arXiv:2511.22331v3 Announce Type: replace-cross
Abstract: Bilevel optimization minimizes an objective function, defined by an upper-level problem whose feasible region is the solution of a lower-level problem. We study the oracle complexity of finding an $\epsilon$-stationary point with first-order methods when the upper-level problem is nonconvex, and the lower-level problem is strongly convex. Recent works (Ji et al., ICML 2021; Arbel and Mairal, ICLR 2022; Chen et al., JMLR 2025) achieve a $\tilde{\mathcal{O}}(\bar \kappa_y^4 \epsilon^{-2})$ upper bound that is near-optimal in $\epsilon$, which can be reduced to $\tilde{\mathcal{O}}(\bar \kappa_y^{7/2} \epsilon^{-2})$ by a naive application of Nesterov acceleration in the inner loop, where $\bar \kappa_y$ is the global condition number. However, the optimal dependency on the condition number is unknown. In this work, we establish a new $\Omega(\kappa_y^{5/2} \epsilon^{-2})$ lower bound, where $\kappa_y < \bar \kappa_y$ is the lower-level condition number that is of the same order as $\bar \kappa_y$ when the smoothness constants are $\mathcal{O}(1)$. Our lower bound establishes the first provable gap in terms of condition number dependency between bilevel problems and minimax problems in this setup. Our lower bounds can be extended to various settings, including high-order smooth functions, stochastic oracles, and convex hyper-objectives: (1) For second-order and arbitrarily smooth problems, we show lower bounds of $\Omega({\kappa_y^{31/14}} \epsilon^{-12/7})$ and $\Omega(\kappa_y^{21/10} \epsilon^{-8/5})$, respectively. (2) For convex-strongly-convex problems, we improve the previously best lower bound (Ji and Liang, JMLR 2022) from $\Omega(\kappa_y /\sqrt{\epsilon})$ to $\Omega(\kappa_y^{3/2} / \sqrt{\epsilon})$. (3) For smooth stochastic problems, we also show a lower bound of $\Omega(\kappa_y^4 \epsilon^{-4})$.
Science Journals
arXiv:2512.09586v2 Announce Type: replace-cross
Abstract: Quantum circuit design is a key bottleneck for practical quantum machine learning on complex, real-world data. We present an automated framework that discovers and refines variational quantum circuits (VQCs) using graph-based Bayesian optimization with a graph neural network (GNN) surrogate. Circuits are represented as graphs and mutated and selected via an expected improvement acquisition function informed by surrogate uncertainty with Monte Carlo dropout. Candidate circuits are evaluated with a hybrid quantum-classical variational classifier on the next generation firewall telemetry and network internet of things (NF-ToN-IoT-V2) cybersecurity dataset, after feature selection and scaling for quantum embedding. We benchmark our pipeline against an MLP-based surrogate, random search, and greedy GNN selection. The GNN-guided optimizer consistently finds circuits with lower complexity and competitive or superior classification accuracy compared to all baselines. Robustness is assessed via a noise study across standard quantum noise channels, including amplitude damping, phase damping, thermal relaxation, depolarizing, and readout bit flip noise. The implementation is fully reproducible, with time benchmarking and export of best found circuits, providing a scalable and interpretable route to automated quantum circuit discovery.
arXiv:2607.09564v2 Announce Type: replace
Abstract: Surface syntax in proof assistants like Rocq, Lean, Agda, and Idris is highly implicit, lacking many details that are needed for user-written code to denote precisely defined mathematical objects. Elaboration is an algorithm that accounts for these details by translating surface syntax to an explicit enough core syntax. The reliability and predictability of elaboration relies on several critical properties of the core type system, including decidability of judgemental equality and the injectivity of type constructors; these dependencies are witnessed in a concrete system by explicit calls to conversion checking and weak-head reduction subroutines.
We introduce a dependently typed monadic domain specific language for the executable specification of correct-by-construction elaboration algorithms that is abstracted from any particular representation of normal forms or algorithm for conversion checking. In particular, we represent a bidirectionally typed surface language for Martin-L\"of type theory by shallow embedding in this DSL so that the translation of surface terms into core terms amounts to elementary equational calculation. This translation is correct by construction in the sense that it cannot produce ill-typed terms, and is automatically stable under judgemental equality of core terms and even under substitution; from the latter property, we obtain a new denotational interpretation of the suspension of elaboration problems. Finally, a concrete elaboration algorithm is extracted by algebraic means from a presheaf model of the DSL built out of the bi-initial natural model of Martin-L\"of type theory.
arXiv:2510.19374v2 Announce Type: replace-cross
Abstract: We revisit Cox's proportional hazards model to improve variable selection in survival analysis. A square-root transformation of the partial likelihood renders the selection of the regularization parameter pivotal, free of the unknown baseline hazard and censoring mechanism. The resulting criterion borrows from information criteria such as BIC and from penalized regression methods such as the lasso, taking the best of both. On simulated and real data, our method substantially improves upon state-of-the-art approaches used daily in support recovery.
arXiv:2607.06817v2 Announce Type: replace-cross
Abstract: Throughout, all graphs are simple, finite and have vertex sets of the form $\{ 0, 1, 2, \ldots, n - 1 \}$ for some $n \in \mathbb{N}$. For graphs $G$ and $H$, and a permutation group $\Gamma$ on the vertex set of $H$, we say that $H$ is $\Gamma$-embeddable in $G$ if there exists a graph homomorphism from $H$ to $G$ of the form $\psi \circ \varphi$, where $\varphi \in \Gamma$ and $\psi$ is an increasing injection. Recently, standard and ordered Ramsey numbers of graphs were unified through the introduction of permutational Ramsey numbers, defined as follows. For graphs $H_1, H_2, \ldots, H_k$ and permutation groups $\Gamma_1, \Gamma_2, \ldots, \Gamma_k$ on their respective vertex sets, the permutational Ramsey number $R(H_1^{\Gamma_1}, H_2^{\Gamma_2}, \ldots, H_k^{\Gamma_k})$ is the minimum $n \in \mathbb{N}$ such that for every $k$-edge-coloring of a complete graph on $n$ vertices, there exists some $j \in \{1, 2, \ldots, k\}$ for which $H_j$ is $\Gamma_j$-embeddable in the spanning subgraph of the complete graph comprising the edges of color $j$.
Here, we consider reflective (resp. dihedral) Ramsey numbers, which are a specific class of permutational Ramsey numbers in which each group $\Gamma_j$ is the reflection group (resp. dihedral group) on the naturally ordered vertex set of $H_j$. Focusing on the two-color case, we apply the SAT-based approach originally proposed by Poljak for ordered Ramsey numbers and recently extended to cyclic Ramsey numbers. We utilize the Kissat SAT solver to obtain exact values and lower bounds for small reflective and dihedral Ramsey numbers whose two arguments belong to the following graph classes: monotone and alternating paths, monotone cycles, start-central stars, complete graphs and nested matchings. We also derive several general results and formulate conjectures based on the computational findings.
arXiv:2607.11871v1 Announce Type: new
Abstract: Existing studies of LLM-as-judge scoring bias work predominantly at the input-output level: they perturb inputs, measure score deltas, and propose prompt-level mitigations. We argue that the same biases admit a representation-level account in the judge's hidden state, complementary to the input-output view and operationally useful in ways it does not afford. We report three findings, across seven judges, seven bias types, and nine benchmarks. Geometry: baseline judging inputs occupy a tight activation manifold while biased inputs are displaced along a low-dimensional, type-specific subspace that sharpens with depth and is recovered consistently by three families of estimators. Causal control: steering hidden states along this subspace drives scoring in both directions, forward shifts reproducing biased scoring on clean inputs and reverse shifts restoring baseline scoring on biased ones, while matched-norm random directions produce shifts an order of magnitude smaller. Operational: a simple linear projection onto the same bias-direction features anticipates judge failures on three entirely unseen benchmarks, substantially outperforming text-based alternatives. Reading bias as activation geometry, rather than as input-output noise, unifies geometric structure, causal control, and operational prediction within a single framework. The project page is available at https://xzx34.github.io/unfair-judge/
arXiv:2607.11660v1 Announce Type: cross
Abstract: The solar chromosphere is permeated by complex magnetic fields that guide plasma flows and energy into the corona. This work presents a detailed analysis of a unique, high-resolution observation of a giant chromospheric spiral structure that emerges due to a large magnetic pore, captured by the Swedish 1-m Solar Telescope (SST). A comprehensive data analysis pipeline is developed to automatically detect the edges of 2255 plasma flows (loops) that constitute the spiral, and these are used to extract the kinematics of flows propagating along the magnetic field. The analysis reveals three primary insights into the spiral's physics. First, magnetic curvature is correlated with oscillatory flow dynamics, i.e. regions of high loop curvature exhibit a statistically significant excess of higher-order oscillation modes compared to straighter loops; it is also correlated with higher intensity and longer periods. Second, spatial distribution of oscillation period shows an inverse trend, decreasing from $\sim$3.5 minutes in the pore to $\sim$3 minutes in the outer spiral arms. This is interpreted as a signature of the overlying trans-equatorial quadrupolar coronal loop system compressing the pore's field lines into a near-horizontal orientation, producing a period gradient that challenges the standard expanding canopy model. Finally, the emission signature confirms that oscillating threads represent localised channels of brightness that lie within cooler, absorbing loop material. This study provides the first statistical analysis of oscillatory flows in a large-scale spiral, probing energy flow through the chromosphere through curved magnetic structure.
arXiv:2505.01258v2 Announce Type: replace-cross
Abstract: Bilevel optimization has recently attracted significant attention in machine learning due to its wide range of applications and advanced hierarchical optimization capabilities. In this paper, we propose a plug-and-play framework, named PnPBO, for developing and analyzing stochastic bilevel optimization methods. This framework integrates both modern unbiased and biased stochastic estimators into the single-loop bilevel optimization framework introduced in [9], with several improvements. In the implementation of PnPBO, all stochastic estimators for different variables can be independently incorporated, and an additional moving average technique is applied when using an unbiased estimator for the upper-level variable. In the theoretical analysis, we provide a unified convergence and complexity analysis for PnPBO, demonstrating that the adaptation of various stochastic estimators (including PAGE, ZeroSARAH, and mixed strategies) within the PnPBO framework achieves optimal sample complexity, comparable to that of single-level optimization. This resolves the open question of whether the optimal complexity bounds for solving bilevel optimization are identical to those for single-level optimization. Finally, we empirically validate our framework, demonstrating its effectiveness on several benchmark problems and confirming our theoretical findings.
arXiv:2504.05349v5 Announce Type: replace-cross
Abstract: Network pruning is used to reduce inference latency and power consumption in large neural networks. However, most methods focus on empirical results at the expense of understanding the pruning process. We introduce Hyperflux, a novel $L_0$ method which models pruning as a continuously evolving system determined by flux, the gradient response to a weight's removal, and pressure, a global regularization driving weights toward pruning. By exploiting this model, Hyperflux's pruning behavior becomes understandable at both microscopic (weight regrowth/pruning) and macroscopic (sparsity convergence, etc.) levels. We also introduce a novel pressure scheduler that reliably targets desired sparsities. Hyperflux achieves competitive results with ResNet-50, VGG-19 and DeiT-T/S on CIFAR-10, CIFAR-100 and ImageNet datasets.
arXiv:2505.24421v2 Announce Type: replace-cross
Abstract: Medical imaging plays a vital role in clinical diagnosis, yet AI-driven imaging methods remain challenged by patient variability, image artifacts, and limited robustness across acquisition conditions. Although deep learning has advanced medical image analysis, 3D image translation remains hindered by limited training data and variability arising from scanner differences, imaging protocols, and patient motion. Conventional data augmentation typically relies on a single transformation pipeline, overlooking augmentation-specific characteristics and limiting representation learning.
To address these challenges, we propose Multi-Encoder Augmentation-Aware Learning (MEAL), which processes multiple augmentation variants through dedicated encoder pathways. Three feature integration strategies are investigated: encoder concatenation (MEAL-CC), fusion layer (MEAL-FL), and an adaptive controller block (MEAL-BD). By dynamically weighting augmentation-specific features before decoding, MEAL-BD preserves complementary representations and improves robustness to clinically relevant variability.
We evaluate MEAL using CT-to-T1-weighted MRI translation, a clinically relevant task when MRI is unavailable, contraindicated, or delayed. Across predefined and unseen test datasets, MEAL-BD consistently outperformed competing approaches under both geometric perturbations and standard imaging conditions, achieving higher peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM). By prioritizing structural fidelity over perceptual realism, MEAL supports clinical interpretation and downstream image analysis rather than replacing diagnostic MRI, demonstrating that augmentation-aware representation learning improves the robustness and clinical applicability of medical image translation.
arXiv:2506.07840v3 Announce Type: replace-cross
Abstract: We introduce new kinetic equations modeling opinion dynamics inside a population of individuals, whose propensity to interact with each other is described by their level of social activity. We show that opinion polarization can arise among agents with a low activity level, while active ones develop a consensus, highlighting the importance of social interactions to prevent the formation of extreme opinions. Moreover, we present a realistic control strategy aimed at reducing the number of inactive agents and increasing the number of socially active ones. At last, we prove several (weak and strong) convergence to equilibrium results for such controlled model. In particular, by considering additional interactions between individuals and opinion leaders capable of steering the average opinion of the population, we use entropy method-like techniques to estimate the relaxation toward equilibrium of solutions to a Fokker-Planck equation with time-dependent coefficients.
arXiv:2508.14838v4 Announce Type: replace-cross
Abstract: A finite relational structure A is called compact if for any infinite relational structure B of the same type, the existence of a homomorphism from B to A is equivalent to the existence of homomorphisms from all finite substructures of B to A. We show that if A has width one, then the compactness of A can be proved in the axiom system of Zermelo and Fraenkel, but otherwise, the compactness of A implies the existence of non-measurable sets in 3-space.
arXiv:2607.11315v1 Announce Type: cross
Abstract: We control the spectral distribution of a spin ensemble by applying a magnetic field gradient using an anti-Helmholtz coil inside a dilution refrigerator, and demonstrate impedance matching between the ensemble and a transmission line, achieving -50 dB absorption of incident radiation. This represents a first step toward a spin-ensemble-based quantum memory for itinerant microwave photons. We further model the spectral distribution under the applied gradient to predict the spin-resonator response, and use the device to systematically tune the weak-to-strong coupling transition in both continuous-wave and time-domain pulsed measurements.
arXiv:2604.02951v2 Announce Type: replace
Abstract: Human data annotation, especially when involving experts, is often treated as an objective reference. However, many annotation tasks are inherently subjective, and annotators' judgments may evolve over time. This study investigates changes in the quality of annotators' work from a competence perspective during a process of social influence recognition. The study involved 25 annotators from five different groups, including both experts and non-experts, who annotated a dataset of 1,021 dialogues with 20 social influence techniques, along with intentions, reactions, and consequences. An initial subset of 150 texts was annotated twice - before and after the main annotation process - to enable comparison. To measure competence shifts, we combined qualitative and quantitative analyses of the annotated data, semi-structured interviews with annotators, self-assessment surveys, and Large Language Model training and evaluation on the comparison dataset. The results indicate a significant increase in annotators' self-perceived competence and confidence. Moreover, observed changes in data quality suggest that the annotation process may enhance annotator competence and that this effect is more pronounced in expert groups. The observed shifts in annotator competence have a visible impact on the performance of LLMs trained on their annotated data.
arXiv:2604.03835v2 Announce Type: replace
Abstract: We demonstrate that the system of fine-tuning constraints for life is overdetermined: the number of inequalities is too large relative to the number of free parameters in the chemical sector and likely not only there. This entails that life-permitting conditions are secured at the level of physics not only by the fine-tuned fundamental constants, but also by a very special form of the laws. In 1960, Eugene Wigner published his essay "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," summarizing his reflections on the miraculous comprehensibility of the mathematical structure of physical laws. The present paper points to another, no less remarkable, aspect of this structure, which may be called as our title suggests.
arXiv:2602.04272v2 Announce Type: replace-cross
Abstract: The Importance-Weighted Evidence Lower Bound (IW-ELBO) has emerged as an effective objective for variational inference (VI), tightening the standard ELBO and mitigating the mode-seeking behaviour.
However, optimizing the IW-ELBO in Euclidean space is often inefficient, as its gradient estimators suffer from a vanishing signal-to-noise ratio (SNR). This paper formulates the optimisation of the IW-ELBO in Bures-Wasserstein space, a manifold of Gaussian distributions equipped with the 2-Wasserstein metric. We derive the Wasserstein gradient of the IW-ELBO and project it onto the Bures-Wasserstein space to yield a tractable algorithm for Gaussian VI.
A pivotal contribution of our analysis concerns the stability of the gradient estimator. While the SNR of the standard Euclidean gradient estimator is known to vanish as the number of importance samples $K$ increases, we prove that the SNR of the Wasserstein gradient scales favourably as $\Omega(\sqrt{K})$, ensuring optimisation efficiency even for large $K$. We further extend this geometric analysis to the Variational R\'enyi Importance-Weighted Autoencoder bound, establishing analogous stability guarantees. Experiments demonstrate that the proposed framework achieves superior approximation performance compared to other baselines.
arXiv:2502.16151v4 Announce Type: replace-cross
Abstract: In Yang-Mills theory on a Euclidean Cauchy surface, the physical gauge group is often taken to be $\mathcal{G}^I/\mathcal{G}^\infty_0$, where $\mathcal{G}^I$ consists of boundary-preserving gauge transformations asymptoting to a constant, and $\mathcal{G}^\infty_0$ consists of transformations generated by the Gauss law constraint. We rigorously derive this physical gauge group for both Abelian and non-Abelian theories. A key result is that restricting to $\mathcal{G}^I$ follows from the structure of the instantaneous state space on which the instantaneous Lagrangian is defined. We extend our analysis to Yang-Mills-Higgs theory, showing that boundary conditions and the physical gauge group differ between the unbroken and broken phases.
arXiv:2607.00586v2 Announce Type: replace-cross
Abstract: We present a simple, yet general approach to study the scaling properties as the dimensionality of Metropolised MCMC sampling algorithms increases. The study relies on the symmetries of the Hamiltonian formalism and ultimately on the symmetry of the Metropolis-Hastings formula. Our findings contain, as particular cases, many known results for the Random Walk Metropolis, MALA and other algorithms. In addition, they provide, in an easy way, new optimal scaling results for a variety of proposal mechanisms, including implicit proposals and proposals generated with the help of differential equation integrators. The analysis applies to targets that are products of a given, not necessarily univariate distribution, and also to cases where the different terms in the product are scaled differently. We show how to construct gradient-based MALA-like proposals where the variance of the proposal as the dimension $d$ increases may be taken as $O(1/d^\mu)$, with $\mu>0$ arbitrarily small, to be compared with the values $\mu = 1$ for Random Walk Metropolis and $\mu=1/3$ for MALA.
arXiv:2607.05153v2 Announce Type: replace-cross
Abstract: Scientists often seek to draw causal inferences from structured data that is not independently and identically distributed, such as spatial data, network data, or molecular data. We develop geometric causal models (GCMs), a framework for causal inference from dependent data that exploits underlying symmetries of the data generating process. For example, in spatial data, we consider processes that are symmetric under translations, or in graph data, symmetric under permutations of the nodes. We show how symmetries, formalized with group theory, can enable causal identification and estimation. We deploy ergodic theory for amenable groups to establish identification, and combine geometric deep learning with scalable Bayesian inference for estimation. We recover i.i.d. causal models and do-calculus when the data is a sequence and the symmetry is permutation equivariance, and find novel types of causal models when we use alternate structures and symmetries. As an example, we construct a causal model that satisfies the symmetries of DNA. This GCM enables new estimators for the effects of genetic variation, combining deep functional genomics models to describe outcomes and DNA language models to describe propensities. We illustrate on semisynthetic data.
arXiv:2603.16883v2 Announce Type: replace
Abstract: Inertial measurement unit-based online handwriting recognition enables the recognition of input signals collected across different writing surfaces but remains challenged by uneven character distributions and inter-writer variability. In this work, we systematically investigate two strategies to address these issues: subword tokenization and concatenation-based data augmentation. Our experiments on the OnHW-Words500 dataset reveal a clear dichotomy between handling inter-writer and intra-writer variance. On the writer-independent split, structural abstraction via Bigram tokenization significantly improves generalization to unseen writing styles, reducing the word error rate (WER) from 15.40% to 12.99%. In contrast, on the writer-dependent split, tokenization degrades performance due to vocabulary distribution shifts between the training and validation sets. Instead, our proposed concatenation-based data augmentation acts as a powerful regularizer, reducing the character error rate by 34.5% and the WER by 25.4%. Further analysis shows that short, low-level tokens benefit model performance and that the performance gains from concatenation-based data augmentation surpass those achieved by proportionally extended training. These findings reveal a clear variance-dependent effect: subword tokenization primarily mitigates inter-writer stylistic variability, whereas concatenation-based data augmentation effectively compensates for intra-writer distributional sparsity.
arXiv:2603.18375v3 Announce Type: replace
Abstract: There has been a growing research interest in Digital Therapeutic Alliance (DTA) as the field of AI-powered conversational agents are being deployed in mental health care, particularly those delivering CBT (Cognitive Behaviour Therapy). Our proposition argues that the current design paradigm which seeks to optimize the bond between a patient in need of support and an AI agent contains a subtle but consequential trap: it risks producing an "appearance of connection" that unintentionally disrupts the fundamental human need for relatedness, which potentially displaces the authentic human relationships upon which long-term psychological recovery depends. We propose a reorientation from designing artificial intelligence tools that simulate relationships to designing AI that scaffolds them. To operationalize our argument, we propose an interdisciplinary model that translates the Responsible AI Six Sphere Framework through the lens of Self-Determination Theory (SDT), with a specific focus on the basic psychological need for relatedness. The resulting model offers the technical and other clinical communities a set of relationship-centered design guidelines and relevant provocations for building AI systems that function not just as companions, but as a catalyst for strengthening a patient's entire relational ecology; their connections with therapists, caregivers, family, and peers. In doing so, we discuss a model towards a more sustainable ecosystem of relationship-centered AI in mental health care.
arXiv:2607.11037v1 Announce Type: cross
Abstract: Chiral nonlinear optical (NLO) responses enable efficient discrimination of circularly polarized light (CPL) and are attracting increasing interest for optical and optoelectronic technologies. However, studies on NLO properties in chiral materials have largely focused on second-order NLO processes, while the role of chirality in third-order NLO processes remains poorly explored. Here, we demonstrate telecom-band CPL detection by third harmonic generation circular dichroism (THG-CD) in the chiral two-dimensional perovskite (R/S-MBACl)2PbI4 and uncover a giant hidden THG-CD anisotropy that is accessible via polarization-resolved detection. Polarization-resolved THG measurements reveal that opposite chiral NLO responses emerge in orthogonal THG polarization channels. Therefore, these chiral anisotropic contributions largely cancel each other in the total-THG signal detection, leading to underestimation of the THG-CD dissymmetry in conventional evaluations based on total-THG intensity. By separating these hidden chiral contributions, we observe exceptionally large dissymmetry factors exceeding 1.9 and achieve selective extraction of chiral NLO responses with opposite handedness, without any structural chiral inversion. These findings highlight the importance of polarization-resolved analysis for evaluating more accurate chiral NLO responses inherent to the material and provide a promising platform for optical information processing, encryption, and anti-counterfeiting technologies at technologically relevant telecommunication wavelengths.
arXiv:2605.15133v2 Announce Type: replace
Abstract: Causal inference, estimating causal effects from observational data, is a fundamental tool in many disciplines. Of particular importance across a variety of domains is the continuous treatment setting, where the variable of intervention has a continuous range. This setting is far less explored and represents a substantial shift from the binary treatment setting, with models needing to represent effects across a continuum of treatment values. In this paper, we present the first causal foundation model for the continuous treatment setting. Our model meta-learns the ability to predict causal effects across a wide variety of unseen tasks without additional training or fine-tuning. First, we design a novel prior over data-generating processes with continuous treatment variables in order to generate a rich causal training corpus. We then train a transformer to reconstruct individual treatment-response curves given only observational data, leveraging in-context learning to amortize expensive Bayesian posterior inference. Our model achieves state-of-the-art performance on individual treatment-response curve reconstruction tasks compared to causal models which are trained specifically for those tasks. Inference code (including trained model weights) can be found at https://github.com/layer6ai-labs/CCPFN-inference .
arXiv:2604.16514v5 Announce Type: replace
Abstract: Autoregressive vision-language models (VLMs) deliver strong multimodal capability, but their token-by-token decoding imposes a fundamental inference bottleneck. Diffusion VLMs offer a more parallel decoding paradigm, yet directly converting a pretrained autoregressive VLM into a large-block diffusion VLM (dVLM) often leads to substantial quality degradation. In this work, we present BARD, a simple and effective bridging framework that converts a pretrained autoregressive VLM into a same-architecture, decoding-efficient dVLM. Our approach combines progressive supervised block merging, which gradually enlarges the decoding block size, with stage-wise intra-dVLM distillation from a fixed small-block diffusion anchor to recover performance lost at larger blocks. We further incorporate a mixed noise scheduler to improve robustness and token revision during denoising, and memory-friendly training to enable efficient training on long multimodal sequences. A key empirical finding is that direct autoregressive-to-diffusion distillation is poorly aligned and can even hurt performance, whereas distillation within the diffusion regime is consistently effective. Experimental results show that, with $\leq$ 4.4M data, BARD-VL transfers strong multimodal capability from Qwen3-VL to a large-block dVLM. Remarkably, BARD-VL establishes a new SOTA among comparable-scale open dVLMs on our evaluation suite at both 4B and 8B scales. At the same time, BARD-VL achieves up to 3$\times$ decoding throughput speedup compared to the source model. Code is available at https://github.com/fudan-generative-vision/Bard-VL.
arXiv:2604.11388v4 Announce Type: replace
Abstract: Consider the classical Min-Sum Set Cover problem: We are given a universe $\mathcal{U}$ of $n$ elements and a collection $\mathcal{S}$ of $k$ subsets of $\mathcal{U}$. The goal is to find a subsequence of sets from $\mathcal{S}$ which covers all elements in $\mathcal{U}$, such that the sum of the covering times of the elements is minimized. This problem can be seen as a scheduling problem on a single machine, where each job represents a set and elements are represented by some kind of utility that is required to be provided by at least one of the jobs. The goal is to schedule the jobs in such a way to minimize the sum of provision times of the utilities. In this paper we consider a natural generalization of this problem to the case of $m$ machines, processing the jobs in parallel. We call this problem Parallel Min-Sum Set Cover.
To obtain approximation algorithms for various variants of this task, we exploit a crucial sub-problem called Parallel Densest Subfamily, where the goal is to find an asignment of sets to the machines that maximizes the ratio of the number of covered elements to the length of the assignment. We prove that an $\alpha$-approximation algorithm for this problem implies a $4\alpha$-approximation algorithm for Parallel Min-Sum Set Cover. Then, we show how to find such an assignment using the well known Maximum Coverage Multiple Knapsack problem. In particular, this yields a $\frac{4e}{e-1}+\epsilon$-approximation for identical machines and an $\frac{8e}{e-1}+\epsilon$-approximation for unrelated machines. If the sets are subject to precedence constraints we give a greedy algorithm for unit cost sets, with an $O(k^{2/3})$ approximation ratio and an $O(\log k)$-approximation algorithm for out-forest precedence constraints and identical machines. The latter algorithm uses a reduction to the Group Steiner Orienteering problem which is of independent interest.