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arXiv2026

Reconstruction-Augmented Visuomotor Pre-Training of 3D-Grounded Bimanual Dexterity from RGB-Only Human Videos

We present SpatialDex, a framework that learns 3D-grounded bimanual dexterity from RGB-only human videos through reconstruction-augmented visuomotor pre-training. The central idea is to learn human behavior together with its spatial context. From each video, we reconstruct the scene geometry and estimate the hand motion, align them at a shared video-level scale using the hand-size prior of 3D hand estimates. We retain the reconstructed geometry as both a policy input and a prediction target. The policy grounds the token grid of a pre-trained vision-language model in this geometry through gated residual fusion, is trained to predict future scene geometry alongside wrist and finger actions, and generates finger motion conditioned on the predicted trajectories of both wrists. Pre-trained on 1M human-video clips and fine-tuned with a small number of robot demonstrations, SpatialDex outperforms the state-of-the-art methods by 16.5 points on nine simulated dexterous tasks across two embodiments and by 38.3 points on six real-world bimanual dexterous tasks. Under a matched comparison, pre-training with reconstructed geometry improves success by 14.2 points over pre-training on hand motion alone.

cs.RO↗
arXiv2026

Scalar-scalar-graviton vertex from Asymptotic Safety

The unitarity and causality properties of asymptotically safe quantum gravity are still unsettled. Scattering amplitudes provide a direct test, but their computation requires fully momentum-dependent correlation functions. In this light, we compute the full scalar-scalar-graviton vertex from Asymptotic Safety within a mostly analytic approximation. Qualitatively, we find the expected logarithmic branch-cut structure, and we correctly recover the double-eikonal soft divergences predicted by Weinberg's soft theorem. Quantitatively, we find that non-minimal operators are generally as important as the minimal vertex stemming from the scalar kinetic term.

hep-th↗
arXiv2026

Semiclassical molecular dynamics simulations of electromagnetically induced transparency cooling of 2D and 3D ion crystals in a Penning trap

Motional modes of trapped-ion crystals in Penning traps can now be cooled to near their ground states via electromagnetically induced transparency (EIT) cooling. Numerical simulations are valuable tools for interpreting EIT cooling results and optimizing experimental protocols, but existing molecular dynamics codes are limited to the simulation of Doppler cooling. In this work, we fill this gap by implementing a semiclassical model of EIT cooling in a novel MD code. By simultaneously evolving the ions' internal quantum states and classical motion, we are able to calculate the instantaneous EIT laser forces acting on the ions. We first validate our code by comparing the single-ion cooling rate to fully quantum simulation results. Next, we analyze cooling of the drumhead modes in planar ion crystals, quantifying the effects of planar ion motion and a finite laser beam width. Finally, we demonstrate efficient EIT cooling of the axial modes in 3D ellipsoidal crystals containing up to 500 ions. Such crystals are a promising platform for future quantum sensing experiments with enhanced sensitivity. We find that the mode spectra of 3D crystals can be engineered to enable sympathetic cooling of the low-frequency $\boldsymbol{E}\times\boldsymbol{B}$ modes. This numerical framework provides a powerful tool for modeling sub-Doppler cooling techniques and for optimizing future quantum sensing and quantum information experiments.

quant-ph↗
arXiv2026

Hydrodynamics of microalgae in sea spray

Airborne transmission of biological matter is likely to cause numerous respiratory distress in coastal populations during certain harmful algal blooms. While we know that dissolved algal toxins aerosolize, the contribution of particle-associated toxins is still unknown. The observation of microalgae in the atmosphere suggests that cells or cell debris could be a carrier. Exchange of particulate matter between ocean and atmosphere is driven by sea spray: microplastics and bacteria aerosolize in jet droplets, following the bursting of air bubbles. However, current models for particle capture only consider surface effects, which fail to explain how large microalgal cells (5-50 um) can be entrapped in jet drops (100-800 um). Here, we demonstrate with a variety of species that microalgae are consistently captured in jet drops, and derive a new particle capture model based on the hydrodynamics of the jet. Using the enrichment factor, which measures the increase in concentration in the first jet drop relative to the bulk, we uncover two regimes. The transition between regimes strongly depends on cell size. In addition, we highlight the dynamics of particles within the jet and derive an enrichment model based on hydrodynamics rather than surface considerations. This work widens and generalizes established results on bacterial and microplastic entrapment in jet drops, resolving discrepancies found in the literature. Finally, we demonstrate that sea spray can aerosolize toxic Ostreopsis cf. ovata cells. This reveals a potential particulate pathway for airborne toxicity during harmful algal blooms and raises the question of the relative contribution of particles to that of dissolved toxins.

cond-mat.soft↗
arXiv2026

Bio-Inspired Auditory Processing: Coupling Parallel Resonate-and-Fire Dynamics with Ternary Recurrent Networks for Speech Recognition

Spiking Neural Networks (SNNs) promise energy-efficient inference through sparse, event-driven computation, yet remain constrained on continuous, context-dependent tasks such as automatic speech recognition (ASR). A key bottleneck is the Leaky Integrate-and-Fire (LIF) neuron, whose membrane decay erases information across pauses and phonetic boundaries while it must both extract features and retain long-range context. Inspired by cortical separation of nonlinear filtering and somatic integration, we introduce the Spiking Ternary GRU (stGRU): a ternary-weight gated recurrent unit performs temporal filtering, while downstream Resonate-and-Fire (RF) neurons generate the binary spike stream driving the next block's event pathway. This makes binary event transmission a native training constraint rather than a separate deployment-time activation quantization step; together with ternary weights, learned projections avoid dense floating-point matrix MACs. Trained end-to-end on LibriSpeech-960, Small, Medium, and Large stGRUs reach 8.09%, 7.04%, and $6.44 \pm 0.17\%$ WER on test-clean without an external language model. To our knowledge, these are the first matrix-MAC-free spiking networks without a learned ANN sequence decoder to achieve single-digit WER on LibriSpeech. The architecture also achieves 10.88% test CER on Aishell-1 (9.28% on dev) when trained from scratch. Internally, trained networks develop a depth-graded hierarchy: shallow layers act as fast acoustic filters, while deep layers form slower semantic integrators whose latent representations segregate into part-of-speech manifolds and word-level spike events. Deep-layer firing rates follow lognormal distributions with a sparsity gradient, mirroring hierarchical processing observed in human cortex in vivo. Our biologically grounded architecture combines competitive ASR with favorable modeled compute and memory cost.

cs.SD↗
arXiv2026

Higher rank spectral projector estimates and a Stein--Tomas restriction theorem

Let $X$ be a compact locally symmetric space of noncompact type. We prove sharp upper bounds for the $L^2\to L^p$ operator norms of spectral projectors for joint eigenfunctions of the full ring of invariant differential operators on $X$. This improves the corresponding result of Marshall, by removing a logarithmic power loss at the critical exponent. Using the same method, we also prove the endpoint case of Mockenhaupt's $(L^2,L^p)$ Fourier restriction theorem.

math.AP↗
arXiv2026

Retrieval Augmented Generation Compositionality

Retrieval Augmented Generation (RAG) grounds large language models in external knowledge. Modern pipelines combine embedding, chunking, retrieval, reranking, query augmentation, context compression, and agentic verification, yet these techniques are typically evaluated one at a time. It remains unclear whether their isolated gains survive composition, whether retrieval quality and answer faithfulness favor the same design choices, and whether conclusions from small corpora hold at large scale. We pre-declare three hypotheses and introduce LASAGNA, an open-source framework for controlled RAG evaluation. We test 450 configurations across eight benchmarks and corpora ranging from 5K to 200K documents. Three findings emerge. First, individually strong techniques from different phases of a RAG pipeline do not necessarily compose: three retrieval techniques predict a +47% combined improvement but deliver only +17% when used together. Second, component gains stack differently for retrieval and faithfulness, and optimizing one can hurt the other. Third, the best composition changes as the corpus grows: the combination that wins on a small corpus may not remain best at large scale. These findings show that gains measured in isolation are not reliable predictors of realistic performance, and that new RAG techniques should be tested with the full surrounding stack. We call on researchers to do so and supply LASAGNA to simplify these experiments.

cs.CL↗
arXiv2026

Accelerated primal-dual dynamics and algorithms for strongly convex-concave bilinear saddle point problems

In this paper, we develop accelerated primal-dual dynamics and algorithms for strongly convex-concave saddle point problems with bilinear coupling. Combining strongly convex Nesterov dynamics with scaled heavy-ball dynamics, we propose a second-order primal-dual dynamical system with constant damping and derive an associated algorithm by time discretization and coefficient adjustment. Under suitable conditions on the continuous scaling function $β(t)$ and the discrete scaling sequence $β_k$, we establish primal-dual gap estimates of $\mathcal O(1/β(t))$ in continuous time and $\mathcal O(1/β_k)$ in discrete time. The maximal admissible growth rates of these scales recover the exponential and linear convergence rates of strongly convex Nesterov methods in continuous and discrete time, respectively. We also prove convergence of the primal-dual trajectory and sequence, even when the dual solution is nonunique. Saddle residual estimates of $\mathcal O(1/\sqrt{β(t)})$ and $\mathcal O(1/\sqrt{β_k})$ hold under globally Lipschitz gradients in continuous time and with a possibly nonsmooth dual potential in discrete time. Numerical experiments illustrate the theoretical results and the performance of the proposed methods.

math.OC↗
arXiv2026

Sufficient and Necessary Causal Explanations for the Analysis of Autonomous Systems

Understanding failures of autonomous systems is challenging, particularly when their behavior depends on black-box components such as neural networks. In this work, we make a distinction between two objectives of failure analysis: reproduction, which seeks to identify conditions sufficient to reproduce an observed failure, and avoidance, which seeks to identify the changes required to prevent it. Previous work on causal explanations of system failures is based on the concept of sufficient explanations and naturally supports reproduction. Nevertheless, we observe that it does not address the problem of avoiding the failure. In this paper, we introduce and formalize the concept of necessary explanations for system analysis as the correct formalism for failure avoidance. We place necessary explanations in the framework of actual causality and show that, together with sufficient explanations, they provide a unified causal framework for addressing both objectives of failure analysis. We present an efficient approximation algorithm for generating necessary explanations based on the notion of causal responsibility. We evaluate the efficiency of our approach across multiple environments. We demonstrate the practical utility of necessary explanations for failure avoidance through counterfactual generation and show that it outperforms existing methods.

cs.RO↗
arXiv2026

Structure-Aware Message Passing on Petri Nets through Directed Walks and Incidence Diffusion

A common application of the process mining discipline is to connect observed event data with Petri nets, which are bipartite, directed graphical process models with rich formal underpinnings. Recent work learns vector representations of Petri nets to retrieve process models and relate them to event logs, but leaves implicit two key aspects hidden within the net's structure: directed cycles (process loops) and invariants recorded by the net's incidence matrix. We expose both of these to message-passing graph neural networks, through a positional encoding built from return probabilities of directed place-transition walks (PNRWPE), and through same-type messages gated by diffusion kernels of the incidence matrix (DA-PNGNN). Our constructions raise macro balanced accuracy in predicting the generation factors of the 96 Process Discovery Contest 2023 models from 0.751 to 0.796 with PNRWPE, which nearly doubles accuracy on process loops, and to 0.830 with DA-PNGNN, which, without retuning, also improves net-to-tree retrieval top-1 accuracy on the self-supervised ProcRosetta benchmark by 4.1 to 5.9 points.

cs.LG↗
arXiv2026

Mellin Moments of Proton Unpolarized GPDs at Nonzero Skewness from Lattice QCD with a Neural-Network Parametrization

We use lattice QCD to determine the generalized form factors (GFFs) entering the first four Mellin moments of the unpolarized isovector $u-d$ proton GPDs at nonzero skewness. The framework combines the polynomiality of the moments in the skewness $ξ$, with the short-distance expansion formalism, allowing the lattice-extracted reduced Ioffe-time distributions (ITDs) to be expressed in terms of GFFs. In order to extract the GFFs by fitting these relations to the lattice data, we parameterize each GFF with an artificial neural network (ANN) as a continuous function of the invariant momentum transfer squared $t$, which accommodates the kinematic coverage of the data in a flexible way. With this fit, we determine the fourteen GFFs that enter the first four Mellin moments, including the skewness-dependent GFFs. From the extracted GFFs, we obtain the quark total angular momentum of the isovector combination, $J^{u-d}=0.296(11)(7)$ in the $\overline{\mathrm{MS}}$ scheme at $μ=2~\mathrm{GeV}$, in agreement with previous lattice determinations based on nonlocal operators and with a smaller total uncertainty. We also determine the impact-parameter distributions of the first three Mellin moments in an unpolarized and in a transversely polarized proton. We finally identify and discuss the principal systematic uncertainties which enter this extraction, and the challenges specific to the nonzero-skewness regime.

hep-lat↗
arXiv2026

Accept or Repair: Preserving Passage-Supported Answers in Contrastive Decoding

Large language models often answer from knowledge learned during training, even when a provided passage contradicts that knowledge. To address this problem, contrastive decoding contrasts the predictions under the full and a modified prompt at every token, but it also alters correct answers that the passage supports. We show that checking answers against the passage removes this trade-off. Based on this observation, we propose Accept-or-Repair (AoR), a training-free procedure. AoR keeps a sampled answer if the passage supports it. Otherwise, it tries up to two replacements with contrastive decoding, returning one as soon as it passes this check. It rejects replacements that repeat the answer generated without the passage when the passage favors another answer. Our experiments show that AoR raises the score over sampling by 12.5 points on counterfactual passages and 2.3 on ordinary ones, surpassing eight contrastive and prompting baselines on both, including when each receives the same rejection rule. Replacing only initial answers that the passage does not support improves the average score of every decoder. These results suggest that models can follow passages that contradict their knowledge while preserving accuracy on passages that agree with it. Code will be released at https://github.com/js-lee-AI/AoR.

cs.CL↗
arXiv2026

Model Predictive Control: Systematic Design Tailored to Nonholonomic Systems

Nonholonomic systems are ubiquitous in applications such as transportation and robotics, yet their control remains challenging. In order to achieve asymptotic stability of a desired equilibrium, model predictive control (MPC) schemes without stabilizing terminal conditions have recently been proposed for nonholonomic kinematic systems. However, this approach still required lengthy system-specific calculations. This paper eliminates the need for these auxiliary calculations, as we propose a streamlined systematic design for MPC stage costs tailored to nonholonomic systems, utilizing the concepts of privileged coordinates and nonholonomic weights. Furthermore, the proposed design methodology is extended beyond purely kinematic models to a wider class of systems with non-negligible dynamics, and we highlight the geometric meaning of the resulting MPC stage costs. The systematic procedure is demonstrated using an articulated vehicle as an example.

math.OC↗
arXiv2026

Intertwined complex orbital order and ferrimagnetism in honeycomb molybdate Fe$_2$Mo$_3$O$_8$

Motivated by the recent experimental interest in honeycomb molybdates A$_2$Mo$_3$O$_8$, we return and develop the minimal models to capture the essential physics for Fe$_2$Mo$_3$O$_8$. It is pointed out that, the magnetism in these materials arises from the mutual induction between the spin-orbit coupling of the tetrahedral sublattice with active orbitals and the superexchange with the spins from the octahedral sublattice. Essentially, the superexchange between the tetrahedral and octahedral sublattices directly drives the ferrimagnetism, and the residual spin-orbit coupling on the tetrahedral sublattice induces the complex orbital order. The hybrid magnon-phonon excitations are further explored together with their resulting Berry curvatures and thermal Hall effect. We discuss the experimental relevance with Fe$_2$Mo$_3$O$_8$, and the framework can be extended to FeNiMo$_3$O$_8$, Ni$_2$Mo$_3$O$_8$ and other isostructural magnets.

cond-mat.str-el↗
arXiv2026

Post-hoc Epistemic Uncertainty for Vision-Language-Action Policies

Vision-language-action (VLA) policies need to recognize gaps in their training knowledge to request useful demonstrations or assistance in new situations, especially when failures are costly. Disagreement within an ensemble of independently trained policies can guide these decisions, but requires training and running multiple policies. We propose post-hoc kernel-variance heads that estimate epistemic uncertainty from the embeddings of a single policy. Each head computes the conditional variance of a Gaussian process conditioned on embeddings from the training demonstrations. Fitting requires no regression targets or gradient updates and leaves the policy unchanged. In experiments with SmolVLA on LIBERO-10, the kernel variance heads perform competitively with two-policy ensemble scores in task-level correlation with task success, in demonstration acquisition during active learning, and in referral to a stronger supervisor policy as a proxy for human assistance. For SmolVLA, the head on the vision-language backbone reduces uncertainty-scoring time by up to approximately a factor of 50 compared with ensemble scores, while also substantially reducing setup costs. We also show that the established evaluation protocol on LIBERO-10 primarily rewards recognition of coverage differences between tasks, while execution variability weakens assessment of within-task rankings. Thus, controlled perturbations provide a complementary evaluation: modality-specific heads identify unfamiliar camera, instruction, or state inputs, while fused heads can detect unfamiliar combinations of individually familiar inputs. With a supervisor proxy trained on the evaluated perturbation families, the decoder head improves within-task referral over ensemble disagreement. These findings show that useful uncertainty estimates for adaptive robot learning can be obtained from a single policy.

cs.RO↗
arXiv2026

Computing the Nucleon of Matching Games

The nucleon is the multiplicative counterpart of the nucleolus: it lexicographically maximizes the fraction of its stand-alone value that each coalition receives. We study exact nucleon computation in matching games and in two extensions: $b$-matching games, in which players may have several partners, and partitioned matching games, in which one player may own several vertices. We resolve three open problems from a recent survey. For ordinary matching games with nonnegative rational weights, we give a polynomial-time combinatorial algorithm using maximum-weight matching, shortest paths, and minimum-cost flow, ; it returns both a nucleon allocation and a compact description of the full nucleon. In contrast, computing any nucleon allocation is NP-hard for unit-weight $b$-matching games with capacities at most three and for unit-weight partitioned matching games of width at most three. Finally, for the unresolved capacity-two case, we show that exact nucleon computation is polynomial-time Turing reducible to SHORTEST NON-ZERO CYCLE.

cs.GT↗
arXiv2026

BCC optimality for the three-dimensional Coulomb lattice energy

We prove that the body-centered cubic lattice uniquely minimizes the renormalized Coulomb energy among three-dimensional Bravais lattices of fixed covolume, up to orthogonal transformations. Using Ewald summation, we write the energy, to within an additive constant, as a sum of two positive, rapidly convergent series in real and reciprocal space. Their positivity provides finite lower bounds for all competitors. A passage to the dual lattice reduces the problem to a face-centered cubic comparison. A short basis vector estimate, a certified local Hessian, and interval bounds on a compact five-dimensional domain complete the computer-assisted proof.

math-ph↗
arXiv2026

SAKURA: Serving Attention Key-Value State Under Rate Adaptation for Private Image Editing on Phones

Diffusion transformers are widely used in image-editing services. To preserve both efficiency and privacy, existing systems commonly rely on cloud-device collaboration. Keeping request-specific inference on the device avoids sending personal images and prompts to the cloud. These workloads often use common templates, such as in face swapping and virtual try-on, enabling KV state to be precomputed and reused across requests. However, this reusable state is large and scales with the number of templates, making it impractical to store all of them on mobile devices. Storing them in the cloud addresses this capacity issue, but cache transfer is placed onto the inference path and can even be slower than on-device computation, especially under fluctuating mobile networks. We introduce SAKURA, a cloud-edge architecture that delivers reusable attention state to mobile devices under a bandwidth budget. It first uses a fine-grained token-importance-aware compression method to preserve image quality under limited transfer budgets. At runtime, SAKURA adaptively selects the cache representation for each upcoming shard based on network bandwidth. To enable efficient execution, we develop a pipelined runtime that overlaps cache transfer and reconstruction with on-device execution. We evaluate SAKURA using three editing tasks and two diffusion models, using a Snapdragon 8 Elite Gen 5 phone. SAKURA reduces latency by 1.82x and 3.27x over CacheGen adapted to DiT and on-device generation, respectively. It also reduces cache storage by 3.06x over uncompressed cache, while preserving image quality.

cs.SE↗