This report provides an overview of the challenge hosted at the OpenSUN3D Workshop on Open-Vocabulary 3D Scene Understanding held in conjunction with ICCV 2023. The goal of this workshop series is to provide a platform for exploration and discussion of open-vocabulary 3D scene understanding tasks, including but not limited to segmentation, detection and mapping. We provide an overview of the challenge hosted at the workshop, present the challenge dataset, the evaluation methodology, and brief descriptions of the winning methods. Additional details are available on the OpenSUN3D workshop website.

Optimal behaviours of a system to perform a specific task can be achieved by leveraging the coupling between trajectory optimization, stabilization, and design optimization. This approach is particularly advantageous for underactuated systems, which are systems that have fewer actuators than degrees of freedom and thus require for more elaborate control systems. This paper proposes a novel co-design algorithm, namely Robust Trajectory Control with Design optimization (RTC-D). An inner optimization layer (RTC) simultaneously performs direct transcription (DIRTRAN) to find a nominal trajectory while computing optimal hyperparameters for a stabilizing time-varying linear quadratic regulator (TVLQR). RTC-D augments RTC with a design optimization layer, maximizing the system's robustness through a time-varying Lyapunov-based region of attraction (ROA) analysis. This analysis provides a formal guarantee of stability for a set of off-nominal states. The proposed algorithm has been tested on two different underactuated systems: the torque-limited simple pendulum and the cart-pole. Extensive simulations of off-nominal initial conditions demonstrate improved robustness, while real-system experiments show increased insensitivity to torque disturbances.

Multi-class classification becomes challenging at test time when the number of classes is very large and testing against every possible class can become computationally infeasible. This problem can be alleviated by imposing (or learning) a structure over the set of classes. We propose an algorithm for learning a treestructure of classifiers which, by optimizing the overall tree loss, provides superior accuracy to existing tree labeling methods. We also propose a method that learns to embed labels in a low dimensional space that is faster than non-embedding approaches and has superior accuracy to existing embedding approaches. Finally we combine the two ideas resulting in the label embedding tree that outperforms alternative methods including One-vs-Rest while being orders of magnitude faster.

Although spectral clustering has enjoyed considerable empirical success in machine learning, its theoretical properties are not yet fully developed. We analyze the performance of a spectral algorithm for hierarchical clustering and show that on a class of hierarchically structured similarity matrices, this algorithm can tolerate noise that grows with the number of data points while still perfectly recovering the hierarchical clusters with high probability. We additionally improve upon previous results for k-way spectral clustering to derive conditions under which spectral clustering makes no mistakes. Further, using minimax analysis, we derive tight upper and lower bounds for the clustering problem and compare the performance of spectral clustering to these information theoretic limits.

Diffusion-based generative models have emerged as powerful tools in the realm of generative modeling. Despite extensive research on denoising across various timesteps and noise levels, a conflict persists regarding the relative difficulties of the denoising tasks. While various studies argue that lower timesteps present more challenging tasks, others contend that higher timesteps are more difficult. To address this conflict, our study undertakes a comprehensive examination of task difficulties, focusing on convergence behavior and changes in relative entropy between consecutive probability distributions across timesteps. Our observational study reveals that denoising at earlier timesteps poses challenges characterized by slower convergence and higher relative entropy, indicating increased task difficulty at these lower timesteps. Building on these observations, we introduce an easy-to-hard learning scheme, drawing from curriculum learning, to enhance the training process of diffusion models. By organizing timesteps or noise levels into clusters and training models with descending orders of difficulty, we facilitate an order-aware training regime, progressing from easier to harder denoising tasks, thereby deviating from the conventional approach of training diffusion models simultaneously across all timesteps. Our approach leads to improved performance and faster convergence by leveraging the benefits of curriculum learning, while maintaining orthogonality with existing improvements in diffusion training techniques. We validate these advantages through comprehensive experiments in image generation tasks, including unconditional, class-conditional, and text-to-image generation.

Sparse learning models typically combine a smooth loss with a nonsmooth penalty, such as trace norm. Although recent developments in sparse approximation have offered promising solution methods, current approaches either apply only to matrix-norm constrained problems or provide suboptimal convergence rates. In this paper, we propose a boosting method for regularized learning that guarantees ɛ accuracy within O(1/ɛ) iterations. Performance is further accelerated by interlacing boosting with fixed-rank local optimization--exploiting a simpler local objective than previous work. The proposed method yields state-of-the-art performance on large-scale problems. We also demonstrate an application to latent multiview learning for which we provide the first efficient weak-oracle.

Kernel-based stochastic factorization (KBSF) is an algorithm for solving reinforcement learning tasks with continuous state spaces which builds a Markov decision process (MDP) based on a set of sample transitions. What sets KBSF apart from other kernel-based approaches is the fact that the size of its MDP is independent of the number of transitions, which makes it possible to control the trade-off between the quality of the resulting approximation and the associated computational cost. However, KBSF's memory usage grows linearly with the number of transitions, precluding its application in scenarios where a large amount of data must be processed. In this paper we show that it is possible to construct KBSF's MDP in a fully incremental way, thus freeing the space complexity of this algorithm from its dependence on the number of sample transitions. The incremental version of KBSF is able to process an arbitrary amount of data, which results in a model-based reinforcement learning algorithm that can be used to solve continuous MDPs in both off-line and on-line regimes. We present theoretical results showing that KBSF can approximate the value function that would be computed by conventional kernel-based learning with arbitrary precision. We empirically demonstrate the effectiveness of the proposed algorithm in the challenging threepole balancing task, in which the ability to process a large number of transitions is crucial for success.

Grasping complex computing concepts often poses a challenge for students who struggle to anchor these new ideas to familiar experiences and understandings. To help with this, a good analogy can bridge the gap between unfamiliar concepts and familiar ones, providing an engaging way to aid understanding. However, creating effective educational analogies is difficult even for experienced instructors. We investigate to what extent large language models (LLMs), specifically ChatGPT, can provide access to personally relevant analogies on demand. Focusing on recursion, a challenging threshold concept, we conducted an investigation analyzing the analogies generated by more than 350 first-year computing students. They were provided with a code snippet and tasked to generate their own recursion-based analogies using ChatGPT, optionally including personally relevant topics in their prompts. We observed a great deal of diversity in the analogies produced with student-prescribed topics, in contrast to the otherwise generic analogies, highlighting the value of student creativity when working with LLMs. Not only did students enjoy the activity and report an improved understanding of recursion, but they described more easily remembering analogies that were personally and culturally relevant.

We study online combinatorial decision problems, where one must make sequential decisions in some combinatorial space without knowing in advance the cost of decisions on each trial; the goal is to minimize the total regret over some sequence of trials relative to the best fixed decision in hindsight. Such problems have been studied mostly in settings where decisions are represented by Boolean vectors and costs are linear in this representation. Here we study a general setting where costs may be linear in any suitable low-dimensional vector representation of elements of the decision space. We give a general algorithm for such problems that we call low-dimensional online mirror descent (LDOMD); the algorithm generalizes both the Component Hedge algorithm of Koolen et al. (2010), and a recent algorithm of Suehiro et al. (2012). Our study offers a unification and generalization of previous work, and emphasizes the role of the convex polytope arising from the vector representation of the decision space; while Boolean representations lead to 0-1 polytopes, more general vector representations lead to more general polytopes. We study several examples of both types of polytopes. Finally, we demonstrate the benefit of having a general framework for such problems via an application to an online transportation problem; the associated transportation polytopes generalize the Birkhoff polytope of doubly stochastic matrices, and the resulting algorithm generalizes the PermELearn algorithm of Helmbold and Warmuth (2009).

To master a discipline such as algebra or physics, students must acquire a set of cognitive skills. Traditionally, educators and domain experts use intuition to determine what these skills are and then select practice exercises to hone a particular skill. We propose a technique that uses student performance data to automatically discover the skills needed in a discipline. The technique assigns a latent skill to each exercise such that a student's expected accuracy on a sequence of same-skill exercises improves monotonically with practice. Rather than discarding the skills identified by experts, our technique incorporates a nonparametric prior over the exerciseskill assignments that is based on the expert-provided skills and a weighted Chinese restaurant process.