In representation learning, uniformity refers to the uniform feature distribution in the latent space (i.e., unit hypersphere). Previous work has shown that improving uniformity contributes to the learning of under-represented classes. However, most of the previous work focused on classification; the representation space of imbalanced regression remains unexplored. Classification-based methods are not suitable for regression tasks because they cluster features into distinct groups without considering the continuous and ordered nature essential for regression. In a geometric aspect, we uniquely focus on ensuring uniformity in the latent space for imbalanced regression through two key losses: enveloping and homogeneity. The enveloping loss encourages the induced trace to uniformly occupy the surface of a hypersphere, while the homogeneity loss ensures smoothness, with representations evenly spaced at consistent intervals. Our method integrates these geometric principles into the data representations via a Surrogate-driven Representation Learning (SRL) framework. Experiments with real-world regression and operator learning tasks highlight the importance of uniformity in imbalanced regression and validate the efficacy of our geometry-based loss functions. Code is available here.

Mathematical reasoning has been challenging for large language models (LLMs), and the introduction of step-by-step Chain-of-Thought (CoT) inference has significantly advanced the mathematical capabilities of LLMs.However, current approaches either necessitate extensive inference datasets for training or depend on few-shot methods that frequently compromise computational accuracy.To address these fundamental limitations, we propose Step Guided Reasoning, a novel training-free adaptation framework that efficiently equips generalpurpose pre-trained language models with enhanced mathematical reasoning capabilities.In this approach, LLMs reflect on small reasoning steps, similar to how humans deliberate and focus attention on what to do next.By incorporating this reflective process into the inference stage, LLMs can effectively guide their reasoning from one step to the next.Through extensive experiments, we demonstrate the significant effect of Step Guided Reasoning in enhancing mathematical performance in state-of-the-art language models -Qwen2-72B-Instruct outperforms its math-specific counterpart, Qwen2.5-72B-Math-Instruct, on MMLU-STEM with a score of 90.9%, compared to 87.3%.The average scores of Qwen2-7B-Instruct and Qwen2-72B-Instruct increase from 27.1% to 36.3% and from 36.5% to 47.4% in the math domain, respectively.

Generalizing to out-of-distribution (OOD) data or unseen domain, termed OOD generalization, still lacks appropriate theoretical guarantees. Canonical OOD bounds focus on different distance measurements between source and target domains but fail to consider the optimization property of the learned model. As empirically shown in recent work, sharpness of learned minimum influences OOD generalization. To bridge this gap between optimization and OOD generalization, we study the effect of sharpness on how a model tolerates data change in domain shift which is usually captured by "robustness" in generalization. In this paper, we give a rigorous connection between sharpness and robustness, which gives better OOD guarantees for robust algorithms. It also provides a theoretical backing for "flat minima leads to better OOD generalization". Overall, we propose a sharpness-based OOD generalization bound by taking robustness into consideration, resulting in a tighter bound than non-robust guarantees. Our findings are supported by the experiments on a ridge regression model, as well as the experiments on deep learning classification tasks.

Mixup is a popular data augmentation technique for training deep neural networks where additional samples are generated by linearly interpolating pairs of inputs and their labels. This technique is known to improve the generalization performance in many learning paradigms and applications. In this work, we first analyze Mixup and show that it implicitly regularizes infinitely many directional derivatives of all orders. Based on this new insight, we propose an improved version of Mixup, theoretically justified to deliver better generalization performance than the vanilla Mixup. To demonstrate the effectiveness of the proposed method, we conduct experiments across various domains such as images, tabular data, speech, and graphs. Our results show that the proposed method improves Mixup across multiple datasets using a variety of architectures, for instance, exhibiting an improvement over Mixup by 0.8% in ImageNet top-1 accuracy.

We present a versatile model, FaceAnime, for various video generation tasks from still images. Video generation from a single face image is an interesting problem and usually tackled by utilizing Generative Adversarial Networks (GANs) to integrate information from the input face image and a sequence of sparse facial landmarks. However, the generated face images usually suffer from quality loss, image distortion, identity change, and expression mismatching due to the weak representation capacity of the facial landmarks. In this paper, we propose to “imagine” a face video from a single face image according to the reconstructed 3D face dynamics, aiming to generate a realistic and identity-preserving face video, with precisely predicted pose and facial expression. The 3D dynamics reveal changes of the facial expression and motion, and can serve as a strong prior knowledge for guiding highly realistic face video generation. In particular, we explore face video prediction and exploit a well-designed 3D dynamic prediction network to predict a 3D dynamic sequence for a single face image. The 3D dynamics are then further rendered by the sparse texture mapping algorithm to recover structural details and sparse textures for generating face frames. Our model is versatile for various AR/VR and entertainment applications, such as face video retargeting and face video prediction. Superior experimental results have well demonstrated its effectiveness in generating high-fidelity, identity-preserving, and visually pleasant face video clips from a single source face image.

Clinical applications that involves risk stratification of patients often predict the likely occurrence of an event such as the development of a complication as well as the time to the next event. Existing approaches that provide individual survival distribution across time often use baseline measurements for the risk prediction of an event occurring, and is unable to estimate the time to next event. Further, they do not deal with the complex and heterogeneous information from past visit records, and hence do not handle repeated events which are common in chronic diseases. We address the above limitations by designing a recurrent temporal time process network that incorporates longitudinal visit information to increase the accuracy of risk predictions for clinical events and to estimate the time to next event. Our proposed solution utilizes a recurrent neural network to learn a latent representation of patient visit history. This representation enables us to approximate the conditional intensity function of the temporal point process, from which we derive the survival probability function to obtain the risk of an event occurring and to estimate the time to next event. We demonstrate our approach on two real-world healthcare datasets and show that the proposed approach is able to achieve a significant performance improvement over state-of-the-art methods.

Few-shot learning ability is heavily desired for machine intelligence. By meta-learning a model initialization from training tasks with fast adaptation ability to new tasks, model-agnostic meta-learning (MAML) has achieved remarkable success in a number of few-shot learning applications. However, theoretical understandings on the learning ability of MAML remain absent yet, hindering developing new and more advanced meta learning methods in a principled way. In this work, we solve this problem by theoretically justifying the fast adaptation capability of MAML when applied to new tasks. Specifically, we prove that the learnt meta-initialization can benefit the fast adaptation to new tasks with only a few steps of gradient descent. This result explicitly reveals the benefits of the unique designs in MAML. Then we propose a theory-inspired task similarity aware MAML which clusters tasks into multiple groups according to the estimated optimal model parameters and learns group-specific initializations. The proposed method improves upon MAML by speeding up the adaptation and giving stronger few-shot learning ability. Experimental results on the few-shot classification tasks testify its advantages.

Despite the great progress made by deep CNNs in image semantic segmentation, they typically require a large number of densely-annotated images for training and are difficult to generalize to unseen object categories. Few-shot segmentation has thus been developed to learn to perform segmentation from only a few annotated examples. In this paper, we tackle the challenging few-shot segmentation problem from a metric learning perspective and present PANet, a novel prototype alignment network to better utilize the information of the support set. Our PANet learns class-specific prototype representations from a few support images within an embedding space and then performs segmentation over the query images through matching each pixel to the learned prototypes. With non-parametric metric learning, PANet offers high-quality prototypes that are representative for each semantic class and meanwhile discriminative for different classes. Moreover, PANet introduces a prototype alignment regularization between support and query. With this, PANet fully exploits knowledge from the support and provides better generalization on few-shot segmentation. Significantly, our model achieves the mIoU score of 48.1% and 55.7% on PASCAL-5i for 1-shot and 5-shot settings respectively, surpassing the state-of-the-art method by 1.8% and 8.6%.