David L. Boothe

Patrick Gillespie, Layal Bou Hamdan, Ioannis Schizas et al.

Equipping graph neural networks with a convolution operation defined in terms of a cellular sheaf offers advantages for learning expressive representations of heterophilic graph data. The most flexible approach to constructing the sheaf is to learn it as part of the network as a function of the node features. However, this leaves the network potentially overly sensitive to the learned sheaf. As a counter-measure, we propose a variational approach to learning cellular sheaves within sheaf neural networks, yielding an architecture we refer to as a Bayesian sheaf neural network. As part of this work, we define a novel family of reparameterizable probability distributions on the rotation group $SO(n)$ using the Cayley transform. We evaluate the Bayesian sheaf neural network on several graph datasets, and show that our Bayesian sheaf models achieve leading performance compared to baseline models and are less sensitive to the choice of hyperparameters under limited training data settings.

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.

Sarah Harkins Dayton, Hayden Everett, Ioannis Schizas et al.

Convolutional neural networks (CNNs) have been established as the main workhorse in image data processing; nonetheless, they require large amounts of data to train, often produce overconfident predictions, and frequently lack the ability to quantify the uncertainty of their predictions. To address these concerns, we propose a new Bayesian topological CNN that promotes a novel interplay between topology-aware learning and Bayesian sampling. Specifically, it utilizes information from important manifolds to accelerate training while reducing calibration error by placing prior distributions on network parameters and properly learning appropriate posteriors. One important contribution of our work is the inclusion of a consistency condition in the learning cost, which can effectively modify the prior distributions to improve the performance of our novel network architecture. We evaluate the model on benchmark image classification datasets and demonstrate its superiority over conventional CNNs, Bayesian neural networks (BNNs), and topological CNNs. In particular, we supply evidence that our method provides an advantage in situations where training data is limited or corrupted. Furthermore, we show that the new model allows for better uncertainty quantification than standard BNNs since it can more readily identify examples of out-of-distribution data on which it has not been trained. Our results highlight the potential of our novel hybrid approach for more efficient and robust image classification.

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.