We introduce Bayesian distributed stochastic gradient descent (BDSGD), a high-throughput algorithm for training deep neural networks on parallel computing clusters. This algorithm uses amortized inference in a deep generative model to perform joint posterior predictive inference of mini-batch gradient computation times in a compute cluster specific manner. Specifically, our algorithm mitigates the straggler effect in synchronous, gradient-based optimization by choosing an optimal cutoff beyond which mini-batch gradient messages from slow workers are ignored. The principle novel contribution and finding of this work goes beyond this by demonstrating that using the predicted run-times from a generative model of cluster worker performance improves over the static-cutoff prior art, leading to higher gradient computation throughput on large compute clusters. In our experiments we show that eagerly discarding the mini-batch gradient computations of stragglers not only increases throughput but sometimes also increases the overall rate of convergence as a function of wall-clock time by virtue of eliminating idleness.

Based on this observation, we propose a new training objective that improves thegeneralization ofamortized inference.

The ability of likelihood-based probabilistic models to generalize to unseen data is central to many machine learning applications such as lossless compression. In this work, we study the generalization of a popular class of probabilistic model - the Variational Auto-Encoder (VAE). We discuss the two generalization gaps that affect VAEs and show that overfitting is usually dominated by amortized inference. Based on this observation, we propose a new training objective that improves the generalization of amortized inference. We demonstrate how our method can improve performance in the context of image modeling and lossless compression.

Inferring causal structure poses a combinatorial search problem that typically involves evaluating structures with a score or independence test. The resulting search is costly, and designing suitable scores or tests that capture prior knowledge is difficult. In this work, we propose to amortize causal structure learning. Rather than searching over structures, we train a variational inference model to directly predict the causal structure from observational or interventional data. This allows our inference model to acquire domain-specific inductive biases for causal discovery solely from data generated by a simulator, bypassing both the hand-engineering of suitable score functions and the search over graphs. The architecture of our inference model emulates permutation invariances that are crucial for statistical efficiency in structure learning, which facilitates generalization to significantly larger problem instances than seen during training. On synthetic data and semisynthetic gene expression data, our models exhibit robust generalization capabilities when subject to substantial distribution shifts and significantly outperform existing algorithms, especially in the challenging genomics domain. Our code and models are publicly available at: https://github.com/larslorch/avici

Cryo-electron microscopy (cryo-EM) is an imaging modality that provides unique insights into the dynamics of proteins and other building blocks of life. The algorithmic challenge of jointly estimating the poses, 3D structure, and conformational heterogeneity of a biomolecule from millions of noisy and randomly oriented 2D projections in a computationally efficient manner, however, remains unsolved. Our method, cryoFIRE, performs ab initio heterogeneous reconstruction with unknown poses in an amortized framework, thereby avoiding the computationally expensive step of pose search while enabling the analysis of conformational heterogeneity. Poses and conformation are jointly estimated by an encoder while a physics-based decoder aggregates the images into an implicit neural representation of the conformational space. We show that our method can provide one order of magnitude speedup on datasets containing millions of images, without any loss of accuracy. We validate that the joint estimation of poses and conformations can be amortized over the size of the dataset. For the first time, we prove that an amortized method can extract interpretable dynamic information from experimental datasets.

Across diverse domains--from complex systems and finance to high-energy physics and astrophysics--scientific inquiry often relies on deriving theoretical parameters from observational data [1]. At the core of this challenge lies the inverse problem: inferring the posterior distribution of theoretical parameters given a set of observables [2]. Traditional approaches for posterior estimation rely on sampling algorithms such as Markov Chain Monte Carlo (MCMC) [3, 4] and Nested Sampling (NS) [5]. In astrophysics and cosmology, implementations like emcee [6] and dynesty [7] have become standard tools. While these frameworks are statistically robust, they suffer significantly from the curse of dimensionality. In real-world scenarios, where the parameter space is high-dimensional and the likelihood function relies on computationally expensive simulators (e.g., in particle physics phenomenology [8]), convergence can take weeks or even months. Recent advances in machine learning have introduced Normalizing Flows (NFs) as a powerful alternative for probabilistic modelling [9, 10]. By learning a bijective mapping between a simple base distribution (e.g., a Gaussian) and the complex target distribution, NFs allow for exact density estimation and efficient sampling [11] from the target distribution. Modern architectures, such as RealNVP [12] and Neural Spline Flows [13], offer enough expressivity to model highly complex distributions.

Probabilistic inference algorithms such as Sequential Monte Carlo (SMC) provide powerful tools for constraining procedural models in computer graphics, but they require many samples to produce desirable results. In this paper, we show how to create procedural models which learn how to satisfy constraints. We augment procedural models with neural networks which control how the model makes random choices based on the output it has generated thus far. We call such models neurally-guided procedural models. As a pre-computation, we train these models to maximize the likelihood of example outputs generated via SMC. They are then used as efficient SMC importance samplers, generating high-quality results with very few samples. We evaluate our method on L-system-like models with image-based constraints. Given a desired quality threshold, neurally-guided models can generate satisfactory results up to 10x faster than unguided models.

Neural Information Processing Systems http://nips.cc/

Typically, inner loops are required to solve the first two sub-minimization problems due to the intractability of the prior and the matrix inversion.