Andrew Davis

Jack T. Beerman, Tyler J. Abele, Mehdi Taghizadeh et al.

Physics-aware recurrent convolutional networks (PARC) have demonstrated strong performance in predicting nonlinear spatiotemporal dynamics by embedding differential operators directly into the computational graph of a neural network. However, pixel-based convolutions are restricted to static, uniform Cartesian grids, making them ill-suited to following evolving localized structures in an efficient manner. Graph neural networks (GNNs) naturally handle irregular spatial discretizations, but existing graph-based physics-aware deep learning (PADL) methods have difficulty handling extreme nonlinear regimes. To address these limitations, we propose Graph PARC (G-PARC), which uses moving least squares (MLS) kernels to approximate spatial derivatives on unstructured graphs, and embeds the derivatives of governing partial differential equations into the network's computational graph. G-PARC achieves better accuracy with 2-3x fewer parameters than MeshGraphNet, MeshGraphKAN, and GraphSAGE, replacing the traditional encoder-processor-decoder framework with analytically computed differential operators. We demonstrate that G-PARC (1) generalizes across nonuniform spatial and temporal discretizations; (2) handles moving meshes required for structural deformation; and (3) outperforms existing graph-based PADL methods on nonlinear benchmarks including fluvial hydrology, planar shock waves, and elastoplastic dynamics. By embedding explicit physical operators within the flexibility of GNNs, G-PARC enables accurate modeling of extreme nonlinear phenomena on complex computational domains, moving PADLbeyond idealized Cartesian grids.

Amelia Kawasaki, Andrew Davis, Houssam Abbas

The widespread adoption of Large Language Models (LLMs), exemplified by OpenAI's ChatGPT, brings to the forefront the imperative to defend against adversarial threats on these models. These attacks, which manipulate an LLM's output by introducing malicious inputs, undermine the model's integrity and the trust users place in its outputs. In response to this challenge, our paper presents an innovative defensive strategy, given white box access to an LLM, that harnesses residual activation analysis between transformer layers of the LLM. We apply a novel methodology for analyzing distinctive activation patterns in the residual streams for attack prompt classification. We curate multiple datasets to demonstrate how this method of classification has high accuracy across multiple types of attack scenarios, including our newly-created attack dataset. Furthermore, we enhance the model's resilience by integrating safety fine-tuning techniques for LLMs in order to measure its effect on our capability to detect attacks. The results underscore the effectiveness of our approach in enhancing the detection and mitigation of adversarial inputs, advancing the security framework within which LLMs operate.

Aleksandr Savchenkov, Andrew Davis, Xuan Zhao

The introduction of cheap RGB-D cameras, stereo cameras, and LIDAR devices has given the computer vision community 3D information that conventional RGB cameras cannot provide. This data is often stored as a point cloud. In this paper, we present a novel method to apply the concept of convolutional neural networks to this type of data. By creating a mapping of nearest neighbors in a dataset, and individually applying weights to spatial relationships between points, we achieve an architecture that works directly with point clouds, but closely resembles a convolutional neural net in both design and behavior. Such a method bypasses the need for extensive feature engineering, while proving to be computationally efficient and requiring few parameters.

Andrew Davis, Itamar Arel

Scalability properties of deep neural networks raise key research questions, particularly as the problems considered become larger and more challenging. This paper expands on the idea of conditional computation introduced by Bengio, et. al., where the nodes of a deep network are augmented by a set of gating units that determine when a node should be calculated. By factorizing the weight matrix into a low-rank approximation, an estimation of the sign of the pre-nonlinearity activation can be efficiently obtained. For networks using rectified-linear hidden units, this implies that the computation of a hidden unit with an estimated negative pre-nonlinearity can be ommitted altogether, as its value will become zero when nonlinearity is applied. For sparse neural networks, this can result in considerable speed gains. Experimental results using the MNIST and SVHN data sets with a fully-connected deep neural network demonstrate the performance robustness of the proposed scheme with respect to the error introduced by the conditional computation process.