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Sampling from diffusion models can be treated as solving the corresponding ordinary differential equations (ODEs), with the aim of obtaining an accurate solution with as few number of function evaluations (NFE) as possible. Recently, various fast samplers utilizing higher-order ODE solvers have emerged and achieved better performance than the initial first-order one. However, these numerical methods inherently result in certain approximation errors, which significantly degrades sample quality with extremely small NFE (e.g., around 5). In contrast, based on the geometric observation that each sampling trajectory almost lies in a two-dimensional subspace embedded in the ambient space, we propose Approximate MEan-Direction Solver (AMED-Solver) that eliminates truncation errors by directly learning the mean direction for fast diffusion sampling. Besides, our method can be easily used as a plugin to further improve existing ODE-based samplers. Extensive experiments on image synthesis with the resolution ranging from 32 to 512 demonstrate the effectiveness of our method. With only 5 NFE, we achieve 6.61 FID on CIFAR-10, 10.74 FID on ImageNet 64$\times$64, and 13.20 FID on LSUN Bedroom. Our code is available at //github.com/zju-pi/diff-sampler.

Models for the dynamics of congestion control generally involve systems of coupled differential equations. Universally, these models assume that traffic sources saturate the maximum transmissions allowed by the congestion control method. This is not suitable for studying congestion control of intermittent but bursty traffic sources. In this paper, we present a characterization of congestion control for arbitrary time-varying traffic that applies to rate-based as well as window-based congestion control. We leverage the capability of network calculus to precisely describe the input-output relationship at network elements for arbitrary source traffic. We show that our characterization can closely track the dynamics of even complex congestion control algorithms.

This paper discusses the theory and numerical method of two-scale analysis for the multiscale Landau-Lifshitz-Gilbert equation in composite ferromagnetic materials. The novelty of this work can be summarized in three aspects: Firstly, the more realistic and complex model is considered, including the effects of the exchange field, anisotropy field, stray field, and external magnetic field. The explicit convergence orders in the $H^1$ norm between the classical solution and the two-scale solution are obtained. Secondly, we propose a robust numerical framework, which is employed in several comprehensive experiments to validate the convergence results for the Periodic and Neumann problems. Thirdly, we design an improved implicit numerical scheme to reduce the required number of iterations and relaxes the constraints on the time step size, which can significantly improve computational efficiency. Specifically, the projection and the expansion methods are given to overcome the inherent non-consistency in the initial data between the multiscale problem and homogenized problem.

We study differentially private (DP) algorithms for recovering clusters in well-clustered graphs, which are graphs whose vertex set can be partitioned into a small number of sets, each inducing a subgraph of high inner conductance and small outer conductance. Such graphs have widespread application as a benchmark in the theoretical analysis of spectral clustering. We provide an efficient ($\epsilon$,$\delta$)-DP algorithm tailored specifically for such graphs. Our algorithm draws inspiration from the recent work of Chen et al., who developed DP algorithms for recovery of stochastic block models in cases where the graph comprises exactly two nearly-balanced clusters. Our algorithm works for well-clustered graphs with $k$ nearly-balanced clusters, and the misclassification ratio almost matches the one of the best-known non-private algorithms. We conduct experimental evaluations on datasets with known ground truth clusters to substantiate the prowess of our algorithm. We also show that any (pure) $\epsilon$-DP algorithm would result in substantial error.

Multiscale problems can usually be approximated through numerical homogenization by an equation with some effective parameters that can capture the macroscopic behavior of the original system on the coarse grid to speed up the simulation. However, this approach usually assumes scale separation and that the heterogeneity of the solution can be approximated by the solution average in each coarse block. For complex multiscale problems, the computed single effective properties/continuum might be inadequate. In this paper, we propose a novel learning-based multi-continuum model to enrich the homogenized equation and improve the accuracy of the single continuum model for multiscale problems with some given data. Without loss of generalization, we consider a two-continuum case. The first flow equation keeps the information of the original homogenized equation with an additional interaction term. The second continuum is newly introduced, and the effective permeability in the second flow equation is determined by a neural network. The interaction term between the two continua aligns with that used in the Dual-porosity model but with a learnable coefficient determined by another neural network. The new model with neural network terms is then optimized using trusted data. We discuss both direct back-propagation and the adjoint method for the PDE-constraint optimization problem. Our proposed learning-based multi-continuum model can resolve multiple interacted media within each coarse grid block and describe the mass transfer among them, and it has been demonstrated to significantly improve the simulation results through numerical experiments involving both linear and nonlinear flow equations.

The scaling laws and extraordinary performance of large foundation models motivate the development and utilization of such large models in biomedicine. However, despite early promising results on some biomedical benchmarks, there are still major challenges that need to be addressed before these models can be used in real-world applications. Frontier models such as GPT-4V still have major competency gaps in multimodal capabilities for biomedical applications. Moreover, pragmatic issues such as access, cost, latency, and compliance make it hard for clinicians to use privately-hosted state-of-the-art large models directly on private patient data. In this paper, we explore training open-source small multimodal models (SMMs) to bridge biomedical competency gaps for unmet clinical needs. To maximize data efficiency, we adopt a modular approach by incorporating state-of-the-art pre-trained models for image and text modalities, and focusing on training a lightweight adapter to ground each modality to the text embedding space. We conduct a comprehensive study of this approach on radiology imaging. For training, we assemble a large dataset with over 1 million image-text pairs. For evaluation, we propose a clinically driven novel approach using GPT-4 and demonstrate its parity with expert evaluation. We also study grounding qualitatively using attention. For best practice, we conduct a systematic ablation study on various choices in data engineering and multimodal training. The resulting LLaVA-Rad (7B) model attains state-of-the-art results on radiology tasks such as report generation and cross-modal retrieval, even outperforming much larger models such as GPT-4V and Med-PaLM M (84B). LLaVA-Rad is fast and can be run on a single V100 GPU in private settings, offering a promising state-of-the-art tool for real-world clinical applications.

Multi-modal emotion recognition has recently gained a lot of attention since it can leverage diverse and complementary relationships over multiple modalities, such as audio, visual, and text. Most state-of-the-art methods for multimodal fusion rely on recurrent networks or conventional attention mechanisms that do not effectively leverage the complementary nature of the modalities. In this paper, we focus on dimensional emotion recognition based on the fusion of facial, vocal, and text modalities extracted from videos. Specifically, we propose a recursive cross-modal attention (RCMA) to effectively capture the complementary relationships across the modalities in a recursive fashion. The proposed model is able to effectively capture the inter-modal relationships by computing the cross-attention weights across the individual modalities and the joint representation of the other two modalities. To further improve the inter-modal relationships, the obtained attended features of the individual modalities are again fed as input to the cross-modal attention to refine the feature representations of the individual modalities. In addition to that, we have used Temporal convolution networks (TCNs) to capture the temporal modeling (intra-modal relationships) of the individual modalities. By deploying the TCNs as well cross-modal attention in a recursive fashion, we are able to effectively capture both intra- and inter-modal relationships across the audio, visual, and text modalities. Experimental results on validation-set videos from the AffWild2 dataset indicate that our proposed fusion model is able to achieve significant improvement over the baseline for the sixth challenge of Affective Behavior Analysis in-the-Wild 2024 (ABAW6) competition.

Time-optimal obstacle avoidance is a prevalent problem encountered in various fields, including robotics and autonomous vehicles, where the task involves determining a path for a moving vehicle to reach its goal while navigating around obstacles within its environment. This problem becomes increasingly challenging as the number of obstacles in the environment rises. We propose an iterative active-inactive obstacle approach, which involves identifying a subset of the obstacles as "active", that considers solely the effect of the "active" obstacles on the path of the moving vehicle. The remaining obstacles are considered "inactive" and are not considered in the path planning process. The obstacles are classified as 'active' on the basis of previous findings derived from prior iterations. This approach allows for a more efficient calculation of the optimal path by reducing the number of obstacles that need to be considered. The effectiveness of the proposed method is demonstrated with two different dynamic models using the various number of obstacles. The results show that the proposed method is able to find the optimal path in a timely manner, while also being able to handle a large number of obstacles in the environment and the constraints on the motion of the object.

Differentially-private (DP) mechanisms can be embedded into the design of a machine learningalgorithm to protect the resulting model against privacy leakage, although this often comes with asignificant loss of accuracy. In this paper, we aim at improving this trade-off for rule lists modelsby establishing the smooth sensitivity of the Gini impurity and leveraging it to propose a DP greedyrule list algorithm. In particular, our theoretical analysis and experimental results demonstrate thatthe DP rule lists models integrating smooth sensitivity have higher accuracy that those using otherDP frameworks based on global sensitivity.

The existence of representative datasets is a prerequisite of many successful artificial intelligence and machine learning models. However, the subsequent application of these models often involves scenarios that are inadequately represented in the data used for training. The reasons for this are manifold and range from time and cost constraints to ethical considerations. As a consequence, the reliable use of these models, especially in safety-critical applications, is a huge challenge. Leveraging additional, already existing sources of knowledge is key to overcome the limitations of purely data-driven approaches, and eventually to increase the generalization capability of these models. Furthermore, predictions that conform with knowledge are crucial for making trustworthy and safe decisions even in underrepresented scenarios. This work provides an overview of existing techniques and methods in the literature that combine data-based models with existing knowledge. The identified approaches are structured according to the categories integration, extraction and conformity. Special attention is given to applications in the field of autonomous driving.