By convention, vectors are column vectors. We first compare the complexities of the incremental EM based methods using the following table which summarizes the state-of-the-art results. The last column is the optimal complexity to reach an -approximate stationary point. Next, we provide the psuedo-codes of several existing incremental EM-based algorithms, following the notations defined in the main paper. Using Lemma 3 below this page, we deduce that SPIDER-EM can be equivalently described by the following algorithm 7. Algorithm 7: The SPIDER-EM algorithm (equivalent description) Lemma 3. Let { The purpose of this section is to show the general convergence results of a SPIDER-EM like algorithm, and these results will be specialized in section 9. T. For some results below, specific assumptions may be introduced on s In addition, since the variance of the sum is the sum of the variance for independent r.v.

The Expectation Maximization (EM) algorithm is of key importance for inference in latent variable models including mixture of regressors and experts, missing observations. This paper introduces a novel EM algorithm, called SPIDER-EM, for inference from a training set of size n, n 1. At the core of our algorithm is an estimator of the full conditional expectation in the E-step, adapted from the stochastic path-integrated differential estimator (SPIDER) technique.

The history of learning for control has been an exciting back and forth between two broad classes of algorithms: planning and reinforcement learning. Planning algorithms effectively reason over long horizons, but assume access to a local policy and distance metric over collision-free paths. Reinforcement learning excels at learning policies and the relative values of states, but fails to plan over long horizons. Despite the successes of each method in various domains, tasks that require reasoning over long horizons with limited feedback and high-dimensional observations remain exceedingly challenging for both planning and reinforcement learning algorithms. Frustratingly, these sorts of tasks are potentially the most useful, as they are simple to design (a human only need to provide an example goal state) and avoid reward shaping, which can bias the agent towards find a suboptimal solution.

We thank the reviewers for their valuable feedback. R2 and R3 had questions about the time complexity of our method. As noted in Appendix A, this computation can be amortized across many goal-reaching tasks. Lastly, we agree with R2 that the construction of "good" replay buffers is an We will clarify this in Section 2.3. We will clarify this in Alg. 1.

There is a rising interest and trend in research towards directly translating speech from one language to another, known as end-to-end speech-to-speech translation. However, most end-to-end models struggle to outperform cascade models, i.e., a pipeline framework by concatenating speech recognition, machine translation, and text-to-speech models. The primary challenges stem from the inherent complexities involved in direct translation tasks and the scarcity of data. In this study, we introduce a novel model framework TransVIP that leverages diverse datasets in a cascade fashion yet facilitates end-to-end inference through joint probability. Furthermore, we propose two separate encoders to preserve the speaker's voice characteristics and isochrony from the source speech during the translation process, making it highly suitable for scenarios such as video dubbing. Our experiments on the French-English language pair demonstrate that our model outperforms the current state-of-the-art speech-to-speech translation model.

In this study, we introduce a unified neural network architecture, the Deep Equilibrium Density Functional Theory Hamiltonian (DEQH) model, which incorporates Deep Equilibrium Models (DEQs) for predicting Density Functional Theory (DFT) Hamiltonians. The DEQH model inherently captures the self-consistency nature of Hamiltonian, a critical aspect often overlooked by traditional machine learning approaches for Hamiltonian prediction. By employing DEQ within our model architecture, we circumvent the need for DFT calculations during the training phase to introduce the Hamiltonian's self-consistency, thus addressing computational bottlenecks associated with large or complex systems. We propose a versatile framework that combines DEQ with off-the-shelf machine learning models for predicting Hamiltonians. When benchmarked on the MD17 and QH9 datasets, DEQHNet, an instantiation of the DEQH framework, has demonstrated a significant improvement in prediction accuracy. Beyond a predictor, the DEQH model is a Hamiltonian solver, in the sense that it uses the fixed-point solving capability of the deep equilibrium model to iteratively solve for the Hamiltonian.

We consider the problem of estimating the mean of a set of vectors, which are stored in a distributed system. This is a fundamental task with applications in distributed SGD and many other distributed problems, where communication is a main bottleneck for scaling up computations. We propose a new sparsity-aware algorithm, which improves previous results both theoretically and empirically. The communication cost of our algorithm is characterized by Hoyer's measure of sparseness. Moreover, we prove that the communication cost of our algorithm is information-theoretic optimal up to a constant factor in all sparseness regime. We have also conducted experimental studies, which demonstrate the advantages of our method and confirm our theoretical findings.

Machine learning as a service has given raise to privacy concerns surrounding clients' data and providers' models and has catalyzed research in private inference (PI): methods to process inferences without disclosing inputs. Recently, researchers have adapted cryptographic techniques to show PI is possible, however all solutions increase inference latency beyond practical limits. This paper makes the observation that existing models are ill-suited for PI and proposes a novel NAS method, named CryptoNAS, for finding and tailoring models to the needs of PI. The key insight is that in PI operator latency costs are inverted: non-linear operations (e.g., ReLU) dominate latency, while linear layers become effectively free. We develop the idea of a ReLU budget as a proxy for inference latency and use CryptoNAS to build models that maximize accuracy within a given budget. CryptoNAS improves accuracy by 3.4% and latency by 2.4 over the state-of-the-art.

Bayesian decision theory outlines a rigorous framework for making optimal decisions based on maximizing expected utility over a model posterior. However, practitioners often do not have access to the full posterior and resort to approximate inference strategies. In such cases, taking the eventual decision-making task into account while performing the inference allows for calibrating the posterior approximation to maximize the utility. We present an automatic pipeline that co-opts continuous utilities into variational inference algorithms to account for decision-making. We provide practical strategies for approximating and maximizing the gain, and empirically demonstrate consistent improvement when calibrating approximations for specific utilities.

The Schrödinger Bridge (SB) problem offers a powerful framework for combining optimal transport and diffusion models. A promising recent approach to solve the SB problem is the Iterative Markovian Fitting (IMF) procedure, which alternates between Markovian and reciprocal projections of continuous-time stochastic processes. However, the model built by the IMF procedure has a long inference time due to using many steps of numerical solvers for stochastic differential equations. To address this limitation, we propose a novel Discrete-time IMF (D-IMF) procedure in which learning of stochastic processes is replaced by learning just a few transition probabilities in discrete time. Its great advantage is that in practice it can be naturally implemented using the Denoising Diffusion GAN (DD-GAN), an already well-established adversarial generative modeling technique. We show that our D-IMF procedure can provide the same quality of unpaired domain translation as the IMF, using only several generation steps instead of hundreds.