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1. Algorithm and Hardware Co-Design for FPGA Acceleration of Hamiltonian Monte Carlo Based No-U-Turn Sampler

   Wang, Y. ; Li, P. ( July 2021 , The 32nd IEEE International Conference on Application-specific Systems, Architectures and Processors)

   null (Ed.)

   Monte Carlo (MC) methods are widely used in many research areas such as physical simulation, statistical analysis, and machine learning. Application of MC methods requires drawing fast mixing samples from a given probability distribution. Among existing sampling methods, the Hamiltonian Monte Carlo (HMC) utilizes gradient information during Hamiltonian simulation and can produce fast mixing samples at the highest efficiency. However, without carefully chosen simulation parameters for a specific problem, HMC generally suffers from simulation locality and computation waste. As a result, the No-U-Turn Sampler (NUTS) has been proposed to automatically tune these parameters during simulation and is the current state-of-the-art sampling algorithm. However, application of NUTS requires frequent gradient calculation of a given distribution and high-volume vector processing, especially for large-scale problems, leading to drawing an expensively large number of samples and a desire of hardware acceleration. While some hardware acceleration works have been proposed for traditional Markov Chain Monte Carlo (MCMC) and HMC methods, there is no existing work targeting hardware acceleration of the NUTS algorithm. In this paper, we present the first NUTS accelerator on FPGA while addressing the high complexity of this state-of-the-art algorithm. Our hardware and algorithm co-optimizations include an incremental resampling technique which leads to a more memory efficient architecture and pipeline optimization for multi-chain sampling to maximize the throughput. We also explore three levels of parallelism in the NUTS accelerator to further boost performance. Compared with optimized C++ NUTS package: RSTAN, our NUTS accelerator can reach a maximum speedup of 50.6X and an energy improvement of 189.7X. 

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2. Provable benefits of annealing for estimating normalizing constants: Importance Sampling, Noise-Contrastive Estimation, and beyond

   Chehab, O ; Hyvärinen, A ; Risteski, A. ( December 2023 , Conference on Neural Information Processing Systems (NeurIPS), 2023)

   Recent research has developed several Monte Carlo methods for estimating the normalization constant (partition function) based on the idea of annealing. This means sampling successively from a path of distributions that interpolate between a tractable "proposal" distribution and the unnormalized "target" distribution. Prominent estimators in this family include annealed importance sampling and annealed noise-contrastive estimation (NCE). Such methods hinge on a number of design choices: which estimator to use, which path of distributions to use and whether to use a path at all; so far, there is no definitive theory on which choices are efficient. Here, we evaluate each design choice by the asymptotic estimation error it produces. First, we show that using NCE is more efficient than the importance sampling estimator, but in the limit of infinitesimal path steps, the difference vanishes. Second, we find that using the geometric path brings down the estimation error from an exponential to a polynomial function of the parameter distance between the target and proposal distributions. Third, we find that the arithmetic path, while rarely used, can offer optimality properties over the universally-used geometric path. In fact, in a particular limit, the optimal path is arithmetic. Based on this theory, we finally propose a two-step estimator to approximate the optimal path in an efficient way. 

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3. A Neural Network MCMC Sampler That Maximizes Proposal Entropy

   https://doi.org/https://doi.org/10.3390/e23030269  

   Li, Zengyi ; Chen, Yubei ; Sommer, Friedrich T. ( February 2021 , Entropy)

   null (Ed.)

   Markov Chain Monte Carlo (MCMC) methods sample from unnormalized probability distributions and offer guarantees of exact sampling. However, in the continuous case, unfavorable geometry of the target distribution can greatly limit the efficiency of MCMC methods. Augmenting samplers with neural networks can potentially improve their efficiency. Previous neural network-based samplers were trained with objectives that either did not explicitly encourage exploration, or contained a term that encouraged exploration but only for well structured distributions. Here we propose to maximize proposal entropy for adapting the proposal to distributions of any shape. To optimize proposal entropy directly, we devised a neural network MCMC sampler that has a flexible and tractable proposal distribution. Specifically, our network architecture utilizes the gradient of the target distribution for generating proposals. Our model achieved significantly higher efficiency than previous neural network MCMC techniques in a variety of sampling tasks, sometimes by more than an order magnitude. Further, the sampler was demonstrated through the training of a convergent energy-based model of natural images. The adaptive sampler achieved unbiased sampling with significantly higher proposal entropy than a Langevin dynamics sample. The trained sampler also achieved better sample quality. 

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4. Variational Marginal Particle Filters

   Lai, Jinlin ; Domke, Justin ; Sheldon, Daniel ( January 2022 , Proceedings of The International Conference on Artificial Intelligence and Statistics (AISTATS))

   Variational inference for state space models (SSMs) is known to be hard in general. Recent works focus on deriving variational objectives for SSMs from unbiased sequential Monte Carlo estimators. We reveal that the marginal particle filter is obtained from sequential Monte Carlo by applying Rao-Blackwellization operations, which sacrifices the trajectory information for reduced variance and differentiability. We propose the variational marginal particle filter (VMPF), which is a differentiable and reparameterizable variational filtering objective for SSMs based on an unbiased estimator. We find that VMPF with biased gradients gives tighter bounds than previous objectives, and the unbiased reparameterization gradients are sometimes beneficial. 

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5. Differentiable Analog Quantum Computing for Optimization and Control

   Leng, Jiaqi ; Peng, Yuxiang ; Qiao, Yi-Ling ; Lin, Ming ; Wu, Xiaodi ( January 2022 , Advances in neural information processing systems)

   We formulate the first differentiable analog quantum computing framework with specific parameterization design at the analog signal (pulse) level to better exploit near-term quantum devices via variational methods. We further propose a scalable approach to estimate the gradients of quantum dynamics using a forward pass with Monte Carlo sampling, which leads to a quantum stochastic gradient descent algorithm for scalable gradient-based training in our framework. Applying our framework to quantum optimization and control, we observe a significant advantage of differentiable analog quantum computing against SOTAs based on parameterized digital quantum circuits by {\em orders of magnitude}. 

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