The brain uses positive signals as a means of signaling. Forward interactions in the early visual cortex are also positive, realized by excitatory synapses. Only local interactions also include inhibition. Non-negative matrix factorization (NMF) captures the biological constraint of positive long-range interactions and can be implemented with stochastic spikes. While NMF can serve as an abstract formalization of early neural processing in the visual system, the performance of deep convolutional networks with NMF modules does not match that of CNNs of similar size. However, when the local NMF modules are each followed by a module that mixes the NMF's positive activities, the performances on the benchmark data exceed that of vanilla deep convolutional networks of similar size. This setting can be considered a biologically more plausible emulation of the processing in cortical (hyper-)columns with the potential to improve the performance of deep networks.

Here we derive optimal gain functions for minimum mean square reconstruction from neural rate responses subjected to Poisson noise. The shape of these functions strongly depends on the length T of the time window within which spikes are counted in order to estimate the underlying firing rate. A phase transition towards pure binary encoding occurs if the maximum mean spike count becomes smaller than approximately three provided the minimum firing rate is zero. For a particular function class, we were able to prove the existence of a second-order phase transition analytically. The critical decoding time window length obtained from the analytical derivation is in precise agreement with the numerical results.

Here we derive optimal gain functions for minimum mean square reconstruction fromneural rate responses subjected to Poisson noise. The shape of these functions strongly depends on the length T of the time window within which spikes are counted in order to estimate the underlying firingrate. A phase transition towards pure binary encoding occurs if the maximum mean spike count becomes smaller than approximately three provided the minimum firing rate is zero. For a particular function class, we were able to prove the existence of a second-order phase transition analytically.The critical decoding time window length obtained from the analytical derivation is in precise agreement with the numerical results. We conclude that under most circumstances relevant to information processingin the brain, rate coding can be better ascribed to a binary (low-entropy) code than to the other extreme ofrich analog coding. 1 Optimal neuronal gain functions for short decoding time windows The use of action potentials (spikes) as a means of communication is the striking feature of neurons in the central nervous system.