Advances in tracking technologies have spurred the rapid growth of large-scale trajectory data. Building a compact collection of pathlets, referred to as a trajectory pathlet dictionary, is essential for supporting mobility-related applications. Existing methods typically adopt a top-down approach, generating numerous candidate pathlets and selecting a subset, leading to high memory usage and redundant storage from overlapping pathlets. To overcome these limitations, we propose a bottom-up strategy that incrementally merges basic pathlets to build the dictionary, reducing memory requirements by up to 24,000 times compared to baseline methods. The approach begins with unit-length pathlets and iteratively merges them while optimizing utility, which is defined using newly introduced metrics of trajectory loss and representability. We develop a deep reinforcement learning framework, PathletRL, which utilizes Deep Q-Networks (DQN) to approximate the utility function, resulting in a compact and efficient pathlet dictionary. Experiments on both synthetic and real-world datasets demonstrate that our method outperforms state-of-the-art techniques, reducing the size of the constructed dictionary by up to 65.8%. Additionally, our results show that only half of the dictionary pathlets are needed to reconstruct 85% of the original trajectory data. Building on PathletRL, we introduce PathletRL++, which extends the original model by incorporating a richer state representation and an improved reward function to optimize decision-making during pathlet merging. These enhancements enable the agent to gain a more nuanced understanding of the environment, leading to higher-quality pathlet dictionaries. PathletRL++ achieves even greater dictionary size reduction, surpassing the performance of PathletRL, while maintaining high trajectory representability.

We introduce a Model Predictive Control (MPC) framework for training deep neural networks, systematically unifying the Back-Propagation (BP) and Forward-Forward (FF) algorithms. At the same time, it gives rise to a range of intermediate training algorithms with varying look-forward horizons, leading to a performance-efficiency trade-off. We perform a precise analysis of this trade-off on a deep linear network, where the qualitative conclusions carry over to general networks. Based on our analysis, we propose a principled method to choose the optimization horizon based on given objectives and model specifications. Numerical results on various models and tasks demonstrate the versatility of our method.

Self-supervised learning (SSL) has proven effective in learning high-quality representations for various downstream tasks, with a primary focus on semantic tasks. However, its application in geometric tasks remains underexplored, partially due to the absence of a standardized evaluation method for geometric representations. To address this gap, we introduce a new pose-estimation benchmark for assessing SSL geometric representations, which demands training without semantic or pose labels and achieving proficiency in both semantic and geometric downstream tasks. On this benchmark, we study enhancing SSL geometric representations without sacrificing semantic classification accuracy. We find that leveraging mid-layer representations improves pose-estimation performance by 10-20%. Further, we introduce an unsupervised trajectory-regularization loss, which improves performance by an additional 4% and improves generalization ability on out-of-distribution data. We hope the proposed benchmark and methods offer new insights and improvements in self-supervised geometric representation learning.

Collaborative Filtering (CF) has been successfully used to help users discover the items of interest. Nevertheless, existing CF methods suffer from noisy data issue, which negatively impacts the quality of recommendation. To tackle this problem, many prior studies leverage adversarial learning to regularize the representations of users/items, which improves both generalizability and robustness. Those methods often learn adversarial perturbations and model parameters under min-max optimization framework. However, there still have two major drawbacks: 1) Existing methods lack theoretical guarantees of why adding perturbations improve the model generalizability and robustness; 2) Solving min-max optimization is time-consuming. In addition to updating the model parameters, each iteration requires additional computations to update the perturbations, making them not scalable for industry-scale datasets. In this paper, we present Sharpness-aware Collaborative Filtering (SharpCF), a simple yet effective method that conducts adversarial training without extra computational cost over the base optimizer. To achieve this goal, we first revisit the existing adversarial collaborative filtering and discuss its connection with recent Sharpness-aware Minimization. This analysis shows that adversarial training actually seeks model parameters that lie in neighborhoods around the optimal model parameters having uniformly low loss values, resulting in better generalizability. To reduce the computational overhead, SharpCF introduces a novel trajectory loss to measure the alignment between current weights and past weights. Experimental results on real-world datasets demonstrate that our SharpCF achieves superior performance with almost zero additional computational cost comparing to adversarial training.

Modern deep neural networks (DNNs) have achieved state-of-the-art performances but are typically over-parameterized. The over-parameterization may result in undesirably large generalization error in the absence of other customized training strategies. Recently, a line of research under the name of Sharpness-Aware Minimization (SAM) has shown that minimizing a sharpness measure, which reflects the geometry of the loss landscape, can significantly reduce the generalization error. However, SAM-like methods incur a two-fold computational overhead of the given base optimizer (e.g. SGD) for approximating the sharpness measure. In this paper, we propose Sharpness-Aware Training for Free, or SAF, which mitigates the sharp landscape at almost zero additional computational cost over the base optimizer. Intuitively, SAF achieves this by avoiding sudden drops in the loss in the sharp local minima throughout the trajectory of the updates of the weights. Specifically, we suggest a novel trajectory loss, based on the KL-divergence between the outputs of DNNs with the current weights and past weights, as a replacement of the SAM's sharpness measure. This loss captures the rate of change of the training loss along the model's update trajectory. By minimizing it, SAF ensures the convergence to a flat minimum with improved generalization capabilities. Extensive empirical results show that SAF minimizes the sharpness in the same way that SAM does, yielding better results on the ImageNet dataset with essentially the same computational cost as the base optimizer.