David L. Boothe

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.

Sarah Harkins Dayton, Layal Bou Hamdan, Ioannis D. Schizas et al.

This chapter explores neural networks, topological data analysis, and topological deep learning techniques, alongside statistical Bayesian methods, for processing images, time series, and graphs to maximize the potential of artificial intelligence in the military domain. Throughout the chapter, we highlight practical applications spanning image, video, audio, and time-series recognition, fraud detection, and link prediction for graphical data, illustrating how topology-aware and uncertainty-aware models can enhance robustness, interpretability, and generalization.

Jared Deighton, Wyatt Mackey, Ioannis Schizas et al.

Mammalian spatial navigation relies on specialized neurons, such as place and grid cells, which encode position based on self-motion and environmental cues. While extensive research has explored the computational role of grid cells, the principles underlying efficient place cell coding remain less understood. Existing spatial information rate measures primarily assess single-neuron encoding, limiting insights into population-level representations, while, the role of correlation in neural coding remains a subject of considerable debate. To address this, we introduce novel, correlation-aware information-theoretic measures that quantify the encoding efficiency of multiple neurons, including the joint stimulus information rate for neuron pairs and the spectral-stimulus information for arbitrary sized populations. The spectral-stimulus information, defined as the leading eigenvalue of the stimulus information matrix, is maximized when neurons exhibit localized, non-overlapping firing fields, mirroring place cell and head direction cell activity. We apply these measures to neural data recorded in mice and monkeys, elucidating differences in encoding efficiency across neuronal pairs and populations. Then, we demonstrate that these measures can be used to train recurrent neural networks (RNNs) via self-supervised learning, leading to the emergence of place cells and head direction cells. Our findings highlight how neural populations collectively encode stimuli, offering a more comprehensive framework for understanding stimulus encoding and optimizing artificial navigation systems in novel environments.

Farzana Nasrin, Christopher Oballe, David L. Boothe et al.

Investigation of human brain states through electroencephalograph (EEG) signals is a crucial step in human-machine communications. However, classifying and analyzing EEG signals are challenging due to their noisy, nonlinear and nonstationary nature. Current methodologies for analyzing these signals often fall short because they have several regularity assumptions baked in. This work provides an effective, flexible and noise-resilient scheme to analyze EEG by extracting pertinent information while abiding by the 3N (noisy, nonlinear and nonstationary) nature of data. We implement a topological tool, namely persistent homology, that tracks the evolution of topological features over time intervals and incorporates individual's expectations as prior knowledge by means of a Bayesian framework to compute posterior distributions. Relying on these posterior distributions, we apply Bayes factor classification to noisy EEG measurements. The performance of this Bayesian classification scheme is then compared with other existing methods for EEG signals.