神经回路中的稀疏无声编码
Sparse and silent coding in neural circuits
摘要：
稀疏编码算法是关于找到一个线性基，其中信号可以由少量的有效（非零）系数表示。这种编码在科学和工程中有许多应用，并且被认为在神经信息处理中起重要作用。然而，由于任务的计算复杂性，只有近似解提供所需的效率（在时间方面）。正如新的结果所示，在特定条件下，存在通过最小化系数的幅度（“$l_1$ -norm”）而不是最小化特征的活动子集的大小（“$l_0$ -norm”）的有效解决方案。这些解决方案的直接神经实现是不可能的，因为它们需要\emph{a priori}对活动特征数量的了解。此外，这些方法利用重建误差的迭代重新评估，这又意味着最终的稀疏形式（具有“群体稀疏性”）只能通过形成一系列非稀疏表示来达到，这与神经系统的整体稀疏功能（“寿命稀疏性”）形成对比。在这篇文章中，我们提出了一种新的算法，它集成了我们以前的“$l_0$ -范数”模型的穗为基础的概率优化稀疏编码的想法来自新的“$l_1$ -范数”的解决方案。由此产生的算法允许神经似是而非的实施，并不需要一个确切定义的稀疏水平，因此它是适合于表示自然刺激与不同数量的功能。我们还表明，组合的方法显着扩展域中的最佳解决方案，可以找到基于“$l_1$规范”的算法。
英文摘要：
Sparse coding algorithms are about finding a linear basis in which signals can be represented by a small number of active (non-zero) coefficients. Such coding has many applications in science and engineering and is believed to play an important role in neural information processing. However, due to the computational complexity of the task, only approximate solutions provide the required efficiency (in terms of time). As new results show, under particular conditions there exist efficient solutions by minimizing the magnitude of the coefficients (`$l_1$-norm') instead of minimizing the size of the active subset of features (`$l_0$-norm'). Straightforward neural implementation of these solutions is not likely, as they require \emph{a priori} knowledge of the number of active features. Furthermore, these methods utilize iterative re-evaluation of the reconstruction error, which in turn implies that final sparse forms (featuring `population sparseness') can only be reached through the formation of a series of non-sparse representations, which is in contrast with the overall sparse functioning of the neural systems (`lifetime sparseness'). In this article we present a novel algorithm which integrates our previous `$l_0$-norm' model on spike based probabilistic optimization for sparse coding with ideas coming from novel `$l_1$-norm' solutions. The resulting algorithm allows neurally plausible implementation and does not require an exactly defined sparseness level thus it is suitable for representing natural stimuli with a varying number of features. We also demonstrate that the combined method significantly extends the domain where optimal solutions can be found by `$l_1$-norm' based algorithms.
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