This paper introduces Bayesian Flow Networks (BFNs), a new class of
generative model in which the parameters of a set of independent distributions
are modified with Bayesian inference in the light of noisy data samples, then
passed as input to a neural network that outputs a second, interdependent
distribution. Starting from a simple prior and iteratively updating the two
distributions yields a generative procedure similar to the reverse process of
diffusion models; however it is conceptually simpler in that no forward process
is required. Discrete and continuous-time loss functions are derived for
continuous, discretised and discrete data, along with sample generation
procedures. Notably, the network inputs for discrete data lie on the
probability simplex, and are therefore natively differentiable, paving the way
for gradient-based sample guidance and few-step generation in discrete domains
such as language modelling. The loss function directly optimises data
compression and places no restrictions on the network architecture. In our
experiments BFNs achieve competitive log-likelihoods for image modelling on
dynamically binarized MNIST and CIFAR-10, and outperform all known discrete
diffusion models on the text8 character-level language modelling task.

该论文介绍了贝叶斯流网络（BFNs），这是一种新的生成模型，通过贝叶斯推理修改一组独立分布的参数，然后将其作为输入传递给神经网络，输出第二个相互依赖的分布。BFNs 在连续数据、离散化数据和离散数据等方面有效，并在图像建模和字符级语言建模任务中实现了有竞争力的对数似然值。

贝叶斯流网络

Bayesian Flow Networks

While recent work on online goal recognition efficiently infers goals under
low observability, comparatively less work focuses on online goal recognition
that works in both discrete and continuous domains. Online goal recognition
approaches often rely on repeated calls to the planner at each new observation,
incurring high computational costs. Recognizing goals online in continuous
space quickly and reliably is critical for any trajectory planning problem
since the real physical world is fast-moving, e.g. robot applications. We
develop an efficient method for goal recognition that relies either on a single
call to the planner for each possible goal in discrete domains or a simplified
motion model that reduces the computational burden in continuous ones. The
resulting approach performs the online component of recognition orders of
magnitude faster than the current state of the art, making it the first online
method effectively usable for robotics applications that require sub-second
recognition.

本研究基于传统调用规划器和简化运动模型，提出了一种高效的在线目标识别方法，可在离散和连续领域内使用，适用于需要亚秒级识别的机器人应用。

基于向量表示的离散和连续域在线目标识别

Online Goal Recognition in Discrete and Continuous Domains Using a  Vectorial Representation

Representing probability distributions by the gradient of their density
functions has proven effective in modeling a wide range of continuous data
modalities. However, this representation is not applicable in discrete domains
where the gradient is undefined. To this end, we propose an analogous score
function called the "Concrete score", a generalization of the (Stein) score for
discrete settings. Given a predefined neighborhood structure, the Concrete
score of any input is defined by the rate of change of the probabilities with
respect to local directional changes of the input. This formulation allows us
to recover the (Stein) score in continuous domains when measuring such changes
by the Euclidean distance, while using the Manhattan distance leads to our
novel score function in discrete domains. Finally, we introduce a new framework
to learn such scores from samples called Concrete Score Matching (CSM), and
propose an efficient training objective to scale our approach to high
dimensions. Empirically, we demonstrate the efficacy of CSM on density
estimation tasks on a mixture of synthetic, tabular, and high-dimensional image
datasets, and demonstrate that it performs favorably relative to existing
baselines for modeling discrete data.

该研究提出了一种在离散领域中类似于 (Stein) 分数的分数函数 ——“Concrete Score”，可以用于离散数据的建模，并且引入了一个新的框架来从样本中学习这样的分数，称为 “Concrete Score Matching（CSM）”，在合成、表格和高维图像数据集的密度估计任务上实验表明，它的性能相对于现有基线表现良好。

具体记分匹配：离散数据的广义记分匹配

Concrete Score Matching: Generalized Score Matching for Discrete Data

We study the problem of learning a distribution from samples, when the
underlying distribution is a mixture of product distributions over discrete
domains. This problem is motivated by several practical applications such as
crowd-sourcing, recommendation systems, and learning Boolean functions. The
existing solutions either heavily rely on the fact that the number of
components in the mixtures is finite or have sample/time complexity that is
exponential in the number of components. In this paper, we introduce a
polynomial time/sample complexity method for learning a mixture of $r$ discrete
product distributions over $\{1, 2, \dots, \ell\}^n$, for general $\ell$ and
$r$. We show that our approach is statistically consistent and further provide
finite sample guarantees.
We use techniques from the recent work on tensor decompositions for
higher-order moment matching. A crucial step in these moment matching methods
is to construct a certain matrix and a certain tensor with low-rank spectral
decompositions. These tensors are typically estimated directly from the
samples. The main challenge in learning mixtures of discrete product
distributions is that these low-rank tensors cannot be obtained directly from
the sample moments. Instead, we reduce the tensor estimation problem to: $a$)
estimating a low-rank matrix using only off-diagonal block elements; and $b$)
estimating a tensor using a small number of linear measurements. Leveraging on
recent developments in matrix completion, we give an alternating minimization
based method to estimate the low-rank matrix, and formulate the tensor
completion problem as a least-squares problem.

提出了一种多项式时间 / 样本复杂度方法来学习离散域上的 $r$ 个离散乘积分布的混合，利用张量分解和矩阵完成方法降低难度，该方法在统计上是一致的，并提供了有限的样本保证。