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McCulloch Pitts attractor networks minimizing probability flow can achieve robust exponential pattern storage.

Fig. 2 Learning critical networks with exponential memory by minimizing probability flow on few training patterns.

Although we have focused on minimizing probability flow to learn parameters in our discrete neural networks, several other strategies exist.

Fig. 3 Distribution of network parameters learned by minimizing probability flow (MPF) sharpens around three critical values.

Here, we discover such networks by minimizing probability flow, a recently proposed objective for estimating parameters in discrete maximum entropy models.

It follows that the optimal setting (7) for x minimizing probability flow gives robust storage (with a single parallel dynamics update) of all k-cliques for (p < 1/4).

We next analytically minimize probability flow to determine explicit networks achieving robust exponential storage.

As a final technical remark about our networks, note that our synapses are actually discrete since the probability flow is minimized at a synaptic ratio equaling a rational number.

It is elementary that a Hopfield network has attractors X if and only if the probability flow (5) can be arbitrarily close to zero, motivating the application of minimizing (5) to find such networks [15].

minimum probability flow.

The probability flow vector J V,I,t) is a measure of the net probability flux in (V,I) space.