Inspired by recent research that recommends starting neural networks training with large learning rates (LRs) to achieve the best generalization, we explore this hypothesis in detail. Our study clarifies the initial LR ranges that provide optimal results for subsequent training with a small LR or weight averaging. We find that these ranges are in fact significantly narrower than generally assumed. We conduct our main experiments in a simplified setup that allows precise control of the learning rate hyperparameter and validate our key findings in a more practical setting.
* Published in Mathematics of Modern Machine Learning Workshop at
NeurIPS 2023. First two authors contributed equally
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 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, it takes around $5 \times 10^5$ additional conformations to match the physical simulator's optimization quality. In this work, we present the Gradual Optimization Learning Framework (GOLF) for energy minimization with neural networks that significantly reduces the required additional data. 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 on par with the oracle on a benchmark of diverse drug-like molecules using $50$x less additional data.
The recently proposed generative flow networks (GFlowNets) are a method of training a policy to sample compositional discrete objects with probabilities proportional to a given reward via a sequence of actions. GFlowNets exploit the sequential nature of the problem, drawing parallels with reinforcement learning (RL). Our work extends the connection between RL and GFlowNets to a general case. We demonstrate how the task of learning a generative flow network can be efficiently redefined as an entropy-regularized RL problem with a specific reward and regularizer structure. Furthermore, we illustrate the practical efficiency of this reformulation by applying standard soft RL algorithms to GFlowNet training across several probabilistic modeling tasks. Contrary to previously reported results, we show that entropic RL approaches can be competitive against established GFlowNet training methods. This perspective opens a direct path for integrating reinforcement learning principles into the realm of generative flow networks.
Diffusion models have shown remarkable performance on many generative tasks. Despite recent success, most diffusion models are restricted in that they only allow linear transformation of the data distribution. In contrast, broader family of transformations can potentially help train generative distributions more efficiently, simplifying the reverse process and closing the gap between the true negative log-likelihood and the variational approximation. In this paper, we present Neural Diffusion Models (NDMs), a generalization of conventional diffusion models that enables defining and learning time-dependent non-linear transformations of data. We show how to optimise NDMs using a variational bound in a simulation-free setting. Moreover, we derive a time-continuous formulation of NDMs, which allows fast and reliable inference using off-the-shelf numerical ODE and SDE solvers. Finally, we demonstrate the utility of NDMs with learnable transformations through experiments on standard image generation benchmarks, including CIFAR-10, downsampled versions of ImageNet and CelebA-HQ. NDMs outperform conventional diffusion models in terms of likelihood and produce high-quality samples.
This paper introduces UnDiff, a diffusion probabilistic model capable of solving various speech inverse tasks. Being once trained for speech waveform generation in an unconditional manner, it can be adapted to different tasks including degradation inversion, neural vocoding, and source separation. In this paper, we, first, tackle the challenging problem of unconditional waveform generation by comparing different neural architectures and preconditioning domains. After that, we demonstrate how the trained unconditional diffusion could be adapted to different tasks of speech processing by the means of recent developments in post-training conditioning of diffusion models. Finally, we demonstrate the performance of the proposed technique on the tasks of bandwidth extension, declipping, vocoding, and speech source separation and compare it to the baselines. The codes will be released soon.
Transfer learning and ensembling are two popular techniques for improving the performance and robustness of neural networks. Due to the high cost of pre-training, ensembles of models fine-tuned from a single pre-trained checkpoint are often used in practice. Such models end up in the same basin of the loss landscape and thus have limited diversity. In this work, we study if it is possible to improve ensembles trained from a single pre-trained checkpoint by better exploring the pre-train basin or a close vicinity outside of it. We show that while exploration of the pre-train basin may be beneficial for the ensemble, leaving the basin results in losing the benefits of transfer learning and degradation of the ensemble quality.
In view synthesis, a neural radiance field approximates underlying density and radiance fields based on a sparse set of scene pictures. To generate a pixel of a novel view, it marches a ray through the pixel and computes a weighted sum of radiance emitted from a dense set of ray points. This rendering algorithm is fully differentiable and facilitates gradient-based optimization of the fields. However, in practice, only a tiny opaque portion of the ray contributes most of the radiance to the sum. We propose an end-to-end differentiable sampling algorithm based on inverse transform sampling. It generates samples according to the probability distribution induced by the density field and picks non-transparent points on the ray. We utilize the algorithm in two ways. First, we propose a novel rendering approach based on Monte Carlo estimates. Such a rendering algorithm allows for optimizing a neural radiance field with just a few radiance field evaluations per ray. Second, we use the sampling algorithm to modify the hierarchical scheme used in the original work on neural radiance fields. In this setup, we were able to train the proposal network end-to-end without any auxiliary losses and improved the baseline performance.
Methods based on Denoising Diffusion Probabilistic Models (DDPM) became a ubiquitous tool in generative modeling. However, they are mostly limited to Gaussian and discrete diffusion processes. We propose Star-Shaped Denoising Diffusion Probabilistic Models (SS-DDPM), a model with a non-Markovian diffusion-like noising process. In the case of Gaussian distributions, this model is equivalent to Markovian DDPMs. However, it can be defined and applied with arbitrary noising distributions, and admits efficient training and sampling algorithms for a wide range of distributions that lie in the exponential family. We provide a simple recipe for designing diffusion-like models with distributions like Beta, von Mises--Fisher, Dirichlet, Wishart and others, which can be especially useful when data lies on a constrained manifold such as the unit sphere, the space of positive semi-definite matrices, the probabilistic simplex, etc. We evaluate the model in different settings and find it competitive even on image data, where Beta SS-DDPM achieves results comparable to a Gaussian DDPM.
Domain adaptation of GANs is a problem of fine-tuning the state-of-the-art GAN models (e.g. StyleGAN) pretrained on a large dataset to a specific domain with few samples (e.g. painting faces, sketches, etc.). While there are a great number of methods that tackle this problem in different ways there are still many important questions that remain unanswered. In this paper, we provide a systematic and in-depth analysis of the domain adaptation problem of GANs, focusing on the StyleGAN model. First, we perform a detailed exploration of the most important parts of StyleGAN that are responsible for adapting the generator to a new domain depending on the similarity between the source and target domains. In particular, we show that affine layers of StyleGAN can be sufficient for fine-tuning to similar domains. Second, inspired by these findings, we investigate StyleSpace to utilize it for domain adaptation. We show that there exist directions in the StyleSpace that can adapt StyleGAN to new domains. Further, we examine these directions and discover their many surprising properties. Finally, we leverage our analysis and findings to deliver practical improvements and applications in such standard tasks as image-to-image translation and cross-domain morphing.