ICLR 2024 论文列表

Maximum mean discrepancy (MMD) flows suffer from high computational costs in large scale computations. In this paper, we show that MMD flows with Riesz kernels $K(x,y) = - \|x-y\|^r$, $r \in (0,2)$ have exceptional properties which allow their efficient computation. We prove that the MMD of Riesz kernels, which is also known as energy distance, coincides with the MMD of their sliced version. As a consequence, the computation of gradients of MMDs can be performed in the one-dimensional setting. Here, for $r=1$, a simple sorting algorithm can be applied to reduce the complexity from $O(MN+N^2)$ to $O((M+N)\log(M+N))$ for two measures with $M$ and $N$ support points. As another interesting follow-up result, the MMD of compactly supported measures can be estimated from above and below by the Wasserstein-1 distance. For the implementations we approximate the gradient of the sliced MMD by using only a finite number $P$ of slices. We show that the resulting error has complexity \smash{$O(\sqrt{d/P})$}, where $d$ is the data dimension. These results enable us to train generative models by approximating MMD gradient flows by neural networks even for image applications. We demonstrate the efficiency of our model by image generation on MNIST, FashionMNIST and CIFAR10.

This paper proposes a novel interpretation technique to explain the behavior of structured output models, which simultaneously learn mappings between an input vector and a set of output variables. As a result of the complex relationships between the computational path of output variables in structured models, a feature may impact an output value via other output variables. We focus on one of the outputs as the target and try to find the most important features adopted by the structured model to decide on the target in each locality of the input space. We consider an arbitrary structured output model available as a black-box and argue that considering correlations among output variables can improve explanation quality. The goal is to train a function as an interpreter for the target output variable over the input space. We introduce an energy-based training process for the interpreter function, which effectively considers the structural information incorporated into the model to be explained. The proposed method's effectiveness is confirmed using various simulated and real data sets.

Molecular conformation optimization is crucial to computer-aided drug discovery and materials design. Traditional energy minimization techniques rely on iterative optimization methods that use molecular forces calculated by a physical simulator (oracle) as anti-gradients. However, this is a computationally expensive approach that requires many interactions with a physical simulator. One way to accelerate this procedure is to replace the physical simulator with a neural network. Despite recent progress in neural networks for molecular conformation energy prediction, such models are prone to errors due to distribution shift, leading to inaccurate energy minimization. We find that the quality of energy minimization with neural networks can be improved by providing optimization trajectories as additional training data. Still, obtaining complete optimization trajectories demands a lot of additional computations. To reduce the required additional data, we present the Gradual Optimization Learning Framework (GOLF) for energy minimization with neural networks. The framework consists of an efficient data-collecting scheme and an external optimizer. The external optimizer utilizes gradients from the energy prediction model to generate optimization trajectories, and the data-collecting scheme selects additional training data to be processed by the physical simulator. Our results demonstrate that the neural network trained with GOLF performs \textit{on par} with the oracle on a benchmark of diverse drug-like molecules using significantly less additional data.

Training energy-based models (EBMs) on high-dimensional data can be both challenging and time-consuming, and there exists a noticeable gap in sample quality between EBMs and other generative frameworks like GANs and diffusion models. To close this gap, inspired by the recent efforts of learning EBMs by maximimizing diffusion recovery likelihood (DRL), we propose cooperative diffusion recovery likelihood (CDRL), an effective approach to tractably learn and sample from a series of EBMs defined on increasingly noisy versons of a dataset, paired with an initializer model for each EBM. At each noise level, the two models are jointly estimated within a cooperative training framework: Samples from the initializer serve as starting points that are refined by a few MCMC sampling steps from the EBM. The EBM is then optimized by maximizing recovery likelihood, while the initializer model is optimized by learning from the difference between the refined samples and the initial samples. In addition, we made several practical designs for EBM training to further improve the sample quality. Combining these advances, we significantly boost the generation performance compared to existing EBM methods on CIFAR-10 and ImageNet 32x32. And we have shown that CDRL has great potential to largely reduce the sampling time. We also demonstrate the effectiveness of our models for several downstream tasks, including classifier-free guided generation, compositional generation, image inpainting and out-of-distribution detection.

Despite the remarkable advances in language modeling, current mainstream decoding methods still struggle to generate texts that align with human texts across different aspects. In particular, sampling-based methods produce less-repetitive texts which are often disjunctive in discourse, while search-based methods maintain topic coherence at the cost of increased repetition. Overall, these methods fall short in achieving holistic alignment across a broad range of aspects. In this work, we frame decoding from a language model as an optimization problem with the goal of strictly matching the expected performance with human texts measured by multiple metrics of desired aspects simultaneously. The resulting decoding distribution enjoys an analytical solution that scales the input language model distribution via a sequence-level energy function defined by these metrics. And most importantly, we prove that this induced distribution is guaranteed to improve the perplexity on human texts, which suggests a better approximation to the underlying distribution of human texts. To facilitate tractable sampling from this globally normalized distribution, we adopt the Sampling-Importance-Resampling technique. Experiments on various domains and model scales demonstrate the superiority of our method in metrics alignment with human texts and human evaluation over strong baselines.