This paper explores the connection between learning trajectories of Deep Neural Networks (DNNs) and their generalization capabilities when optimized using (stochastic) gradient descent algorithms. Instead of concentrating solely on the generalization error of the DNN post-training, we present a novel perspective for analyzing generalization error by investigating the contribution of each update step to the change in generalization error. This perspective enable a more direct comprehension of how the learning trajectory influences generalization error. Building upon this analysis, we propose a new generalization bound that incorporates more extensive trajectory information. Our proposed generalization bound depends on the complexity of learning trajectory and the ratio between the bias and diversity of training set. Experimental observations reveal that our method effectively captures the generalization error throughout the training process. Furthermore, our approach can also track changes in generalization error when adjustments are made to learning rates and label noise levels. These results demonstrate that learning trajectory information is a valuable indicator of a model's generalization capabilities.

Despite the availability of international prize-money competitions, scaled vehicles, and simulation environments, research on autonomous racing and the control of sports cars operating close to the limit of handling has been limited by the high costs of vehicle acquisition and management, as well as the limited physics accuracy of open-source simulators. In this paper, we propose a racing simulation platform based on the simulator Assetto Corsa to test, validate, and benchmark autonomous driving algorithms, including reinforcement learning (RL) and classical Model Predictive Control (MPC), in realistic and challenging scenarios. Our contributions include the development of this simulation platform, several state-of-the-art algorithms tailored to the racing environment, and a comprehensive dataset collected from human drivers. Additionally, we evaluate algorithms in the offline RL setting.

Heatmap regression has dominated human pose estimation due to its superior performance and strong generalization. To meet the requirements of traditional explicit neural networks for output form, existing heatmap-based methods discretize the originally continuous heatmap representation into 2D pixel arrays, which leads to performance degradation due to the introduction of quantization errors. This problem is significantly exacerbated as the size of the input image decreases, which makes heatmap-based methods not much better than coordinate regression on low-resolution images. In this paper, we propose a novel neural representation for human pose estimation called NerPE to achieve continuous heatmap regression. Given any position within the image range, NerPE regresses the corresponding confidence scores for body joints according to the surrounding image features, which guarantees continuity in space and confidence during training. Thanks to the decoupling from spatial resolution, NerPE can output the predicted heatmaps at arbitrary resolution during inference without retraining, which easily achieves sub-pixel localization precision. To reduce the computational cost, we design progressive coordinate decoding to cooperate with continuous heatmap regression, in which localization no longer requires the complete generation of high-resolution heatmaps.

Recent advancements in models linking natural language with human motions have shown significant promise in motion generation and editing based on instructional text. Motivated by applications in sports coaching and motor skill learning, we investigate the inverse problem: generating corrective instructional text, leveraging motion editing and generation models. We introduce a novel approach that, given a user's current motion (source) and the desired motion (target), generates text instructions to guide the user towards achieving the target motion. We leverage large language models to generate corrective texts and utilize existing motion generation and editing frameworks to compile datasets of triplets (source motion, target motion, and corrective text). Using this data, we propose a new motion-language model for generating corrective instructions. We present both qualitative and quantitative results across a diverse range of applications that largely improve upon baselines. Our approach demonstrates its effectiveness in instructional scenarios, offering text-based guidance to correct and enhance user performance.

Deep neural networks have been increasingly used in real-world applications, making it critical to ensure their ability to adapt to new, unseen data. In this paper, we study the generalization capability of neural networks trained with (stochastic) gradient flow. We establish a new connection between the loss dynamics of gradient flow and general kernel machines by proposing a new kernel, called loss path kernel. This kernel measures the similarity between two data points by evaluating the agreement between loss gradients along the path determined by the gradient flow. Based on this connection, we derive a new generalization upper bound that applies to general neural network architectures. This new bound is tight and strongly correlated with the true generalization error. We apply our results to guide the design of neural architecture search (NAS) and demonstrate favorable performance compared with state-of-the-art NAS algorithms through numerical experiments.

Humans have a powerful and mysterious capacity to reason. Working through a set of mental steps enables us to make inferences we would not be capable of making directly even though we get no additional data from the world. Similarly, when large language models generate intermediate steps (a chain of thought) before answering a question, they often produce better answers than they would directly. We investigate why and how chain-of-thought reasoning is useful in language models, testing the hypothesis that reasoning is effective when training data consists of overlapping local clusters of variables that influence each other strongly. These training conditions enable the chaining of accurate local inferences to estimate relationships between variables that were not seen together in training.

Sharpness-aware minimization (SAM) has well documented merits in enhancing generalization of deep neural networks, even without sizable data augmentation. Embracing the geometry of the loss function, where neighborhoods of'flat minima' heighten generalization ability, SAM seeks'flat valleys' by minimizing the maximum loss caused by an adversary perturbing parameters within the neighborhood. Although critical to account for sharpness of the loss function, such an'over-friendly adversary' can curtail the outmost level of generalization. The novel approach of this contribution fosters stabilization of adversaries through variance suppression (VaSSO) to avoid such friendliness.

Sharpness-aware minimization (SAM) has well documented merits in enhancing generalization of deep neural networks, even without sizable data augmentation. Embracing the geometry of the loss function, where neighborhoods of'flat minima' heighten generalization ability, SAM seeks'flat valleys' by minimizing the maximum loss caused by an adversary perturbing parameters within the neighborhood. Although critical to account for sharpness of the loss function, such an'over-friendly adversary' can curtail the outmost level of generalization. The novel approach of this contribution fosters stabilization of adversaries through variance suppression (VaSSO) to avoid such friendliness.