Momentum-based optimizers are widely adopted for training neural networks. However, the optimal selection of momentum coefficients remains elusive. This uncertainty impedes a clear understanding of the role of momentum in stochastic gradient methods. In this paper, we present a frequency domain analysis framework that interprets the momentum method as a time-variant filter for gradients, where adjustments to momentum coefficients modify the filter characteristics. Our experiments support this perspective and provide a deeper understanding of the mechanism involved. Moreover, our analysis reveals the following significant findings: high-frequency gradient components are undesired in the late stages of training; preserving the original gradient in the early stages, and gradually amplifying low-frequency gradient components during training both enhance performance. Based on these insights, we propose Frequency Stochastic Gradient Descent with Momentum (FSGDM), a heuristic optimizer that dynamically adjusts the momentum filtering characteristic with an empirically effective dynamic magnitude response. Experimental results demonstrate the superiority of FSGDM over conventional momentum optimizers.

Target localization technology is widely applied in various applications, such as rescue missions, robot navigation, and the Internet of Things. However, in some scenarios, the positions of sensors are unknown due to the load limitation of the sensor carriers and environmental interferences, resulting in the instability of the global navigation satellite system (GNSS). This paper focuses on optimal angle-of-arrival (AOA) sensor placement using multiple position-unknown sensors for target localization accuracy improvement. To guarantee the uniqueness of the target coordinate, at least two anchors are needed. The anchors are some static benchmark objects in the environment with priori known positions. Firstly, a new optimization problem for AOA target localization accuracy improvement incorporating position-unknown sensors and anchors is formulated. Secondly, the optimal theoretical localization accuracies of the unknown sensors and target are derived by minimizing the trace of the Cramér-Rao lower bounds (CRLBs). Thirdly, a mixture optimization method, including a geometrical initialization and the new proposed simultaneous perturbation stochastic approximation and adaptive momentum estimation (SPSA-Adam) algebraic algorithm, is developed. Then, the correctness of the new theoretical findings and the effectiveness of the proposed sensor placement optimization method are verified by simulation examples.

Most of existing graph processing systems essentially follow pull-based computation model to handle compute-intensive parts of graph iteration for high parallelism. Considering all vertices and edges are processed in each iteration, pull model may suffers from a large number of invalid (vertex/edge) operations that do not contribute to graph convergence, leading to potential performance degradation. In this paper, we have the insight that these invalid operations can be filtered by leveraging a small fraction of critical information. However, most of critical information are often beyond the visibility of active vertices being processed. We present two novel filtration approaches to (cooperatively) identify out-of-visibility critical information with boundary-cut heuristics and speculative prediction for many graph algorithms. We have integrated both approaches and their hybrid solution into three state-of-art graph processing systems (including Ligra, Gemini, and Polymer). Experimental results using a wide variety of graph algorithms on both real-world and synthetic graph datasets show that neither of these approaches can have an absolute win for all graph algorithms. Boundary-cut, predictive, and hybrid approaches can improve the performance by 115.1, 38.1, and 136.6 percent on average.

Existing graph processing frameworks greatly improve the performance of memory subsystem, but they are still subject to the underlying modern processor, resulting in the potential inefficiencies for graph processing in the sense of low instruction level parallelism and high branch misprediction. These inefficiencies, in accordance with our comprehensive micro-architectural study, mainly arise out of a wealth of dependencies, serial semantic of instruction streams, and complex conditional instructions in graph processing. In this paper, we propose that a fundamental shift of approach is necessary to break through the inefficiencies of the underlying processor via the dataflow paradigm. It is verified that the idea of applying dataflow approach into graph processing is extremely appealing for the following two reasons. First, as the execution and retirement of instructions only depend on the availability of input data in dataflow model, a high degree of parallelism can be therefore provided to relax the heavy dependency and serial semantic. Second, dataflow is guaranteed to make it possible to reduce the costs of branch misprediction by simultaneously executing all branches of a conditional instruction. Consequently, we make the preliminary attempt to develop the dataflow insight into a specialized graph accelerator. We believe that our work would open a wide range of opportunities to improve the performance of computation and memory access for large-scale graph processing.