Dataset Condensation is a newly emerging technique aiming at learning a tiny dataset that captures the rich information encoded in the original dataset.

We study the optimization problem associated with fitting two-layer ReLU neural networks with respect to the squared loss, where labels are generated by a target network. Use is made of the rich symmetry structure to develop a novel set of tools for studying the mechanism by which over-parameterization annihilates spurious minima through. Sharp analytic estimates are obtained for the loss and the Hessian spectrum at different minima, and it is shown that adding neurons can turn symmetric spurious minima into saddles through a local mechanism that does not generate new spurious minima; minima of smaller symmetry require more neurons. Using Cauchy's interlacing theorem, we prove the existence of descent directions in certain subspaces arising from the symmetry structure of the loss function. This analytic approach uses techniques, new to the field, from algebraic geometry, representation theory and symmetry breaking, and confirms rigorously the effectiveness of over-parameterization in making the associated loss landscape accessible to gradient-based methods. For a fixed number of neurons and inputs, the spectral results remain true under symmetry breaking perturbation of the target.

We study the optimization problem associated with fitting two-layer ReLU neural networks with respect to the squared loss, where labels are generated by a target network. We make use of the rich symmetry structure to develop a novel set of tools for studying families of spurious minima. In contrast to existing approaches which operate in limiting regimes, our technique directly addresses the nonconvex loss landscape for finite number of inputs $d$ and neurons $k$, and provides analytic, rather than heuristic, information. In particular, we derive analytic estimates for the loss at different minima, and prove that, modulo $O(d^{-1/2})$-terms, the Hessian spectrum concentrates near small positive constants, with the exception of $\Theta(d)$ eigenvalues which grow linearly with~$d$. We further show that the Hessian spectrum at global and spurious minima coincide to $O(d^{-1/2})$-order, thus challenging our ability to argue about statistical generalization through local curvature. Lastly, our technique provides the exact \emph{fractional} dimensionality at which families of critical points turn from saddles into spurious minima. This makes possible the study of the creation and the annihilation of spurious minima using powerful tools from equivariant bifurcation theory.

We consider the optimization problem associated with fitting two-layers ReLU networks with respect to the squared loss, where labels are generated by a target network. We leverage the rich symmetry structure to analytically characterize the Hessian at various families of spurious minima in the natural regime where the number of inputs $d$ and the number of hidden neurons $k$ is finite. In particular, we prove that for $d\ge k$ standard Gaussian inputs: (a) of the $dk$ eigenvalues of the Hessian, $dk - O(d)$ concentrate near zero, (b) $\Omega(d)$ of the eigenvalues grow linearly with $k$. Although this phenomenon of extremely skewed spectrum has been observed many times before, to our knowledge, this is the first time it has been established {rigorously}. Our analytic approach uses techniques, new to the field, from symmetry breaking and representation theory, and carries important implications for our ability to argue about statistical generalization through local curvature.

Generative models for materials, especially inorganic crystals, hold potential to transform the theoretical prediction of novel compounds and structures. Advancement in this field depends on robust benchmarks and minimal, information-rich datasets that enable meaningful model evaluation. This paper critically examines common datasets and reported metrics for a crystal structure prediction task$\unicode{x2014}$generating the most likely structures given the chemical composition of a material. We focus on three key issues: First, materials datasets should contain unique crystal structures; for example, we show that the widely-utilized carbon-24 dataset only contains $\approx$40% unique structures. Second, materials datasets should not be split randomly if polymorphs of many different compositions are numerous, which we find to be the case for the perov-5 and MP-20 datasets. Third, benchmarks can mislead if used uncritically, e.g., reporting a match rate metric without considering the structural variety exhibited by identical building blocks. To address these oft-overlooked issues, we introduce several fixes. We provide revised versions of the carbon-24 dataset: one with duplicates removed, one deduplicated and split by number of atoms $N$, one with enantiomorphs, and two containing only identical structures but with different unit cells. We also propose new splits for datasets with polymorphs, ensuring that polymorphs are grouped within each split subset, setting a more sensible standard for benchmarking model performance. Finally, we present METRe and cRMSE, new model evaluation metrics that can correct existing issues with the match rate metric.

Boltzmann machines (BMs) are powerful energy-based generative models, but their heavy training cost has largely confined practical use to Restricted BMs (RBMs) trained with an efficient learning method called contrastive divergence. More accurate learning typically requires Markov chain Monte Carlo (MCMC) Boltzmann sampling, but it is time-consuming due to the difficulty of parallelization for more expressive models. To address this limitation, we first propose a new Boltzmann sampler inspired by a quantum-inspired combinatorial optimization called simulated bifurcation (SB). This SB-inspired approach, which we name Langevin SB (LSB), enables parallelized sampling while maintaining accuracy comparable to MCMC. Furthermore, this is applicable not only to RBMs but also to BMs with general couplings. However, LSB cannot control the inverse temperature of the output Boltzmann distribution, which hinders learning and degrades performance. To overcome this limitation, we also developed an efficient method for estimating the inverse temperature during the learning process, which we call conditional expectation matching (CEM). By combining LSB and CEM, we establish an efficient learning framework for BMs with greater expressive power than RBMs. We refer to this framework as sampler-adaptive learning (SAL). SAL opens new avenues for energy-based generative modeling beyond RBMs.

The boundary element method (BEM) provides an efficient numerical framework for solving multiple scattering problems in unbounded homogeneous domains, since it reduces the discretization to the domain boundaries, thereby condensing the computational complexity. The procedure first consists in determining the solution trace on the boundaries of the domain by solving a boundary integral equation, after which the volumetric solution can be recovered at low computational cost with a boundary integral representation. As the first step of the BEM represents the main computational bottleneck, we introduce PIBNet, a learning-based approach designed to approximate the solution trace. The method leverages a physics-inspired graph-based strategy to model obstacles and their long-range interactions efficiently. Then, we introduce a novel multiscale graph neural network architecture for simulating the multiple scattering. To train and evaluate our network, we present a benchmark consisting of several datasets of different types of multiple scattering problems. The results indicate that our approach not only surpasses existing state-of-the-art learning-based methods on the considered tasks but also exhibits superior generalization to settings with an increased number of obstacles. github.com/ENSTA-U2IS-AI/pibnet

Abstract-- Inspecting large-scale industrial surfaces like aircraft fuselages for quality control requires precise, high-resolution 3D geometry. Vision-based tactile sensors (VBTSs) offer high local resolution but require slow'press-and-lift' measurements for large areas. Sliding or roller/belt VBTS designs provide continuous measurement but face significant challenges: sliding suffers from friction/wear, while both are speed-limited by camera frame rates and motion blur . Thus, a rapid, continuous, high-resolution method is needed. We introduce a novel neuromorphic tactile roller sensor . It uses a modified event-based multi-view stereo algorithm for 3D reconstruction, leveraging high temporal resolution and motion blur robustness. This reconstruction is most effective for surfaces with distinct edges or sharp features, which are often the most critical for defect detection in industrial inspection tasks. We demonstrate 0.5 m/s scanning speeds with MAE below 100 µm (11x faster than prior methods). A multi-reference Bayesian fusion strategy reduces MAE by 25.2% (vs. Surface metrology and surface inspection are crucial elements in quality assurance across diverse industries, particularly aerospace and automotive manufacturing. Precise inspection is required to identify characteristics like paint quality, coating integrity, and subtle defects such as cracks, nicks, and dents [1], [2], [3]. Often, achieving a resolution of 0.1 mm or lower is necessary to accurately classify these features and ensure component integrity and safety [4]. Traditional contact-based methods, including high-precision profilometers [5], [6] or microscopic techniques [7], [8], [9], offer high resolution locally but become exceedingly time-consuming when applied to large surface areas due to their sequential, point-by-point or small-patch measurement nature. Non-contact optical methods, such as cameras, laser scanners, or structured light systems [2], [10], [11], [12], [13], [14], can significantly accelerate inspection by capturing data over wider areas. However, these methods often lack robustness; their performance can be compromised by variations in ambient lighting, motion blur when attempting high-speed scanning, or challenging surface optical properties like high reflectivity or transparency [15].

Recent progress in 4D representations, such as Dynamic NeRF and 4D Gaussian Splatting (4DGS), has enabled dynamic 4D scene reconstruction. However, text-driven 4D scene editing remains under-explored due to the challenge of ensuring both multi-view and temporal consistency across space and time during editing. Existing studies rely on 2D diffusion models that edit frames independently, often causing motion distortion, geometric drift, and incomplete editing. We introduce Dynamic-eDiTor, a training-free text-driven 4D editing framework leveraging Multimodal Diffusion Transformer (MM-DiT) and 4DGS. This mechanism consists of Spatio-Temporal Sub-Grid Attention (STGA) for locally consistent cross-view and temporal fusion, and Context Token Propagation (CTP) for global propagation via token inheritance and optical-flow-guided token replacement. Together, these components allow Dynamic-eDiTor to perform seamless, globally consistent multi-view video without additional training and directly optimize pre-trained source 4DGS. Extensive experiments on multi-view video dataset DyNeRF demonstrate that our method achieves superior editing fidelity and both multi-view and temporal consistency prior approaches. Project page for results and code: https://di-lee.github.io/dynamic-eDiTor/