End-to-End Mesh Optimization of a Hybrid Deep Learning Black-Box PDE Solver

Deep learning has been widely applied to solve partial differential equations (PDEs) in computational fluid dynamics. Recent research proposed a PDE correction framework that leverages deep learning to correct the solution obtained by a PDE solver on a coarse mesh. However, end-to-end training of such a PDE correction model over both solver-dependent parameters such as mesh parameters and neural network parameters requires the PDE solver to support automatic differentiation through the iterative numerical process. Such a feature is not readily available in many existing solvers. In this study, we explore the feasibility of end-to-end training of a hybrid model with a black-box PDE solver and a deep learning model for fluid flow prediction. Specifically, we investigate a hybrid model that integrates a black-box PDE solver into a differentiable deep graph neural network. To train this model, we use a zeroth-order gradient estimator to differentiate the PDE solver via forward propagation. Although experiments show that the proposed approach based on zeroth-order gradient estimation underperforms the baseline that computes exact derivatives using automatic differentiation, our proposed method outperforms the baseline trained with a frozen input mesh to the solver. Moreover, with a simple warm-start on the neural network parameters, we show that models trained by these zeroth-order algorithms achieve an accelerated convergence and improved generalization performance.

Convergence Guarantees for RMSProp and Adam in Generalized-smooth Non-convex Optimization with Affine Noise Variance

This paper provides the first tight convergence analyses for RMSProp and Adam in non-convex optimization under the most relaxed assumptions of coordinate-wise generalized smoothness and affine noise variance. We first analyze RMSProp, which is a special case of Adam with adaptive learning rates but without first-order momentum. Specifically, to solve the challenges due to dependence among adaptive update, unbounded gradient estimate and Lipschitz constant, we demonstrate that the first-order term in the descent lemma converges and its denominator is upper bounded by a function of gradient norm. Based on this result, we show that RMSProp with proper hyperparameters converges to an $\epsilon$-stationary point with an iteration complexity of $\mathcal O(\epsilon^{-4})$. We then generalize our analysis to Adam, where the additional challenge is due to a mismatch between the gradient and first-order momentum. We develop a new upper bound on the first-order term in the descent lemma, which is also a function of the gradient norm. We show that Adam with proper hyperparameters converges to an $\epsilon$-stationary point with an iteration complexity of $\mathcal O(\epsilon^{-4})$. Our complexity results for both RMSProp and Adam match with the complexity lower bound established in \cite{arjevani2023lower}.

Large-Scale Non-convex Stochastic Constrained Distributionally Robust Optimization

Distributionally robust optimization (DRO) is a powerful framework for training robust models against data distribution shifts. This paper focuses on constrained DRO, which has an explicit characterization of the robustness level. Existing studies on constrained DRO mostly focus on convex loss function, and exclude the practical and challenging case with non-convex loss function, e.g., neural network. This paper develops a stochastic algorithm and its performance analysis for non-convex constrained DRO. The computational complexity of our stochastic algorithm at each iteration is independent of the overall dataset size, and thus is suitable for large-scale applications. We focus on the general Cressie-Read family divergence defined uncertainty set which includes $\chi^2$-divergences as a special case. We prove that our algorithm finds an $\epsilon$-stationary point with a computational complexity of $\mathcal O(\epsilon^{-3k_*-5})$, where $k_*$ is the parameter of the Cressie-Read divergence. The numerical results indicate that our method outperforms existing methods.} Our method also applies to the smoothed conditional value at risk (CVaR) DRO.

HIMap: HybrId Representation Learning for End-to-end Vectorized HD Map Construction

Vectorized High-Definition (HD) map construction requires predictions of the category and point coordinates of map elements (e.g. road boundary, lane divider, pedestrian crossing, etc.). State-of-the-art methods are mainly based on point-level representation learning for regressing accurate point coordinates. However, this pipeline has limitations in obtaining element-level information and handling element-level failures, e.g. erroneous element shape or entanglement between elements. To tackle the above issues, we propose a simple yet effective HybrId framework named HIMap to sufficiently learn and interact both point-level and element-level information. Concretely, we introduce a hybrid representation called HIQuery to represent all map elements, and propose a point-element interactor to interactively extract and encode the hybrid information of elements, e.g. point position and element shape, into the HIQuery. Additionally, we present a point-element consistency constraint to enhance the consistency between the point-level and element-level information. Finally, the output point-element integrated HIQuery can be directly converted into map elements' class, point coordinates, and mask. We conduct extensive experiments and consistently outperform previous methods on both nuScenes and Argoverse2 datasets. Notably, our method achieves $77.8$ mAP on the nuScenes dataset, remarkably superior to previous SOTAs by $8.3$ mAP at least.

Evaluating Unsupervised Dimensionality Reduction Methods for Pretrained Sentence Embeddings

Sentence embeddings produced by Pretrained Language Models (PLMs) have received wide attention from the NLP community due to their superior performance when representing texts in numerous downstream applications. However, the high dimensionality of the sentence embeddings produced by PLMs is problematic when representing large numbers of sentences in memory- or compute-constrained devices. As a solution, we evaluate unsupervised dimensionality reduction methods to reduce the dimensionality of sentence embeddings produced by PLMs. Our experimental results show that simple methods such as Principal Component Analysis (PCA) can reduce the dimensionality of sentence embeddings by almost $50\%$, without incurring a significant loss in performance in multiple downstream tasks. Surprisingly, reducing the dimensionality further improves performance over the original high-dimensional versions for the sentence embeddings produced by some PLMs in some tasks.

Transfer Learning-Enhanced Instantaneous Multi-Person Indoor Localization by CSI

Passive indoor localization, integral to smart buildings, emergency response, and indoor navigation, has traditionally been limited by a focus on single-target localization and reliance on multi-packet CSI. We introduce a novel Multi-target loss, notably enhancing multi-person localization. Utilizing this loss function, our instantaneous CSI-ResNet achieves an impressive 99.21% accuracy at 0.6m precision with single-timestamp CSI. A preprocessing algorithm is implemented to counteract WiFi-induced variability, thereby augmenting robustness. Furthermore, we incorporate Nuclear Norm-Based Transfer Pre-Training, ensuring adaptability in diverse environments, which provides a new paradigm for indoor multi-person localization. Additionally, we have developed an extensive dataset, surpassing existing ones in scope and diversity, to underscore the efficacy of our method and facilitate future fingerprint-based localization research.

EDTC: enhance depth of text comprehension in automated audio captioning

Modality discrepancies have perpetually posed significant challenges within the realm of Automated Audio Captioning (AAC) and across all multi-modal domains. Facilitating models in comprehending text information plays a pivotal role in establishing a seamless connection between the two modalities of text and audio. While recent research has focused on closing the gap between these two modalities through contrastive learning, it is challenging to bridge the difference between both modalities using only simple contrastive loss. This paper introduces Enhance Depth of Text Comprehension (EDTC), which enhances the model's understanding of text information from three different perspectives. First, we propose a novel fusion module, FUSER, which aims to extract shared semantic information from different audio features through feature fusion. We then introduced TRANSLATOR, a novel alignment module designed to align audio features and text features along the tensor level. Finally, the weights are updated by adding momentum to the twin structure so that the model can learn information about both modalities at the same time. The resulting method achieves state-of-the-art performance on AudioCaps datasets and demonstrates results comparable to the state-of-the-art on Clotho datasets.

Brain-Inspired Two-Stage Approach: Enhancing Mathematical Reasoning by Imitating Human Thought Processes

Although large language models demonstrate emergent abilities in solving math word problems, there is a challenging task in complex multi-step mathematical reasoning tasks. To improve model performance on mathematical reasoning tasks, previous work has conducted supervised fine-tuning on open-source models by improving the quality and quantity of data. In this paper, we propose a novel approach, named Brain, to imitate human thought processes to enhance mathematical reasoning abilities, using the Frontal Lobe Model to generate plans, and then employing the Parietal Lobe Model to generate code and execute to obtain answers. First, we achieve SOTA performance in comparison with Code LLaMA 7B based models through this method. Secondly, we find that plans can be explicitly extracted from natural language, code, or formal language. Our code and data are publicly available at https://github.com/cyzhh/Brain.

An Empirical Study of Data Ability Boundary in LLMs' Math Reasoning

Large language models (LLMs) are displaying emergent abilities for math reasoning tasks,and there is a growing attention on enhancing the ability of open-source LLMs through supervised fine-tuning (SFT).In this paper, we aim to explore a general data strategy for supervised data to help optimize and expand math reasoning ability.Firstly, we determine the ability boundary of reasoning paths augmentation by identifying these paths' minimal optimal set.Secondly, we validate that different abilities of the model can be cumulatively enhanced by Mix of Minimal Optimal Sets of corresponding types of data, while our models MMOS achieve SOTA performance on series base models under much lower construction costs.Besides, we point out GSM-HARD is not really hard and today's LLMs no longer lack numerical robustness.Also, we provide an Auto Problem Generator for robustness testing and educational applications.Our code and data are publicly available at https://github.com/cyzhh/MMOS.