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Formal theorem proving, a field at the intersection of mathematics and computer science, has seen renewed interest with advancements in large language models (LLMs). This paper introduces SubgoalXL, a novel approach that synergizes subgoal-based proofs with expert learning to enhance LLMs' capabilities in formal theorem proving within the Isabelle environment. SubgoalXL addresses two critical challenges: the scarcity of specialized mathematics and theorem-proving data, and the need for improved multi-step reasoning abilities in LLMs. By optimizing data efficiency and employing subgoal-level supervision, SubgoalXL extracts richer information from limited human-generated proofs. The framework integrates subgoal-oriented proof strategies with an expert learning system, iteratively refining formal statement, proof, and subgoal generators. Leveraging the Isabelle environment's advantages in subgoal-based proofs, SubgoalXL achieves a new state-of-the-art performance of 56.1\% in Isabelle on the standard miniF2F dataset, marking an absolute improvement of 4.9\%. Notably, SubgoalXL successfully solves 41 AMC12, 9 AIME, and 3 IMO problems from miniF2F. These results underscore the effectiveness of maximizing limited data utility and employing targeted guidance for complex reasoning in formal theorem proving, contributing to the ongoing advancement of AI reasoning capabilities. The implementation is available at \url{//github.com/zhaoxlpku/SubgoalXL}.

As digital twins (DTs) to physical communication systems, network simulators can aid the design and deployment of communication networks. However, time-consuming simulations must be run for every new set of network configurations. Learnable digital twins (LDTs), in contrast, can be trained offline to emulate simulation outcomes and serve as a more efficient alternative to simulation-based DTs at runtime. In this work, we propose GLANCE, a communication LDT that learns from the simulator ns-3. It can evaluate network key performance indicators (KPIs) and assist in network management with exceptional efficiency. Leveraging graph learning, we exploit network data characteristics and devise a specialized architecture to embed sequential and topological features of traffic flows within the network. In addition, multi-task learning (MTL) and transfer learning (TL) are leveraged to enhance GLANCE's generalizability to unseen inputs and efficacy across different tasks. Beyond end-to-end KPI prediction, GLANCE can be deployed within an optimization framework for network management. It serves as an efficient or differentiable evaluator in optimizing network configurations such as traffic loads and flow destinations. Through numerical experiments and benchmarking, we verify the effectiveness of the proposed LDT architecture, demonstrate its robust generalization to various inputs, and showcase its efficacy in network management applications.

Sequential recommendation, where user preference is dynamically inferred from sequential historical behaviors, is a critical task in recommender systems (RSs). To further optimize long-term user engagement, offline reinforcement-learning-based RSs have become a mainstream technique as they provide an additional advantage in avoiding global explorations that may harm online users' experiences. However, previous studies mainly focus on discrete action and policy spaces, which might have difficulties in handling dramatically growing items efficiently. To mitigate this issue, in this paper, we aim to design an algorithmic framework applicable to continuous policies. To facilitate the control in the low-dimensional but dense user preference space, we propose an \underline{\textbf{E}}fficient \underline{\textbf{Co}}ntinuous \underline{\textbf{C}}ontrol framework (ECoC). Based on a statistically tested assumption, we first propose the novel unified action representation abstracted from normalized user and item spaces. Then, we develop the corresponding policy evaluation and policy improvement procedures. During this process, strategic exploration and directional control in terms of unified actions are carefully designed and crucial to final recommendation decisions. Moreover, beneficial from unified actions, the conservatism regularization for policies and value functions are combined and perfectly compatible with the continuous framework. The resulting dual regularization ensures the successful offline training of RL-based recommendation policies. Finally, we conduct extensive experiments to validate the effectiveness of our framework. The results show that compared to the discrete baselines, our ECoC is trained far more efficiently. Meanwhile, the final policies outperform baselines in both capturing the offline data and gaining long-term rewards.

Generative, temporal network models play an important role in analyzing the dependence structure and evolution patterns of complex networks. Due to the complicated nature of real network data, it is often naive to assume that the underlying data-generative mechanism itself is invariant with time. Such observation leads to the study of changepoints or sudden shifts in the distributional structure of the evolving network. In this paper, we propose a likelihood-based methodology to detect changepoints in undirected, affine preferential attachment networks, and establish a hypothesis testing framework to detect a single changepoint, together with a consistent estimator for the changepoint. Such results require establishing consistency and asymptotic normality of the MLE under the changepoint regime, which suffers from long range dependence. The methodology is then extended to the multiple changepoint setting via both a sliding window method and a more computationally efficient score statistic. We also compare the proposed methodology with previously developed non-parametric estimators of the changepoint via simulation, and the methods developed herein are applied to modeling the popularity of a topic in a Twitter network over time.

Quantum network simulation is an essential step towards developing applications for quantum networks and determining minimal requirements for the network hardware. As it is with classical networking, a simulation ecosystem allows for application development, standardization, and overall community building. Currently, there is limited traction towards building a quantum networking community-there are limited open-source platforms, challenging frameworks with steep learning curves, and strong requirements of software engineering skills. Our Quantum Network Development Kit (QNDK) project aims to solve these issues. It includes a graphical user interface to easily develop and run quantum network simulations with very little code. It integrates various quantum network simulation engines and provides a single interface to them, allowing users to use the features from any of them. Further, it deploys simulation execution in a cloud environment, offloading strong computing requirements to a high-performance computing system. In this paper, we detail the core features of the QNDK and outline the development roadmap to enabling virtual quantum testbeds.

The universal approximation theorem states that a neural network with one hidden layer can approximate continuous functions on compact sets with any desired precision. This theorem supports using neural networks for various applications, including regression and classification tasks. Furthermore, it is valid for real-valued neural networks and some hypercomplex-valued neural networks such as complex-, quaternion-, tessarine-, and Clifford-valued neural networks. However, hypercomplex-valued neural networks are a type of vector-valued neural network defined on an algebra with additional algebraic or geometric properties. This paper extends the universal approximation theorem for a wide range of vector-valued neural networks, including hypercomplex-valued models as particular instances. Precisely, we introduce the concept of non-degenerate algebra and state the universal approximation theorem for neural networks defined on such algebras.

Technological advances facilitate the ability to acquire multimodal data, posing a challenge for recognition systems while also providing an opportunity to use the heterogeneous nature of the information to increase the generalization capability of models. An often overlooked issue is the cost of the labeling process, which is typically high due to the need for a significant investment in time and money associated with human experts. Existing semi-supervised learning methods often focus on operating in the feature space created by the fusion of available modalities, neglecting the potential for cross-utilizing complementary information available in each modality. To address this problem, we propose Cross-Modality Clustering-based Self-Labeling (CMCSL). Based on a small set of pre-labeled data, CMCSL groups instances belonging to each modality in the deep feature space and then propagates known labels within the resulting clusters. Next, information about the instances' class membership in each modality is exchanged based on the Euclidean distance to ensure more accurate labeling. Experimental evaluation conducted on 20 datasets derived from the MM-IMDb dataset indicates that cross-propagation of labels between modalities -- especially when the number of pre-labeled instances is small -- can allow for more reliable labeling and thus increase the classification performance in each modality.

Spiking neural networks (SNNs), known for their low-power, event-driven computation and intrinsic temporal dynamics, are emerging as promising solutions for processing dynamic, asynchronous signals from event-based sensors. Despite their potential, SNNs face challenges in training and architectural design, resulting in limited performance in challenging event-based dense prediction tasks compared to artificial neural networks (ANNs). In this work, we develop an efficient spiking encoder-decoder network (SpikingEDN) for large-scale event-based semantic segmentation tasks. To enhance the learning efficiency from dynamic event streams, we harness the adaptive threshold which improves network accuracy, sparsity and robustness in streaming inference. Moreover, we develop a dual-path Spiking Spatially-Adaptive Modulation module, which is specifically tailored to enhance the representation of sparse events and multi-modal inputs, thereby considerably improving network performance. Our SpikingEDN attains a mean intersection over union (MIoU) of 72.57\% on the DDD17 dataset and 58.32\% on the larger DSEC-Semantic dataset, showing competitive results to the state-of-the-art ANNs while requiring substantially fewer computational resources. Our results shed light on the untapped potential of SNNs in event-based vision applications. The source code will be made publicly available.

Unsupervised domain adaptation has recently emerged as an effective paradigm for generalizing deep neural networks to new target domains. However, there is still enormous potential to be tapped to reach the fully supervised performance. In this paper, we present a novel active learning strategy to assist knowledge transfer in the target domain, dubbed active domain adaptation. We start from an observation that energy-based models exhibit free energy biases when training (source) and test (target) data come from different distributions. Inspired by this inherent mechanism, we empirically reveal that a simple yet efficient energy-based sampling strategy sheds light on selecting the most valuable target samples than existing approaches requiring particular architectures or computation of the distances. Our algorithm, Energy-based Active Domain Adaptation (EADA), queries groups of targe data that incorporate both domain characteristic and instance uncertainty into every selection round. Meanwhile, by aligning the free energy of target data compact around the source domain via a regularization term, domain gap can be implicitly diminished. Through extensive experiments, we show that EADA surpasses state-of-the-art methods on well-known challenging benchmarks with substantial improvements, making it a useful option in the open world. Code is available at //github.com/BIT-DA/EADA.

Ensembles over neural network weights trained from different random initialization, known as deep ensembles, achieve state-of-the-art accuracy and calibration. The recently introduced batch ensembles provide a drop-in replacement that is more parameter efficient. In this paper, we design ensembles not only over weights, but over hyperparameters to improve the state of the art in both settings. For best performance independent of budget, we propose hyper-deep ensembles, a simple procedure that involves a random search over different hyperparameters, themselves stratified across multiple random initializations. Its strong performance highlights the benefit of combining models with both weight and hyperparameter diversity. We further propose a parameter efficient version, hyper-batch ensembles, which builds on the layer structure of batch ensembles and self-tuning networks. The computational and memory costs of our method are notably lower than typical ensembles. On image classification tasks, with MLP, LeNet, and Wide ResNet 28-10 architectures, our methodology improves upon both deep and batch ensembles.