#01Aug 13, 2026
cond-mat.stat-mech
Equivariant learning of a transferable three-dimensional classical density functional
Bingqing Cheng
Liquids exhibit collective behavior that depends sensitively on thermodynamic conditions, interfaces and confinement, yet predicting each new state commonly requires a separate atomistic simulation. Classical density functional theory offers a reusable variational description, but its central excess free-energy functional is generally unknown, and learned approximations have largely remained restricted to planar or lower-dimensional settings. Here we show that this functional can be learned directly from fully three-dimensional equilibrium density fields while preserving spatial symmetry and variational consistency, without free-energy or chemical-potential labels. A single learned functional transfers across temperatures, system sizes and statistical ensembles, and recovers structure factors, the equation of state, liquid--vapor coexistence and interfacial broadening, none of which are used as training targets. Applied to complex three-dimensional geometries, it predicts the non-monotonic force associated with formation and rupture of a solvent-depleted bridge between colloids and adsorption in an interconnected gyroid pore. These results demonstrate that equilibrium density data can be converted into a transferable thermodynamic generator connecting microscopic liquid structure to response, phase behavior and collective phenomena.
#02Aug 13, 2026
cs.LG
Sparse Orthogonal Regression Technique: A Spectral Framework for Equation Discovery, Approximation, and Integration
Sabin Roman, Ljupco Todorovski, Saso Dzeroski
We develop the Sparse Orthogonal Regression Technique (SORT), a sparse spectral framework for learning orthonormal-basis expansions from noisy and irregularly sampled data. SORT estimates expansion coefficients directly from observations using L1-regularized regression, avoiding explicit quadrature or analytic inner-product evaluation. The central application is data-driven discovery of ordinary differential equations: vector fields are represented in chosen orthogonal bases and learned as sparse coefficient expansions. This provides a complementary route to symbolic regression, grammar-based discovery, and SINDy-style sparse identification by first recovering a compact spectral representation, which can later guide searches for simpler analytic forms. Across the dynamical-system experiments, SORT matches or improves upon library-based sparse-regression baselines when the basis is well adapted to the problem, and shows more stable degradation under sparse sampling, noisy derivative estimates, and representation mismatch. Specific examples illustrate why this representation is useful: if a finite library misses the problem-specific nonlinearity, the resulting model can fail. SORT is not immune to mismatch, but it shifts the problem away from brittle selection among generic terms to basis design adapted to the problem domain. The experiments also show that dominant low-order coefficients persist as model order increases, supporting order-consistent model growth. Beyond equation discovery, the same learned expansion supports nonlinear approximation and estimation of complex, high-dimensional integrals by coefficient readout. Overall, SORT provides a reusable intermediate representation for system identification, approximation, and integration, while making basis design an explicit part of the scientific modeling problem.
#03Aug 13, 2026
cs.CL
Measuring Task-Agnostic Training Data Influence Across Language Model Pretraining
Yuto Nishida, Hirokazu Kiyomaru, Yusuke Oda and 6 more
Measuring training data influence consistently across language model pretraining is challenging. It is difficult to select downstream tasks or validation sets representative of a model's general capabilities, and reliance on task performance at intermediate checkpoints complicates comparisons across training. We propose a measure of training data influence that does not require selecting a downstream task or validation set as the attribution target. Specifically, we define an example's influence by how much its gradient update reduces the squared distance to the final parameters of a given pretraining run, and estimate this quantity from intermediate checkpoints without retraining. Applying the method to 18 configurations from the Pythia and PolyPythia suites, we find systematic temporal changes in influential data. Early in training, literature-related data are more strongly aligned with the trajectory toward the final parameters, whereas STEM data become more strongly aligned in later stages. This qualitative crossover is broadly consistent across model configurations. Our results provide a tractable trajectory-level view of how influential data change throughout pretraining, complementing influence analyses defined with respect to specific downstream tasks or validation sets.
#04Aug 13, 2026
cs.CV
SCULPT: Subtractive Composition for 3D Part Generation
Sikuang Li, Chen Yang, Jiemin Fang and 5 more
Part-aware 3D generation aims to create digital assets that are coherent as complete objects while exposing structural parts for editing, material assignment, animation, and reuse. Existing methods impose this structure outside the native generation loop: segmentation-based methods partition an already generated shape, while additive methods synthesize parts from predefined layouts, boxes, or tokens and then reconcile them into a whole. The former preserves the generated geometry but fixes the object before part boundaries are determined; the latter exposes part cardinality but often leaves shared boundaries vulnerable to gaps, interpenetrations, and material discontinuities. In this paper, we propose SCULPT, a framework that addresses these challenges through subtractive composition. Given a complete object represented in a structured 3D latent space, SCULPT iteratively applies a joint split predictor to generate one extracted part together with the remaining object. The predictor performs a coupled denoising process conditioned on both the image and the current 3D state, so the extracted part and updated remainder are generated together rather than reconciled after generation. The joint split predictor processes both outputs on the union of their native sparse 3D supports, allowing neighboring supports to overlap rather than imposing a disjoint voxel partition. The rollout ends when the remainder support becomes empty or reaches a fixed safety cap, allowing the number of generated parts to adapt to each object within that bound. Extensive experiments demonstrate state-of-the-art geometry on PartObjaverse while preserving strong complete-object reconstruction after part assembly. Results on four dataset images, one text-to-image-generated input, and one real-world photograph further show fine-grained textured part decomposition beyond the benchmark.
#05Aug 13, 2026
cs.CV
V-RAE: Rethinking Video Latent Spaces for Generation
Minghui Guo, Shengqiong Wu, Hao Fei
Latent video generation relies on autoencoders to define a compact space in which generative models operate. Although video autoencoder architectures have evolved substantially, their latent spaces are still optimized primarily for pixel-level reconstruction and provide limited high-level semantic organization. A reconstruction-optimal latent space, however, need not be well suited to generative modeling. We propose V-RAE, a video representation autoencoder that builds compact generative latents on top of frozen vision foundation model representations. A lightweight temporal pooling module removes temporal redundancy while preserving semantic structure, and a video decoder reconstructs continuous motion from the compressed features. We evaluate V-RAE with four representative frozen encoders on video reconstruction, semantic probing, and class-conditional generation. V-RAE achieves 2.13 rFVD on K600, outperforming all evaluated large-scale pretrained video VAEs. Its latents retain substantially more semantic information than conventional video tokenizer latents. Under matched generation settings, our best variant achieves gFVD scores of 117.86 and 19.16 on UCF101 and K600, respectively, while converging up to 6x faster}. We further show that reconstruction quality alone is insufficient to characterize generative utility and introduce tFVD, a temporal-coherence diagnostic that correlates more reliably with downstream generation quality. Beyond video generation, V-RAE also improves future video prediction on Cityscapes over the Wan 2.2 VAE latent space under matched prediction settings. Taken together, the experiments show that frozen semantic representations can support video reconstruction, generation, and predictive modeling. The project page: https://v-rae.github.io/.