What makes an artificial system a good model of intelligence? The classical test proposed by Alan Turing focuses on behavior, requiring that an artificial agent's behavior be indistinguishable from that of a human. While behavioral similarity provides a strong starting point, two systems with very different internal representations can produce the same outputs. Thus, in modeling biological intelligence, the field of NeuroAI often aims to go beyond behavioral similarity and achieve representational convergence between a model's activations and the measured activity of a biological system. This position paper argues that the standard definition of the Turing Test is incomplete for NeuroAI, and proposes a stronger framework called the ``NeuroAI Turing Test'', a benchmark that extends beyond behavior alone and \emph{additionally} requires models to produce internal neural representations that are empirically indistinguishable from those of a brain up to measured individual variability, i.e. the differences between a computational model and the brain is no more than the difference between one brain and another brain. While the brain is not necessarily the ceiling of intelligence, it remains the only universally agreed-upon example, making it a natural reference point for evaluating computational models. By proposing this framework, we aim to shift the discourse from loosely defined notions of brain inspiration to a systematic and testable standard centered on both behavior and internal representations, providing a clear benchmark for neuroscientific modeling and AI development.

Image representations (artificial or biological) are often compared in terms of their global geometry; however, representations with similar global structure can have strikingly different local geometries. Here, we propose a framework for comparing a set of image representations in terms of their local geometries. We quantify the local geometry of a representation using the Fisher information matrix, a standard statistical tool for characterizing the sensitivity to local stimulus distortions, and use this as a substrate for a metric on the local geometry in the vicinity of a base image. This metric may then be used to optimally differentiate a set of models, by finding a pair of "principal distortions" that maximize the variance of the models under this metric. We use this framework to compare a set of simple models of the early visual system, identifying a novel set of image distortions that allow immediate comparison of the models by visual inspection. In a second example, we apply our method to a set of deep neural network models and reveal differences in the local geometry that arise due to architecture and training types. These examples highlight how our framework can be used to probe for informative differences in local sensitivities between complex computational models, and suggest how it could be used to compare model representations with human perception. Biological and artificial neural networks transform sensory stimuli into high-dimensional internal representations that support downstream tasks, and these representations are often described in terms of their neural population geometry (Chung & Abbott, 2021). Are these models functionally interchangeable, or are the datasets and methods that are used to test them simply insufficient to reveal their differences?

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 properties of the model and the target. We apply this theory to the case of regression between model activations and neural responses and decompose the neural prediction error in terms of the model eigenspectra, alignment of model eigenvectors and neural responses, and the training set size. Using this decomposition, we introduce geometrical measures to interpret the neural prediction error. 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.