Extraction of latent sources of complex stimuli is critical for making sense of the world. While the brain solves this blind source separation (BSS) problem continuously, its algorithms remain unknown. Previous work on biologically-plausible BSS algorithms assumed that observed signals are linear mixtures of statistically independent or uncorrelated sources, limiting the domain of applicability of these algorithms. To overcome this limitation, we propose novel biologically-plausible neural networks for the blind separation of potentially dependent/correlated sources. Differing from previous work, we assume some general geometric, not statistical, conditions on the source vectors allowing separation of potentially dependent/correlated sources. Concretely, we assume that the source vectors are sufficiently scattered in their domains which can be described by certain polytopes. Then, we consider recovery of these sources by the Det-Max criterion, which maximizes the determinant of the output correlation matrix to enforce a similar spread for the source estimates. Starting from this normative principle, and using a weighted similarity matching approach that enables arbitrary linear transformations adaptable by local learning rules, we derive two-layer biologically-plausible neural network algorithms that can separate mixtures into sources coming from a variety of source domains. We demonstrate that our algorithms outperform other biologically-plausible BSS algorithms on correlated source separation problems.
翻译:挖掘复杂刺激的潜伏来源对于理解世界至关重要。 虽然大脑不断解决盲源分离问题, 但它的算法仍然未知。 生物可变性BSS算法的先前工作假设, 观察到的信号是统计上独立或不相干来源的线性混合物, 限制了这些算法的适用范围。 为了克服这一限制, 我们提出新的生物可变性神经网络, 以便盲目分离潜在依赖/ 相关来源。 与以往工作不同, 我们假设来源矢量的一些一般几何而非统计条件, 允许将潜在依赖/ 相关来源分离。 具体地说, 我们假设, 源矢量分散在它们的域中, 可以由某些多面图加以描述。 然后, 我们考虑利用Det- Max 标准恢复这些来源, 最大限度地确定输出相关关系矩阵的决定因素, 以强制源值估算。 从这一规范原则开始, 并使用一种加权相似的匹配方法, 使得源量直线性变化能够通过本地学习规则加以调整。 我们假设源量源的两层生物可分解的分子算法, 我们从生物可分解的模型的网络, 。