Ioannis Schizas

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.

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.

Wyatt Mackey, Ioannis Schizas, Jared Deighton et al.

A common technique for ameliorating the computational costs of running large neural models is sparsification, or the pruning of neural connections during training. Sparse models are capable of maintaining the high accuracy of state of the art models, while functioning at the cost of more parsimonious models. The structures which underlie sparse architectures are, however, poorly understood and not consistent between differently trained models and sparsification schemes. In this paper, we propose a new technique for sparsification of recurrent neural nets (RNNs), called moduli regularization, in combination with magnitude pruning. Moduli regularization leverages the dynamical system induced by the recurrent structure to induce a geometric relationship between neurons in the hidden state of the RNN. By making our regularizing term explicitly geometric, we provide the first, to our knowledge, a priori description of the desired sparse architecture of our neural net, as well as explicit end-to-end learning of RNN geometry. We verify the effectiveness of our scheme under diverse conditions, testing in navigation, natural language processing, and addition RNNs. Navigation is a structurally geometric task, for which there are known moduli spaces, and we show that regularization can be used to reach 90% sparsity while maintaining model performance only when coefficients are chosen in accordance with a suitable moduli space. Natural language processing and addition, however, have no known moduli space in which computations are performed. Nevertheless, we show that moduli regularization induces more stable recurrent neural nets, and achieves high fidelity models above 90% sparsity.

Tuan Ho, Ioannis Schizas, K. R. Rao et al.

Dual-fisheye lens cameras are becoming popular for 360-degree video capture, especially for User-generated content (UGC), since they are affordable and portable. Images generated by the dual-fisheye cameras have limited overlap and hence require non-conventional stitching techniques to produce high-quality 360x180-degree panoramas. This paper introduces a novel method to align these images using interpolation grids based on rigid moving least squares. Furthermore, jitter is the critical issue arising when one applies the image-based stitching algorithms to video. It stems from the unconstrained movement of stitching boundary from one frame to another. Therefore, we also propose a new algorithm to maintain the temporal coherence of stitching boundary to provide jitter-free 360-degree videos. Results show that the method proposed in this paper can produce higher quality stitched images and videos than prior work.