cumulant tensors using $\ell_1$-based diagonalization over the orthogonal or unitary group. We propose Jacobi-SubG, a Jacobi-type framework that selects index pairs using Riemannian subdifferential information and performs plane rotations with a refinement step that preserves nonzero diagonal contractions. For the general tensor model, we prove global convergence of the entire iterate sequence from any initialization with nonzero diagonal contractions, provided that the subproblem solvers satisfy a uniform sufficient-ascent estimate. For real and complex third- and fourth-order cumulant tensors, which are widely used in ICA, we develop specialized subproblem solvers satisfying these conditions. The resulting algorithms thus enjoy global convergence under the simple initialization condition that all diagonal contractions are nonzero. Numerical experiments on ICA and tensor diagonalization show that the proposed Jacobi-SubG variants achieve better source recovery and higher final objective values in several settings, particularly at the higher tested noise levels.

Machine translation (MT) is increasingly utilized in multilingual crisis communication, yet conventional evaluation does not directly assess whether translated emergency messages preserve their actionability. We introduce SIREN (Situation-aware Index for Response and Emergency ActioNability), a human evaluation framework assessing whether translation choices compromise protective action, directive force, and urgency of the source text. We evaluate SIREN in two complementary settings. At the error level, we apply it to HOPE-annotated Italian–English translations produced by ChatGPT-4o and Google Translate: 31.63% and 48.73% of errors, respectively, compromise actionability, predominantly by affecting the protective action. At the message level, we evaluate English–French translations produced by TranslateGemma-4B and Google Translate, with actionability preserved in 85.34% and 92.67% of translations, respectively. TranslateGemma-4B failures predominantly weaken directive force, whereas Google Translate failures more often compromise protective actions and receive Major impact ratings. These findings show that translation systems can differ not only in how often actionability is lost, but also in the nature and functional impact of these failures. Alongside SIREN, we contribute an English–French crisis-translation resource with human actionability annotations and post-edited reference translations, supporting further research on function-oriented evaluation for crisis communication. Our experimental data is available at https://github.com/mcstaiano/SIREN.

Recovering divergence-free velocity fields from sparse and corrupted observations requires reconciling physical consistency, expressive representations, and robustness to missing data. We introduce DFK-Former, a set-to-field transformer that reconstructs divergence-free velocity fields from sparse, noisy, and irregularly sampled 3D observations. The model is inherently invariant to the number and ordering of input samples and predicts the parameters of a divergence-free kernel representation, producing continuous, mesh-free velocity fields that satisfy incompressibility exactly by construction rather than approximately through soft constraints or projection operators. Unlike existing divergence-free kernel approaches, which estimate kernel coefficients via a separate optimization for each field, DFK-Former predicts these coefficients directly in a single forward pass. This eliminates costly iterative fitting while providing a learned prior that enables accurate reconstruction even when observations are insufficient to uniquely determine the field. To enhance representational power, we introduce adaptive and anisotropic divergence-free kernels that preserve exact incompressibility guarantees while capturing more complex flow structures. Extensive experiments across varying levels of sparsity, noise, and occlusion, including transfer to real Direct Numerical Simulation (DNS) turbulence data, demonstrate substantial gains in both accuracy and efficiency. DFK-Former reduces endpoint error by up to 4.6x compared to per-field divergence-free-kernel optimization, while reconstructing each field in 7.5 ms instead of 9.8 s, yielding a speedup of more than three orders of magnitude. These results establish direct, feed-forward prediction of divergence-free kernel parameters as a practical and effective paradigm for physically consistent velocity-field reconstruction from sparse observations.

Learning a response law for continuous decisions from observational time series is central to many real-world decision systems, yet temporal non-stationarity poses a fundamental challenge: as outcomes drift over time, naively pooled models can conflate action effects with shifting baselines and even reverse action rankings. Even when the one-step response is identifiable, unrestricted cross-time generalization remains fundamentally ill-posed. We therefore seek the part of the response that remains stable for decisions even when outcome levels do not. We propose deployable causal action geometry: the action-response shape that remains after anchoring away action-independent level shifts on a selected link scale and profiling out positive amplitude variation. Building on this target, we develop a two-stage orthogonal estimator that first obtains cross-fitted pilot estimates of anchored responses and then performs honest profiled selection over link, representation, and shape classes. The resulting estimator admits oracle guarantees for the restricted target and, under approximate persistence, produces decision rules that remain near optimal in future periods. Experiments on synthetic data and Dominick's support the proposed target and its transfer behavior. In a randomized Taobao A/B test, the deployed system improves GMV and purchase counts by \(1.16\%\) and \(1.70\%\).

The deep hole problem is a fundamental problem in coding theory, and it has many important applications in code constructions and cryptography. The deep hole problem of Reed-Solomon codes has gained a lot of attention. As a generalization of Reed-Solomon codes under Hamming metric, we study the covering radius and deep holes of Hyperderivative Reed-Solomon (HRS) codes under the Niederreiter-Rosenbloom-Tsfasman (NRT) metric. We determine the NRT covering radius of HRS code and characterize its NRT deep holes via Maximum Distance Separable (MDS) extensions and polynomial remainder conditions. We further relate the enumeration of NRT deep holes to the characteristic polynomial of an associated hyperplane arrangement. We also provide three classes of explicit NRT deep-hole constructions, propose a Cheng-Murray type conjecture for HRS codes under the NRT metric and obtain a conditional low-layer description. Using these characterizations, we derive exact enumeration formulas in several special cases.

Cross-task generalization remains difficult for world action models (WAMs), even when their predicted futures depict plausible manipulation. This gap can be attributed directly: we make this gap directly testable by decoupling a WAM into a world model and an inverse-dynamics model (IDM), then holding the IDM fixed while replacing the source of future images. We introduce Align Once, Evaluate Everywhere (AoE), a camera-space inverse-dynamics model pretrained on large-scale robot data, which provides this recovery interface for different future sources across tasks and environments. Through it, we find that actions recovered from recorded futures of unseen tasks execute almost as well as replayed demonstrations, whereas futures predicted by world models collapse across benchmarks. The failures are not generic: they concentrate on the gripper and interaction geometry while generation capacity is spent on task-irrelevant background. This diagnosis suggests that supervision should target exactly these regions. We therefore introduce the vision-to-action (VITA) loss, which passes generated futures through the frozen AoE and penalizes discrepancies in the recovered actions, redirecting generation toward action-relevant detail. Across two world models and three manipulation benchmarks, this simple change raises the execution success of generated futures from near zero to 47.0%. The same loss also transfers to WAMs and yields consistent gains in native control.

Science maps describe relationships between papers. Text embedding models build these relationships by turning a paper's text into a list of numbers that gives it a position. Would another model give the same picture? I compare ten models using titles and abstracts of 500,000 publications from the OpenAlex bibliographic catalogue, published in 2000-2024 across 26 disciplines, including Medicine and Physics. Representing each discipline by its papers' average position produces similar arrangements across models, including when other papers are selected. Yet within a discipline and period, two models share, on average, only eight of the 25 papers closest to a given paper. Supplying titles alone also changes much of that list, with effects that vary between models. Models can also disagree about which discipline's papers are more spread out. One measure of spread compares angles between lines drawn from a common point to each paper's position. Moving that point can reverse which discipline appears more spread out, even when selecting other papers leaves the answer unchanged. The broad arrangement can remain similar while answers about nearby papers and differences between disciplines depend on the model, the text it receives and how its output is processed.

We present the first dynamic maximal independent set (MIS) of a graph with $n$ vertices and up to $m$ edges under edge updates in the prediction model, where a predicted update sequence is available for offline preprocessing before the real updates arrive online. We consider the incremental (insertion-only), decremental (deletions-only), and fully dynamic (insertions and deletions) models. Without predictions, deterministic algorithms need worst-case update time of $O(n)$ for decremental and $O(m)$ for incremental and fully dynamic settings. Bernstein et al.~[SODA26] proved under the combinatorial BMM conjecture, combinatorial incremental algorithms against an adaptive adversary require $\Omega(n^{1-o(1)})$ amortized update time. We present deterministic incremental, decremental, and fully dynamic algorithms whose update times depend on the prediction error. This error is measured by the number $\eta_e$ of mispredicted updates, and by the number $\eta_v$ and total degree $\eta_v^*$ of vertices whose MIS membership was mispredicted. With $O(mn)$ preprocessing, our decremental and incremental algorithms achieve worst-case update times $O(\eta_v)$ and $O(\eta_e+\eta_v^*)$, respectively. Our fully dynamic algorithm achieves $O(\eta_e+\eta_v^*)$ worst-case update time with $O(un)$ preprocessing for $u$ updates. We also give space-efficient variants using $O(m)$ space for the decremental and $O(m\sqrt{m})$ for the incremental setting, at the cost of a logarithmic overhead in worst-case update time. Our algorithms satisfy consistency, robustness, and smooth degradation, the required properties of algorithms with predictions. They can also utilize the general error correction framework of Khan et al.~[Arxiv26], relaxing the error measures from first point of difference to prefix matching (for partially dynamic) and set edit distance (for fully dynamic), maintaining the same bounds.

State space models provide efficient linear-complexity processing for long sequences, but their performance frequently degrades as context length grows. We propose SuPER-Mamba, a training-free framework that uses Surprisal as a model-intrinsic signal for long-range state routing in pretrained Mamba models. SuPER-Mamba computes position-wise Surprisal from next-token predictions, aggregates neighboring responses through Local Pooling, and uses the resulting scores to prioritize Global-Channel updates without query-dependent scoring or additional training. We evaluate SuPER-Mamba on three state-space models across the LongBench-E benchmark. The results show that SuPER-Mamba improves the average score from 8.06 to 15.69, corresponding to a 94.7% relative gain over the Base Models and a 13.1% improvement over the state-of-the-art prior baseline. Ablation and length-wise analyses further support the effectiveness of the proposed routing framework.

Natural-language self-consistency and executable programs provide complementary test-time evidence for mathematical reasoning, yet either channel may support the same semantic error. Thus we propose ACED, a reference-anchored framework that treats the self-consistency answer as the default and executable outputs as supporting evidence rather than interchangeable votes. ACED converts source-specific answer counts into smoothed supports, combines them through a weighted logarithmic pool, and overrides the reference only when a calibrated relative-evidence margin is exceeded. The same rule supports both candidate selection and admission of executable-only answers. Across five math word-problem benchmarks, ACED matches or outperforms the corresponding baselines. On GSM8K, ACED-CANDIDATE recovers 89.7% of the attainable candidate-set gain with only three damaging overrides, while ACED-ALL reaches 86.9% accuracy versus 82.6% for direct Program-of-Thought aggregation. These results show that preserving evidence provenance enables more reliable integration of natural-language and executable reasoning.

Recent Vision-Language-Action (VLA) models increasingly use natural-language instructions to condition autonomous driving behavior. Yet existing closed-loop benchmarks primarily measure route completion, safety, and rule compliance, leaving a fundamental question unresolved: does language actually determine which feasible behavior the vehicle executes? A trajectory may be safe and successful while still violating or even ignoring the passenger's instruction. To address this, we introduce \ltd, a benchmark designed to directly test this capability. Its key evaluation unit, the paired counterfactual unit (PCU), holds the initial driving scene fixed while changing only the instruction. This design enables us to distinguish isolated instruction success from counterfactual paired success across four instruction-following scopes. To test whether this distinction persists across evaluation regimes, we instantiate Language2Drive in complementary closed-loop CARLA simulation, reconstructed real-world scenes, and open-loop driving benchmarks, including our released CARLA-Language2Drive simulator with purpose-built maps. Evaluating representative driving VLAs across these settings reveals a striking mismatch between strong driving competence and weak language control: 93.2% of successful rollouts do not have a successful counterpart under the alternative feasible instruction. This failure is dominated by one-sided completion, where a model repeatedly executes one preferred behavior but fails when the same scene requires the counterfactual alternative. These results expose two fundamental limitations of current evaluation: isolated success and driving scores, which are widely used by conventional driving benchmarks, can substantially overstate language-following capability, while current driving VLAs themselves lack reliable instruction following under matched counterfactual tests.

Memory-based long-video generation aims to combine user control with long-range visual consistency. We organize this process into three functional components: a planner, an adapter, and a generator. Representative multi-shot systems couple memory to generator-specific interfaces or use predefined agent workflows, rather than independently training a memory policy for cross-shot objectives. We introduce REEL, a general-purpose visual-memory planner. Through a unified tool interface, REEL learns to retrieve references, create missing visual evidence, and update persistent memory. Backend-specific adapters translate its evidence plans into supported conditioning inputs, allowing the same policy to guide different black-box video generators. To train REEL, we construct two high-quality datasets, REEL-SFT-4k and REEL-RL-1k, covering diverse interaction patterns and prompt types. Training proceeds in three stages: supervised fine-tuning, single-shot Group Relative Policy Optimization (GRPO), and multi-shot GRPO. Multi-shot GRPO carries policy-generated memory across consecutive shots, so later outcomes guide earlier reference selection and memory updates. REEL-Bench tests identity preservation and intended state changes under text-only requests and timed reference-image uploads. On JoyAI-Echo~1.5 and MiniMax-H3, REEL improves cross-shot consistency on ST-Bench by 15.1% and 20.7%, and Core-100 on our proposed REEL-Bench by 2.41 and 8.32 points, respectively, over the no-memory baseline.