We introduce Stanford-ORB, a new real-world 3DObject inverse Rendering Benchmark. Recent advances in inverse rendering have enabled a wide range of real-world applications in 3D content generation, moving rapidly from research and commercial use cases to consumer devices. While the results continue to improve, there is no real-world benchmark that can quantitatively assess and compare the performance of various inverse rendering methods. Existing real-world datasets typically consist only of the shape and multi-view images of objects, which are not sufficient for evaluating the quality of material recovery and object relighting. Methods capable of recovering material and lighting often resort to synthetic data for quantitative evaluation, which on the other hand does not guarantee generalization to complex real-world environments. We introduce a new dataset of real-world objects captured under a variety of natural scenes with ground-truth 3D scans, multi-view images, and environment lighting. Using this dataset, we establish the first comprehensive real-world evaluation benchmark for object inverse rendering tasks from in-thewild scenes and compare the performance of various existing methods. All data, code, and models can be accessed at https://stanfordorb.github.io/.

Conditional independence is central to modern statistics, but beyond special parametric families it rarely admits an exact covariance characterization. We introduce the binary expansion group intersection network (BEGIN), a distribution-free graphical representation for multivariate binary data and bit-encoded multinomial variables. For arbitrary binary random vectors and bit representations of multinomial variables, we prove that conditional independence is equivalent to a sparse linear representation of conditional expectations, to a block factorization of the corresponding interaction covariance matrix, and to block diagonality of an associated generalized Schur complement. The resulting graph is indexed by the intersection of multiplicative groups of binary interactions, yielding an analogue of Gaussian graphical modeling beyond the Gaussian setting. This viewpoint treats data bits as atoms and local BEGIN molecules as building blocks for large Markov random fields. We also show how dyadic bit representations allow BEGIN to approximate conditional independence for general random vectors under mild regularity conditions. A key technical device is the Hadamard prism, a linear map that links interaction covariances to group structure.

Molecule inverse folding has been a long-standing challenge in chemistry and biology, with the potential to revolutionize drug discovery and material science. Despite specified models have been proposed for different small-or macro-molecules, few have attempted to unify the learning process, resulting in redundant efforts. Complementary to recent advancements in molecular structure prediction, such as RoseTTAFold All-Atom and AlphaFold3, we propose the unified model UniIF for the inverse folding of all molecules. We do such unification in two levels: 1) Data-Level: We propose a unified block graph data form for all molecules, including the local frame building and geometric feature initialization.

Implicit representation has opened up new possibilities for inverse rendering. However, existing implicit neural inverse rendering methods struggle to handle strongly illuminated scenes with significant shadows and slight reflections. The existence of shadows and reflections can lead to an inaccurate understanding of the scene, making precise factorization difficult. To this end, we present RobIR, an implicit inverse rendering approach that uses ACES tone mapping and regularized visibility estimation to reconstruct accurate BRDF of the object. By accurately modeling the indirect radiance field, normal, visibility, and direct light simultaneously, we are able to accurately decouple environment lighting and the object's PBR materials without imposing strict constraints on the scene. Even in high-illumination scenes with shadows and specular reflections, our method can recover high-quality albedo and roughness with no shadow interference. RobIR outperforms existing methods in both quantitative and qualitative evaluations.

In this paper, we analyze the sample and communication complexity of the federated linear stochastic approximation (FedLSA) algorithm. We explicitly quantify the effects of local training with agent heterogeneity. We show that the communication complexity of FedLSA scales polynomially with the inverse of the desired accuracy ϵ. To overcome this, we propose SCAFFLSA a new variant of FedLSA that uses control variates to correct for client drift, and establish its sample and communication complexities. We show that for statistically heterogeneous agents, its communication complexity scales logarithmically with the desired accuracy, similar to Scaffnew. An important finding is that, compared to the existing results for Scaffnew, the sample complexity scales with the inverse of the number of agents, a property referred to as linear speed-up. Achieving this linear speed-up requires completely new theoretical arguments. We apply the proposed method to federated temporal difference learning with linear function approximation and analyze the corresponding complexity improvements.

This paper considers a number of related inverse filtering problems for hidden Markov models (HMMs). In particular, given a sequence of state posteriors and the system dynamics; i) estimate the corresponding sequence of observations, ii) estimate the observation likelihoods, and iii) jointly estimate the observation likelihoods and the observation sequence. We show how to avoid a computationally expensive mixed integer linear program (MILP) by exploiting the algebraic structure of the HMM filter using simple linear algebra operations, and provide conditions for when the quantities can be uniquely reconstructed. We also propose a solution to the more general case where the posteriors are noisily observed. Finally, the proposed inverse filtering algorithms are evaluated on real-world polysomnographic data used for automatic sleep segmentation.

The covariance matrix adaptation evolution strategy (CMA-ES) is arguably one of the most powerful real-valued derivative-free optimization algorithms, finding many applications in machine learning. The CMA-ES is a Monte Carlo method, sampling from a sequence of multi-variate Gaussian distributions. Given the function values at the sampled points, updating and storing the covariance matrix dominates the time and space complexity in each iteration of the algorithm. We propose a numerically stable quadratic-time covariance matrix update scheme with minimal memory requirements based on maintaining triangular Cholesky factors. This requires a modification of the cumulative step-size adaption (CSA) mechanism in the CMA-ES, in which we replace the inverse of the square root of the covariance matrix by the inverse of the triangular Cholesky factor. Because the triangular Cholesky factor changes smoothly with the matrix square root, this modification does not change the behavior of the CMA-ES in terms of required objective function evaluations as verified empirically. Thus, the described algorithm can and should replace the standard CMA-ES if updating and storing the covariance matrix matters.

However, the generalization properties of second-order methods are still being debated.

Neural operators [Kovachki et al., 2021a,b] are neural networks that take a