Generative models for materials, especially inorganic crystals, hold potential to transform the theoretical prediction of novel compounds and structures. Advancement in this field depends critically 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--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 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.

Online Continual Learning (OCL) requires models to learn sequentially from data streams with limited memory. Rehearsal-based methods, particularly Experience Replay (ER), are commonly used in OCL scenarios. This paper revisits ER through the lens of $\epsilon$-constraint optimization, revealing that ER implicitly employs a soft constraint on past task performance, with its weighting parameter post-hoc defining a slack variable. While effective, ER's implicit and fixed slack strategy has limitations: it can inadvertently lead to updates that negatively impact generalization, and its fixed trade-off between plasticity and stability may not optimally balance current streaming with memory retention, potentially overfitting to the memory buffer. To address these shortcomings, we propose the \textbf{G}radient-Guided \textbf{E}psilon \textbf{C}onstraint (\textbf{GEC}) method for online continual learning. GEC explicitly formulates the OCL update as an $\epsilon$-constraint optimization problem, which minimize the loss on the current task data and transform the stability objective as constraints and propose a gradient-guided method to dynamically adjusts the update direction based on whether the performance on memory samples violates a predefined slack tolerance $\bar{\varepsilon}$: if forgetting exceeds this tolerance, GEC prioritizes constraint satisfaction; otherwise, it focuses on the current task while controlling the rate of increase in memory loss. Empirical evaluations on standard OCL benchmarks demonstrate GEC's ability to achieve a superior trade-off, leading to improved overall performance.

Diffusion models are powerful generative models but suffer from slow sampling, often taking 1000 sequential denoising steps for one sample. As a result, considerable efforts have been directed toward reducing the number of denoising steps, but these methods hurt sample quality. Instead of reducing the number of denoising steps (trading quality for speed), in this paper we explore an orthogonal approach: can we run the denoising steps in parallel (trading compute for speed)? In spite of the sequential nature of the denoising steps, we show that surprisingly it is possible to parallelize sampling via Picard iterations, by guessing the solution of future denoising steps and iteratively refining until convergence. With this insight, we present ParaDiGMS, a novel method to accelerate the sampling of pretrained diffusion models by denoising multiple steps in parallel. ParaDiGMS is the first diffusion sampling method that enables trading compute for speed and is even compatible with existing fast sampling techniques such as DDIM and DPMSolver. Using ParaDiGMS, we improve sampling speed by 2-4x across a range of robotics and image generation models, giving state-of-the-art sampling speeds of 0.2s on 100-step DiffusionPolicy and 14.6s on 1000-step StableDiffusion-v2 with no measurable degradation of task reward, FID score, or CLIP score.1

Population risk is always of primary interest in machine learning; however, learning algorithms only have access to the empirical risk. Even for applications with nonconvex non-smooth losses (such as modern deep networks), the population risk is generally significantly more well behaved from an optimization point of view than the empirical risk. In particular, sampling can create many spurious local minima. We consider a general framework which aims to optimize a smooth nonconvex function $F$ (population risk) given only access to an approximation $f$ (empirical risk) that is pointwise close to $F$ (i.e., $\norm{F-f}_{\infty} \le \nu$). Our objective is to find the $\epsilon$-approximate local minima of the underlying function $F$ while avoiding the shallow local minima---arising because of the tolerance $\nu$---which exist only in $f$. We propose a simple algorithm based on stochastic gradient descent (SGD) on a smoothed version of $f$ that is guaranteed to achieve our goal as long as $\nu \le O(\epsilon^{1.5}/d)$. We also provide an almost matching lower bound showing that our algorithm achieves optimal error tolerance $\nu$ among all algorithms making a polynomial number of queries of $f$. As a concrete example, we show that our results can be directly used to give sample complexities for learning a ReLU unit.

As such, we prevent policies from merely exploiting heuristic rewards without improving the task reward.

Before defining our algorithm at each iterationt we first lighten our notation with a shorthandba(X) = b(ˆp(t 1)(X),a) (at different iterationt, ba denotes different functions), andb(X) is the vector of (b1(X),,bK(X)). For the intuition of the algorithm, consider the t-th iteration where the current prediction function is ˆp(t 1). Thestatement of the theorem is identical; the proof is also essentially the same except for the use of some new technicaltools. Conversely, if ˆp is LB decision calibrated, then kE[p (X) ˆp(X)|U]k1 = 0 almost surely (because if the expectation of a non-negative random variable is zero, the random variable must be zero almost surely), which implies thatˆp is distributioncalibrated. For BKa we use the VC dimension approach.