Over the past few years, research on deep graph learning has shifted from static graphs to temporal graphs in response to real-world complex systems that exhibit dynamic behaviors. In practice, temporal graphs are formalized as an ordered sequence of static graph snapshots observed at discrete time points. Sequence models such as RNNs or Transformers have long been the predominant backbone networks for modeling such temporal graphs. Yet, despite the promising results, RNNs struggle with long-range dependencies, while transformers are burdened by quadratic computational complexity. Recently, state space models (SSMs), which are framed as discretized representations of an underlying continuous-time linear dynamical system, have garnered substantial attention and achieved breakthrough advancements in independent sequence modeling. In this work, we undertake a principled investigation that extends SSM theory to temporal graphs by integrating structural information into the online approximation objective via the adoption of a Laplacian regularization term.

In this paper, we propose a neural network-based approach for learning to represent the behavior of plastic solid materials ranging from rubber and metal to sand and snow. Unlike elastic forces such as spring forces, these plastic forces do not result from the positional gradient of any potential energy, imposing great challenges on the stability and flexibility of their simulation. Our method effectively resolves this issue by learning a generalizable plastic energy whose derivative closely matches the analytical behavior of plastic forces. Our method, for the first time, enables the simulation of a wide range of arbitrary elasticity-plasticity combinations using time step-independent, unconditionally stable optimization-based time integrators. We demonstrate the efficacy of our method by learning and producing challenging 2D and 3D effects of metal, sand, and snow with complex dynamics.

This paper makes a step towards modeling the modality discrepancy in the crossspectral re-identification task. Based on the Lambertain model, we observe that the non-linear modality discrepancy mainly comes from diverse linear transformations acting on the surface of different materials. From this view, we unify all data augmentation strategies for cross-spectral re-identification by mimicking such local linear transformations and categorizing them into moderate transformation and radical transformation. By extending the observation, we propose a Random Linear Enhancement (RLE) strategy which includes Moderate Random Linear Enhancement (MRLE) and Radical Random Linear Enhancement (RRLE) to push the boundaries of both types of transformation. Moderate Random Linear Enhancement is designed to provide diverse image transformations that satisfy the original linear correlations under constrained conditions, whereas Radical Random Linear Enhancement seeks to generate local linear transformations directly without relying on external information. The experimental results not only demonstrate the superiority and effectiveness of RLE but also confirm its great potential as a general-purpose data augmentation for cross-spectral re-identification. The code is available at https://github.com/stone96123/RLE.

The third inequality follows from identifying that for a given λ, the best policy may be defined pointwise as the argument of the maximum written in the expectation. Thus, only the middle equality () deserves a proof. We obtain it by applying a general theorem of strong duality (which requires feasibility for slightly smaller cost constraints). We restate a result extracted from the monograph by Luenberger [1969]. It relies on the dual functional φ, whose expression we recall below.

This work presents general upper and lower bounds on the Kullback-Leibler (KL) divergence of coreset approximations that reflect the full range of applicability of Bayesian coresets.

An important unresolved challenge in the theory of regularization is to set the regularization coefficients of popular techniques like the ElasticNet with general provable guarantees. We consider the problem of tuning the regularization parameters of Ridge regression, LASSO, and the ElasticNet across multiple problem instances, a setting that encompasses both cross-validation and multi-task hyperparameter optimization. We obtain a novel structural result for the ElasticNet which characterizes the loss as a function of the tuning parameters as a piecewise-rational function with algebraic boundaries. We use this to bound the structural complexity of the regularized loss functions and show generalization guarantees for tuning the ElasticNet regression coefficients in the statistical setting. We also consider the more challenging online learning setting, where we show vanishing average expected regret relative to the optimal parameter pair.

Simulation-based inference (SBI) is constantly in search of more expressive and efficient algorithms to accurately infer the parameters of complex simulation models. In line with this goal, we present consistency models for posterior estimation (CMPE), a new conditional sampler for SBI that inherits the advantages of recent unconstrained architectures and overcomes their sampling inefficiency at inference time. CMPE essentially distills a continuous probability flow and enables rapid few-shot inference with an unconstrained architecture that can be flexibly tailored to the structure of the estimation problem. We provide hyperparameters and default architectures that support consistency training over a wide range of different dimensions, including low-dimensional ones which are important in SBI workflows but were previously difficult to tackle even with unconditional consistency models. Our empirical evaluation demonstrates that CMPE not only outperforms current state-of-the-art algorithms on hard low-dimensional benchmarks, but also achieves competitive performance with much faster sampling speed on two realistic estimation problems with high data and/or parameter dimensions.

The Area Under the ROC Curve (AUC) is a well-known metric for evaluating instance-level long-tail learning problems. In the past two decades, many AUC optimization methods have been proposed to improve model performance under long-tail distributions. In this paper, we explore AUC optimization methods in the context of pixel-level long-tail semantic segmentation, a much more complicated scenario. This task introduces two major challenges for AUC optimization techniques. On one hand, AUC optimization in a pixel-level task involves complex coupling across loss terms, with structured inner-image and pairwise inter-image dependencies, complicating theoretical analysis. On the other hand, we find that mini-batch estimation of AUC loss in this case requires a larger batch size, resulting in an unaffordable space complexity.