Identifying Interpretable Visual Features in Artificial and Biological Neural Systems

Single neurons in neural networks are often interpretable in that they represent individual, intuitively meaningful features. However, many neurons exhibit mixed selectivity, i.e., they represent multiple unrelated features. A recent hypothesis proposes that features in deep networks may be represented in superposition, i.e., on non-orthogonal axes by multiple neurons, since the number of possible interpretable features in natural data is generally larger than the number of neurons in a given network. Accordingly, we should be able to find meaningful directions in activation space that are not aligned with individual neurons. Here, we propose (1) an automated method for quantifying visual interpretability that is validated against a large database of human psychophysics judgments of neuron interpretability, and (2) an approach for finding meaningful directions in network activation space. We leverage these methods to discover directions in convolutional neural networks that are more intuitively meaningful than individual neurons, as we confirm and investigate in a series of analyses. Moreover, we apply the same method to three recent datasets of visual neural responses in the brain and find that our conclusions largely transfer to real neural data, suggesting that superposition might be deployed by the brain. This also provides a link with disentanglement and raises fundamental questions about robust, efficient and factorized representations in both artificial and biological neural systems. One of the oldest ideas in neuroscience is Cajal's single neuron doctrine (Finger, 2001) and its application to perception (Barlow, 1972), i.e., the hypothesis that individual sensory neurons encode individually meaningful features. The idea dates back to the early 1950s, when researchers began to find evidence of neurons that reliably and selectively fire in response to particular stimuli, such as dots on a contrasting background (Barlow, 1953) and lines of particular orientation and width (Hubel & Wiesel, 1959). These findings gave rise to the standard model of the ventral visual stream as a process of hierarchical feature extraction and pooling (Hubel & Wiesel, 1968; Gross et al., 1972; In this work, we adopt a pragmatic definition of feature based on human discernability, measured through psychophysics experiments (see below). For an attempt at a more formal definition see Elhage et al. (2022). Neurons in the early stages extract simple features, such as oriented lines, while neurons at later stages combine simple features to construct more complex composite features. In the highest stages, complex features are combined to yield representations of entire objects encoded by single neurons--the shape of a hand, or the face of a friend.