Summary:
Challenging a long-standing principle in sensory neuroscience, researchers discovered that correlated “noise” among fluctuating neurons does not place an absolute ceiling on the sensory information large neural networks can encode. Analyzing over 20,000 visual cortex neurons across mammalian models, the team identified invariant scaling power laws showing that information capacity continues to expand as neural populations grow.
Key Facts:
- Overturning a 30-Year Hypothesis: Theoretical neuroscience has widely assumed that shared trial-to-trial fluctuations (noise correlations) inevitably impose a hard ceiling on sensory population coding.
- Discovery of Invariant Power Laws: By evaluating visual cortex recordings across tens of thousands of neurons, the team identified two scale-invariant power laws that govern noise strength distribution and its alignment with stimulus signals.
- Infinite Scaling Potential: While shared noise slows the rate at which information accumulates as neurons are added, the stimulus signal extends into quiet, low-variability dimensions, preventing information saturation.
Source: Kyoto University
The Puzzle of Unreliable Neurons
The human brain constructs an internal representation of sensory reality through the collective firing of billions of cortical neurons. Yet at the individual cellular level, single neurons respond with notorious unreliability: present the exact same sensory image repeatedly, and an isolated neuron’s firing rate will fluctuate significantly from trial to trial.
To overcome this biological variability, the nervous system employs population coding—distributing sensory information across thousands or millions of interconnected cells to average out individual errors.
However, neurons within cortical networks do not operate in isolation; their membrane potentials and spike times often rise and fall together. For the past three decades, computational neuroscientists have argued that this shared fluctuation, termed “noise correlation”, presents an insurmountable barrier. If shared biological noise overlaps with the patterns of activity that encode sensory signals, theoretical models predicted that adding more neurons would eventually yield diminishing returns, ultimately hitting a hard informational ceiling.
“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, Ph.D., of the University of California, Los Angeles (UCLA).
Mapping 20,000 Visual Cortex Neurons
To resolve this paradox, an international consortium of researchers from Kyoto University, Harvard University, and UCLA reanalyzed large-scale, two-photon calcium imaging and electrophysiological datasets capturing between 18,000 and 21,000 neurons simultaneously within the primary visual cortex (V1) of mice discriminating fine differences between visual stimuli.
The investigators assessed how much visual information could be linearly decoded as they sampled progressively larger sub-ensembles of cortical neurons.
By iteratively isolating random subpopulations across multiple scales and decomposing their collective noise into distinct mathematical activity patterns (eigenmodes), the researchers uncovered two distinct power laws that retained an invariant mathematical form regardless of population size:
- Noise Amplitude Scaling: A power law describing the distribution of noise strengths across network modes.
- Signal-Noise Alignment: A power law describing how closely each noise pattern aligned with the sensory stimulus axis.
Combining these scaling laws with subsampling constraints enabled the investigators to mathematically extrapolate how information scales beyond physically recorded population boundaries.
Information Slows Down, But Never Stops Growing
Across all animal subjects, the empirical power-law exponents contradicted the classic saturation hypothesis. While the strongest noise components did align more closely with the sensory signal, the signal simultaneously projected across a vast subspace of lower-variability, quieter activity modes.
Consequently, while correlated noise slows down the rate of information accumulation as neural networks expand, it does not bring information growth to a halt.
“For three decades, shared neural fluctuations were widely expected to make information saturate,” explained Hideaki Shimazaki, Ph.D., of Kyoto University. “Our results show that this is not inevitable.”
Blueprints for Fault-Tolerant Computing
Beyond resolving a foundational mystery of sensory neurobiology, the team’s mathematical framework provides a universal theory for how linearly decodable information scales in complex, stochastic networks.
These insights have direct applications for neuromorphic hardware, distributed artificial intelligence architectures, and quantum-adjacent noisy computing systems. Engineers grappling with shared noise in dense silicon circuits can leverage these biological scaling principles to design fault-tolerant computational architectures where adding processing units continues to enhance precision indefinitely.
Editorial Notes:
- This article was edited by a Neuroscience News editor.
- Journal paper reviewed in full.
- Additional context added by our staff.
About this Theoretical Neuroscience Research:
- Media Contact: Whitney Hubbell
- Source: Kyoto University
- Image Credit: Image credited to Neuroscience News
- Original Research is Open Access: Science Advances (Sept 25, 2026). “Population coding under the scale invariance of high-dimensional noise.” Authors: S. Amin Moosavi, Sai Sumedh R. Hindupur, and Hideaki Shimazaki.
- DOI: 10.1126/sciadv.adz9632
Abstract
Population coding under the scale invariance of high-dimensional noise
High-dimensional scale-invariant neural activity is ubiquitous across brain regions and species, but its implications for information coding remain unclear.
Here, we ask how stimulus information in the high-dimensional activity of mouse V1 scales with neuron number: Does it saturate due to noise correlations or increase without bound as subpopulations grow?
Contrary to previous reports, we find that leading noise components that scale linearly with population size, and thus can limit information, are not sufficiently aligned with the signal to impose a bound. This conclusion follows from two scale-invariant power-law properties of neuronal responses in mouse V1: the noise eigenspectrum and alignment of noise components with the signal.
We show that population subsampling links the observed power-law exponents to information boundedness and that information scaling depends on the full eigenspectrum rather than its leading modes. Last, we prove that, under subsampling, information-limiting correlations, if present, are differential correlations.
Our findings clarify how information scales in high-dimensional neuronal activity under scale-invariant noise.
