Seeing Is Believing: Brain-Inspired Modular Training for Mechanistic Interpretability.

We introduce Brain-Inspired Modular Training (BIMT), a method for making neural networks more modular and interpretable. Inspired by brains, BIMT embeds neurons in a geometric space and augments the loss function with a cost proportional to the length of each neuron connection. This is inspired by the idea of minimum connection cost in evolutionary biology, but we are the first the combine this idea with training neural networks with gradient descent for interpretability. We demonstrate that BIMT discovers useful modular neural networks for many simple tasks, revealing compositional structures in symbolic formulas, interpretable decision boundaries and features for classification, and mathematical structure in algorithmic datasets. Qualitatively, BIMT-trained networks have modules readily identifiable by the naked eye, but regularly trained networks seem much more complicated. Quantitatively, we use Newman's method to compute the modularity of network graphs; BIMT achieves the highest modularity for all our test problems. A promising and ambitious future direction is to apply the proposed method to understand large models for vision, language, and science.

Tracking single fluorescent particles in three dimensions via extremum seeking.

The ability to track single fluorescent particles in three-dimensions with sub-diffraction limit precision as well as sub-millisecond temporal resolution has enabled the understanding of many biophysical phenomena at the nanometer scale. While there are several techniques for achieving this, most require complicated experimental setups that are expensive to implement. These methods can offer superb performance but their complexity may be overwhelming to the end-user whose aim is only to understand the feature being imaged. In this work, we describe a method for tracking a single fluorescent particle using a standard confocal or multi-photon microscope configuration. It relies only on the assumption that the relative position of the measurement point and the particle can be actuated and that the point spread function has a global maximum that coincides with the particle's position. The method uses intensity feedback to calculate real-time position commands that "seek" the extremum of the point spread function as the particle moves through its environment. We demonstrate the method by tracking a diffusing quantum dot in a hydrogel on a standard epifluorescent confocal microscope.