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We present a framework for learning Hamiltonian systems using data. This work is based on a lifting hypothesis, which posits that nonlinear Hamiltonian systems can be written as nonlinear systems with cubic Hamiltonians. By leveraging this, we obtain quadratic dynamics that are Hamiltonian in a transformed coordinate system. To that end, for given generalized position and momentum data, we propose a methodology to learn quadratic dynamical systems, enforcing the Hamiltonian structure in combination with a weakly-enforced symplectic auto-encoder. The obtained Hamiltonian structure exhibits long-term stability of the system, while the cubic Hamiltonian function provides relatively low model complexity. For low-dimensional data, we determine a higher-dimensional transformed coordinate system, whereas for high-dimensional data, we find a lower-dimensional coordinate system with the desired properties. We demonstrate the proposed methodology by means of both low-dimensional and high-dimensional nonlinear Hamiltonian systems.

A pivotal aspect in the design of neural networks lies in selecting activation functions, crucial for introducing nonlinear structures that capture intricate input-output patterns. While the effectiveness of adaptive or trainable activation functions has been studied in domains with ample data, like image classification problems, significant gaps persist in understanding their influence on classification accuracy and predictive uncertainty in settings characterized by limited data availability. This research aims to address these gaps by investigating the use of two types of adaptive activation functions. These functions incorporate shared and individual trainable parameters per hidden layer and are examined in three testbeds derived from additive manufacturing problems containing fewer than one hundred training instances. Our investigation reveals that adaptive activation functions, such as Exponential Linear Unit (ELU) and Softplus, with individual trainable parameters, result in accurate and confident prediction models that outperform fixed-shape activation functions and the less flexible method of using identical trainable activation functions in a hidden layer. Therefore, this work presents an elegant way of facilitating the design of adaptive neural networks in scientific and engineering problems.

Foundation models, such as Large language Models (LLMs), have attracted significant amount of interest due to their large number of applications. Existing works show that appropriate prompt design, such as Chain-of-Thoughts, can unlock LLM's powerful capacity in diverse areas. However, when handling tasks involving repetitive sub-tasks and/or deceptive contents, such as arithmetic calculation and article-level fake news detection, existing prompting strategies either suffers from insufficient expressive power or intermediate errors triggered by hallucination. To make LLM more discerning to such intermediate errors, we propose to guide LLM with a Divide-and-Conquer program that simultaneously ensures superior expressive power and disentangles task decomposition, sub-task resolution, and resolution assembly process. Theoretic analysis reveals that our strategy can guide LLM to extend the expressive power of fixed-depth Transformer. Experiments indicate that our proposed method can achieve better performance than typical prompting strategies in tasks bothered by intermediate errors and deceptive contents, such as large integer multiplication, hallucination detection and misinformation detection.

Several works related to spatial crowdsourcing have been proposed in the direction where the task executers are to perform the tasks within the stipulated deadlines. Though the deadlines are set, it may be a practical scenario that majority of the task executers submit the tasks as late as possible. This situation where the task executers may delay their task submission is termed as procrastination in behavioural economics. In many applications, these late submission of tasks may be problematic for task providers. So here, the participating agents (both task providers and task executers) are articulated with the procrastination issue. In literature, how to prevent this procrastination within the deadline is not addressed in spatial crowdsourcing scenario. However, in a bipartite graph setting one procrastination aware scheduling is proposed but balanced job (task and job will synonymously be used) distribution in different slots (also termed as schedules) is not considered there. In this paper, a procrastination aware scheduling of jobs is proliferated by proposing an (randomized) algorithm in spatial crowdsourcing scenario. Our algorithm ensures that balancing of jobs in different schedules are maintained. Our scheme is compared with the existing algorithm through extensive simulation and in terms of balancing effect, our proposed algorithm outperforms the existing one. Analytically it is shown that our proposed algorithm maintains the balanced distribution.

Deep reinforcement learning (DRL) has shown remarkable success in complex autonomous driving scenarios. However, DRL models inevitably bring high memory consumption and computation, which hinders their wide deployment in resource-limited autonomous driving devices. Structured Pruning has been recognized as a useful method to compress and accelerate DRL models, but it is still challenging to estimate the contribution of a parameter (i.e., neuron) to DRL models. In this paper, we introduce a novel dynamic structured pruning approach that gradually removes a DRL model's unimportant neurons during the training stage. Our method consists of two steps, i.e. training DRL models with a group sparse regularizer and removing unimportant neurons with a dynamic pruning threshold. To efficiently train the DRL model with a small number of important neurons, we employ a neuron-importance group sparse regularizer. In contrast to conventional regularizers, this regularizer imposes a penalty on redundant groups of neurons that do not significantly influence the output of the DRL model. Furthermore, we design a novel structured pruning strategy to dynamically determine the pruning threshold and gradually remove unimportant neurons with a binary mask. Therefore, our method can remove not only redundant groups of neurons of the DRL model but also achieve high and robust performance. Experimental results show that the proposed method is competitive with existing DRL pruning methods on discrete control environments (i.e., CartPole-v1 and LunarLander-v2) and MuJoCo continuous environments (i.e., Hopper-v3 and Walker2D-v3). Specifically, our method effectively compresses $93\%$ neurons and $96\%$ weights of the DRL model in four challenging DRL environments with slight accuracy degradation.

This paper presents an innovative approach to recognizing personality traits using deep learning (DL) methods applied to electrocardiogram (ECG) signals. Within the framework of detecting the big five personality traits model encompassing extra-version, neuroticism, agreeableness, conscientiousness, and openness, the research explores the potential of ECG-derived spectrograms as informative features. Optimal window sizes for spectrogram generation are determined, and a convolutional neural network (CNN), specifically Resnet-18, and visual transformer (ViT) are employed for feature extraction and personality trait classification. The study utilizes the publicly available ASCERTAIN dataset, which comprises various physiological signals, including ECG recordings, collected from 58 participants during the presentation of video stimuli categorized by valence and arousal levels. The outcomes of this study demonstrate noteworthy performance in personality trait classification, consistently achieving F1-scores exceeding 0.9 across different window sizes and personality traits. These results emphasize the viability of ECG signal spectrograms as a valuable modality for personality trait recognition, with Resnet-18 exhibiting effectiveness in discerning distinct personality traits.

Spectral clustering (SC) is a popular clustering technique to find strongly connected communities on a graph. SC can be used in Graph Neural Networks (GNNs) to implement pooling operations that aggregate nodes belonging to the same cluster. However, the eigendecomposition of the Laplacian is expensive and, since clustering results are graph-specific, pooling methods based on SC must perform a new optimization for each new sample. In this paper, we propose a graph clustering approach that addresses these limitations of SC. We formulate a continuous relaxation of the normalized minCUT problem and train a GNN to compute cluster assignments that minimize this objective. Our GNN-based implementation is differentiable, does not require to compute the spectral decomposition, and learns a clustering function that can be quickly evaluated on out-of-sample graphs. From the proposed clustering method, we design a graph pooling operator that overcomes some important limitations of state-of-the-art graph pooling techniques and achieves the best performance in several supervised and unsupervised tasks.

Translational distance-based knowledge graph embedding has shown progressive improvements on the link prediction task, from TransE to the latest state-of-the-art RotatE. However, N-1, 1-N and N-N predictions still remain challenging. In this work, we propose a novel translational distance-based approach for knowledge graph link prediction. The proposed method includes two-folds, first we extend the RotatE from 2D complex domain to high dimension space with orthogonal transforms to model relations for better modeling capacity. Second, the graph context is explicitly modeled via two directed context representations. These context representations are used as part of the distance scoring function to measure the plausibility of the triples during training and inference. The proposed approach effectively improves prediction accuracy on the difficult N-1, 1-N and N-N cases for knowledge graph link prediction task. The experimental results show that it achieves better performance on two benchmark data sets compared to the baseline RotatE, especially on data set (FB15k-237) with many high in-degree connection nodes.

Incorporating knowledge graph into recommender systems has attracted increasing attention in recent years. By exploring the interlinks within a knowledge graph, the connectivity between users and items can be discovered as paths, which provide rich and complementary information to user-item interactions. Such connectivity not only reveals the semantics of entities and relations, but also helps to comprehend a user's interest. However, existing efforts have not fully explored this connectivity to infer user preferences, especially in terms of modeling the sequential dependencies within and holistic semantics of a path. In this paper, we contribute a new model named Knowledge-aware Path Recurrent Network (KPRN) to exploit knowledge graph for recommendation. KPRN can generate path representations by composing the semantics of both entities and relations. By leveraging the sequential dependencies within a path, we allow effective reasoning on paths to infer the underlying rationale of a user-item interaction. Furthermore, we design a new weighted pooling operation to discriminate the strengths of different paths in connecting a user with an item, endowing our model with a certain level of explainability. We conduct extensive experiments on two datasets about movie and music, demonstrating significant improvements over state-of-the-art solutions Collaborative Knowledge Base Embedding and Neural Factorization Machine.

Recently, deep learning has achieved very promising results in visual object tracking. Deep neural networks in existing tracking methods require a lot of training data to learn a large number of parameters. However, training data is not sufficient for visual object tracking as annotations of a target object are only available in the first frame of a test sequence. In this paper, we propose to learn hierarchical features for visual object tracking by using tree structure based Recursive Neural Networks (RNN), which have fewer parameters than other deep neural networks, e.g. Convolutional Neural Networks (CNN). First, we learn RNN parameters to discriminate between the target object and background in the first frame of a test sequence. Tree structure over local patches of an exemplar region is randomly generated by using a bottom-up greedy search strategy. Given the learned RNN parameters, we create two dictionaries regarding target regions and corresponding local patches based on the learned hierarchical features from both top and leaf nodes of multiple random trees. In each of the subsequent frames, we conduct sparse dictionary coding on all candidates to select the best candidate as the new target location. In addition, we online update two dictionaries to handle appearance changes of target objects. Experimental results demonstrate that our feature learning algorithm can significantly improve tracking performance on benchmark datasets.