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Students find their first course in Formal Languages and Automata Theory challenging. In addition to the development of formal arguments, most students struggle to understand nondeterministic computation models. In part, the struggle stems from the course exposing them for the first time to nondeterminism. Often, students find it difficult to understand why a nondeterministic machine accepts or rejects a word. Furthermore, they may feel uncomfortable with there being multiple computations on the same input and with a machine not consuming all of its input. This article describes a visualization tool developed to help students understand nondeterministic behavior. The tool is integrated into, FSM, a domain-specific language for the Automata Theory classroom. The strategy is based on the automatic generation of computation graphs given a machine and an input word. Unlike previous visualization tools, the computation graphs generated reflect the structure of the given machine's transition relation and not the structure of the computation tree.

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Large discrete action spaces (LDAS) remain a central challenge in reinforcement learning. Existing solution approaches can handle unstructured LDAS with up to a few million actions. However, many real-world applications in logistics, production, and transportation systems have combinatorial action spaces, whose size grows well beyond millions of actions, even on small instances. Fortunately, such action spaces exhibit structure, e.g., equally spaced discrete resource units. With this work, we focus on handling structured LDAS (SLDAS) with sizes that cannot be handled by current benchmarks: we propose Dynamic Neighborhood Construction (DNC), a novel exploitation paradigm for SLDAS. We present a scalable neighborhood exploration heuristic that utilizes this paradigm and efficiently explores the discrete neighborhood around the continuous proxy action in structured action spaces with up to $10^{73}$ actions. We demonstrate the performance of our method by benchmarking it against three state-of-the-art approaches designed for large discrete action spaces across two distinct environments. Our results show that DNC matches or outperforms state-of-the-art approaches while being computationally more efficient. Furthermore, our method scales to action spaces that so far remained computationally intractable for existing methodologies.

Recent advancements in model-free deep reinforcement learning have enabled efficient agent training. However, challenges arise when determining the region of attraction for these controllers, especially if the region does not fully cover the desired area. This paper addresses this issue by introducing a feedback motion control algorithm that utilizes data-driven techniques and neural networks. The algorithm constructs a graph of connected reinforcement-learning based controllers, each with its own defined region of attraction. This incremental approach effectively covers a bounded region of interest, creating a trajectory of interconnected nodes that guide the system from an initial state to the goal. Two approaches are presented for connecting nodes within the algorithm. The first is a tree-structured method, facilitating "point-to-point" control by constructing a tree connecting the initial state to the goal state. The second is a graph-structured method, enabling "space-to-space" control by building a graph within a bounded region. This approach allows for control from arbitrary initial and goal states. The proposed method's performance is evaluated on a first-order dynamic system, considering scenarios both with and without obstacles. The results demonstrate the effectiveness of the proposed algorithm in achieving the desired control objectives.

In goal-conditioned reinforcement learning (GCRL), sparse rewards present significant challenges, often obstructing efficient learning. Although multi-step GCRL can boost this efficiency, it can also lead to off-policy biases in target values. This paper dives deep into these biases, categorizing them into two distinct categories: "shooting" and "shifting". Recognizing that certain behavior policies can hasten policy refinement, we present solutions designed to capitalize on the positive aspects of these biases while minimizing their drawbacks, enabling the use of larger step sizes to speed up GCRL. An empirical study demonstrates that our approach ensures a resilient and robust improvement, even in ten-step learning scenarios, leading to superior learning efficiency and performance that generally surpass the baseline and several state-of-the-art multi-step GCRL benchmarks.

Differentially Private Stochastic Gradient Descent with gradient clipping (DPSGD-GC) is a powerful tool for training deep learning models using sensitive data, providing both a solid theoretical privacy guarantee and high efficiency. However, using DPSGD-GC to ensure Differential Privacy (DP) comes at the cost of model performance degradation due to DP noise injection and gradient clipping. Existing research has extensively analyzed the theoretical convergence of DPSGD-GC, and has shown that it only converges when using large clipping thresholds that are dependent on problem-specific parameters. Unfortunately, these parameters are often unknown in practice, making it hard to choose the optimal clipping threshold. Therefore, in practice, DPSGD-GC suffers from degraded performance due to the {\it constant} bias introduced by the clipping. In our work, we propose a new error-feedback (EF) DP algorithm as an alternative to DPSGD-GC, which not only offers a diminishing utility bound without inducing a constant clipping bias, but more importantly, it allows for an arbitrary choice of clipping threshold that is independent of the problem. We establish an algorithm-specific DP analysis for our proposed algorithm, providing privacy guarantees based on R{\'e}nyi DP. Additionally, we demonstrate that under mild conditions, our algorithm can achieve nearly the same utility bound as DPSGD without gradient clipping. Our empirical results on Cifar-10/100 and E2E datasets, show that the proposed algorithm achieves higher accuracies than DPSGD while maintaining the same level of DP guarantee.

Performance bounds for parameter estimation play a crucial role in statistical signal processing theory and applications. Two widely recognized bounds are the Cram\'{e}r-Rao bound (CRB) in the non-Bayesian framework, and the Bayesian CRB (BCRB) in the Bayesian framework. However, unlike the CRB, the BCRB is asymptotically unattainable in general, and its equality condition is restrictive. This paper introduces an extension of the Bobrovsky--Mayer-Wolf--Zakai class of bounds, also known as the weighted BCRB (WBCRB). The WBCRB is optimized by tuning the weighting function in the scalar case. Based on this result, we propose an asymptotically tight version of the bound called AT-BCRB. We prove that the AT-BCRB is asymptotically attained by the maximum {\it a-posteriori} probability (MAP) estimator. Furthermore, we extend the WBCRB and the AT-BCRB to the case of vector parameters. The proposed bounds are evaluated in several fundamental signal processing examples, such as variance estimation of white Gaussian process, direction-of-arrival estimation, and mean estimation of Gaussian process with unknown variance and prior statistical information. It is shown that unlike the BCRB, the proposed bounds are asymptotically attainable and coincide with the expected CRB (ECRB). The ECRB, which imposes uniformly unbiasedness, cannot serve as a valid lower bound in the Bayesian framework, while the proposed bounds are valid for any estimator.

With the rise of powerful pre-trained vision-language models like CLIP, it becomes essential to investigate ways to adapt these models to downstream datasets. A recently proposed method named Context Optimization (CoOp) introduces the concept of prompt learning -- a recent trend in NLP -- to the vision domain for adapting pre-trained vision-language models. Specifically, CoOp turns context words in a prompt into a set of learnable vectors and, with only a few labeled images for learning, can achieve huge improvements over intensively-tuned manual prompts. In our study we identify a critical problem of CoOp: the learned context is not generalizable to wider unseen classes within the same dataset, suggesting that CoOp overfits base classes observed during training. To address the problem, we propose Conditional Context Optimization (CoCoOp), which extends CoOp by further learning a lightweight neural network to generate for each image an input-conditional token (vector). Compared to CoOp's static prompts, our dynamic prompts adapt to each instance and are thus less sensitive to class shift. Extensive experiments show that CoCoOp generalizes much better than CoOp to unseen classes, even showing promising transferability beyond a single dataset; and yields stronger domain generalization performance as well. Code is available at //github.com/KaiyangZhou/CoOp.

To date, most existing self-supervised learning methods are designed and optimized for image classification. These pre-trained models can be sub-optimal for dense prediction tasks due to the discrepancy between image-level prediction and pixel-level prediction. To fill this gap, we aim to design an effective, dense self-supervised learning method that directly works at the level of pixels (or local features) by taking into account the correspondence between local features. We present dense contrastive learning, which implements self-supervised learning by optimizing a pairwise contrastive (dis)similarity loss at the pixel level between two views of input images. Compared to the baseline method MoCo-v2, our method introduces negligible computation overhead (only <1% slower), but demonstrates consistently superior performance when transferring to downstream dense prediction tasks including object detection, semantic segmentation and instance segmentation; and outperforms the state-of-the-art methods by a large margin. Specifically, over the strong MoCo-v2 baseline, our method achieves significant improvements of 2.0% AP on PASCAL VOC object detection, 1.1% AP on COCO object detection, 0.9% AP on COCO instance segmentation, 3.0% mIoU on PASCAL VOC semantic segmentation and 1.8% mIoU on Cityscapes semantic segmentation. Code is available at: //git.io/AdelaiDet

Graph Convolutional Networks (GCNs) have received increasing attention in recent machine learning. How to effectively leverage the rich structural information in complex graphs, such as knowledge graphs with heterogeneous types of entities and relations, is a primary open challenge in the field. Most GCN methods are either restricted to graphs with a homogeneous type of edges (e.g., citation links only), or focusing on representation learning for nodes only instead of jointly optimizing the embeddings of both nodes and edges for target-driven objectives. This paper addresses these limitations by proposing a novel framework, namely the GEneralized Multi-relational Graph Convolutional Networks (GEM-GCN), which combines the power of GCNs in graph-based belief propagation and the strengths of advanced knowledge-base embedding methods, and goes beyond. Our theoretical analysis shows that GEM-GCN offers an elegant unification of several well-known GCN methods as specific cases, with a new perspective of graph convolution. Experimental results on benchmark datasets show the advantageous performance of GEM-GCN over strong baseline methods in the tasks of knowledge graph alignment and entity classification.

Learning with limited data is a key challenge for visual recognition. Few-shot learning methods address this challenge by learning an instance embedding function from seen classes and apply the function to instances from unseen classes with limited labels. This style of transfer learning is task-agnostic: the embedding function is not learned optimally discriminative with respect to the unseen classes, where discerning among them is the target task. In this paper, we propose a novel approach to adapt the embedding model to the target classification task, yielding embeddings that are task-specific and are discriminative. To this end, we employ a type of self-attention mechanism called Transformer to transform the embeddings from task-agnostic to task-specific by focusing on relating instances from the test instances to the training instances in both seen and unseen classes. Our approach also extends to both transductive and generalized few-shot classification, two important settings that have essential use cases. We verify the effectiveness of our model on two standard benchmark few-shot classification datasets --- MiniImageNet and CUB, where our approach demonstrates state-of-the-art empirical performance.

Policy gradient methods are often applied to reinforcement learning in continuous multiagent games. These methods perform local search in the joint-action space, and as we show, they are susceptable to a game-theoretic pathology known as relative overgeneralization. To resolve this issue, we propose Multiagent Soft Q-learning, which can be seen as the analogue of applying Q-learning to continuous controls. We compare our method to MADDPG, a state-of-the-art approach, and show that our method achieves better coordination in multiagent cooperative tasks, converging to better local optima in the joint action space.

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