A silting theorem was established by Buan and Zhou as a generalisation of the classical tilting theorem of Brenner and Butler. In this paper, we give an alternative proof of the theorem by using differential graded algebras.
3D multi-object tracking in LiDAR point clouds is a key ingredient for self-driving vehicles. Existing methods are predominantly based on the tracking-by-detection pipeline and inevitably require a heuristic matching step for the detection association. In this paper, we present SimTrack to simplify the hand-crafted tracking paradigm by proposing an end-to-end trainable model for joint detection and tracking from raw point clouds. Our key design is to predict the first-appear location of each object in a given snippet to get the tracking identity and then update the location based on motion estimation. In the inference, the heuristic matching step can be completely waived by a simple read-off operation. SimTrack integrates the tracked object association, newborn object detection, and dead track killing in a single unified model. We conduct extensive evaluations on two large-scale datasets: nuScenes and Waymo Open Dataset. Experimental results reveal that our simple approach compares favorably with the state-of-the-art methods while ruling out the heuristic matching rules.
Policy gradient (PG) methods are popular reinforcement learning (RL) methods where a baseline is often applied to reduce the variance of gradient estimates. In multi-agent RL (MARL), although the PG theorem can be naturally extended, the effectiveness of multi-agent PG (MAPG) methods degrades as the variance of gradient estimates increases rapidly with the number of agents. In this paper, we offer a rigorous analysis of MAPG methods by, firstly, quantifying the contributions of the number of agents and agents explorations to the variance of MAPG estimators. Based on this analysis, we derive the optimal baseline (OB) that achieves the minimal variance. In comparison to the OB, we measure the excess variance of existing MARL algorithms such as vanilla MAPG and COMA. Considering using deep neural networks, we also propose a surrogate version of OB, which can be seamlessly plugged into any existing PG methods in MARL. On benchmarks of Multi-Agent MuJoCo and StarCraft challenges, our OB technique effectively stabilises training and improves the performance of multi-agent PPO and COMA algorithms by a significant margin.
Safety is a critical concern for the next generation of autonomy that is likely to rely heavily on deep neural networks for perception and control. Formally verifying the safety and robustness of well-trained DNNs and learning-enabled systems under attacks, model uncertainties, and sensing errors is essential for safe autonomy. This research proposes a framework to repair unsafe DNNs in safety-critical systems with reachability analysis. The repair process is inspired by adversarial training which has demonstrated high effectiveness in improving the safety and robustness of DNNs. Different from traditional adversarial training approaches where adversarial examples are utilized from random attacks and may not be representative of all unsafe behaviors, our repair process uses reachability analysis to compute the exact unsafe regions and identify sufficiently representative examples to enhance the efficacy and efficiency of the adversarial training. The performance of our framework is evaluated on two types of benchmarks without safe models as references. One is a DNN controller for aircraft collision avoidance with access to training data. The other is a rocket lander where our framework can be seamlessly integrated with the well-known deep deterministic policy gradient (DDPG) reinforcement learning algorithm. The experimental results show that our framework can successfully repair all instances on multiple safety specifications with negligible performance degradation. In addition, to increase the computational and memory efficiency of the reachability analysis algorithm, we propose a depth-first-search algorithm that combines an existing exact analysis method with an over-approximation approach based on a new set representation. Experimental results show that our method achieves a five-fold improvement in runtime and a two-fold improvement in memory usage compared to exact analysis.
Building robust deep learning-based models requires diverse training data, ideally from several sources. However, these datasets cannot be combined easily because of patient privacy concerns or regulatory hurdles, especially if medical data is involved. Federated learning (FL) is a way to train machine learning models without the need for centralized datasets. Each FL client trains on their local data while only sharing model parameters with a global server that aggregates the parameters from all clients. At the same time, each clients data can exhibit differences and inconsistencies due to the local variation in the patient population, imaging equipment, and acquisition protocols. Hence, the federated learned models should be able to adapt to the local particularities of a clients data. In this work, we combine FL with an AutoML technique based on local neural architecture search by training a supernet. Furthermore, we propose an adaptation scheme to allow for personalized model architectures at each FL clients site. The proposed method is evaluated on four different datasets from 3D prostate MRI and shown to improve the local models performance after adaptation through selecting an optimal path through the AutoML supernet.
Deep learning models for medical image segmentation are primarily data-driven. Models trained with more data lead to improved performance and generalizability. However, training is a computationally expensive process because multiple hyper-parameters need to be tested to find the optimal setting for best performance. In this work, we focus on accelerating the estimation of hyper-parameters by proposing two novel methodologies: proxy data and proxy networks. Both can be useful for estimating hyper-parameters more efficiently. We test the proposed techniques on CT and MR imaging modalities using well-known public datasets. In both cases using one dataset for building proxy data and another data source for external evaluation. For CT, the approach is tested on spleen segmentation with two datasets. The first dataset is from the medical segmentation decathlon (MSD), where the proxy data is constructed, the secondary dataset is utilized as an external validation dataset. Similarly, for MR, the approach is evaluated on prostate segmentation where the first dataset is from MSD and the second dataset is PROSTATEx. First, we show higher correlation to using full data for training when testing on the external validation set using smaller proxy data than a random selection of the proxy data. Second, we show that a high correlation exists for proxy networks when compared with the full network on validation Dice score. Third, we show that the proposed approach of utilizing a proxy network can speed up an AutoML framework for hyper-parameter search by 3.3x, and by 4.4x if proxy data and proxy network are utilized together.
Deep convolutional neural networks have been widely employed as an effective technique to handle complex and practical problems. However, one of the fundamental problems is the lack of formal methods to analyze their behavior. To address this challenge, we propose an approach to compute the exact reachable sets of a network given an input domain, where the reachable set is represented by the face lattice structure. Besides the computation of reachable sets, our approach is also capable of backtracking to the input domain given an output reachable set. Therefore, a full analysis of a networks behavior can be realized. In addition, an approach for fast analysis is also introduced, which conducts fast computation of reachable sets by considering selected sensitive neurons in each layer. The exact pixel-level reachability analysis method is evaluated on a CNN for the CIFAR10 dataset and compared to related works. The fast analysis method is evaluated over a CNN CIFAR10 dataset and VGG16 architecture for the ImageNet dataset.
Trust region methods are widely applied in single-agent reinforcement learning problems due to their monotonic performance-improvement guarantee at every iteration. Nonetheless, when applied in multi-agent settings, the guarantee of trust region methods no longer holds because an agents payoff is also affected by other agents adaptive behaviors. To tackle this problem, we conduct a game-theoretical analysis in the policy space, and propose a multi-agent trust region learning method (MATRL), which enables trust region optimization for multi-agent learning. Specifically, MATRL finds a stable improvement direction that is guided by the solution concept of Nash equilibrium at the meta-game level. We derive the monotonic improvement guarantee in multi-agent settings and empirically show the local convergence of MATRL to stable fixed points in the two-player rotational differential game. To test our method, we evaluate MATRL in both discrete and continuous multiplayer general-sum games including checker and switch grid worlds, multi-agent MuJoCo, and Atari games. Results suggest that MATRL significantly outperforms strong multi-agent reinforcement learning baselines.
When solving two-player zero-sum games, multi-agent reinforcement learning (MARL) algorithms often create populations of agents where, at each iteration, a new agent is discovered as the best response to a mixture over the opponent population. Within such a process, the update rules of who to compete with (i.e., the opponent mixture) and how to beat them (i.e., finding best responses) are underpinned by manually developed game theoretical principles such as fictitious play and Double Oracle. In this paper we introduce a framework, LMAC, based on meta-gradient descent that automates the discovery of the update rule without explicit human design. Specifically, we parameterise the opponent selection module by neural networks and the best-response module by optimisation subroutines, and update their parameters solely via interaction with the game engine, where both players aim to minimise their exploitability. Surprisingly, even without human design, the discovered MARL algorithms achieve competitive or even better performance with the state-of-the-art population-based game solvers (e.g., PSRO) on Games of Skill, differentiable Lotto, non-transitive Mixture Games, Iterated Matching Pennies, and Kuhn Poker. Additionally, we show that LMAC is able to generalise from small games to large games, for example training on Kuhn Poker and outperforming PSRO on Leduc Poker. Our work inspires a promising future direction to discover general MARL algorithms solely from data.
Attosecond science promises to reveal the most fundamental electronic dynamics occurring in matter and it can develop further by meeting two linked technological goals related to high-order harmonic sources: higher photon flux (permitting to measure low cross-section processes) and improved spectral tunability (allowing selectivity in addressing specific electronic transitions). New developments come through parametric waveform synthesis, which provides control over the shape of high-energy electric field transients, enabling the creation of highly-tunable isolated attosecond pulses via high-harmonic generation. Here we show that central energy, spectral bandwidth/shape and temporal duration of the attosecond pulses can be controlled by shaping the laser pulse waveform via two key parameters: the relative-phase between two halves of the multi-octave spanning optical spectrum, and the overall carrier-envelope phase. These results not only promise to expand the experimental possibilities in attosecond science, but also demonstrate coherent strong-field control of free-electron trajectories using tailored optical waveforms.
