DVMNet: Computing Relative Pose for Unseen Objects Beyond Hypotheses

Determining the relative pose of an object between two images is pivotal to the success of generalizable object pose estimation. Existing approaches typically approximate the continuous pose representation with a large number of discrete pose hypotheses, which incurs a computationally expensive process of scoring each hypothesis at test time. By contrast, we present a Deep Voxel Matching Network (DVMNet) that eliminates the need for pose hypotheses and computes the relative object pose in a single pass. To this end, we map the two input RGB images, reference and query, to their respective voxelized 3D representations. We then pass the resulting voxels through a pose estimation module, where the voxels are aligned and the pose is computed in an end-to-end fashion by solving a least-squares problem. To enhance robustness, we introduce a weighted closest voxel algorithm capable of mitigating the impact of noisy voxels. We conduct extensive experiments on the CO3D, LINEMOD, and Objaverse datasets, demonstrating that our method delivers more accurate relative pose estimates for novel objects at a lower computational cost compared to state-of-the-art methods. Our code is released at: https://github.com/sailor-z/DVMNet/.

Accurately Predicting Probabilities of Safety-Critical Rare Events for Intelligent Systems

Intelligent systems are increasingly integral to our daily lives, yet rare safety-critical events present significant latent threats to their practical deployment. Addressing this challenge hinges on accurately predicting the probability of safety-critical events occurring within a given time step from the current state, a metric we define as 'criticality'. The complexity of predicting criticality arises from the extreme data imbalance caused by rare events in high dimensional variables associated with the rare events, a challenge we refer to as the curse of rarity. Existing methods tend to be either overly conservative or prone to overlooking safety-critical events, thus struggling to achieve both high precision and recall rates, which severely limits their applicability. This study endeavors to develop a criticality prediction model that excels in both precision and recall rates for evaluating the criticality of safety-critical autonomous systems. We propose a multi-stage learning framework designed to progressively densify the dataset, mitigating the curse of rarity across stages. To validate our approach, we evaluate it in two cases: lunar lander and bipedal walker scenarios. The results demonstrate that our method surpasses traditional approaches, providing a more accurate and dependable assessment of criticality in intelligent systems.

FACT: Fast and Active Coordinate Initialization for Vision-based Drone Swarms

Swarm robots have sparked remarkable developments across a range of fields. While it is necessary for various applications in swarm robots, a fast and robust coordinate initialization in vision-based drone swarms remains elusive. To this end, our paper proposes a complete system to recover a swarm's initial relative pose on platforms with size, weight, and power (SWaP) constraints. To overcome limited coverage of field-of-view (FoV), the drones rotate in place to obtain observations. To tackle the anonymous measurements, we formulate a non-convex rotation estimation problem and transform it into a semi-definite programming (SDP) problem, which can steadily obtain global optimal values. Then we utilize the Hungarian algorithm to recover relative translation and correspondences between observations and drone identities. To safely acquire complete observations, we actively search for positions and generate feasible trajectories to avoid collisions. To validate the practicability of our system, we conduct experiments on a vision-based drone swarm with only stereo cameras and inertial measurement units (IMUs) as sensors. The results demonstrate that the system can robustly get accurate relative poses in real time with limited onboard computation resources. The source code is released.

Centroidal State Estimation based on the Koopman Embedding for Dynamic Legged Locomotion

In this paper, we introduce a novel approach to centroidal state estimation, which plays a crucial role in predictive model-based control strategies for dynamic legged locomotion. Our approach uses the Koopman operator theory to transform the robot's complex nonlinear dynamics into a linear system, by employing dynamic mode decomposition and deep learning for model construction. We evaluate both models on their linearization accuracy and capability to capture both fast and slow dynamic system responses. We then select the most suitable model for estimation purposes, and integrate it within a moving horizon estimator. This estimator is formulated as a convex quadratic program, to facilitate robust, real-time centroidal state estimation. Through extensive simulation experiments on a quadruped robot executing various dynamic gaits, our data-driven framework outperforms conventional filtering techniques based on nonlinear dynamics. Our estimator addresses challenges posed by force/torque measurement noise in highly dynamic motions and accurately recovers the centroidal states, demonstrating the adaptability and effectiveness of the Koopman-based linear representation for complex locomotive behaviors. Importantly, our model based on dynamic mode decomposition, trained with two locomotion patterns (trot and jump), successfully estimates the centroidal states for a different motion (bound) without retraining.

Kernel Multigrid: Accelerate Back-fitting via Sparse Gaussian Process Regression

Additive Gaussian Processes (GPs) are popular approaches for nonparametric feature selection. The common training method for these models is Bayesian Back-fitting. However, the convergence rate of Back-fitting in training additive GPs is still an open problem. By utilizing a technique called Kernel Packets (KP), we prove that the convergence rate of Back-fitting is no faster than $(1-\mathcal{O}(\frac{1}{n}))^t$, where $n$ and $t$ denote the data size and the iteration number, respectively. Consequently, Back-fitting requires a minimum of $\mathcal{O}(n\log n)$ iterations to achieve convergence. Based on KPs, we further propose an algorithm called Kernel Multigrid (KMG). This algorithm enhances Back-fitting by incorporating a sparse Gaussian Process Regression (GPR) to process the residuals subsequent to each Back-fitting iteration. It is applicable to additive GPs with both structured and scattered data. Theoretically, we prove that KMG reduces the required iterations to $\mathcal{O}(\log n)$ while preserving the time and space complexities at $\mathcal{O}(n\log n)$ and $\mathcal{O}(n)$ per iteration, respectively. Numerically, by employing a sparse GPR with merely 10 inducing points, KMG can produce accurate approximations of high-dimensional targets within 5 iterations.

RL in Markov Games with Independent Function Approximation: Improved Sample Complexity Bound under the Local Access Model

Efficiently learning equilibria with large state and action spaces in general-sum Markov games while overcoming the curse of multi-agency is a challenging problem. Recent works have attempted to solve this problem by employing independent linear function classes to approximate the marginal $Q$-value for each agent. However, existing sample complexity bounds under such a framework have a suboptimal dependency on the desired accuracy $\varepsilon$ or the action space. In this work, we introduce a new algorithm, Lin-Confident-FTRL, for learning coarse correlated equilibria (CCE) with local access to the simulator, i.e., one can interact with the underlying environment on the visited states. Up to a logarithmic dependence on the size of the state space, Lin-Confident-FTRL learns $\epsilon$-CCE with a provable optimal accuracy bound $O(\epsilon^{-2})$ and gets rids of the linear dependency on the action space, while scaling polynomially with relevant problem parameters (such as the number of agents and time horizon). Moreover, our analysis of Linear-Confident-FTRL generalizes the virtual policy iteration technique in the single-agent local planning literature, which yields a new computationally efficient algorithm with a tighter sample complexity bound when assuming random access to the simulator.

Real-Time Adaptive Safety-Critical Control with Gaussian Processes in High-Order Uncertain Models

This paper presents an adaptive online learning framework for systems with uncertain parameters to ensure safety-critical control in non-stationary environments. Our approach consists of two phases. The initial phase is centered on a novel sparse Gaussian process (GP) framework. We first integrate a forgetting factor to refine a variational sparse GP algorithm, thus enhancing its adaptability. Subsequently, the hyperparameters of the Gaussian model are trained with a specially compound kernel, and the Gaussian model's online inferential capability and computational efficiency are strengthened by updating a solitary inducing point derived from new samples, in conjunction with the learned hyperparameters. In the second phase, we propose a safety filter based on high-order control barrier functions (HOCBFs), synergized with the previously trained learning model. By leveraging the compound kernel from the first phase, we effectively address the inherent limitations of GPs in handling high-dimensional problems for real-time applications. The derived controller ensures a rigorous lower bound on the probability of satisfying the safety specification. Finally, the efficacy of our proposed algorithm is demonstrated through real-time obstacle avoidance experiments executed using both a simulation platform and a real-world 7-DOF robot.

Mitigating the Bias in the Model for Continual Test-Time Adaptation

Continual Test-Time Adaptation (CTA) is a challenging task that aims to adapt a source pre-trained model to continually changing target domains. In the CTA setting, a model does not know when the target domain changes, thus facing a drastic change in the distribution of streaming inputs during the test-time. The key challenge is to keep adapting the model to the continually changing target domains in an online manner. We find that a model shows highly biased predictions as it constantly adapts to the chaining distribution of the target data. It predicts certain classes more often than other classes, making inaccurate over-confident predictions. This paper mitigates this issue to improve performance in the CTA scenario. To alleviate the bias issue, we make class-wise exponential moving average target prototypes with reliable target samples and exploit them to cluster the target features class-wisely. Moreover, we aim to align the target distributions to the source distribution by anchoring the target feature to its corresponding source prototype. With extensive experiments, our proposed method achieves noteworthy performance gain when applied on top of existing CTA methods without substantial adaptation time overhead.

Unraveling the Mystery of Scaling Laws: Part I

Scaling law principles indicate a power-law correlation between loss and variables such as model size, dataset size, and computational resources utilized during training. These principles play a vital role in optimizing various aspects of model pre-training, ultimately contributing to the success of large language models such as GPT-4, Llama and Gemini. However, the original scaling law paper by OpenAI did not disclose the complete details necessary to derive the precise scaling law formulas, and their conclusions are only based on models containing up to 1.5 billion parameters. Though some subsequent works attempt to unveil these details and scale to larger models, they often neglect the training dependency of important factors such as the learning rate, context length and batch size, leading to their failure to establish a reliable formula for predicting the test loss trajectory. In this technical report, we confirm that the scaling law formulations proposed in the original OpenAI paper remain valid when scaling the model size up to 33 billion, but the constant coefficients in these formulas vary significantly with the experiment setup. We meticulously identify influential factors and provide transparent, step-by-step instructions to estimate all constant terms in scaling-law formulas by training on models with only 1M~60M parameters. Using these estimated formulas, we showcase the capability to accurately predict various attributes for models with up to 33B parameters before their training, including (1) the minimum possible test loss; (2) the minimum required training steps and processed tokens to achieve a specific loss; (3) the critical batch size with an optimal time/computation trade-off at any loss value; and (4) the complete test loss trajectory with arbitrary batch size.

Relational Representation Learning Network for Cross-Spectral Image Patch Matching

Recently, feature relation learning has drawn widespread attention in cross-spectral image patch matching. However, existing related research focuses on extracting diverse relations between image patch features and ignores sufficient intrinsic feature representations of individual image patches. Therefore, an innovative relational representation learning idea is proposed for the first time, which simultaneously focuses on sufficiently mining the intrinsic features of individual image patches and the relations between image patch features. Based on this, we construct a lightweight Relational Representation Learning Network (RRL-Net). Specifically, we innovatively construct an autoencoder to fully characterize the individual intrinsic features, and introduce a Feature Interaction Learning (FIL) module to extract deep-level feature relations. To further fully mine individual intrinsic features, a lightweight Multi-dimensional Global-to-Local Attention (MGLA) module is constructed to enhance the global feature extraction of individual image patches and capture local dependencies within global features. By combining the MGLA module, we further explore the feature extraction network and construct an Attention-based Lightweight Feature Extraction (ALFE) network. In addition, we propose a Multi-Loss Post-Pruning (MLPP) optimization strategy, which greatly promotes network optimization while avoiding increases in parameters and inference time. Extensive experiments demonstrate that our RRL-Net achieves state-of-the-art (SOTA) performance on multiple public datasets. Our code will be made public later.