Tatsukawa Tsuyoshi, Teramae Jun-Nosuke
Department of Advanced Mathematical Sciences, Graduate School of Informatics, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan.
Proc Natl Acad Sci U S A. 2025 May 27;122(21):e2418218122. doi: 10.1073/pnas.2418218122. Epub 2025 May 23.
A recent study has suggested that the stimulus responses of cortical neural populations follow a critical power law. More precisely, the power spectrum of the covariance matrix of neural responses follows a power law with an exponent indicating that the neural manifold lies on the edge of differentiability. This criticality is hypothesized to balance expressivity and robustness in neural encoding, as population responses on a nondifferential fractal manifold are thought to be overly sensitive to perturbations. However, contrary to this hypothesis, we prove that neural coding is far more robust than previously assumed. We develop a theoretical framework that provides an analytical expression for the Fisher information of population coding under the small noise assumption. Our results reveal that, due to its intrinsic high dimensionality, population coding maintains reliability even on a nondifferentiable fractal manifold, despite its sensitivity to perturbations. Furthermore, the theory reveals that the trade-off between energetic cost and information makes the critical power-law coding the optimal neural encoding of sensory information for a wide range of conditions. In this derivation, we highlight the essential role of a neural correlation, known as differential correlation, in power-law population coding. By uncovering the nontrivial nature of high-dimensional information coding, this work deepens our understanding of criticality and power laws in both biological and artificial neural computation.
最近的一项研究表明，皮层神经群体的刺激反应遵循临界幂律。更确切地说，神经反应协方差矩阵的功率谱遵循幂律，其指数表明神经流形位于可微性边缘。据推测，这种临界性在神经编码中平衡了表现力和鲁棒性，因为非微分分形流形上的群体反应被认为对扰动过于敏感。然而，与这一假设相反，我们证明神经编码比之前假设的要稳健得多。我们开发了一个理论框架，在小噪声假设下为群体编码的费希尔信息提供了一个解析表达式。我们的结果表明，由于其固有的高维性，群体编码即使在不可微的分形流形上也能保持可靠性，尽管它对扰动敏感。此外，该理论表明，能量成本和信息之间的权衡使得临界幂律编码在广泛的条件下成为感觉信息的最优神经编码。在这个推导过程中，我们强调了一种称为微分相关的神经相关性在幂律群体编码中的重要作用。通过揭示高维信息编码的非平凡性质，这项工作加深了我们对生物和人工神经计算中临界性和幂律的理解。
