We present a novel algorithm for parameter learning in generic deep
generative models that builds upon the predictive coding (PC) framework of
computational neuroscience. Our approach modifies the standard PC algorithm to
bring performance on-par and exceeding that obtained from standard variational
auto-encoder (VAE) training. By injecting Gaussian noise into the PC inference
procedure we re-envision it as an overdamped Langevin sampling, which
facilitates optimisation with respect to a tight evidence lower bound (ELBO).
We improve the resultant encoder-free training method by incorporating an
encoder network to provide an amortised warm-start to our Langevin sampling and
test three different objectives for doing so. Finally, to increase robustness
to the sampling step size and reduce sensitivity to curvature, we validate a
lightweight and easily computable form of preconditioning, inspired by Riemann
Manifold Langevin and adaptive optimizers from the SGD literature. We compare
against VAEs by training like-for-like generative models using our technique
against those trained with standard reparameterisation-trick-based ELBOs. We
observe our method out-performs or matches performance across a number of
metrics, including sample quality, while converging in a fraction of the number
of SGD training iterations.

我们提出了一种新颖的算法，用于在通用深度生成模型中学习参数，该算法基于计算神经科学的预测编码 (PC) 框架。通过将高斯噪声注入 PC 推理过程，我们重新构想它作为过阻尼 Langevin 采样，从而实现对紧密证据下界 (ELBO) 的优化。我们通过将编码器网络纳入到我们的 Langevin 采样中，提供一个得到温和起步的改进的编码器自由训练方法，并测试了三种不同的目标。最后，为了增加对采样步长的鲁棒性，并减少对曲率的敏感性，我们验证了一种轻量级且易于计算的预条件形式，受到 Riemann 流形 Langevin 和 SGD 文献中的自适应优化器的启发。我们通过使用我们的技术和使用标准重参数化技巧的 ELBO 训练的模型进行训练，在许多指标上观察到我们的方法优于或与其性能相匹配，并且收敛迭代次数仅为其一部分。

用朗之万动力学进行预测编码采样

Sample as You Infer: Predictive Coding With Langevin Dynamics

In sampling-based Bayesian models of brain function, neural activities are
assumed to be samples from probability distributions that the brain uses for
probabilistic computation. However, a comprehensive understanding of how
mechanistic models of neural dynamics can sample from arbitrary distributions
is still lacking. We use tools from functional analysis and stochastic
differential equations to explore the minimum architectural requirements for
$\textit{recurrent}$ neural circuits to sample from complex distributions. We
first consider the traditional sampling model consisting of a network of
neurons whose outputs directly represent the samples (sampler-only network). We
argue that synaptic current and firing-rate dynamics in the traditional model
have limited capacity to sample from a complex probability distribution. We
show that the firing rate dynamics of a recurrent neural circuit with a
separate set of output units can sample from an arbitrary probability
distribution. We call such circuits reservoir-sampler networks (RSNs). We
propose an efficient training procedure based on denoising score matching that
finds recurrent and output weights such that the RSN implements Langevin
sampling. We empirically demonstrate our model's ability to sample from several
complex data distributions using the proposed neural dynamics and discuss its
applicability to developing the next generation of sampling-based brain models.

使用功能分析和随机微分方程的工具，探索基于采样的脑功能贝叶斯模型中神经动力学机制在复杂分布中的采样能力的最小体系结构要求，并提出了能够从任意概率分布中进行采样的储液器 - 采样网络（RSN）以及基于去噪评分匹配的有效训练过程，从而实现 Langevin 采样，并在实验中展示了该模型从多个复杂数据分布中进行采样的能力，探讨了其在开发基于采样的大脑模型的潜力。

递归神经网络中的表达性概率抽样

Expressive probabilistic sampling in recurrent neural networks

In this work, we propose \texttt{TimeGrad}, an autoregressive model for
multivariate probabilistic time series forecasting which samples from the data
distribution at each time step by estimating its gradient. To this end, we use
diffusion probabilistic models, a class of latent variable models closely
connected to score matching and energy-based methods. Our model learns
gradients by optimizing a variational bound on the data likelihood and at
inference time converts white noise into a sample of the distribution of
interest through a Markov chain using Langevin sampling. We demonstrate
experimentally that the proposed autoregressive denoising diffusion model is
the new state-of-the-art multivariate probabilistic forecasting method on
real-world data sets with thousands of correlated dimensions. We hope that this
method is a useful tool for practitioners and lays the foundation for future
research in this area.

本研究提出了一种基于 TimeGrad 的自回归模型，用于多元概率时间序列预测，该模型在每个时间步长从数据分布中采样，通过估计梯度进行采样，采用扩散概率模型，优化可变界，通过 Langevin 采样将白噪声转换为感兴趣的分布样本，在实验中表明，该模型是当前实现多元概率预测的最佳方法之一，可实际应用于数千个相关维度的真实数据集。