# Why is PES biologically plausible?

The NEF puts great emphasis on biological plausibility. However, I'm not clear on why the Prescribed Error Sensitivity (PES) learning rule, used in many NEF-based models, is considered to be biologically plausible. I've heard that:

• It doesn't rely on any globally shared information between neurons
• It empirically replicated various aspects of STDP

But I'm not sure how it does these things or why that's important. Specifically, what would an alternative to PES have to demonstrate to show they had improved biological plausibility?

## 1 Answer

For a learning rule to be biologically plausible, it has to only depend on knowledge/information local to the neuron (no global information about the neuron population) and has to match experimental neuroscience data.

# Only Neuron-Local Information

As discussed in "Simultaneous unsupervised and supervised learning of cognitive functions in biologically plausible spiking neural networks" by Bekolay et al., the effect of the PES learning rule on the decoders $\Delta \mathbf{d}_i$ is formulated as:

$$\Delta \mathbf{d}_i=\kappa \mathbf{E}a_i$$

• $\mathbf{E}$ is the error vector is mapped onto individual neurons which also represent vectors of the same dimension. Biologically, the error vector is theorized to be dopamine levels.
• $a_i$ is each neuron activity level, which in the NEF is defined as a combination of the neuron's encoder and it's activation function. See Principle 1 of the NEF for more detail.
• $\mathbf{\kappa}$ is the error scaling factor

All of these variables only require information local to the neuron. From the paper:

The key difference between this rule and backpropagation is that the global-to- local mapping is done by imposing the portion of the error vector space each neuron is sensitive to via its encoder. This limits flexibility, but removes the dependency on global information, making the rule biologically plausible.

# Matching Neuroscience Experiments

To actually match experimental STDP spiking data, PES must be combined with the Bienenstock, Cooper, Munro (BCM) learning rule to enforce sparsity on the encoders. This creates the homeostatic PES rule (hPES).

This matches the following experiments from "Synaptic modification by correlated activity: Hebb’s postulate revisited" by Bi and Poo.

# Other Replications

In addition to these experiments, there are various papers that use the PES learning rule to replicate things such as a model of Fear Conditioning and a model N-Armed Bandit Task, however this evidence isn't necessarily unique to the PES learning rule.