Papers

Closed bosonic lattice systems do not generally admit operator norm Lieb-Robinson bounds uniformly in the initial state. The reason is that the information propagation velocity can grow with the local boson occupancy, which can be macroscopically large. Here, we show that local dissipation restores an operator-norm Lieb-Robinson bound. We consider the dissipative Bose-Hubbard model described by a Lindbladian operator with on-site $\ell$-photon loss, $\ell>2$. For our main result, we establish an almost-ballistic Lieb-Robinson bound. Dissipation rapidly depletes highly occupied sites, thus regularizing the state on the Sobolev-type scale of local particle moments. The resulting moment bounds diverge as time approaches zero but remain integrable near zero at sufficiently low orders, which is crucial for our argument. We extend these ideas to treat cat-code dissipation and, for initial states in the code space, we prove a local adiabatic approximation uniform in the total volume. Further consequences include local channel approximation, a thermodynamic limit, and efficient hybrid bosonic-qubit simulation. The point is that these applications are now available uniformly in the input state, as for quantum spin systems, but in contrast to closed Bose-Hubbard systems.

Bio-inspired tendon-driven rigid-soft coupled dexterous fingers exhibit strong nonlinearity and configuration-dependent sensitivity, making accurate modeling challenging. In discrete-time control, Jacobian-based kinematic algorithms typically rely on point-wise local linear approximations, which makes their performance sensitive to sensor sampling frequency and controller update frequency. To address this issue, we propose Jacobian Flow Matching (JFM), a structured learning framework based on Conditional Flow Matching (CFM), to learn a resolution-consistent Jacobian field that models actuation-to-motion transitions as a dynamical flow. The proposed framework supports both single-step prediction and continuous rollout via ODE integration, enabling consistent inference across temporal resolutions. Experiments on a tendon-driven rigid-soft finger show that the proposed method suppresses outlier errors and improves single-step prediction accuracy, reducing the global average RMSE by over 53% compared with a baseline discrete Jacobian learning approach. For long-horizon prediction, trajectories recovered via ODE integration achieve higher fidelity under sparse sampling (Stride = 8), reducing the RMSE median by 14.43% and the error variance by 24.87%. These results demonstrate that the learned flow-based Jacobian field provides an effective local model for offline multi-step trajectory optimization in rigid-soft coupled nonlinear systems.

Large language Models (LLMs) are increasingly used to simulate human decision-making, yet their outputs often under-represent human behavioural heterogeneity. We investigate whether conditioning LLMs on Social Value Orientation (SVO, a measure of how individuals value their own outcomes relative to others') can better reproduce human behaviour in a sequential social dilemma. Using experimental data from two variants of the Centipede Game (CG) as reference, we compare the default behaviour of eight LLMs with behaviour generated after conditioning them on SVO profiles drawn from the human sample. We find that the default strategies vary substantially across models, but are generally distant from the reference distributions. However, conditioning them on SVO profiles systematically steers their strategic behaviour, improving alignment with the human reference by up to 70% with respect to the default. Across models, higher induced SVO values decrease the probability of stopping the game, reproducing the relationship between prosociality and cooperation observed in human behaviour. Together with the sensitivity of LLMs' elicited SVO to prompt and order effects, these results suggest that the usefulness of SVO for behavioural simulation does not depend on LLMs possessing stable social preferences, but rather on their ability to map social preferences onto corresponding strategic choices.

Motivated by hyperconnected urban parcel networks for same-day and time-sensitive delivery, we study the fixed-line routing problem that arises when evaluating a candidate set of recurring inter-hub vehicle services. Vehicles follow predefined cyclic sequences of service points, or lines, and parcels may transfer between lines. Such transfers expand path choice but require loading and unloading operations that make vehicles dwell at service points. Because handled volumes are routing-dependent, dwell times become endogenous, linking routing decisions to line cycle times, effective service frequencies, and transfer waiting times. We introduce the Routing in Line Networks with Handling Times (RLN-HT) problem and formulate it as a bilinear generalized capacity-flow assignment model. We characterize optimal dwell times and the resulting frequencies as functions of handling workloads, enabling a reformulation solely in terms of commodity flows. We exploit its convex substructure to derive two second-order conic relaxations that preserve the original feasible region and therefore yield feasible incumbent solutions along with valid lower bounds. We also develop a residual-frontier framework that characterizes the tradeoff between the convex relaxation objective and the remaining nonconvex residual, yielding a general mechanism for constructing lower-bound certificates. Computational experiments show that ignoring handling times can yield poor or infeasible routing, whereas accounting for endogenous dwell times can improve average parcel travel times by up to 26.5%. In instances with up to 257 nodes and 25 lines, the relaxations solve quickly, yield near-optimal routing, and obtain small optimality gaps, whereas off-the-shelf spatial branch-and-bound struggles to produce useful bounds.

This work presents a unified inflationary and late-time cosmology, developed within Einstein-Gauss-Bonnet gravity coupled to three scalar fields, governed by a single potential and coupling function throughout cosmic history. Permitting the Gauss-Bonnet coupling to depend on the field content, rather than assigning it arbitrarily, produces a two-phase inflationary scenario: the higher-curvature term initially drives expansion and later becomes a subdominant. The initial super-inflationary stage ends dynamically when the geometrically induced stabilization of the waterfall field fails, at a field value determined by the combination $(n-1)Q$. Coherent oscillations of the waterfall condensate serve as the initial radiation source, replacing conventional reheating and establishing the thermal bath necessary for the subsequent warm phase. Utilizing a two-stage dissipation mechanism with $\Gamma_\phi\propto T^3$, the scalar and tensor spectra are derived while retaining Gauss-Bonnet contributions, demonstrating that the growth of inflaton fluctuations is regulated by the shear viscosity of the bath, which is essential for model viability. A quartic potential, previously excluded in the cold scenario, becomes viable, with $n_s$ within the Planck $1\sigma$ band and $r$ suppressed. Agreement with the spectral index is generic, while internal consistency confines the model to a narrow band in $(n-1)Q$. Finally, the release of the third scalar near matter-radiation equality transforms a very small mass scale into a very large coupling by a logic inverse to the seesaw mechanism. At late times, the inflaton persists as dark energy.

Code detectors can become obsolete as code-generating models evolve: a detector validated on one generation of models may not transfer to the next. We call this limited useful life a detector half-life. We evaluate eight general-purpose LLM judges and three dedicated detectors on human-written code and code produced by seven generators across C++, Java, and Python. Our results reveal two problems. First, performance varies considerably across generators and prompting strategies, suggesting that some detectors rely on generator-specific patterns rather than general evidence of code provenance. Second, accuracy can conceal severe prediction bias. DetectCodeGPT and GPT-Sniffer achieved an accuracy of 0.50 but an F1 score of 0.00 across all generators because they classified almost every sample as AI-generated. However, general-purpose LLM judges achieved stronger accuracy and F1 scores. Our results show that general-purpose LLMs are promising training-free judges of code provenance and can outperform dedicated detectors. However, their reliability depends on the judge model, the code generator, and the prompting strategy. We therefore recommend evaluating LLM judges across multiple generators and reporting macro-F1 alongside class-specific precision and recall.

Biomolecular therapeutics often start from known sequences and require targeted editing to improve multiple properties while satisfying hard biochemical and manufacturability constraints. However, existing generative methods do not jointly support multi-objective optimization, hard feasibility, and sequence editing in discrete, variable-length biological spaces. In this work, we introduce Pareto-Constrained Molecule Editing (pCoMole), a framework built on discrete flow matching that steers a pre-trained Edit Flow toward user-specified preferences while enforcing terminal feasibility. pCoMole defines a feasibility-gated terminal distribution using an augmented Tchebycheff utility and realizes the resulting preference tilt through a Doob-h transform of the underlying edit process. To make this construction practical, we approximate the required harmonic function using short Monte Carlo rollouts over candidate edits, yielding an efficient guided editor with provable preference consistency. We validate pCoMole by shrinking GFP while retaining fluorescence-related properties, shortening diverse Cas9 orthologs while preserving PAM specificity, and compressing peptide binders into short peptidomimetics that optimize seven drug-related properties under hard constraints. In wet lab testing, two 229-residue pCoMole-designed eGFP variants retained clear green fluorescence in BL21 cells after 10 deletions, with either one or two substitutions. Together, pCoMole enables constraint-aware, Pareto-aligned editing of biomolecular sequences in discrete, variable-length spaces.

We establish complexity lower bounds for stochastic first-order algorithms in nonconvex–concave minimax optimization, allowing algorithms to use variance reduction. Our main contribution is a lower bound for a zero-respecting algorithm class that permits variance reduction, extending beyond the algorithmic restrictions imposed by some existing lower bounds. We consider objectives with an $L$-Lipschitz continuous joint gradient, a compact convex dual domain of Euclidean radius at most $D_Y$, and a primal value function, defined by maximizing the objective over the dual variable, with initial suboptimality at most $\Delta$. The target accuracy $\varepsilon$ is measured by the gradient norm of the Moreau envelope of the constrained primal value function with parameter $1/(2L)$. Under an unbiased stochastic first-order oracle with variance at most $\sigma^2$ and mean-squared smoothness, we prove the lower bound $\Omega\!\left(L^2D_Y\Delta\varepsilon^{-3}+L^3D_Y^2\Delta\sigma^2\varepsilon^{-6}\right)$. This result quantifies the dependence on accuracy, dual-domain radius, and oracle noise even when variance reduction is allowed. We also establish complementary lower bounds for nonconvex–strongly-concave minimax optimization. With dual strong-concavity parameter $\mu>0$ and condition number $\kappa:=L/\mu$, we obtain $\Omega\!\left(L\Delta\sqrt{\kappa}\,\varepsilon^{-2}+L\Delta\kappa\sigma^2\varepsilon^{-4}\right)$ under the bounded-variance oracle model. Under the additional mean-squared smoothness condition with constant $\bar L$, we obtain $\Omega\!\left(L\Delta\sqrt{\kappa}\,\varepsilon^{-2}+\Delta\bar L\sigma\kappa^{3/2}\varepsilon^{-3}\right)$. Together, these results identify complexity barriers across the concave and strongly concave regimes, with the main nonconvex–concave bound remaining valid for algorithms that use variance reduction.

Despite remarkable progress, video generation models often produce highly similar outputs when repeatedly sampled from the same prompt, limiting their usefulness for creative exploration. Existing diversity evaluations primarily rely on global scalar metrics, which obscure where diversity collapses in the spatiotemporal space of videos. We introduce DiVid, a dimension-level diagnostic framework that decomposes video generation diversity into six interpretable dimensions: Semantic, Style, Subject, Scene, Motion, and Camera. Each dimension is measured through a reproducible computer-vision pipeline and analyzed alongside quality and instruction faithfulness to examine potential trade-offs. Systematic evaluation of representative video generation models reveals that diversity is highly dimension-specific: models with strong global diversity scores still collapse on specific factors, particularly Motion and Camera. These rankings persist after filtering unfaithful generations, indicating genuine capability differences rather than off-prompt outputs. Beyond measurement, controlled prompt interventions identify two fundamental bottlenecks: default mode convergence, where models fall back to dominant patterns under open-ended prompts; and realization gaps, where models fail to faithfully realize diverse, explicitly requested alternatives, particularly for temporal factors. The larger faithfulness losses for temporal factors highlight the difficulty of controlling motion and camera variation through text alone. DiVid thus shifts the study of diversity from measuring whether it exists to diagnosing where and why it collapses, and provides actionable directions for dimension-aware training objectives and control signals. The framework will be released to facilitate future research on diverse and controllable video generation.

For a third-order symmetric tensor, the Comon rank gap is the difference between its CP rank and its symmetric rank. We study direct sums of Lovitz's rational $27$-dimensional tensor, whose two ranks are $55$ and $56$. Two copies have ranks $110$ and $112$, and three copies have ranks $165$ and $168$, over both the real and the complex fields. Thus direct sums yield concise cubic tensors on spaces of dimensions $54$ and $81$ with Comon rank gaps two and three.

Event-chain Monte Carlo (ECMC) has revolutionised computational sampling over recent years, providing a powerful alternative to the molecular-dynamics (MD) and Hamiltonian Monte Carlo (HMC) algorithms. Each method outperforms the ubiquitous random-walk Metropolis algorithm by advancing particles along deterministic trajectories, but ECMC achieves this without being constrained by Newtonian dynamics. Recent advances exploited this dynamical freedom to induce a collective particle dynamics that relax local density variations on fast timescales. In a foundational model of $N$ pairwise-interacting particles on the 1D torus, this led to an $O(N^{3/4})$ improvement on the industry-leading computational efficiency of MD and HMC - but with an impractically small prefactor at low/high mean particle density for general attractive/repulsive interactions. Here we present a universal framework that generalises this high-efficiency sampling strategy to all translationally symmetric pairwise models on the torus - creating the potential to surpass MD and HMC as the state of the art. We also numerically elucidate the collective particle dynamics and discuss broad impact across the physical sciences and computational statistics.

Given a symmetric simple random walk $(X_n)_{n \ge 0}$, the family of all symmetric simple random walks $(Y_n)_{n \ge 0}$ adapted to the filtration of $(X_n)_{n \ge 0}$ was studied in Collevecchio et al. (2022). In particular, the authors established necessary and sufficient conditions under which the suitably normalized two-dimensional process $((X_n, Y_n))_{n \ge 0}$ converges weakly to a two-dimensional Brownian motion. When this occurs, we say that the random walk $(Y_n)_n$ is normal (with respect to $(X_n)_n$). In this paper, we investigate whether a "randomly selected" $(Y_n)_{n \ge 0}$ is normal. We consider a very general randomization procedure and look at both the quenched and annealed settings.

Jin, Milojević, Tomon and Zhang established a powerful recursive estimate relating the positive eigenvalues of a graph whose least eigenvalue is small in absolute value. We establish a refinement of this result, yielding improved estimates across spectral graph theory and discrepancy theory, and for Chowla's cosine problem. Recent results of Janzer, Tomon and Yip allow us to directly transfer least eigenvalue estimates to the corresponding surplus estimates. Using these tools, we fully resolve a conjecture of Räty, Sudakov and Tomon. We show that, for an $n$-vertex graph $G$ with least eigenvalue $\lambda_n$ and surplus $\operatorname{sp}(G)$, if $G$ is $\epsilon$-far from all disjoint unions of cliques, then $|\lambda_n|\geq \Omega_\epsilon(n^{1/4})$ and $\operatorname{sp}(G)\geq \Omega_\epsilon(n^{5/4})$. Furthermore, we show that when $G$ is $n^{-o(1)}$-far from all disjoint unions of cliques, we have $|\lambda_n|\geq n^{1/4 - o(1)}$ and $\operatorname{sp}(G)\geq n^{5/4 - o(1)}$. Finally, we show that the surplus of a $K_t$-free graph with $m$ edges is at least $m^{0.614 - o(1)}$ as $m$ tends to infinity.

This paper is concerned with establishing estimates on averaged Green's functions for a uniformly elliptic divergence form partial difference equation with random coefficients on the $d$ dimensional integer lattice $\mathbb{Z}^d$. It has previously been shown that the averaged Green's function is point-wise well approximated by the homogenized Green's function at large length scales. Corresponding results also hold for (fractional) derivatives of the averaged Green's function up to but not including the second derivative. Second derivative results have been established when the elliptic equation generates a positive semi-group, as in the diagonal case. Here the second derivative result is shown more generally by using an insight of Bourgain.

Real images often exhibit unknown and mixed degradations, making restoration substantially more challenging than single-task image restoration because multiple distortion types interact within the same observation. Consequently, existing methods often rely on prior knowledge of the degradation type or separate task-specific models, which may oversmooth fine structures or leave residual artifacts, motivating a compact model-driven alternative. We propose the Multi-Degradation Image Restoration Network (MDIRNET), a unified framework that combines a model-driven low-rank prior with end-to-end learning. Here, unified refers to joint training on three degradation types: noise, rain, and blur. A single MDIRNET model restores all three without requiring task-specific models, modules, or branches at inference. The low-rank prior exploits the redundancy and compact structure of natural image patches. To identify this underlying low-dimensional representation, we formalize restoration via Orthogonal Variational PCA (OVPCA) and translate its iterative inference into a deep unfolding network. To handle spatially non-uniform corruption and local content variability, we further introduce a learnable patch-partitioning strategy and a lightweight dynamic rank-allocation module that predicts the appropriate subspace dimension for each region. Spatially adaptive reconstruction refinement is performed using a supervised attention module. Extensive experiments on standard denoising, deblurring, and deraining benchmarks show that MDIRNET achieves competitive or superior performance over strong baselines across most metrics, while controlled mixed-degradation experiments demonstrate consistent performance across the evaluated synthetic degradation combinations. The code is available at https://github.com/ScholarForge/mdirnet.git.

Refreshment samples are the standard remedy for panel attrition, and the identification results behind them maintain that participation does not change measurement. We characterize what a refreshment sample identifies about panel conditioning, modelled as a deterministic monotone map at reinterview, when attrition is unrestricted. A candidate map is consistent with the data if and only if the retention-scaled distribution of the stayers' implied latent outcomes is setwise dominated by the refreshment distribution; every such map is rationalized by an explicit attrition process. Without attrition the map is identified on the latent-outcome support; with attrition, a density-ratio condition governs the identified set, and tail behaviour alone does not determine it. For an unrestricted map the survivors' mean effect has the familiar trimming bounds; for an item with all categories reported, the model reduces to a test of no conditioning. Within a cohort, other waves, dropout patterns and entry-wave items leave the set unchanged unless restrictions link selection across waves. Under explicit selection restrictions, survival matching, symmetric matching and entry-wave correction identify survivor effects. We derive their biases and give rank conditions under which refreshment schedules identify curvature in the conditioning path. A Japanese panel illustrates the results.

The honeycomb and Kelvin problems ask how space can be partitioned into cells of equal volume with the least surface area. We resolve this question in four dimensions for convex bodies that tile space by translations, showing that the regular $24$-cell uniquely minimizes surface area at fixed volume. We develop a framework combining an exact deficit identity, valid in every dimension, with a descent argument. As a consequence, the regular $24$-cell also minimizes surface area among such tiles containing a fixed ball.

Structured policies improve efficiency, robustness, and interpretability in imitation learning by introducing task-specific inductive bias, but existing structure generation methods rely either on extensive human input or on static domain knowledge encoded in LLMs, which may be inconsistent with the expert demonstrations. We propose a closed-loop framework that iteratively refines structured policies using LLM-guided analysis of policy rollouts. By logging rollouts as semantically meaningful tabular data and prompting the LLM to generate diagnostic analysis code, our method identifies suboptimalities in the policy structure and iteratively corrects them without requiring human instruction. Experiments on car racing and door opening tasks show that our approach improves imitation learning performance by up to 15% over zero-shot LLM-generated structures and requires 75% less compute to achieve the same reinforcement learning performance. These results demonstrate that tabular rollout analysis provides an effective feedback signal to align LLM-generated policy structures with expert demonstrations, and we can utilize it to generate good policy structures automatically.

We prove asymptotic bias bounds for stochastic gradient Langevin dynamics in Wasserstein distance of order two. We assume that the negative log-density is strongly convex with a Lipschitz gradient, and that the stochastic gradient estimator is unbiased with an error satisfying a mean-square Lipschitz condition. The bounds are of order $h$ under a fourth moment assumption on the stochastic gradient error and of order $h^{1/2}$ under only a second moment assumption, where $h$ is the stepsize. A spiked-noise example shows that a second moment assumption alone is insufficient for a bound of order $h$ that is uniform over noise distributions with a fixed variance.

The increasing prevalence of decentralized data has led to a growing interest in federated learning, which enables collaborative model training without clients sharing their sensitive local data. However, FL alone does not sufficiently protect sensitive training data and is generally coupled with privacy-preserving techniques, such as differential privacy and homomorphic encryption. Although powerful, these techniques address separate concerns via different mechanisms, so relying on just one might prove insufficient or impractical for addressing challenges associated with federated learning. In this work, we propose a privacy-preserving federated learning framework that combines homomorphic encryption-based training with differential privacy-based model inspection and release. We adopt a Markov chain Monte Carlo-based Bayesian privacy estimation method to estimate the privacy of our proposed framework. Our results show that this method improves both model utility and estimated privacy over the baseline method that relies solely on differential privacy for training. In our experiments with the FEMNIST dataset, by the end of training, our method reaches a test loss of $1.09$, compared to $2.37$ for the differential privacy-only approach, while providing stronger estimated privacy protection, with the estimated posterior mean of the privacy parameter $\epsilon$ of $4.32$, compared to $7.26$ for the differential privacy-only approach. We also show that intermittent model monitoring can preserve the encrypted training trajectory while, under our evaluated experimental setting, providing estimated privacy comparable to or stronger than the differential privacy-only approach.

Weight-space networks operate directly on parameters of other neural networks, enabling tasks such as predicting model properties, editing trained models, and generating weights. Weight-space symmetries such as neuron permutations make equivariance a key design principle. However, existing equivariant weight-space architectures have primarily been studied for transformations that preserve the network architecture. In contrast, many practical transformations, including model compression and upscaling, map a trained source network into a target network with a different architecture. In this setting, the source and target permutation symmetries act on different parameter spaces, making equivariance less straightforward to formulate. Our key idea for addressing this mismatch is to reformulate cross-architecture operators with two inputs: a trained source network and an initialization of the target network. This lets us define equivariant cross-architecture operators that refine the initialization of the target network using information from the source network, while being invariant to source-network permutations and equivariant to target-network permutations. Based on this formulation, we introduce CrossGMN, a graph metanetwork that jointly processes both networks through symmetry-preserving cross-network message passing. We prove CrossGMN is universal for continuous cross-architecture operators on compact sets under a general-position assumption. We evaluate CrossGMN for model compression, predicting a smaller network's parameters to accelerate subsequent knowledge distillation. Across 2-D and 3-D INRs and image classification with MLPs, CNNs, and Vision Transformers, CrossGMN speeds up distillation by up to 8.89x, transfers across datasets without retraining (3.78x), and a single model can accelerate compression from heterogeneous source architectures into a common target architecture.

An assignment of tasks to servers can resist every small improvement and still make tasks wait longer than necessary. We determine exactly how inefficient such an assignment can be when each task requires one unit of service and the eligibility constraints permit all tasks to use distinct servers. For every move size $r$ and maximum current server load $K$, we give a closed formula for the worst ratio between locally optimal and globally optimal total completion time. Local optimality here allows every feasible reassignment changing at most $r$ tasks. Every finite-cap bound is attained on a tree where each task has at most two eligible servers. Thus the worst behavior already occurs under simple eligibility constraints. At load cap two, the exact ratio is $1+1/(r+2)$, attained on a path with $r+2$ tasks. Without a load cap, the worst-case supremum is $3/2$ for single-task moves and approximately $1.294503159$ for two-task moves; its excess above one is $1/(r+2)+O(2^{-r}/r)$ as $r$ grows. The proof uses an explicit rational potential on a comparison graph and matching extremal constructions. These results give sharp guarantees for bounded-size local search on matchable semi-matchings, including exact guarantees under degree bounds.

In this article, we present our vision and recent advancements toward creating a decentralized system capable of learning from real-time data within buildings to support sustainable and privacy-preserving smart environments. Our approach promotes the concept of the building itself as the data center, aligning with the principles of edge computing to safeguard confidentiality and reduce reliance on external cloud infrastructure. This is particularly valuable in humanitarian contexts, where data sovereignty, energy efficiency, and infrastructure constraints are critical. We detail a lightweight, "Kubernetes-like" orchestration framework for deploying AI services within such environments and demonstrate our progress in implementing AI algorithms on low-power, cost-effective microcontrollers such as those in the Arduino ecosystem. By enabling in-situ learning directly on sensors or microcontrollers, our work aims to bring intelligent services to resource-limited settings, fostering autonomy, resilience, and sustainable development in vulnerable or underserved communities. The contributions in this article are related, firstly, to our project "Online Machine Learning Algorithms for Embedded Systems" and the evaluation of two new online algorithms. Secondly, we envision a cloud-fog-edge architecture based on the KOptim and FIWARE components, and we propose a methodology for coupling them. Experimental results of the online algorithms are also presented, showcasing real-world traces.

Data lakes contain a plethora of attributes scattered across many tables that, when combined, provide enhanced assets for data analysis. Nonetheless, deciding which attributes belong together in meaningful relations remains a manual, per-task effort. Merging by joinability alone provides no guarantees regarding attribute relevance, while selecting features against a single target discards attributes useful to other tasks. To address this gap, we introduce the data composition problem: organizing a fragmented, heterogeneous lake into meaningful relations, agnostic of any particular analytical task so that the resulting organization can serve as a common foundation for diverse downstream analyses. We propose DIADA, a composition system that employs multivariate dependence as the criterion for assessing the meaningfulness of a relation and approximates it by hypothesizing independence among attributes and identifying those sets that violate this hypothesis. To do so, we map the attributes to a predicate space, forming a lattice under inclusion and mining those predicate sets that exhibit dependence among their constituents. We contribute a dedicated and scalable algorithm to effectively explore this space, outscaling classical algorithms for mining relationships, thus discovering dependencies that would otherwise be impractical to identify. We demonstrate that applying a single data composition process benefits diverse potential downstream tasks. This is the result of providing a subset of low-noise, statistically relevant attributes that increases the confidence that detected patterns are grounded in real relationships, thus preventing common modeling issues in large-scale environments.

Fairness conclusions in clinical prediction can depend strongly on both the metrics reported and the demographic resolution at which performance is evaluated. We revisit these evaluation choices for ICU mortality prediction on MIMIC-IV, comparing predictive-utility and subgroup-error metrics across several fairness interventions. As a complementary case study, we introduce a lightweight adaptation strategy that jointly balances ethnicity–gender–insurance representation without conditioning on mortality outcomes, allowing demographic representation balancing to be examined separately from outcome-conditioned or direct error-rate interventions. We evaluate its behavior at both marginal and corresponding three-way intersectional subgroup levels, while accounting for the statistical support of finer-grained estimates. The results show that interventions can receive substantially different assessments across accuracy/AUROC, sensitivity, and false-positive rate, and that marginal demographic summaries can conceal heterogeneous error profiles within their constituent intersections, including among larger subgroups. These findings highlight the importance of evaluating fairness interventions at both complementary metric and subgroup resolutions, while accounting for the intervention target and the reliability of subgroup estimates.

Autonomous underwater vehicles (AUVs) assisting human divers must continuously track not only the diver's 3D position but also their full-body orientation. However, vision-based perception is unreliable underwater, and forward-looking sonar – despite being widely used – discards the elevation information needed for orientation estimation, posing a fundamental limitation. Recently commercialized 3D sonar preserves elevation but produces sparse, noisy returns, and existing detectors are built for dense LiDAR data and for targets that remain upright and rotate only about the yaw axis (e.g., vehicles, pedestrians), making them unable to represent a freely pitching and rolling diver. To address this gap, we present two contributions. First, SonarVoxNet adapts a voxel-based encoder and an anchor-free center-based detection head to 3D sonar data, replacing the conventional yaw-only rotation representation with a continuous 6D rotation parameterization to predict full 9-DoF oriented bounding boxes – to our knowledge, the first 3D sonar diver detector to do so. Second, Diver3D is the first public 3D sonar dataset with full 3D orientation labels for divers in diverse, non-upright poses, collected at a natural cave-diving site. Through controlled ablations over the backbone and detection head, we show that the dominant factor behind accurate 3D sonar-based diver detection is the transition from yaw-only rotation to full-SO(3) rotation. This transition substantially improves detection accuracy and reduces orientation error. These results demonstrate that full-body diver orientation is recoverable from 3D sonar alone, laying the groundwork for future work on diver pose estimation and diver-robot interaction.

We establish a Type I curvature bound for finite-time volume-collapsing Kähler–Ricci flows on compact Kähler surfaces. No symmetry assumption is imposed, and the initial Kähler class need not be rational. The proof combines local symplectic topology with the classification of gradient Kähler–Ricci shrinking solitons. Bamler's compactness and structure theory provides the shrinking limits used in the argument.

Let $T$ be a non-invertible surjective continuous endomorphism of the group $\ttf^d\,:= \rrf^d/\zzf^d$. Then $T$ preserves the Haar measure, is associated to some $d \times d$ matrix $A$ with integer coefficients and is $r$-to-one, where $r = |\det A| \ge 2$. In~\cite{Krzyzewski}, Krzyżewski gives a necessary and sufficient condition for $T$ to be exact, and shows that $T$ – viewed as a measure-preserving map – is isomorphic to the direct product of some (possibly trivial) toral automorphism by some exact toral endomorphism. We re-prove these results by more elementary and constructive methods, whereas Krzyżewski actually works with endomorphisms of compact Abelian groups and relies on non-constructive theorems. Krzyżewski's exactness condition and Mihailescu's papers ~\cite{Mihailescu 2012} and~\cite{Mihailescu 2013} show that $T$ is isomorphic to the one-sided uniform Bernoulli shift on $\odc 0,r-1 \fdc^{\zzf\_+}$ if and only if $A$ is expanding (i.e. the modulus of each eigenvalue is $>1$). When $A$ is not expanding and hyperbolic (i.e. all eigenvalues have modulus different from $1$), Mihailescu~\cite{Mihailescu 2012} shows that $T$ cannot have a generating Rokhlin partition. More generally, when $A$ is not expanding (whether hyperbolic or not), we show that the endomorphism $T$ cannot have a smooth finite generator (whether independent or not).

Modern machine-learning models often contain strongly dependent or redundant features, making feature attribution difficult because shared predictive information can be distributed across correlated predictors. Existing methods such as SHAP, LIME, HSIC, MI/CMI, and SAGE may therefore produce unstable rankings under multicollinearity or near-duplicate predictors. We propose the Mutual Correlation Impact Ratio Method (MCIR-M), a dependence-aware global feature-importance approach that quantifies the unique predictive information contributed by each feature beyond a selected dependence neighbourhood. MCIR-M introduces the Mutual Correlation Impact Ratio (MCIR), which conditions each feature on strongly dependent neighbours and computes a normalized ratio of conditional to block-level information. The population score lies in [0,1] and equals zero under exact conditional redundancy. We also introduce a lightweight estimation procedure that computes MCIR using a fraction of the available data and evaluates agreement with full-data explanations. Across controlled synthetic redundancy experiments and the UCI HAR benchmark, MCIR shows dependence-aware ranking behaviour, with its clearest advantage under injected near-duplicate predictors. Comparisons with independent and conditional SHAP, SAGE, HSIC, MI-based scores, and CIR-family baselines are mixed across real-data criteria. Reduced explanation samples lower computational burden in the evaluated configurations, while agreement with full-data explanations is assessed separately through ranking, head-set, and faithfulness diagnostics. Overall, MCIR-M provides a practical dependence-aware diagnostic for global explanation under strong feature dependence.

Vision-language models (VLMs) face a fixed-budget trade-off between processing more visual information for fine-grained perception and using a larger language backbone for complex reasoning. Existing studies do not tell us which combination of backbone size and input resolution to deploy, especially in high-resolution deployments. To address this gap, we propose the Separable Law that describes how VLM performance changes with language backbone size and visual token count. We fit the law to measurements from 26 InternVL and QwenVL models, with language backbone sizes from 1B to 72B, on four high-resolution benchmarks with image sizes from 224 pixels to 8K. We find that the questions responding to scaling can be predicted from the skill they require, while a substantial fraction never responds at all. We also find that the two model families gain similarly from a larger backbone, while their gains from more visual tokens differ sharply. Combined with a cost law, the Separable Law gives a closed-form rule for allocating compute between backbone size and visual tokens. When deployment is limited to available configurations, the law identifies model and image sizes that perform close to the best feasible choice under the same budget. We hope our work offers a principled way to decide how much a model should be allowed to see at high resolution, given what it must reason about.