Brittany Story

Edward C. Mitchell, Brittany Story, David Boothe et al.

The brain's spatial orientation system uses different neuron ensembles to aid in environment-based navigation. Two of the ways brains encode spatial information is through head direction cells and grid cells. Brains use head direction cells to determine orientation whereas grid cells consist of layers of decked neurons that overlay to provide environment-based navigation. These neurons fire in ensembles where several neurons fire at once to activate a single head direction or grid. We want to capture this firing structure and use it to decode head direction grid cell data. Understanding, representing, and decoding these neural structures requires models that encompass higher order connectivity, more than the 1-dimensional connectivity that traditional graph-based models provide. To that end, in this work, we develop a topological deep learning framework for neural spike train decoding. Our framework combines unsupervised simplicial complex discovery with the power of deep learning via a new architecture we develop herein called a simplicial convolutional recurrent neural network. Simplicial complexes, topological spaces that use not only vertices and edges but also higher-dimensional objects, naturally generalize graphs and capture more than just pairwise relationships. Additionally, this approach does not require prior knowledge of the neural activity beyond spike counts, which removes the need for similarity measurements. The effectiveness and versatility of the simplicial convolutional neural network is demonstrated on head direction and trajectory prediction via head direction and grid cell datasets.

Mikolaj Walczak, Romina Aalishah, Wyatt Mackey et al.

Deep reinforcement learning agents are often fragile while humans remain adaptive and flexible to varying scenarios. To bridge this gap, we present EDEN, a biologically inspired navigation framework that integrates learned entorhinal-like grid cell representations and reinforcement learning to enable autonomous navigation. Inspired by the mammalian entorhinal-hippocampal system, EDEN allows agents to perform path integration and vector-based navigation using visual and motion sensor data. At the core of EDEN is a grid cell encoder that transforms egocentric motion into periodic spatial codes, producing low-dimensional, interpretable embeddings of position. To generate these activations from raw sensory input, we combine fiducial marker detections in the lightweight MiniWorld simulator and DINO-based visual features in the high-fidelity Gazebo simulator. These spatial representations serve as input to a policy trained with Proximal Policy Optimization (PPO), enabling dynamic, goal-directed navigation. We evaluate EDEN in both MiniWorld, for rapid prototyping, and Gazebo, which offers realistic physics and perception noise. Compared to baseline agents using raw state inputs (e.g., position, velocity) or standard convolutional image encoders, EDEN achieves a 99% success rate, within the simple scenarios, and >94% within complex floorplans with occluded paths with more efficient and reliable step-wise navigation. In addition, as a replacement of ground truth activations, we present a trainable Grid Cell encoder enabling the development of periodic grid-like patterns from vision and motion sensor data, emulating the development of such patterns within biological mammals. This work represents a step toward biologically grounded spatial intelligence in robotics, bridging neural navigation principles with reinforcement learning for scalable deployment.

Teresa Heiss, Sarah Tymochko, Brittany Story et al.

Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging. A high resolution means longer image acquisition and larger data requirements for a given sample, but if the resolution is too low, significant information may be lost. This paper studies the impact of changes in resolution on persistent homology, a tool from topological data analysis that provides a signature of structure in an image across all length scales. Given prior information about a function, the geometry of an object, or its density distribution at a given resolution, we provide methods to select the coarsest resolution yielding results within an acceptable tolerance. We present numerical case studies for an illustrative synthetic example and samples from porous materials where the theoretical bounds are unknown.

Henry Adams, Elin Farnell, Brittany Story

A support vector machine (SVM) is an algorithm that finds a hyperplane which optimally separates labeled data points in $\mathbb{R}^n$ into positive and negative classes. The data points on the margin of this separating hyperplane are called support vectors. We connect the possible configurations of support vectors to Radon's theorem, which provides guarantees for when a set of points can be divided into two classes (positive and negative) whose convex hulls intersect. If the convex hulls of the positive and negative support vectors are projected onto a separating hyperplane, then the projections intersect if and only if the hyperplane is optimal. Further, with a particular type of general position, we show that (a) the projected convex hulls of the support vectors intersect in exactly one point, (b) the support vectors are stable under perturbation, (c) there are at most $n+1$ support vectors, and (d) every number of support vectors from 2 up to $n+1$ is possible. Finally, we perform computer simulations studying the expected number of support vectors, and their configurations, for randomly generated data. We observe that as the distance between classes of points increases for this type of randomly generated data, configurations with fewer support vectors become more likely.