A simple self-decoding model for neural coding

Neural coding is an important tool to discover the inner workings of mind. In this work, we propose and consider a simple but novel self-decoding model for neural coding based on the principle that the neuron body represents ongoing stimulus while dendrites are used to store that stimulus as a memory. In particular, suppose t spiking presynaptic neurons transmit any stimulus directly to a population of n postsynaptic neurons, a postsynaptic neuron spikes if it does not connect to an inhibitory presynaptic neuron, and every stimulus is represented by up to d spiking postsynaptic neurons. Our hypothesis is that the brain is organized to functionally satisfy the following six criteria: (i) decoding objective, i.e., there are up to r-1 [≥] 0 additional spiking postsynaptic neurons in response to a stimulus along with the spiking postsynaptic neurons representing the stimulus, (ii) smoothness, i.e., similar stimuli are encoded similarly by the presynaptic neurons, (iii) optimal information transmission, i.e., t is minimized, (iv) optimal energetic cost, i.e., only the t presynaptic neurons and the postsynaptic neurons representing a stimulus spike, (v) low-dimensional representation, i.e., d = o(n), and (vi) sparse coding, i.e., t = o(n). Our finding is that some criteria cause or correlate with others. Let the characteristic set of a postsynaptic neuron be the set of the presynaptic neurons it connects with. We prove that (i) holds if and only if the union of the r characteristic sets of any r postsynaptic neurons is not included in the union of the d characteristic sets of d other postsynaptic neurons. Consequently, (ii) is attained. More importantly, we suggest that the decoding objective (i) and optimal information transmission (iii) play a fundamental role in neural computation, while (v) and (vi) correlate to each other and correlate with (iii) and (iv). We examine our hypothesis by statistically testing functional connectivity network and the presynaptic-postsynaptic connectivity in layer 2 of the medial entorhinal cortex of a rat.