Porr Bernd, Wörgötter Florentin
Department of Electronics and Electrical Engineering, University of Glasgow, Glasgow, GT12 8LT, Scotland.
Neural Comput. 2006 Jun;18(6):1380-412. doi: 10.1162/neco.2006.18.6.1380.
Currently all important, low-level, unsupervised network learning algorithms follow the paradigm of Hebb, where input and output activity are correlated to change the connection strength of a synapse. However, as a consequence, classical Hebbian learning always carries a potentially destabilizing autocorrelation term, which is due to the fact that every input is in a weighted form reflected in the neuron's output. This self-correlation can lead to positive feedback, where increasing weights will increase the output, and vice versa, which may result in divergence. This can be avoided by different strategies like weight normalization or weight saturation, which, however, can cause different problems. Consequently, in most cases, high learning rates cannot be used for Hebbian learning, leading to relatively slow convergence. Here we introduce a novel correlation-based learning rule that is related to our isotropic sequence order (ISO) learning rule (Porr & Wörgötter, 2003a), but replaces the derivative of the output in the learning rule with the derivative of the reflex input. Hence, the new rule uses input correlations only, effectively implementing strict heterosynaptic learning. This looks like a minor modification but leads to dramatically improved properties. Elimination of the output from the learning rule removes the unwanted, destabilizing autocorrelation term, allowing us to use high learning rates. As a consequence, we can mathematically show that the theoretical optimum of one-shot learning can be reached under ideal conditions with the new rule. This result is then tested against four different experimental setups, and we will show that in all of them, very few (and sometimes only one) learning experiences are needed to achieve the learning goal. As a consequence, the new learning rule is up to 100 times faster and in general more stable than ISO learning.
目前，所有重要的、低级的、无监督网络学习算法都遵循赫布范式，即输入和输出活动相互关联，以改变突触的连接强度。然而，结果是，经典的赫布学习总是带有一个潜在的不稳定自相关项，这是因为每个输入都以加权形式反映在神经元的输出中。这种自相关会导致正反馈，即权重增加会增加输出，反之亦然，这可能导致发散。这可以通过不同的策略来避免，如权重归一化或权重饱和，然而，这可能会导致不同的问题。因此，在大多数情况下，赫布学习不能使用高学习率，导致收敛相对较慢。在这里，我们引入了一种新的基于相关性的学习规则，它与我们的各向同性序列顺序（ISO）学习规则（Porr & Wörgötter，2003a）相关，但在学习规则中用反射输入的导数代替了输出的导数。因此，新规则仅使用输入相关性，有效地实现了严格的异突触学习。这看起来像是一个小修改，但却带来了显著改善的特性。从学习规则中消除输出消除了不需要的、不稳定的自相关项，使我们能够使用高学习率。因此，我们可以从数学上证明，在理想条件下，新规则可以达到一次性学习的理论最优值。然后针对四种不同的实验设置对这一结果进行了测试，我们将表明，在所有这些设置中，只需很少（有时只需一次）的学习经验就能实现学习目标。因此，新的学习规则比ISO学习快100倍，并且总体上更稳定。
