AI 中文总结
该研究揭示跨维推断中学习型提议在平衡态最优，通过实验验证其加速模型阶数混合的效果，开发了开源工具HyperWave，可跨领域应用于源计数与信号重建。
AI 中文摘要
从图像中源的计数到混合模型，在推断模型维度（解释数据所需的分量数量）的同时推断参数是一个普遍存在的问题，可逆跳转马尔可夫链蒙特卡罗（reversible-jump Markov chain Monte Carlo）可精确求解该问题，但混合速度较慢。学习型提议在固定维度场景中已得到广泛应用，但其能否加速维度变换移动本身在很大程度上仍未得到验证。我们表明，答案具有结构性起源：维度变换的出生移动（birth move）的最优提议在运行的不同阶段是不同的对象。在拟合模型的构建过程中，它必须匹配当前残差——这是一个状态依赖量，无状态依赖的网络无法表示；但在平衡态时，它退化为后验分布的单分量边际，而这正是自适应归一化流（adaptive normalizing flow）从采样器自身历史中学习的分布。因此，无状态依赖的学习型出生提议在一个阶段无用，而在另一阶段最优。受控实验证实了这一归因：应用精确的Metropolis--Hastings校正（该校正对任意网络均保持目标分布不变）时，学习型出生移动虽未改变接受率，但加速了模型阶数混合——在十次种子基准测试中，它在十次运行中的六次达到了预设的停止规则，通常速度快数倍，而一个经过强调优的手动基线仅在一次运行中达到该规则（单侧p值为0.03）；一项隔离实验显示，在模型内部部署相同的流无任何增益。该方法未做特定领域假设，可在科学领域（包括地面和空间探测器的引力波、头皮脑电图记录）的含噪图像中计数源并重建信号，我们将该方法作为开源包HyperWave发布。
英文摘要
Inferring the dimension of a model - the number of components needed to explain data - jointly with the parameters is a pervasive problem, from counting sources in an image to mixture modeling, and reversible-jump Markov chain Monte Carlo solves it exactly but mixes slowly. Learned proposals are well established at fixed dimension, but whether they can accelerate the dimension-changing moves themselves has remained largely untested. We show that the answer has a structural origin: the optimal proposal for the dimension-changing birth move is a different object in different phases of the run. While the fit is being assembled it must match the current residual - a state-dependent quantity no state-independent network can represent - but at equilibrium it degenerates to the posterior's single-component marginal, which is exactly the distribution an adaptive normalizing flow learns from the sampler's own history. A learned state-independent birth proposal is therefore useless in one phase and optimal in the other. Controlled experiments confirm the attribution: applied with an exact Metropolis--Hastings correction that leaves the target invariant for any network, the learned births leave acceptance rates unchanged yet accelerate model-order mixing - in a ten-seed benchmark they meet a pre-specified stopping rule in six of ten runs, typically several times sooner, where a strong hand-tuned baseline meets it in one (one-sided p=0.03) - and an isolation experiment shows the same flow deployed within-model buys nothing. Making no domain-specific assumptions, the same sampler counts sources in a noisy image and reconstructs signals across scientific domains, including gravitational waves from ground- and space-based detectors and a scalp EEG recording. We release the method as HyperWave, an open-source package.
Comments23 pages, 5 figures, 2 tables
