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   Many theories assume that a sensory neuron’s higher firing rate indicates a greater probability of its preferred stimulus. However, this contradicts 1) the adaptation phenomena where prolonged exposure to, and thus increased probability of, a stimulus reduces the firing rates of cells tuned to the stimulus; and 2) the observation that unexpected (low probability) stimuli capture attention and increase neuronal firing. Other theories posit that the brain builds predictive/efficient codes for reconstructing sensory inputs. However, they cannot explain that the brain preserves some information while discarding other. We propose that in sensory areas, projection neurons’ firing rates are proportional to optimal code length (i.e., negative log estimated probability), and their spike patterns are the code, for useful features in inputs. This hypothesis explains adaptation-induced changes of V1 orientation tuning curves, and bottom-up attention. We discuss how the modern minimum-description-length (MDL) principle may help understand neural codes. Because regularity extraction is relative to a model class (defined by cells) via its optimal universal code (OUC), MDL matches the brain’s purposeful, hierarchical processing without input reconstruction. Such processing enables input compression/understanding even when model classes do not contain true models. Top-down attention modifies lower-level OUCs via feedback connections to enhance transmission of behaviorally relevant information. Although OUCs concern lossless data compression, we suggest possible extensions to lossy, prefix-free neural codes for prompt, online processing of most important aspects of stimuli while minimizing behaviorally relevant distortion. Finally, we discuss how neural networks might learn MDL’s normalized maximum likelihood (NML) distributions from input data. 

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4. Fast-slow analysis as a technique for understanding the neuronal response to current ramps

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5. Compressive Sensing Inference of Neuronal Network Connectivity in Balanced Neuronal Dynamics

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