计算智能的生成泛函：Fisher信息作为自限Hebbian学习规则的目标函数
Generating functionals for computational intelligence: the Fisher information as an objective function for self-limiting Hebbian learning rules
摘要：
生成泛函可以引导动力系统的演化，并构成处理与计算智能相关的神经网络复杂性的可能途径。我们提出并探索了一个新的目标函数，它允许获得传入突触权重的可塑性规则。自适应规则是赫布的，自限性的，并导致从最小化的Fisher信息相对于突触通量。我们进行了一系列的模拟，检查在各种情况下的新的学习规则的行为。突触权重的向量与输入活动的主方向对齐，无论何时出现。当有两个或两个以上的主方向时，进行线性判别;具有双峰发射率分布的方向，其特征在于负过剩峰度，是优选的。我们发现强大的性能和完整的稳态适应的突触权重结果作为一个副产品的突触通量最小化。这种自限制行为允许在任意持续时间内进行稳定的在线学习。当输入活动的统计数据在模拟的某个点发生变化时，神经元会获得新的信息，然而，这显示出一种明显的弹性，可以忘记以前获得的知识。当从随机抽取的突触权重开始时，学习是快速的，而当突触权重已经完全适应时，学习则慢得多。
英文摘要：
Generating functionals may guide the evolution of a dynamical system and constitute a possible route for handling the complexity of neural networks as relevant for computational intelligence. We propose and explore a new objective function, which allows to obtain plasticity rules for the afferent synaptic weights. The adaption rules are Hebbian, self-limiting, and result from the minimization of the Fisher information with respect to the synaptic flux. We perform a series of simulations examining the behavior of the new learning rules in various circumstances. The vector of synaptic weights aligns with the principal direction of input activities, whenever one is present. A linear discrimination is performed when there are two or more principal directions; directions having bimodal firing-rate distributions, being characterized by a negative excess kurtosis, are preferred. We find robust performance and full homeostatic adaption of the synaptic weights results as a by-product of the synaptic flux minimization. This self-limiting behavior allows for stable online learning for arbitrary durations. The neuron acquires new information when the statistics of input activities is changed at a certain point of the simulation, showing however, a distinct resilience to unlearn previously acquired knowledge. Learning is fast when starting with randomly drawn synaptic weights and substantially slower when the synaptic weights are already fully adapted.
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