Research Papers

arXiv:2605.25303v1 Announce Type: cross Abstract: The $2 \rightarrow q$ norm of a matrix $X \in \mathbb{R}^{n \times d}$ is defined as $\lVert X \rVert_{2 \rightarrow q} = \sup_{\lVert v \rVert_2 = 1} \lVert Xv \rVert_q$. We give polynomial-time multiplicative approximation algorithms for this norm when $q > 2$ (i.e. in the hypercontractive setting). This problem either directly captures or is closely related to long-standing open problems in combinatorial optimization and hardness of approximation (e.g. Small Set Expansion), quantum information (e.g. Best Separable State), and algorithmic statistics. Very little is known about what approximation factors we can achieve for this problem in polynomial time, even though such approximations have significant downstream consequences. Barak, Brand\~{a}o, Harrow, Kelner, Steurer, and Zhou showed that no polynomial-time algorithm can achieve an approximation factor better than $2^{\sqrt{\log n}}$, assuming the Exponential Time Hypothesis (FOCS'

arXiv:2605.25347v1 Announce Type: cross Abstract: We introduce ERNIE-Image, an open-source text-to-image generation model built upon an 8B single-stream DiT architecture. ERNIE-Image aims to bridge the gap between current open-source models and leading closed-source systems through more effective mining of large-scale pre-training data and improved supervision quality throughout training. During pre-training, we adopt a bottom-up data construction pipeline that combines fine-grained image categorization, rich caption annotation, aesthetic assessment, and hierarchical sampling. This strategy reduces data noise while preserving long-tail concepts and detailed real-world knowledge, providing a stronger foundation for complex generation tasks. In the post-training stage, we use a top-down data construction pipeline for high-demand scenarios, diversify prompt annotations to better match real user inputs, and apply a stabilized DPO strategy to align the model with human aesthetic preferences

arXiv:2605.25383v1 Announce Type: cross Abstract: We consider graph diffusion processes constructed from finite i.i.d. samples drawn from an unknown manifold embedded in ambient Euclidean space, where the graph affinity is defined by an ambient Gaussian kernel matrix. We show that the manifold heat semigroup $Q_t = e^{t\Delta}$ can be approximated directly by iterating the graph transition matrix $P$, under only low regularity assumptions on the test function $f$, including the case $f \in L^\infty$. We bound $\| P^n f - Q_t f \|$ in $\infty$-norm, with the operator application to $f$ properly defined, and we recover the classical graph-Laplacian pointwise rate $O(N^{-2/(d+6)})$ up to logarithmic factors, for diffusion times $t $ up to $O(1)$ and longer. The rate holds for in-sample error as well as out-of-sample generalization, where the estimator of $Q_t f$ at a new point is defined via kernel convolution. To handle non-uniform sampling densities on the manifold, we introduce a right

arXiv:2605.25418v1 Announce Type: cross Abstract: Generating 3D models from face sketches is an active topic of research in Computer Graphics due to its potential to tremendously facilitate the modeling of faces for both professional 3D arists and novices. Motivated by the observation that facial expressions are responsible for significantly altering and shaping the contours in our faces, we combine both expression detection and 3D model generation in our approach. The result is a novel approach to generating 3D models from sketches which relies on three components: Convolutional Neural Networks, a parametric 3D face model (Valley Girl), and Active Snake Contours. For the first time in the literature, CNNs are trained (using our own generated dataset) to detect the expression in the given sketch through detecting the active FACS Action Units. The expression is then duplicated on Valley Girl to obtain a 3D model with a similar expression. Active Snake Contours are then used to find the

arXiv:2605.25452v1 Announce Type: cross Abstract: Graph Neural Networks (GNN) are currently the most popular approach for learning and prediction on graph-structured data and are deployed in various fields, from social network analysis to drug discovery. However, there is limited mathematical understanding of the performance of GNNs. We discuss the various perspectives used to study statistical generalisation in GNNs. We identify three broad frameworks. The first approach, rooted in learning theory, relies on uniform convergence bounds and the complexity of the hypothesis class of specific GNN architectures. This approach also builds on the expressivity of GNNs, typically studied through the lens of graph isomorphism tests. The second principle is to simplify the neural architecture by analysing GNNs under the asymptotics of infinitely many parameters or infinite graph size. This approach approximates GNNs using Gaussian processes, neural tangent kernels or graphon neural network opera

arXiv:2605.25460v1 Announce Type: cross Abstract: Removing noise is difficult, but adding noise is easy. In this work, we show how to eliminate mean-shift noisy components from PCA by deliberately introducing knockoff mean-shift perturbation. Standard PCA is highly sensitive to shifts in the sample mean: a small fraction of samples from a shifted distribution can cause large deviations in the leading principal components. In high-dimensional regimes, existing Robust PCA approaches cannot handle the mean-shift contamination structure inherent in the mixture model. Using tools from Random Matrix Theory, we prove that the mean-shift spikes are spectrally separable from the stable eigenvalues of the original covariance. Furthermore, the original eigenspace remains asymptotically invariant to the contamination, independent of the mixture weight. Exploiting this spectral stability, we propose a simple, two-stage PCA algorithm by adding knockoff mean that identifies and removes the mean-shift

arXiv:2605.25509v1 Announce Type: cross Abstract: Reconstructing PDE solutions from sparse observations is a core challenge in scientific computing. We present FM4PDE, a flow-matching generative framework that learns the joint distribution of PDE coefficients (or initial states) and solutions (or final states), enabling both forward simulation and inverse recovery with limited paired data. At inference, sampling is guided by a composite loss that enforces agreement with sparse measurements and reduces the PDE residual; we support deterministic, stochastic, and hybrid samplers. We provide error guarantees for these guided procedures. For the deterministic optimizer, a coercivity condition ensures trajectory boundedness and a phase-wise contraction yields logarithmic complexity in the target accuracy. For the stochastic sampler, we introduce adaptive guidance and assume dissipativity of the velocity field to obtain uniform moment bounds independent of the noise-floor parameter. This lead

arXiv:2605.25526v1 Announce Type: cross Abstract: We study the geometry of determinantal point processes (DPPs) through the spectral decomposition $L=U\Lambda U^{\top}$. The spectrum $\Lambda$ governs the cardinality distribution via elementary symmetric polynomials, while the eigenspace orientation $U$ governs the conditional law within each fixed-cardinality stratum. Conditioning on cardinality $k$ yields the $k$-DPP, for which the identifiability structure changes fundamentally: the spectral parameter becomes identifiable only up to a common scale, and the eigenspace rotation parameter is identifiable only through squared minors of the eigenvector matrix. We characterize the identifiability gap precisely, via three explicit invariances (scale, sign similarity, and eigenspace rotation) and a dimension-counting theorem showing the existence of additional continuous non-identifiability whenever $\binom{N}{k}<N(N+1)/2$. In contrast, for the full DPP the non-identifiability comes only fr

arXiv:2605.25540v1 Announce Type: cross Abstract: Alzheimer's disease (AD) is a progressive neurodegenerative disorder and the leading cause of dementia, affecting memory, reasoning, communication, and daily functioning. Early diagnosis is particularly important, as timely intervention may help slow cognitive decline and improve patient care. Recent studies have demonstrated that spontaneous speech contains valuable linguistic and acoustic biomarkers associated with dementia. However, existing approaches often rely on independently trained modality-specific models, feature concatenation strategies, ensemble methods, or attention-based fusion mechanisms that do not explicitly maximize the dependency between speech and transcript representations. In this work, we propose a multimodal deep learning framework for automatic dementia detection that jointly exploits speech and transcript information in an end-to-end trainable manner. Specifically, speech recordings are divided into 10-second

arXiv:2605.25590v1 Announce Type: cross Abstract: We study nonstationary generalized linear bandits (GLBs), where the expected reward is modeled through a nonlinear link function with an unknown time-varying parameter. This framework encompasses a broad class of reward models, including linear, Bernoulli, and binomial rewards. Existing approaches are predominantly based on maximum-likelihood estimation (MLE), using sliding-window, restart, or discounting mechanisms to handle nonstationarity. Although these methods achieve statistically efficient regret guarantees, they generally require revisiting past observations at every round, which leads to computation and memory costs that grow with time; moreover, several of them rely on a non-convex projection step. In this paper, we propose DOMD-GLB, a new algorithm for nonstationary GLBs that utilizes discounted online mirror descent (DOMD) for parameter estimation, thereby incurring only $O(1)$ computation and memory costs per round. We prov

arXiv:2605.25592v1 Announce Type: cross Abstract: We study optimal experimental design for multinomial logit (MNL) bandits, where an agent repeatedly selects a subset of $K$ items from a ground set of size $N$ and observes single-choice feedback. Unlike linear or generalized linear bandits, MNL bandits have a combinatorial action space, which makes classical optimal design approaches and naive optimization over all subsets computationally intractable. We propose a computationally efficient optimal design framework for MNL models that achieves both statistical efficiency and scalability through two complementary approaches: (i) an exact or certified-approximate reformulation of the design oracle as a $0$-$1$ mixed-integer linear program (MILP) with solver-certified early stopping, and (ii) a fully polynomial-time lifted design that replaces the nonlinear objective with a tractable surrogate. Using the Kiefer-Wolfowitz equivalence theorem, we establish near G-optimality guarantees and ch

arXiv:2605.25604v1 Announce Type: cross Abstract: Reinforcement Learning has become a standard paradigm for aligning Large Language Models with human intent and task requirements. While Group Relative Policy Optimization offers an efficient, value-model-free alternative to Proximal Policy Optimization, adapting it to real-world multi-reward settings remains challenging. Standard scalarization practices, such as Reward Combination and Advantage Combination, suffer from significant drawbacks: Reward Combination frequently generates advantages with excessively large squared magnitudes that lead to training instability, while Advantage Combination relies on static hyperparameters and ignores cross-objective correlations. To address these limitations, we propose Dynamic Variance-adaptive Advantage Optimization (DVAO), which dynamically adjusts combination weights based on the empirical reward variance of each objective within a rollout group, effectively up-weighting objectives with a stron

arXiv:2605.25605v1 Announce Type: cross Abstract: In the past decade, numerous studies have applied deep neural networks (DNNs) to decode auditory attention (AAD) from Electroencephalogram (EEG) signals via stimulus reconstruction. However, the influence of dataset balance on the decoding performance of stimulus reconstruction-based AAD remains unexplored. In this study, three publicly available EEG-AAD datasets - KUL, DTU, and NJU cEEGrid - are used to construct both balanced and unbalanced experimental conditions. We hypothesize and demonstrate that stimulus reconstruction-based DNN decoders tend to produce overestimated decoding performance on unbalanced datasets. To address this issue, we propose a leave-one-paired-envelope-out (LOPEO) cross-validation protocol. Experimental results confirm that LOPEO effectively prevents inflated decoding accuracy on unbalanced datasets. While balanced datasets are generally preferred in experimental design, LOPEO provides a principled evaluation

arXiv:2605.25608v1 Announce Type: cross Abstract: The ability of deep neural networks to learn hierarchical features is widely regarded as a key mechanism underlying their success in high-dimensional learning. Existing theory partially supports this view by establishing approximation rates based on parameter counts and sample complexity guarantees for compositional models without incurring the curse of dimensionality (CoD). To study overparameterized regimes, where the number of parameters exceeds the sample size, we develop a framework that measures complexity via the parameter norm. Within this approach, we establish approximation rates and excess risk bounds for learning sparse compositional functions whose compositional structure is represented by directed acyclic graphs (DAGs), using Frobenius norm-constrained deep neural networks. Our results have broad applicability since every function that is efficiently Turing computable admits sparse compositional representations. In particu

arXiv:2605.24339v1 Announce Type: new Abstract: We present IsaacIPC, a robotic simulation framework that couples GPU accelerated incremental potential contact (IPC) with IsaacSim/Lab. IsaacIPC maps simulated deformation between simulation and visual meshes, enabling real-time realistic rendering with applications to data collection and policy evaluation. For tactile sensing, we introduce the geometric mortar contact potential (GMCP), which defines a barrier potential over contact samples on tactile surfaces to better resolve contact-pressure distributions. We evaluate GMCP on contact benchmarks and demonstrate IsaacIPC on rigid-deformable robotic simulations including a quadruped robot, a dexterous hand, and a universal manipulation interface (UMI) gripper.