The representations of neural networks are often compared to those of biological systems by performing regression between the neural network responses and those measured from biological systems. Many different state-of-the-art deep neural networks yield similar neural predictions, but it remains unclear how to differentiate among models that perform equally well at predicting neural responses. To gain insight into this, we use a recent theoretical framework that relates the generalization error from regression to the spectral bias of the model activations and the alignment of the neural responses onto the learnable subspace of the model. We extend this theory to the case of regression between model activations and neural responses, and define geometrical properties describing the error embedding geometry. We test a large number of deep neural networks that predict visual cortical activity and show that there are multiple types of geometries that result in low neural prediction error as measured via regression. The work demonstrates that carefully decomposing representational metrics can provide interpretability of how models are capturing neural activity and points the way towards improved models of neural activity.

翻译：神经网络表征常通过与生物系统响应的回归分析进行比较。许多不同的先进深度神经网络能产生相似的神经预测，但如何区分在预测神经响应方面表现同样良好的模型仍不清楚。为深入探讨此问题，我们采用近期建立的理论框架，该框架将回归的泛化误差与模型激活的谱偏差及神经响应在模型可学习子空间上的对齐程度相关联。我们将该理论扩展至模型激活与神经响应之间的回归场景，并定义了描述误差嵌入几何结构的几何特性。我们测试了大量预测视觉皮层活动的深度神经网络，结果表明存在多种几何结构可通过回归分析实现低神经预测误差。这项工作证明，精细分解表征指标可揭示模型捕获神经活动的方式，并为改进神经活动模型指明方向。