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Abstract:
Living organisms are constantly exposed to sensory stimuli with complex, high-dimensional statistics. Properly reacting to these stimuli is essential for the organism to survive. However, already the encoding of stimulus intensity bears problems, as intensities are often distributed over multiple orders of magnitude. The capability to process these broad distributions can be quantified by the dynamic range. For recurrent neural networks, it was shown that the dynamic range of the neural response is maximized at criticality [1,2]. Here, we note that an optimal neural response to real complex stimulus statistics does not only require a sufficiently large dynamic range, but also requires to cover those intensities that are relevant. We quantify the intensities covered by the dynamic range with what we call the discriminable interval. For a single network near criticality, we show analytically that this discriminable interval cannot be tuned to cover all possible stimulus intensities. As a result, some intensities cannot be encoded – although they are potentially essential for the organism to survive. To resolve this problem, we derive a rule for activity-dependent synaptic adaptation that allows the network to fine-tune the discriminable interval. We demonstrate that an ensemble of such networks with specifically fine-tuned discriminable intervals can generate an optimal response to complex stimulus statistics.
