Abstract: A quaternion deep neural network (QTDNN) includes a plurality of modular hidden layers, each comprising a set of QT computation sublayers, including a quaternion (QT) general matrix multiplication sublayer, a QT non-linear activations sublayer, and a QT sampling sublayer arranged along a forward signal propagation path. Each QT computation sublayer of the set has a plurality of QT computation engines. In each modular hidden layer, a steering sublayer precedes each of the QT computation sublayers along the forward signal propagation path. The steering sublayer directs a forward-propagating quaternion-valued signal to a selected at least one QT computation engine of a next QT computation subsequent sublayer.

Abstract: A machine-learning system includes a quaternion (QT) computation engine. Input data to the QT computation engine includes quaternion values, each comprising a real component and three imaginary components, represented as a set of real-valued tensors. A single quaternion value is represented as a 1-dimensional real-valued tensor having four real-valued components, wherein a first real-valued component represents the real component of the single quaternion value, and wherein a second, a third, and a fourth real-valued component each respectively represents one of the imaginary components. A quaternion-valued vector having a size N is represented as a 2-dimensional real-valued tensor comprising N 1-dimensional real-valued tensors. A quaternion-valued matrix having N×M dimensions is represented as a 3-dimensional real-valued tensor comprising M 2-dimensional real-valued tensors comprising N 1-dimensional real-valued tensors.

Abstract: A deep neural network (DNN) includes hidden layers arranged along a forward propagation path between an input layer and an output layer. The input layer accepts training data comprising quaternion values, outputs a quaternion-valued signal along the forward path to at least one of the hidden layers. At least some of the hidden layers include quaternion layers to execute consistent quaternion (QT) forward operations based on one or more variable parameters. A loss function engine produces a loss function representing an error between the DNN result and an expected result. QT backpropagation-based training operations include computing layer-wise QT partial derivatives, consistent with an orthogonal basis of quaternion space, of the loss function with respect to a QT conjugate of the one or more variable parameters and of respective inputs to the quaternion layers.

Abstract: A quaternion deep neural network (QTDNN) includes a plurality of modular hidden layers, each comprising a set of QT computation sublayers, including a quaternion (QT) general matrix multiplication sublayer, a QT non-linear activations sublayer, and a QT sampling sublayer arranged along a forward signal propagation path. Each QT computation sublayer of the set has a plurality of QT computation engines. In each modular hidden layer, a steering sublayer precedes each of the QT computation sublayers along the forward signal propagation path. The steering sublayer directs a forward-propagating quaternion-valued signal to a selected at least one QT computation engine of a next QT computation subsequent sublayer.

Abstract: A deep neural network (DNN) includes hidden layers arranged along a forward propagation path between an input layer and an output layer. The input layer accepts training data comprising quaternion values, outputs a quaternion-valued signal along the forward path to at least one of the hidden layers. At least some of the hidden layers include quaternion layers to execute consistent quaternion (QT) forward operations based on one or more variable parameters. A loss function engine produces a loss function representing an error between the DNN result and an expected result. QT backpropagation-based training operations include computing layer-wise QT partial derivatives, consistent with an orthogonal basis of quaternion space, of the loss function with respect to a QT conjugate of the one or more variable parameters and of respective inputs to the quaternion layers.

Abstract: A machine-learning system includes a quaternion (QT) computation engine. Input data to the QT computation engine includes quaternion values, each comprising a real component and three imaginary components, represented as a set of real-valued tensors. A single quaternion value is represented as a 1-dimensional real-valued tensor having four real-valued components, wherein a first real-valued component represents the real component of the single quaternion value, and wherein a second, a third, and a fourth real-valued component each respectively represents one of the imaginary components. A quaternion-valued vector having a size N is represented as a 2-dimensional real-valued tensor comprising N 1-dimensional real-valued tensors. A quaternion-valued matrix having N×M dimensions is represented as a 3-dimensional real-valued tensor comprising M 2-dimensional real-valued tensors comprising N 1-dimensional real-valued tensors.

Abstract: Various systems and methods for implementing context-based digital signal processing are described herein. An object detection system includes a processor to: access sensor data from a first sensor and a second sensor integrated in a vehicle; access an operating context of the vehicle; assign a first weight to a first object detection result from sensor data of the first sensor, the first weight adjusted based on the operating context; assign a second weight to a second object detection result from sensor data of the second sensor, the second weight adjusted based on the operating context; and perform a combined object detection technique by combining the first object detection result weighted by the first weight and the second object detection result weighted by the second weight.

Abstract: Various systems and methods for implementing context-based digital signal processing are described herein. An object detection system includes a processor to: access sensor data from a first sensor and a second sensor integrated in a vehicle; access an operating context of the vehicle; assign a first weight to a first object detection result from sensor data of the first sensor, the first weight adjusted based on the operating context; assign a second weight to a second object detection result from sensor data of the second sensor, the second weight adjusted based on the operating context; and perform a combined object detection technique by combining the first object detection result weighted by the first weight and the second object detection result weighted by the second weight.