Power laws from about 20,000 mouse neurons predict sensory information keeps rising with population size

Single neurons are unreliable reporters. Show one the same image over and over and its firing rate swings from trial to trial. The standard fix is population coding: spread the signal across many cells so that individual errors average out ^[10]. That only works if the errors are independent, and cortical neurons tend to rise and fall together. As the release describes it, computational neuroscience has held for about 30 years that this shared noise sets a limit ^[8]. If the noise overlaps the activity patterns that carry the stimulus, each added neuron contributes less, and eventually information hits a hard ceiling ^[8].

"We face a fundamental question: why does the brain have so many neurons if shared fluctuations impose a ceiling on information?" said S. Amin Moosavi of the University of California, Los Angeles ^[9].

The team from Kyoto University, Harvard and UCLA tackled the question by studying how information scales ^[2]. They reanalysed two-photon calcium imaging and electrophysiology datasets, each covering 18,000 to 21,000 neurons recorded at once in the primary visual cortex of mice discriminating fine differences between stimuli ^[1]. From each dataset they drew random subpopulations of increasing size and measured how much stimulus information a linear decoder could read out ^[3]. They also broke the shared noise into eigenmodes, the distinct patterns in which the population fluctuates together ^[4].

Two regularities came out. Noise strength across the modes followed a power law. So did the alignment of each mode with the stimulus axis, and neither law changed form as the subsample grew ^[4]. That invariance is what lets the curve be extended. Combined with subsampling constraints, the fitted laws let the team estimate information beyond the number of cells they actually recorded ^[5].

The old worry was partly right. The strongest noise modes did line up more closely with the stimulus signal ^[6]. But the signal also ran through a large subspace of quiet, low-variability modes, where shared noise does less damage ^[6]. According to the release, the exponents in every animal contradicted the saturation hypothesis. Correlated noise slows the rate at which information builds up as neurons are added, but does not stop it ^[7].

The thing this doesn't tell you is what happens far beyond 21,000 cells. Past the recorded range, the no-ceiling result is a fitted power law carried forward. If the curve bent at larger scales, a ceiling would come back ^[5]. How much growth slows depends on the exponents, and bigger recordings can check them directly. The readout is also narrow: linear decoding of a fine discrimination task in mouse V1 ^[1][3].

The release, issued by Kyoto University, opens with the human brain's billions of cortical neurons and says the analysis spans "mammalian models" ^[11][12]. The recordings it describes are from mice ^[1].