Segment Any Object Model (SAOM): Real-to-Simulation Fine-Tuning Strategy for Multi-Class Multi-Instance Segmentation

Multi-class multi-instance segmentation is the task of identifying masks for multiple object classes and multiple instances of the same class within an image. The foundational Segment Anything Model (SAM) is designed for promptable multi-class multi-instance segmentation but tends to output part or sub-part masks in the "everything" mode for various real-world applications. Whole object segmentation masks play a crucial role for indoor scene understanding, especially in robotics applications. We propose a new domain invariant Real-to-Simulation (Real-Sim) fine-tuning strategy for SAM. We use object images and ground truth data collected from Ai2Thor simulator during fine-tuning (real-to-sim). To allow our Segment Any Object Model (SAOM) to work in the "everything" mode, we propose the novel nearest neighbour assignment method, updating point embeddings for each ground-truth mask. SAOM is evaluated on our own dataset collected from Ai2Thor simulator. SAOM significantly improves on SAM, with a 28% increase in mIoU and a 25% increase in mAcc for 54 frequently-seen indoor object classes. Moreover, our Real-to-Simulation fine-tuning strategy demonstrates promising generalization performance in real environments without being trained on the real-world data (sim-to-real). The dataset and the code will be released after publication.

Resolution invariant deep operator network for PDEs with complex geometries

Neural operators (NO) are discretization invariant deep learning methods with functional output and can approximate any continuous operator. NO have demonstrated the superiority of solving partial differential equations (PDEs) over other deep learning methods. However, the spatial domain of its input function needs to be identical to its output, which limits its applicability. For instance, the widely used Fourier neural operator (FNO) fails to approximate the operator that maps the boundary condition to the PDE solution. To address this issue, we propose a novel framework called resolution-invariant deep operator (RDO) that decouples the spatial domain of the input and output. RDO is motivated by the Deep operator network (DeepONet) and it does not require retraining the network when the input/output is changed compared with DeepONet. RDO takes functional input and its output is also functional so that it keeps the resolution invariant property of NO. It can also resolve PDEs with complex geometries whereas NO fail. Various numerical experiments demonstrate the advantage of our method over DeepONet and FNO.

Sparse discovery of differential equations based on multi-fidelity Gaussian process

Sparse identification of differential equations aims to compute the analytic expressions from the observed data explicitly. However, there exist two primary challenges. Firstly, it exhibits sensitivity to the noise in the observed data, particularly for the derivatives computations. Secondly, existing literature predominantly concentrates on single-fidelity (SF) data, which imposes limitations on its applicability due to the computational cost. In this paper, we present two novel approaches to address these problems from the view of uncertainty quantification. We construct a surrogate model employing the Gaussian process regression (GPR) to mitigate the effect of noise in the observed data, quantify its uncertainty, and ultimately recover the equations accurately. Subsequently, we exploit the multi-fidelity Gaussian processes (MFGP) to address scenarios involving multi-fidelity (MF), sparse, and noisy observed data. We demonstrate the robustness and effectiveness of our methodologies through several numerical experiments.

Conformal Prediction for Deep Classifier via Label Ranking

Conformal prediction is a statistical framework that generates prediction sets containing ground-truth labels with a desired coverage guarantee. The predicted probabilities produced by machine learning models are generally miscalibrated, leading to large prediction sets in conformal prediction. In this paper, we empirically and theoretically show that disregarding the probabilities' value will mitigate the undesirable effect of miscalibrated probability values. Then, we propose a novel algorithm named $\textit{Sorted Adaptive prediction sets}$ (SAPS), which discards all the probability values except for the maximum softmax probability. The key idea behind SAPS is to minimize the dependence of the non-conformity score on the probability values while retaining the uncertainty information. In this manner, SAPS can produce sets of small size and communicate instance-wise uncertainty. Theoretically, we provide a finite-sample coverage guarantee of SAPS and show that the expected value of set size from SAPS is always smaller than APS. Extensive experiments validate that SAPS not only lessens the prediction sets but also broadly enhances the conditional coverage rate and adaptation of prediction sets.

Physics-informed invertible neural network for the Koopman operator learning

In Koopman operator theory, a finite-dimensional nonlinear system is transformed into an infinite but linear system using a set of observable functions. However, manually selecting observable functions that span the invariant subspace of the Koopman operator based on prior knowledge is inefficient and challenging, particularly when little or no information is available about the underlying systems. Furthermore, current methodologies tend to disregard the importance of the invertibility of observable functions, which leads to inaccurate results. To address these challenges, we propose the so-called FlowDMD, a Flow-based Dynamic Mode Decomposition that utilizes the Coupling Flow Invertible Neural Network (CF-INN) framework. FlowDMD leverages the intrinsically invertible characteristics of the CF-INN to learn the invariant subspaces of the Koopman operator and accurately reconstruct state variables. Numerical experiments demonstrate the superior performance of our algorithm compared to state-of-the-art methodologies.

Augmented Message Passing Stein Variational Gradient Descent

Stein Variational Gradient Descent (SVGD) is a popular particle-based method for Bayesian inference. However, its convergence suffers from the variance collapse, which reduces the accuracy and diversity of the estimation. In this paper, we study the isotropy property of finite particles during the convergence process and show that SVGD of finite particles cannot spread across the entire sample space. Instead, all particles tend to cluster around the particle center within a certain range and we provide an analytical bound for this cluster. To further improve the effectiveness of SVGD for high-dimensional problems, we propose the Augmented Message Passing SVGD (AUMP-SVGD) method, which is a two-stage optimization procedure that does not require sparsity of the target distribution, unlike the MP-SVGD method. Our algorithm achieves satisfactory accuracy and overcomes the variance collapse problem in various benchmark problems.

TransFusionOdom: Interpretable Transformer-based LiDAR-Inertial Fusion Odometry Estimation

Multi-modal fusion of sensors is a commonly used approach to enhance the performance of odometry estimation, which is also a fundamental module for mobile robots. However, the question of \textit{how to perform fusion among different modalities in a supervised sensor fusion odometry estimation task?} is still one of challenging issues remains. Some simple operations, such as element-wise summation and concatenation, are not capable of assigning adaptive attentional weights to incorporate different modalities efficiently, which make it difficult to achieve competitive odometry results. Recently, the Transformer architecture has shown potential for multi-modal fusion tasks, particularly in the domains of vision with language. In this work, we propose an end-to-end supervised Transformer-based LiDAR-Inertial fusion framework (namely TransFusionOdom) for odometry estimation. The multi-attention fusion module demonstrates different fusion approaches for homogeneous and heterogeneous modalities to address the overfitting problem that can arise from blindly increasing the complexity of the model. Additionally, to interpret the learning process of the Transformer-based multi-modal interactions, a general visualization approach is introduced to illustrate the interactions between modalities. Moreover, exhaustive ablation studies evaluate different multi-modal fusion strategies to verify the performance of the proposed fusion strategy. A synthetic multi-modal dataset is made public to validate the generalization ability of the proposed fusion strategy, which also works for other combinations of different modalities. The quantitative and qualitative odometry evaluations on the KITTI dataset verify the proposed TransFusionOdom could achieve superior performance compared with other related works.

Describing and Localizing Multiple Changes with Transformers

Change captioning tasks aim to detect changes in image pairs observed before and after a scene change and generate a natural language description of the changes. Existing change captioning studies have mainly focused on scenes with a single change. However, detecting and describing multiple changed parts in image pairs is essential for enhancing adaptability to complex scenarios. We solve the above issues from three aspects: (i) We propose a CG-based multi-change captioning dataset; (ii) We benchmark existing state-of-the-art methods of single change captioning on multi-change captioning; (iii) We further propose Multi-Change Captioning transformers (MCCFormers) that identify change regions by densely correlating different regions in image pairs and dynamically determines the related change regions with words in sentences. The proposed method obtained the highest scores on four conventional change captioning evaluation metrics for multi-change captioning. In addition, existing methods generate a single attention map for multiple changes and lack the ability to distinguish change regions. In contrast, our proposed method can separate attention maps for each change and performs well with respect to change localization. Moreover, the proposed framework outperformed the previous state-of-the-art methods on an existing change captioning benchmark, CLEVR-Change, by a large margin (+6.1 on BLEU-4 and +9.7 on CIDEr scores), indicating its general ability in change captioning tasks.