This paper introduces a local planner that synergizes the decision making and trajectory planning modules towards autonomous driving. The decision making and trajectory planning tasks are jointly formulated as a nonlinear programming problem with an integrated objective function. However, integrating the discrete decision variables into the continuous trajectory optimization leads to a mixed-integer programming (MIP) problem with inherent nonlinearity and nonconvexity. To address the challenge in solving the problem, the original problem is decomposed into two sub-stages, and a two-stage optimization (TSO) based approach is presented to ensure the coherence in outcomes for the two stages. The optimization problem in the first stage determines the optimal decision sequence that acts as an informed initialization. With the outputs from the first stage, the second stage necessitates the use of a high-fidelity vehicle model and strict enforcement of the collision avoidance constraints as part of the trajectory planning problem. We evaluate the effectiveness of our proposed planner across diverse multi-lane scenarios. The results demonstrate that the proposed planner simultaneously generates a sequence of optimal decisions and the corresponding trajectory that significantly improves driving performance in terms of driving safety and traveling efficiency as compared to alternative methods. Additionally, we implement the closed-loop simulation in CARLA, and the results showcase the effectiveness of the proposed planner to adapt to changing driving situations with high computational efficiency.
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This work addresses the path planning problem for a group of unmanned aerial vehicles (UAVs) to maintain a desired formation during operation. Our approach formulates the problem as an optimization task by defining a set of fitness functions that not only ensure the formation but also include constraints for optimal and safe UAV operation. To optimize the fitness function and obtain a suboptimal path, we employ the teaching-learning-based optimization algorithm and then further enhance it with mechanisms such as mutation, elite strategy, and multi-subject combination. A number of simulations and experiments have been conducted to evaluate the proposed method. The results demonstrate that the algorithm successfully generates valid paths for the UAVs to fly in a triangular formation for an inspection task.
This paper discusses our recent generalized optimal algebraic multigrid (AMG) convergence theory applied to the steady-state Stokes equations discretized using Taylor-Hood elements ($\pmb{ \mathbb{P}}_2/\mathbb{P}_{1}$). The generalized theory is founded on matrix-induced orthogonality of the left and right eigenvectors of a generalized eigenvalue problem involving the system matrix and relaxation operator. This framework establishes a rigorous lower bound on the spectral radius of the two-grid error-propagation operator, enabling precise predictions of the convergence rate for symmetric indefinite problems, such as those arising from saddle-point systems. We apply this theory to the recently developed monolithic smooth aggregation AMG (SA-AMG) solver for Stokes, constructed using evolution-based strength of connection, standard aggregation, and smoothed prolongation. The performance of these solvers is evaluated using additive and multiplicative Vanka relaxation strategies. Additive Vanka relaxation constructs patches algebraically on each level, resulting in a nonsymmetric relaxation operator due to the partition of unity being applied on one side of the block-diagonal matrix. Although symmetry can be restored by eliminating the partition of unity, this compromises convergence. Alternatively, multiplicative Vanka relaxation updates velocity and pressure sequentially within each patch, propagating updates multiplicatively across the domain and effectively addressing velocity-pressure coupling, ensuring a symmetric relaxation. We demonstrate that the generalized optimal AMG theory consistently provides accurate lower bounds on the convergence rate for SA-AMG applied to Stokes equations. These findings suggest potential avenues for further enhancement in AMG solver design for saddle-point systems.
The paper investigates the problem of path planning techniques for multi-copter uncrewed aerial vehicles (UAV) cooperation in a formation shape to examine surrounding surfaces. We first describe the problem as a joint objective cost for planning a path of the formation centroid working in a complicated space. The path planning algorithm, named the generalized particle swarm optimization algorithm, is then presented to construct an optimal, flyable path while avoiding obstacles and ensuring the flying mission requirements. A path-development scheme is then incorporated to generate a relevant path for each drone to maintain its position in the formation configuration. Simulation, comparison, and experiments have been conducted to verify the proposed approach. Results show the feasibility of the proposed path-planning algorithm with GEPSO.
This paper explores the application of Explainable AI (XAI) techniques to improve the transparency and understanding of predictive models in control of automated supply air temperature (ASAT) of Air Handling Unit (AHU). The study focuses on forecasting of ASAT using a linear regression with Huber loss. However, having only a control curve without semantic and/or physical explanation is often not enough. The present study employs one of the XAI methods: Shapley values, which allows to reveal the reasoning and highlight the contribution of each feature to the final ASAT forecast. In comparison to other XAI methods, Shapley values have solid mathematical background, resulting in interpretation transparency. The study demonstrates the contrastive explanations--slices, for each control value of ASAT, which makes it possible to give the client objective justifications for curve changes.
Due to their robustness and flexibility, neural-driven beamformers are a popular choice for speech separation in challenging environments with a varying amount of simultaneous speakers alongside noise and reverberation. Time-frequency masks and relative directions of the speakers regarding a fixed spatial grid can be used to estimate the beamformer's parameters. To some degree, speaker-independence is achieved by ensuring a greater amount of spatial partitions than speech sources. In this work, we analyze how to encode both mask and positioning into such a grid to enable joint estimation of both quantities. We propose mask-weighted spatial likelihood coding and show that it achieves considerable performance in both tasks compared to baseline encodings optimized for either localization or mask estimation. In the same setup, we demonstrate superiority for joint estimation of both quantities. Conclusively, we propose a universal approach which can replace an upstream sound source localization system solely by adapting the training framework, making it highly relevant in performance-critical scenarios.
We present an approach to modifying Transformer architectures by integrating graph-aware relational reasoning into the attention mechanism, merging concepts from graph neural networks and language modeling. Building on the inherent connection between attention and graph theory, we reformulate the Transformer's attention mechanism as a graph operation and propose Graph-Aware Isomorphic Attention. This method leverages advanced graph modeling strategies, including Graph Isomorphism Networks (GIN) and Principal Neighborhood Aggregation (PNA), to enrich the representation of relational structures. Our approach captures complex dependencies and generalizes across tasks, as evidenced by a reduced generalization gap and improved learning performance. Additionally, we expand the concept of graph-aware attention to introduce Sparse GIN-Attention, a fine-tuning approach that employs sparse GINs. By interpreting attention matrices as sparse adjacency graphs, this technique enhances the adaptability of pre-trained foundational models with minimal computational overhead, endowing them with graph-aware capabilities. Sparse GIN-Attention fine-tuning achieves improved training dynamics and better generalization compared to alternative methods like low-rank adaption (LoRA). We discuss latent graph-like structures within traditional attention mechanisms, offering a new lens through which Transformers can be understood. By evolving Transformers as hierarchical GIN models for relational reasoning. This perspective suggests profound implications for foundational model development, enabling the design of architectures that dynamically adapt to both local and global dependencies. Applications in bioinformatics, materials science, language modeling, and beyond could benefit from this synthesis of relational and sequential data modeling, setting the stage for interpretable and generalizable modeling strategies.
This paper introduces a novel algorithm designed for speech synthesis from neural activity recordings obtained using invasive electroencephalography (EEG) techniques. The proposed system offers a promising communication solution for individuals with severe speech impairments. Central to our approach is the integration of time-frequency features in the high-gamma band computed from EEG recordings with an advanced NeuroIncept Decoder architecture. This neural network architecture combines Convolutional Neural Networks (CNNs) and Gated Recurrent Units (GRUs) to reconstruct audio spectrograms from neural patterns. Our model demonstrates robust mean correlation coefficients between predicted and actual spectrograms, though inter-subject variability indicates distinct neural processing mechanisms among participants. Overall, our study highlights the potential of neural decoding techniques to restore communicative abilities in individuals with speech disorders and paves the way for future advancements in brain-computer interface technologies.
Recently, it can be noticed that most models based on spiking neural networks (SNNs) only use a same level temporal resolution to deal with speech classification problems, which makes these models cannot learn the information of input data at different temporal scales. Additionally, owing to the different time lengths of the data before and after the sub-modules of many models, the effective residual connections cannot be applied to optimize the training processes of these models.To solve these problems, on the one hand, we reconstruct the temporal dimension of the audio spectrum to propose a novel method named as Temporal Reconstruction (TR) by referring the hierarchical processing process of the human brain for understanding speech. Then, the reconstructed SNN model with TR can learn the information of input data at different temporal scales and model more comprehensive semantic information from audio data because it enables the networks to learn the information of input data at different temporal resolutions. On the other hand, we propose the Non-Aligned Residual (NAR) method by analyzing the audio data, which allows the residual connection can be used in two audio data with different time lengths. We have conducted plentiful experiments on the Spiking Speech Commands (SSC), the Spiking Heidelberg Digits (SHD), and the Google Speech Commands v0.02 (GSC) datasets. According to the experiment results, we have achieved the state-of-the-art (SOTA) result 81.02\% on SSC for the test classification accuracy of all SNN models, and we have obtained the SOTA result 96.04\% on SHD for the classification accuracy of all models.
Mean Field Control Games (MFCGs) provide a powerful theoretical framework for analyzing systems of infinitely many interacting agents, blending elements from Mean Field Games (MFGs) and Mean Field Control (MFC). However, solving the coupled Hamilton-Jacobi-Bellman and Fokker-Planck equations that characterize MFCG equilibria remains a significant computational challenge, particularly in high-dimensional or complex environments. This paper presents a scalable deep Reinforcement Learning (RL) approach to approximate equilibrium solutions of MFCGs. Building on previous works, We reformulate the infinite-agent stochastic control problem as a Markov Decision Process, where each representative agent interacts with the evolving mean field distribution. We use the actor-critic based algorithm from a previous paper (Angiuli et.al., 2024) as the baseline and propose several versions of more scalable and efficient algorithms, utilizing techniques including parallel sample collection (batching); mini-batching; target network; proximal policy optimization (PPO); generalized advantage estimation (GAE); and entropy regularization. By leveraging these techniques, we effectively improved the efficiency, scalability, and training stability of the baseline algorithm. We evaluate our method on a linear-quadratic benchmark problem, where an analytical solution to the MFCG equilibrium is available. Our results show that some versions of our proposed approach achieve faster convergence and closely approximate the theoretical optimum, outperforming the baseline algorithm by an order of magnitude in sample efficiency. Our work lays the foundation for adapting deep RL to solve more complicated MFCGs closely related to real life, such as large-scale autonomous transportation systems, multi-firm economic competition, and inter-bank borrowing problems.
We study the classic matrix cross approximation based on the maximal volume submatrices. Our main results consist of an improvement of the classic estimate for matrix cross approximation and a greedy approach for finding the maximal volume submatrices. More precisely, we present a new proof of the classic estimate of the inequality with an improved constant. Also, we present a family of greedy maximal volume algorithms to improve the computational efficiency of matrix cross approximation. The proposed algorithms are shown to have theoretical guarantees of convergence. Finally, we present two applications: image compression and the least squares approximation of continuous functions. Our numerical results at the end of the paper demonstrate the effective performance of our approach.
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