Lian Yanbo, Burkitt Anthony N
Department of Biomedical Engineering, The University of Melbourne, Parkville, Victoria, Australia.
Graeme Clark Institute for Biomedical Engineering, The University of Melbourne, Parkville, Victoria, Australia.
PLoS Comput Biol. 2025 May 27;21(5):e1013059. doi: 10.1371/journal.pcbi.1013059. eCollection 2025 May.
Sparse coding, predictive coding and divisive normalization have each been found to be principles that underlie the function of neural circuits in many parts of the brain, supported by substantial experimental evidence. However, the connections between these related principles are still poorly understood. Sparse coding and predictive coding can be reconciled into a learning framework with predictive structure and sparse responses, termed as sparse/predictive coding. However, how sparse/predictive coding (a learning model) is connected with divisive normalization (not a learning model) is still not well investigated. In this paper, we show how sparse coding, predictive coding, and divisive normalization can be described within a unified framework, and illustrate this explicitly within the context of a two-layer neural learning model of sparse/predictive coding. This two-layer model is constructed in a way that implements sparse coding with a network structure that is constructed by implementing predictive coding. We demonstrate how a homeostatic function that regulates neural responses in the model can shape the nonlinearity of neural responses in a way that replicates different forms of divisive normalization. Simulations show that the model can learn simple cells in the primary visual cortex with the property of contrast saturation, which has previously been explained by divisive normalization. In summary, the study demonstrates that the three principles of sparse coding, predictive coding, and divisive normalization can be connected to provide a learning framework based on biophysical properties, such as Hebbian learning and homeostasis, and this framework incorporates both learning and more diverse response nonlinearities observed experimentally. This framework has the potential to also be used to explain how the brain learns to integrate input from different sensory modalities.
稀疏编码、预测编码和归一化除法各自被发现是大脑许多部位神经回路功能的基础原则，并有大量实验证据支持。然而，这些相关原则之间的联系仍知之甚少。稀疏编码和预测编码可以整合到一个具有预测结构和稀疏响应的学习框架中，称为稀疏/预测编码。然而，稀疏/预测编码（一种学习模型）与归一化除法（不是一种学习模型）之间是如何联系的，仍未得到充分研究。在本文中，我们展示了稀疏编码、预测编码和归一化除法如何在一个统一框架内进行描述，并在稀疏/预测编码的两层神经学习模型的背景下进行了明确说明。这个两层模型的构建方式是，通过实现预测编码来构建网络结构，从而实现稀疏编码。我们展示了一种调节模型中神经响应的稳态功能如何以复制不同形式的归一化除法的方式塑造神经响应的非线性。模拟表明，该模型可以学习具有对比度饱和特性的初级视觉皮层中的简单细胞，这一特性此前已通过归一化除法得到解释。总之，该研究表明，稀疏编码、预测编码和归一化除法这三个原则可以相互联系，以提供一个基于生物物理特性（如赫布学习和稳态）的学习框架，并且这个框架既包含学习，又包含实验中观察到的更多样化的响应非线性。这个框架还有潜力用于解释大脑如何学习整合来自不同感觉模态的输入。
