Abstract. Given a collection [Formula: see text] of graphs on the common vertex set [Formula: see text] of size [Formula: see text], an [Formula: see text]-edge graph [Formula: see text] with vertices in [Formula: see text] is a transversal in [Formula: see text] if there exists a bijection [Formula: see text] such that [Formula: see text] for all [Formula: see text]. Denote [Formula: see text]. In this paper, we first establish a minimum degree condition for the existence of transversal Hamilton paths in [Formula: see text]: if [Formula: see text] and [Formula: see text], then [Formula: see text] contains a transversal Hamilton path. This solves a problem proposed by [L. Li, P. Li, and X. Li, J. Graph Theory, 104 (2023), pp. 341–359]. As a continuation of the transversal version of Dirac’s theorem [F. Joos and J. Kim, Bull. Lond. Math. Soc., 52 (2020), 498–504] and the stability result for transversal Hamilton cycles [Y. Cheng and K. Staden, Electron. J. Combin., 32 (2025), P4.36], our second result characterizes all graph collections with minimum degree at least [Formula: see text] and without transversal Hamilton cycles. We obtain an analogous result for transversal Hamilton paths. The proof is a combination of the stability result for transversal Hamilton paths and cycles and the transversal blow-up lemma, along with some structural analysis.

Abstract. A [Formula: see text]-graph system [Formula: see text] is a family of not necessarily distinct [Formula: see text]-graphs on the same [Formula: see text]-vertex set [Formula: see text], and a [Formula: see text]-graph [Formula: see text] on [Formula: see text] is said to be [Formula: see text]-transversal provided that there exists an injection [Formula: see text] such that [Formula: see text] for all [Formula: see text]. We show that given [Formula: see text], sufficiently large [Formula: see text], and an [Formula: see text]-vertex [Formula: see text]-graph system [Formula: see text], if [Formula: see text] for each [Formula: see text], then there exists an [Formula: see text]-transversal tight Hamilton cycle. This extends the result of Rödl, Ruciński, and Szemerédi [ Combinatorica, 28 (2008), pp. 229–260] on single [Formula: see text]-graphs.

Abstract. Thomassé conjectured the following strengthening of the well-known Caccetta–Häaggkvist conjecture: any digraph with minimum out-degree [Formula: see text] and girth [Formula: see text] contains a directed path of length [Formula: see text]. Bai and Manoussakis [ SIAM J. Discrete Math., 33 (2019), pp. 2444–2451] gave counterexamples to Thomassé’s conjecture for every even [Formula: see text]. In this note, we first generalize their counterexamples to show that Thomassé’s conjecture is false for every [Formula: see text]. We also obtain the positive result that any digraph with minimum out-degree [Formula: see text] and girth [Formula: see text] contains a directed path of [Formula: see text]. For small [Formula: see text] we obtain better bounds; e.g., for [Formula: see text] we show that oriented graph with minimum out-degree [Formula: see text] contains a directed path of length [Formula: see text]. Furthermore, we show that each [Formula: see text]-regular digraph with girth [Formula: see text] contains a directed path of length [Formula: see text]. Our results give the first nontrivial bounds for these problems.

Spatiotemporal prediction is challenging due to the complex dynamic motion and appearance changes. Existing work concentrates on embedding additional cells into the standard ConvLSTM to memorize spatial appearances during the prediction. These models always rely on the convolution layers to capture the spatial dependence, which are local and inefficient. However, long-range spatial dependencies are significant for spatial applications. To extract spatial features with both global and local dependencies, we introduce the self-attention mechanism into ConvLSTM. Specifically, a novel self-attention memory (SAM) is proposed to memorize features with long-range dependencies in terms of spatial and temporal domains. Based on the self-attention, SAM can produce features by aggregating features across all positions of both the input itself and memory features with pair-wise similarity scores. Moreover, the additional memory is updated by a gating mechanism on aggregated features and an established highway with the memory of the previous time step. Therefore, through SAM, we can extract features with long-range spatiotemporal dependencies. Furthermore, we embed the SAM into a standard ConvLSTM to construct a self-attention ConvLSTM (SA-ConvLSTM) for the spatiotemporal prediction. In experiments, we apply the SA-ConvLSTM to perform frame prediction on the MovingMNIST and KTH datasets and traffic flow prediction on the TexiBJ dataset. Our SA-ConvLSTM achieves state-of-the-art results on both datasets with fewer parameters and higher time efficiency than previous state-of-the-art method.

Recently, Recurrent Neural Network (RNN) based methods and Self-Attention (SA) based methods have achieved promising performance in Video Question Answering (VideoQA). Despite the success of these works, RNN-based methods tend to forget the global semantic contents due to the inherent drawbacks of the recurrent units themselves, while SA-based methods cannot precisely capture the dependencies of the local neighborhood, leading to insufficient modeling for temporal order. To tackle these problems, we propose a novel VideoQA framework which progressively refines the representations of videos and questions from fine to coarse grain in a sequence-sensitive manner. Specifically, our model improves the feature representations via the following two steps: (1) introducing two fine-grained feature-augmented memories to strengthen the information augmentation of video and text which can improve memory capacity by memorizing more relevant and targeted information. (2) appending the self-attention and co-attention module to the memory output thus the module is able to capture global interaction between high-level semantic informations. Experimental results show that our approach achieves state-of-the-art performance on VideoQA benchmark datasets.

Learning related tasks in various domains and transferring exploited knowledge to new situations is a significant challenge in Reinforcement Learning (RL). However, most RL algorithms are data inefficient and fail to generalize in complex environments, limiting their adaptability and applicability in multi-task scenarios. In this paper, we propose SelfSupervised Mixture-of-Experts (SUM), an effective algorithm driven by predictive uncertainty estimation for multitask RL. SUM utilizes a multi-head agent with shared parameters as experts to learn a series of related tasks simultaneously by Deep Deterministic Policy Gradient (DDPG). Each expert is extended by predictive uncertainty estimation on known and unknown states to enhance the Q-value evaluation capacity against overfitting and the overall generalization ability. These enable the agent to capture and diffuse the common knowledge across different tasks improving sample efficiency in each task and the effectiveness of expert scheduling across multiple tasks. Instead of task-specific design as common MoEs, a self-supervised gating network is adopted to determine a potential expert to handle each interaction from unseen environments and calibrated completely by the uncertainty feedback from the experts without explicit supervision. To alleviate the imbalanced expert utilization as the crux of MoE, optimization is accomplished via decayedmasked experience replay, which encourages both diversification and specialization of experts during different periods. We demonstrate that our approach learns faster and achieves better performance by efficient transfer and robust generalization, outperforming several related methods on extended OpenAI Gym’s MuJoCo multi-task environments.

Frame-to-frame uncertainty is a major challenge in video prediction. The use of the deterministic models always leads to averaging of future states. Some methods draw samples from a prior at each time step to deal with the uncertainty of the future states, such as the SVG model [1]. However, these models always use only one set of latent variables to represent the whole stochastic part in a video clip whereas sequential data often involves multiple independent factors. In this paper, we exploit the complex representation of information in video sequences by formulating it explicitly with a disentangled-representation stochastic video generation (DR-SVG) model that imposes sequence-dependent prior and sequence-independent prior to different sets of latent variables. Through a variational lower-bound and adversarial objective functions in latent space, our model can produce crisper frames with clear content and pose which indicate the sequence-dependent and sequence-independent component respectively.

Automatically generating natural language descriptions of images is a fundamental problem in artificial intelligence that connects computer vision and natural language processing. In recent years tremendous success has been shown in image captioning under the encoder-decoder framework, in which decoders are often chain-structured with Recurrent Neural Networks(RNNs), treating sentences as sequences. However, natural sentences are not inherently linear structures, but hierarchical structures. In this paper, we for the first time proposed a model with tree-structured decoder for image captioning(Image-to-Tree), which does not directly generate sentences but instead explicitly generates their dependency trees in a top-down manner. Inspired by the success of attention mechanism in image captioning, we also proposed a corresponding attention-based model for Image-to-Tree. Experiments on MSCOCO dataset demonstrate that our model can achieve comparable results to chain-structured models of different language metrics.

Deep Deterministic Policy Gradient (DDPG) algorithm has been successful for state-of-the-art performance in high-dimensional continuous control tasks. However, due to the complexity and randomness of the environment, DDPG tends to suffer from inefficient exploration and unstable training. In this work, we propose Self-Adaptive Double Bootstrapped DDPG (SOUP), an algorithm that extends DDPG to bootstrapped actor-critic architecture. SOUP improves the efficiency of exploration by multiple actor heads capturing more potential actions and multiple critic heads evaluating more reasonable Q-values collaboratively. The crux of double bootstrapped architecture is to tackle the fluctuations in performance, caused by multiple heads of spotty capacity varying throughout training. To alleviate the instability, a self-adaptive confidence mechanism is introduced to dynamically adjust the weights of bootstrapped heads and enhance the ensemble performance effectively and efficiently. We demonstrate that SOUP achieves faster learning by at least 45% while improving cumulative reward and stability substantially in comparison to vanilla DDPG on OpenAI Gym's MuJoCo environments.