基于对称矩阵分解的Hebbian/Anti-Hebbian在线稀疏字典学习网络
A Hebbian/Anti-Hebbian Network for Online Sparse Dictionary Learning Derived from Symmetric Matrix Factorization
摘要：
Olshausen和Field（OF）提出，初级视觉皮层（V1）中的神经计算可以部分地通过稀疏字典学习来建模。通过最小化正则化表示误差，他们推导出一种在线算法，该算法从与生理实验一致的自然图像集合中学习Gabor滤波器感受野。虽然OF算法可以映射到单层神经网络中的动态和突触可塑性，但导出的学习规则是非局部的-突触权重更新取决于神经元的活动，而不仅仅是突触前和突触后的神经元-因此在生物学上是不可信的。在这里，为了克服这个问题，我们从一个新的成本函数-输入的相似性矩阵的对称因式分解的正则化错误中获得稀疏字典学习。我们的算法映射到一个神经网络的相同架构的OF，但只使用生物合理的本地学习规则。当在自然图像上训练时，我们的网络学习Gabor滤波器感受野，并再现OF网络中硬连接的突触权重之间的相关性。因此，在线对称矩阵分解可以作为神经计算的算法理论。
英文摘要：
Olshausen and Field (OF) proposed that neural computations in the primary visual cortex (V1) can be partially modeled by sparse dictionary learning. By minimizing the regularized representation error they derived an online algorithm, which learns Gabor-filter receptive fields from a natural image ensemble in agreement with physiological experiments. Whereas the OF algorithm can be mapped onto the dynamics and synaptic plasticity in a single-layer neural network, the derived learning rule is nonlocal - the synaptic weight update depends on the activity of neurons other than just pre- and postsynaptic ones - and hence biologically implausible. Here, to overcome this problem, we derive sparse dictionary learning from a novel cost-function - a regularized error of the symmetric factorization of the input's similarity matrix. Our algorithm maps onto a neural network of the same architecture as OF but using only biologically plausible local learning rules. When trained on natural images our network learns Gabor-filter receptive fields and reproduces the correlation among synaptic weights hard-wired in the OF network. Therefore, online symmetric matrix factorization may serve as an algorithmic theory of neural computation.
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