Problems involving geometric data arise in physics, chemistry, robotics, computer vision, and many other fields. Such data can take numerous forms, for instance points, direction vectors, translations, or rotations, but to date there is no single architecture that can be applied to such a wide variety of geometric types while respecting their symmetries. In this paper we introduce the Geometric Algebra Transformer (GATr), a general-purpose architecture for geometric data. GATr represents inputs, outputs, and hidden states in the projective geometric (or Clifford) algebra, which offers an efficient 16-dimensional vector-space representation of common geometric objects as well as operators acting on them. GATr is equivariant with respect to E(3), the symmetry group of 3D Euclidean space. As a Transformer, GATr is versatile, efficient, and scalable. We demonstrate GATr in problems from n-body modeling to wall-shear-stress estimation on large arterial meshes to robotic motion planning. GATr consistently outperforms both non-geometric and equivariant baselines in terms of error, data efficiency, and scalability.

Problems involving geometric data arise in physics, chemistry, robotics, computer vision, and many other fields. Such data can take numerous forms, for instance points, direction vectors, translations, or rotations, but to date there is no single architecture that can be applied to such a wide variety of geometric types while respecting their symmetries. In this paper we introduce the Geometric Algebra Transformer (GATr), a general-purpose architecture for geometric data. GATr represents inputs, outputs, and hidden states in the projective geometric (or Clifford) algebra, which offers an efficient 16-dimensional vector-space representation of common geometric objects as well as operators acting on them. GATr is equivariant with respect to E(3), the symmetry group of 3D Euclidean space.

Adding explanations to audio deepfake detection (ADD) models will boost their real-world application by providing insight on the decision making process. In this paper, we propose a relevancy-based explainable AI (XAI) method to analyze the predictions of transformer-based ADD models. We compare against standard Grad-CAM and SHAP-based methods, using quantitative faithfulness metrics as well as a partial spoof test, to comprehensively analyze the relative importance of different temporal regions in an audio. We consider large datasets, unlike previous works where only limited utterances are studied, and find that the XAI methods differ in their explanations. The proposed relevancy-based XAI method performs the best overall on a variety of metrics. Further investigation on the relative importance of speech/non-speech, phonetic content, and voice onsets/offsets suggest that the XAI results obtained from analyzing limited utterances don't necessarily hold when evaluated on large datasets.

Problems involving geometric data arise in physics, chemistry, robotics, computer vision, and many other fields. Such data can take numerous forms, for instance points, direction vectors, translations, or rotations, but to date there is no single architecture that can be applied to such a wide variety of geometric types while respecting their symmetries. In this paper we introduce the Geometric Algebra Transformer (GATr), a general-purpose architecture for geometric data. GATr represents inputs, outputs, and hidden states in the projective geometric (or Clifford) algebra, which offers an efficient 16-dimensional vector-space representation of common geometric objects as well as operators acting on them. GATr is equivariant with respect to E(3), the symmetry group of 3D Euclidean space.

Problems involving geometric data arise in physics, chemistry, robotics, computer vision, and many other fields. Such data can take numerous forms, for instance points, direction vectors, translations, or rotations, but to date there is no single architecture that can be applied to such a wide variety of geometric types while respecting their symmetries. In this paper we introduce the Geometric Algebra Transformer (GATr), a general-purpose architecture for geometric data. GATr represents inputs, outputs, and hidden states in the projective geometric (or Clifford) algebra, which offers an efficient 16-dimensional vector-space representation of common geometric objects as well as operators acting on them. GATr is equivariant with respect to E(3), the symmetry group of 3D Euclidean space. As a Transformer, GATr is versatile, efficient, and scalable. We demonstrate GATr in problems from n-body modeling to wall-shear-stress estimation on large arterial meshes to robotic motion planning. GATr consistently outperforms both non-geometric and equivariant baselines in terms of error, data efficiency, and scalability.

The model, Global Automated Target Recognition (GATR), runs in the cloud, using Maxar Technologies' Geospatial Big Data platform (GBDX) to access Maxar's 100 petabyte satellite imagery library and millions of curated data labels across dozens of categories that expedite the training of deep learning algorithms. Fast GPUs enable GATR to scan a large area very quickly, while deep learning methods automate object recognition and reduce the need for extensive algorithm training. The tool teaches itself what the identifying characteristics of an object area or target, for example, learning how to distinguish between a cargo plane and a military transport jet. The system then scales quickly to scan large areas, such as entire countries. GATR uses common deep learning techniques found in the commercial sector and can identify airplanes, ships,, buildings, seaports, etc. "There's more commercial satellite data than ever available today, and up until now, identifying objects has been a largely manual process," says Maria Demaree, vice president and general manager of Lockheed Martin Space Mission Solutions.