The interaction of a protein with its environment can be understood and controlled via its 3D structure. Experimental methods for protein structure determination, such as X-ray crystallography or cryogenic electron microscopy, shed light on biological processes but introduce challenging inverse problems. Learning-based approaches have emerged as accurate and efficient methods to solve these inverse problems for 3D structure determination, but are specialized for a predefined type of measurement. Here, we introduce a versatile framework to turn raw biophysical measurements of varying types into 3D atomic models. Our method combines a physics-based forward model of the measurement process with a pretrained generative model providing a task-agnostic, data-driven prior. Our method outperforms posterior sampling baselines on both linear and non-linear inverse problems. In particular, it is the first diffusion-based method for refining atomic models from cryo-EM density maps.

X-ray free-electron lasers (XFELs) offer unique capabilities for measuring the structure and dynamics of biomolecules, helping us understand the basic building blocks of life. Notably, high-repetition-rate XFELs enable single particle imaging (X-ray SPI) where individual, weakly scattering biomolecules are imaged under near-physiological conditions with the opportunity to access fleeting states that cannot be captured in cryogenic or crystallized conditions. Existing X-ray SPI reconstruction algorithms, which estimate the unknown orientation of a particle in each captured image as well as its shared 3D structure, are inadequate in handling the massive datasets generated by these emerging XFELs. Here, we introduce X-RAI, an online reconstruction framework that estimates the structure of a 3D macromolecule from large X-ray SPI datasets. X-RAI consists of a convolutional encoder, which amortizes pose estimation over large datasets, as well as a physics-based decoder, which employs an implicit neural representation to enable high-quality 3D reconstruction in an end-to-end, self-supervised manner. We demonstrate that X-RAI achieves state-of-the-art performance for small-scale datasets in simulation and challenging experimental settings and demonstrate its unprecedented ability to process large datasets containing millions of diffraction images in an online fashion. These abilities signify a paradigm shift in X-ray SPI towards real-time capture and reconstruction.

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.