Papers

A connected skew brace of finite Morley rank is left nilpotent (resp. weakly soluble) whenever the additive and multiplicative groups are nilpotent (resp. are soluble and the left chief length is at most 3).

Group recommender systems typically rely on either aggregating individual preferences or treating groups as distinct meta-users. However, these methods often suffer from static aggregation strategies or data sparsity issues within group histories. This paper introduces a novel approach, that relies on a GNN-based architecture to learn a dual representation of each user's preferences, capturing their behavior as an independent individual from one side and as a member of a collective from the other side. By performing a differential analysis of these individual and group-oriented preferences, our system then determines the behavioral profile of each user when joining a group. Finally, specific preference aggregation strategies are defined to cope with the behavioral profiles of the users composing a group. Consequently, the system is equally capable of delivering precise recommendations to individuals and to arbitrary groups, effectively unifying the two traditional paradigms of recommendation. Experiments on synthetic data simulating diverse group settings and behaviors confirm the flexibility and relevance of the proposed approach compared to state-of-the-art methods.

The interactions between post-asymptotic giant branch (post-AGB) binaries and their circumbinary disks play a central role in shaping the evolution of these systems. Circumbinary disks around post-AGB binaries are stable, though relatively short-lived structures ($10^4-10^5$ years) and their physical properties and evolution remain poorly understood. In this study, we target IRAS 08544-4431, one of the best-studied post-AGB binaries. This system has well-constrained stellar and orbital parameters, exhibits well-defined characteristic refractory-depleted photospheric chemistry, and hosts a stable, sub-Keplerian circumbinary disk extending from a well-resolved sublimation rim at approximately 8 au to outer radii of approximately 1 000 au. We probe the disk layers close to the midplane using ALMA Band 7 continuum and $^{12}$CO $J=3-2$ observations of IRAS 08544-4431 obtained with baselines up to 16.2 km. These data provide the finest angular resolution yet achieved with ALMA for dust-continuum observations of post-AGB binaries with a (almost) face-on disk (15 au; 10 mas). The resulting map of dust continuum enabled resolving disk inner rim, a largely smooth radial profile, and a prominent azimuthal asymmetry at a radius of $\sim$45 mas. Notably, the location of this dust asymmetry coincides with the forward-scattering peak reported in SPHERE/VLT observations of IRAS 08544-4431. The $^{12}$CO emission is more extended than the dust continuum and confirms the disk rotation in this system. However, the global $^{12}$CO map shows indications of a spatial offset from the dust asymmetry, suggesting some degree of gas-dust decoupling. Together, these observations establish IRAS 08544-4431 as a key laboratory for studying disk and dust evolution in a parameter space distinct from that of young stars with protoplanetary disks.

Privacy-sensitive organizations may run large language models (LLMs) in restricted or air-gapped environments while exporting selected diagnostic artifacts. We show that a compromised runtime component can hide sensitive information in intermediate activations that are allowed to leave the restricted environment. An offline observer can recover this information with a simple linear decoder. The attack requires no model retraining or weight modification, no attacker-controlled egress, and no control over the recorder or transfer process. We introduce a residual-stream covert-channel attack that maps messages to codewords and injects them into an intermediate residual stream through a compromised runtime hook. To maintain recoverability, the injection strength is scaled with the local residual norm using the signal-to-residual-norm ratio. Across eleven models from seven architecture families, our evaluation shows 91–100% recovery on nine models with KL divergence 0.001–0.007, while evaluated activation-level detectors remain close to random guessing (AUC <= 0.56). Tested post-hoc defenses do not reliably eliminate the channel. Thus, an activation artifact can be schema-valid while carrying information that is not authorized to cross the boundary.

The anisotropic evolution of relativistic particles in magnetically dominated Alfvénic turbulence is a fundamental process governing nonthermal emissions in high-energy astrophysical environments. In this work, we develop a theoretical framework by deriving scaling equations that characterize the pitch-angle dynamics of leptons and photons across both weak- and strong-radiative cooling regimes. Our model reveals a universal coupling between particle energy and angular distribution, arising from the interplay of field-aligned accelerations, perpendicular drift motions, and radiation reactions. The model can uniquely identify “turning-point energies" that exhibit a nonlinear dependence on the local magnetic field and the energy-injection scale. The validity of this scaling model is confirmed through radiative particle-in-cell simulations. We show that the electron pitch-angle distribution fundamentally dictates photon emission characteristics, further revealing a pronounced statistical correlation between high-energy photon emission and turbulent vortices in the reconnection regions. By bridging the gap between small-scale kinetic interactions and broad-band spectral characteristics, this work provides a quantitative basis for interpreting the hardening of radiation spectra and complex polarization signatures in sources such as pulsar wind nebulae and gamma-ray bursts.

Financial institutions are beginning to deploy agentic workflows in credit, fraud, collections, compliance, and operational control. Governance remains largely component-centric: each model or agent is specified, tested, authorized, and monitored locally. That is insufficient when institutional risk arises from the joint behavior of many locally acceptable components. We call this gap constitutional non-compositionality: local compliance checks need not compose into acceptable collective outcomes such as bounded disparate impact, market integrity, or traceable accountability. We propose ARIA as a finance-specific reference architecture and falsifiable research agenda for agent-population governance. It organizes six capabilities across normative-accountability, execution-control, and assurance-learning planes: policy specification, population-level observed-versus-expected behavior monitoring (M2), bounded authority, runtime containment, adaptive policy change, and preserved human oversight competence. Two simulations illustrate shared-signal thin-file exclusion under local controls and earlier warning from observed-versus-expected distributional monitoring in a constructed drift regime. The contribution maps these controls to fair-lending, EU AI Act, model-risk, and conduct-supervision evidence needs, and closes with a validation agenda rather than a production-effectiveness claim.

We establish a sufficient condition under which overlapping PEPS boundary states satisfy the approximate factorization criterion for a spectral gap. The condition is formulated in terms of the boundary response induced by cutting bonds through the center of a rectangular region. We decompose this response into a contribution common to all four associated regions and a remainder measured in the instantaneous boundary metric. A single linear transport absorbs the common contribution and yields compatible factorization operators, with an error controlled solely by the remainder. We apply this framework to Ising PEPS and to the spin-3/2 AKLT model on the hexagonal lattice. For Ising PEPS, the required boundary-response estimate reduces to a Dobrushin-Shlosman-type condition. For the hexagonal AKLT model, a rooted expansion in paths and loops isolates the common response, while a local comparison of boundary states together with a scalar Kotecký-Preiss estimate controls the remaining terms. In both cases, the factorization error decays exponentially with the overlap width, up to a prefactor proportional to the cut length. For AKLT, we establish the corresponding physical projector estimate and obtain a uniform spectral gap. For Ising PEPS, the gap implication additionally requires compatible injective regional contractions, as specified in the paper. More generally, the method provides a systematic route from locality of PEPS boundary response to spectral gaps of two-dimensional parent Hamiltonians.

When do orthogonal measurements extract all accessible information? We introduce a posterior algebra for full-rank ensembles. Its commutativity determines whether an information bound is attained; its joint eigenspaces then classify optimal finite-outcome measurements. For two states, we constructively prove Shor's conjecture in finite dimension, including singular states. Orthogonal measurements can fail at fixed guessing error: a discontinuous basis switch forces some qubit pairs to need three outcomes. A Tsallis information score can require three outcomes even without an error constraint.

We settle three conjectures concerning a doubly symmetric binary source $(X,Y)$ with crossover $p$. Consider Markov chains $U - X - Y - V$ with $U,V$ binary, and let $\mathcal{A}$ be the set of rate triples $(I(U;V),I(U;X),I(Y;V))$ attainable with arbitrary binary channels $X\to U$, $Y\to V$, and $\mathcal{B}$ the subset attainable with binary symmetric channels. The averaged BSC conjecture, Conjecture 5.2 of Pichler, Piantanida and Matz (2022), asserts $\operatorname{conv}\mathcal{A}=\operatorname{conv}\mathcal{B}$. We prove this for every $p\in[0,1]$. Two conjectures of Dikshtein, Ordentlich and Shamai (2022) concern the double-sided information bottleneck at $p=0$, where $Y=X$ and the two channels see the same source: their Conjecture 1 identifies the exact maximum of $I(U;V)$ at prescribed rates $I(U;X)$ and $I(Y;V)$, and their Conjecture 2 the exact minimum. We prove both for binary $U,V$: the two extrema are attained by the same pair of Z/S-channels, in opposite orientation for the maximum and in the same orientation for the minimum. The proofs were found with substantial AI assistance, and all three theorems are formalised in Lean 4 with Mathlib, depending only on the standard axioms. The development is available at https://github.com/g-pichler/bsc-averaging . The proof of Conjecture 1 of Dikshtein, Ordentlich and Shamai (2022) contains three certified computations, a polynomial bound, an interval sweep and a polynomial positivity certificate, all of which are checked in Lean.

In this work, we investigate the dynamics of a scalar particle in a black-hole spacetime surrounded by a cosmological constant and an anisotropic fluid. By solving the Klein–Gordon equation through a power series approach, we obtain quasibound states and the corresponding energy quasispectrum. We find that the quasispectrum can exhibit both real and imaginary components, depending on the model parameters, with the real component existing only under specific conditions. The numerical analysis shows that decreasing the cosmological constant and the anisotropic fluid parameter enhances the energy and increases the radiation in the region outside the event horizon, whereas stronger contributions from these surrounding fields tend to suppress the emitted radiation. We also analyze several asymptotic limits and recover the corresponding results for the Kiselev, de Sitter, and Schwarzschild black holes, providing consistency checks for our solutions. These results highlight the role of the surrounding matter distribution and cosmological contribution in modifying the dynamics and radiation of scalar fields in black hole spacetimes.

Rapid growth of data centers and artificial-intelligence services is producing computational loads at scales once associated mainly with largest power plants. Recent grid events show that a routine transmission disturbance can cause several gigawatts of data-center demand to disconnect or transfer to backup nearly at once. This article revisits the classical synchronization and transient-stability theory needed to reason about such events. We organize four lines of work—graph-based synchronization conditions, winding-number descriptions of nonlinear power flow, separable convex network optimization, and direct energy methods—into a single cycle-space certificate framework for the lossless fixed-voltage model. The static layer gives an exact strict-cohesion test within a prescribed winding cell and reveals the widely used Dörfler–Chertkov–Bullo test as a quadratic surrogate of the same convex problem. The dynamic layer converts the critical-energy calculation into a finite family of convex boundary problems. Standard MATPOWER benchmarks illustrate both what the stronger static test gains and where it gains nothing: the 118-bus case admits $16.2\%$ more loading than the sufficient screen, while the 39-bus case is bridge-limited and the thresholds coincide. A stylized $2.7$-GW 39-bus event further shows that transient margin can change by about a factor of two depending on where balancing power is supplied, even when every final balanced operating point remains statically feasible. The result is a tutorial synthesis and an extensible deterministic certificate for emerging gigawatt-scale computational-load contingencies.

Methods operating on Vision Transformer (ViT) feature spaces typically rely on Euclidean distance or cosine similarity. This assumes that every direction is equally meaningful, but there is no reason to believe the true task geometry has this property. The task-sensitive geometry of the feature space is given by the pullback metric $g(F) = J(F)^\top J(F)$, where $J$ is the Jacobian of the decoder's output fed to a task-specific distance, with respect to the features. Storing the full $g$ is infeasible at modern scales, and for dense outputs such as depth maps even forming $J$ is impractical. We show that whether a low-rank approximation of this metric can be learned depends on the model-decoder pair, and we characterize this with a matrix-free diagnostic $\kappa_{cap}(r)$ computable with a low number of Jacobian-vector products. For tractable pairs, we develop the Spectral Pullback Network (SPN), which learns a low-rank version of the metric from randomized power iteration, and we distill it into a $310$K-parameter importance head that predicts token importance directly from the features. When the Jacobian spectrum is too spread out for a low-rank approximation, passing the decoder's input features through a VAE bottleneck can restore tractability. Across DPT, DINOv2, CLIP, and VGGT backbones, $\kappa_{cap}(r)$ predicts which learned-metric architectures are viable. The importance head reaches Spearman $\rho = 0.998$ on DINOv2 CLS, and our geometric token pruning reduces the additional depth error of ToMe-based token selection by $25\%$ on DPT depth at prune ratio $0.5$, without fine-tuning the ViT. Project page: https://cyberiada.github.io/TaskInducedViTs/

Large language models (LLMs) have made substantial progress on medical question-answering, yet effective medical dialogue also requires learning to ask questions that uncover relevant patient information. To train such dialogue policies, a common pipeline combines supervised fine-tuning with reinforcement learning (RL) based on final diagnostic correctness. However, this outcome-based supervision does not directly distinguish the contributions of individual questions and provides no question-level feedback for unexecuted alternatives. To address this gap, we introduce PCQC (Privileged Counterfactual Question Credit), which uses privileged patient information during training to learn from questions never asked. During training, PCQC makes alternative questions directly comparable at the same dialogue state by using privileged patient facts to construct their answers. A frozen diagnostic scorer evaluates the diagnostic utility of each resulting question-answer pair by how strongly it supports the correct diagnosis. PCQC turns these comparisons into relative question credit that teaches the policy which questions to favor, directly supervising both executed and unexecuted questions alongside outcome-based RL without requiring complete rollouts for the unexecuted alternatives. Extensive experiments across four medical benchmarks demonstrate that PCQC achieves 63.10% mean diagnostic accuracy, outperforming GRPO and ATPO by 4.38 and 4.21 percentage points, respectively. These gains are achieved with 33.1% fewer inquiry turns than GRPO.

Accurate remaining discharge time (RDT) prediction is challenging in real-world battery applications because future load profiles are unknown and highly dynamic. To address the uncertainty of continuous RDT regression, this paper introduces Relative Discharge Stage (RDS), a battery-management indicator that represents the remaining discharge condition using five interpretable classes: Normal, Good, Moderate, Low, and Recharge Required. Unlike state of charge (SOC), which reflects the current charge level, RDS characterizes the remaining discharge process without requiring future-current information during inference. A physics-informed RDS classification framework is proposed, combining SOC estimation with lightweight temporal learning. The SOC-estimation component includes second-order ECM state and terminal-voltage prediction, hysteresis and OCV temperature correction, core-temperature estimation, and AEKF state correction, supported by OCV evaluation, online STC-ECM parameter adaptation, and pretrained neural residual-voltage correction. The measured current, terminal voltage, surface temperature, and estimated SOC are arranged into a sliding observation window and processed by a lightweight temporal convolutional network. Experiments on two public lithium-ion battery datasets demonstrate robust RDS classification, with accuracy exceeding 80% under varying load and thermal conditions.

Transverse momentum dependent parton distributions are objects that have gained substantial attention in the recent past as they are crucial for studying the 3-D structure of proton. These distributions at twist-3 are important for understanding phenomena like beam single spin asymmetries, which are observed in high-energy scattering experiments. However, due to the unavailability of direct phenomenological fits, currently one has to rely on simplified models of the proton in order to obtain these twist-3 distributions. In this work, we present the calculation of T-even twist-3 quark distributions using the quark target model.

In this paper, we consider the complexity of enumerating inclusion minimal defensive alliances. We present a polynomial-delay algorithm on graphs with maximum degree 5. We complement this result by proving that there is no output-polynomial algorithm on bipartite graphs with maximum degree 6 and degeneracy 2, unless P = NP. Furthermore, there is an FPT-delay algorithm when parameterized by neighborhood diversity. This result is the first exploit of a recently published enumeration algorithm for ILPs. By way of contrast, we prove that, for the parameter pathwidth, there is no FPT-delay algorithm for enumerating all inclusion minimal defensive alliances (unless FPT = W[1]). To the best of our knowledge, this is the first non-enumerability result using parameterized complexity for variations of Another/Next-problems.

We introduce cavity Rydberg quantum photonics as a novel platform for generating hybrid entangled states of optical photons. The system achieves world-record sizes of these states and has the potential to produce yet larger states in the future. In the hybrid entangled state produced here, a superposition of two coherent states is entangled with a polarization qubit carried by a photon in another beam path. We perform quantum state tomography of this hybrid entangled state and evaluate various key properties. By optimizing the decoherence we increase the size compared to previous hybrid entangled states, reaching a size of $\alpha^2= 2.4$. Besides the fundamental interest in Schrödinger cat states, this work is interesting because of potential applications in the field of quantum information processing.

In this paper, we are concerned with matrices formed by block-diagonal factors interleaved with fixed permutations – a flexible family of structured matrices. This class has recently drawn interest in deep learning architectures for its balanced expressivity-efficiency trade-off, yet efficient computational strategies for working with it remain to be found. We approach this problem through Riemannian geometry and examine under what conditions this class admits a smooth manifold structure. For the practically important case of orthogonal two-factor matrices, we derive the essential Riemannian tools and propose efficient algorithms for their implementation. The algorithms leverage automatic differentiation, support parameter sharing within each factor, and avoid explicit dense matrix construction. We test them within the Riemannian optimization framework on the best matrix approximation problem and for parameter-efficient fine-tuning of large language models. Beyond the two-factor setting, we study the geometric and matrix-theoretic properties of factorizations with a larger number of block-diagonal factors.

KV-cache eviction is typically evaluated through average quality-memory trade-offs, yet a small average loss can hide requests whose utility degrades materially. We reformulate eviction as a deployment risk-control problem: a material degradation occurs when eviction lowers task utility by more than a deployment-specified tolerance relative to full-KV inference on the same request, and deployment risk is the population frequency of such events. Given a reliability contract specifying a target risk level and confidence requirement, we use a compressor-agnostic post-hoc certification procedure to select a retention policy from calibration data with a finite-sample guarantee, falling back to full KV when no compressed policy is certified. Across multiple eviction methods, Llama and Mistral models, and LongBench and RULER-32K, the same contract supports substantially different levels of eviction: on Llama, it certifies SnapKV at 75% retention on LongBench but no tested compressed policy on RULER-32K, triggering full-KV fallback. Policies with empirical degradation rates below the 5% target can still fail finite-sample certification; on Llama LongBench, empirical thresholding selects uncertified policies that retain 5-10 percentage points less cache across fixed-budget methods. The proposed framework converts a deployment-level reliability requirement into a KV-memory operating point.

Pruning large pre-trained transformer-based ASR models such as OpenAI's Whisper has seen great adoption, as pruning the decoder led to significant end-to-end transcription speedups. For instance, the whisper-large-v3-turbo variant reduced the decoder from 32 to 4 layers, while Distill-Whisper similarly reduced the decoder to only 2 layers. Although some attention has been put towards reducing the size of the encoder, no approach has seen wide adoption. This could be due to the need for custom inference implementations to take advantage of the compressed model. We present an approach that ranks encoder layers by the leave-one-layer-out change in Word Error Rate (WER). The six layers that cause the least change are removed, corresponding to $18.5\%$ of the encoder stack. The pruned model requires no custom inference code as it is simply a more shallow encoder with fewer layers. We further distill using unlabeled monolingual speech data to recover performance degradation caused by the zero-shot layer pruning. Mean WER across four languages increases to $20.1\%$ after distillation, compared to $21.9\%$ zero-shot, going from a baseline of $18.2\%$. We release all of our code (https://github.com/rasgaard/whisper-encoder-layer-prune) and the pruned model (https://huggingface.co/rasgaard/whisper-large-v3-turbo-encoder-pruned).

We study a one-parameter family of SO(4)-invariant pluriclosed Hermitian metrics $g_c$ with vanishing Bismut Ricci form on the affine quadric $Q_3\cong TS^3$, previously described in the physics literature. For every real parameter $c$, we prove local existence and uniqueness of a real-analytic solution to the defining singular initial-value problem, together with positivity of the associated metric near the singular orbit $S^3$. We then establish global existence and completeness for $|c|\leq1$ and finite-time degeneration for $|c|>1$. The complete family exhausts all SO(4)-invariant Bismut Hermitian-Einstein metrics on the affine quadric $Q_3$, and joins Stenzel's Kähler Ricci-flat to a metric that was first considered by Chamseddine-Volkov/Maldacena-Nuñez. We also determine the leading asymptotics and derive an explicit scalar curvature formula, proving strict positivity for the non-Kähler members and identifying the change in asymptotic scalar curvature at the endpoint $c=1$. Finally, we show that all these metrics are not Bismut flat and have full Bismut holonomy SU(3), providing new examples of such manifolds.

Supercooled phase transitions can generate observable gravitational waves, but their bubble dynamics may also imprint large spatial inhomogeneities in the baryon asymmetry. For phase transitions below the TeV scale, ordinary baryon diffusion can be too slow to erase such inhomogeneities before Big Bang Nucleosynthesis, potentially leading to stringent constraints from the observed light-element abundances. We show that this problem can be naturally avoided in darkogenesis scenarios, where the phase transition first generates an asymmetry in a dark-sector particle that is subsequently transferred to visible baryons. The dark-sector particle can travel over much larger distances than ordinary baryons before decaying, erasing the inhomogeneity before the baryon asymmetry is established. We derive the conditions for efficient erasure in both the diffusive and collisionless transport regimes and translate them into constraints on the dark-sector interactions. For a representative dark phase transition with a reheating temperature of $\mathcal{O}(1) \,\mathrm{GeV}$, $\beta/H \simeq 10$, and a dark-sector particle lifetime of $0.1\,\mathrm{s}$, we find that the inhomogeneity is efficiently erased for a viable range of the interactions. Importantly, baryogenesis before the phase transition is challenged both by dilution from strong supercooling and by the subsequent imprinting of spatial inhomogeneities. This points toward darkogenesis associated with the phase transition as a consistent framework, in which dark-sector transport erases the inhomogeneity before it is transferred to visible baryons.

Bayesian Federated Inference (BFI) estimates statistical models from multicenter data when individual-level observations cannot be combined across centers. We present \pkg{BFI}, an \proglang{R} package that implements this methodology for Gaussian, binomial logistic, and survival regression models. Each center performs a Bayesian maximum a posteriori analysis and sends only parameter estimates and curvature information to a central server, where these summaries are combined to approximate the analysis of the combined data. The package supports prior specification, structured forms of between-center heterogeneity, several parametric and flexible baseline-hazard models for survival analysis, and treatment-effect estimation for observational and randomized studies. We describe the software design and the information exchanged between centers, give reproducible workflows for these analyses, and compare the federated results with pooled-data analyses for Gaussian, logistic, and survival models.

Video is a rich representation of a physical event, capturing appearance, geometry, motion, and temporal evolution. Other modalities, such as 3D body motion or audio, encode narrower aspects of the same event. We find that joint multimodal diffusion transformers exhibit a corresponding asymmetry in cross-modal correspondence: companion modalities develop strong correspondences to video, but the reciprocal correspondences through which they constrain video remain substantially weaker. We express both directions as comparable correspondence distributions over video tokens and define their disagreement as the reciprocal correspondence gap. We introduce RecCAR, standing for Reciprocal Cross-modal Attention Regularization, a KL regularizer that uses the well-established video-to-modality correspondence as a fixed reference and aligns the weaker modality-to-video correspondence toward it. Across joint video-motion and video-audio generation, RecCAR improves the Human Anatomy score from 0.69 to 0.75 and reduces audio-video desynchronization from 0.804 to 0.752, while improving overall generation

We prove that $S^1$, ${\rm SU}(2)$, and ${\rm SO}(3)$ are compact amalgamation bases: for each of these groups, any two compact groups with specified embedded copies of it embed in a compact group in which those copies agree. For compact Lie groups, the amalgam can be chosen to be a finite-dimensional unitary group. This research was conducted with substantial AI assistance, including in the development of mathematical constructions and proof arguments.

We study the topological non-Abelian string and its classical stability in models with two Higgs fields to achieve the symmetry breaking of ${\rm SU}(N) \otimes {\rm U}(1)_X\to {\rm SU}(N-1) \otimes {\rm U}(1)_{X^\prime}$. The topological origin is due to the global $\widetilde {\rm U}(1)$ symmetry and its breaking in the scalar potential. The most generic winding configurations of arbitrary integers of $(n_1\,, n_2)$ are considered. The stability of the topological string is analyzed based on the time-dependent perturbations to the string background and numerical solutions to the coupled Helmholtz equations of the perturbed Fourier modes. We present the constraints on the stable regions for the $(n_1\,, 0)$ configuration (or equivalently the $(0\,, n_2)$ configuration). For the general winding configurations of $(n_1\neq 0\,, n_2\neq 0)$, we point out the stable regions only exist in the semilocal limit of the large mixing angle of $\vartheta_N\to \frac{\pi}{2}$.

In this work, we consider the problem of uncertainty estimation of the results obtained through theoretical calculations using a composite quantum chemistry scheme. Each component of the composite scheme carries its own individual uncertainty, originating principally from a finite size of the basis set used in the calculations. Of practical interest is the total uncertainty, i.e. the uncertainty of the sum of all components. We first show that the conventional error propagation rules that treat each component as a statistically uncorrelated variable are not well-justified in practice. To remedy this, we propose a method of estimating the total uncertainty of the composite scheme which does not rely on the assumption that the components are independent. It is formulated as a series of random walks with different starting values that represent the uncertainty of each component of the composite scheme. This method is first applied to two example composite schemes for the water dimer and the nitrogen molecule that illustrate its most salient features and allow for a deeper analysis. Next, the method is tested for a larger set of interaction energies from the S66 dataset for which trustworthy reference data are available and the error can be assessed unambiguously. It is shown that the method provides reliable and reasonably tight uncertainty estimates at an arbitrary predefined confidence level required in a given application. While the focus of the paper is on composite schemes, we believe that the general idea can be useful more broadly in computational chemistry and physics.

The surge in AI-assisted generation of educational materials has outpaced our capacity to validate their pedagogical quality. Automated evaluation using Bloom Classifier models is a promising approach to assess educational materials at scale. These models show high accuracy within-distribution dataset (IID Dataset). However, applying the same models to new out-of-distribution (OOD) datasets such as AI-assisted generated questions could show performance degradation. To identify robust classifiers under dataset shift, we evaluated traditional Machine Learning (ML), transformer, and Large Language models on the Bloom level classification task. We also explored feature-engineering strategies incorporating NLP metrics, appending the learning objectives as part of the input, and text splicing to stabilize OOD performance. Our baseline tests show that TFPOS-IDF ML models perform poorly on OOD (Macro F1-score 0.48) compared to BERT (0.55) and LLMs (0.79). Text splicing improved macro F1-score performance of ML and BERT models (0.59 and 0.62, respectively). Appending the learning objectives with the input increased model performance on specific dataset. Model retraining provided the largest improvement across models and datasets. Overall, these findings highlight the trade-off on the use of pre-trained models with novel AI-assisted educational questions and how strategic feature enhancements help address loss in performance.

In an $n$-dimensional cropped hypercube each of the $2^n$ cropping inequalities chops off a single corner of the $0$–$1$ hypercube by an $\ell_1$-distance $\rho$. The case $\rho = 1/2$ has been extensively studied in the literature. This paper shows that the Lasserre rank of the $n$-dimensional cropped hypercube where $\rho = 1/2$, $n \geq 2$, is the smallest integer $0\leq t \leq n$ such that $\Delta_t < 0$ in the recurrence $\Delta_{-1} = 1$, $\Delta_{0} = n-1$, $\Delta_t = (n-1)\Delta_{t-1} - t(n-t+1)\Delta_{t-2}$. It follows that the Lasserre rank can be computed in time $O(n^2 \log^2 n)$. Asymptotically, the rank is $\frac{n}{2} + c_{1/2}\sqrt{n} + o(\sqrt{n})$, where $c_{1/2}$ is the unique zero of a given function. Numerically, $c_{1/2} \approx 0.3825$. In fact, we prove such results for any fixed $0 < \rho < 1$.

Vision-language-action models (VLA) promise human-steerable autonomous driving, but their training is bottlenecked by the scarcity of frames paired with natural-language instructions: while camera streams and expert trajectories are logged at scale, language annotations (e.g., turn left at the intersection) remain scarce and expensive to acquire. To address this challenge, we introduce Latent Action Driving Annotations (LADA), a three-stage pipeline that transforms abundant unlabelled observation-trajectory pairs into a substrate for language-conditioned control. First, we train a latent action model with a vector-quantised bottleneck, producing a compact codebook of high-level vehicle intents. Second, a small language-annotated subset is used to train a vision-language translator to map observations and language instructions into this codebook. Third, we train a driving VLA on observation-latent-action pairs over the full unlabelled corpus. Using fewer than 5% of language annotations and without leveraging any auxiliary chain-of-thought reasoning or visual question answering streams, LADA achieves a Driving Score of 87.98 and a Success Rate of 70.46% on the closed-loop Bench2Drive benchmark, matching or surpassing fully supervised baselines.