We propose a new metric for robot state estimation based on the recently introduced $\text{SE}_2(3)$ Lie group definition. Our metric is related to prior metrics for SLAM but explicitly takes into account the linear velocity of the state estimate, improving over current pose-based trajectory analysis. This has the benefit of providing a single, quantitative metric to evaluate state estimation algorithms against, while being compatible with existing tools and libraries. Since ground truth data generally consists of pose data from motion capture systems, we also propose an approach to compute the ground truth linear velocity based on polynomial interpolation. Using Chebyshev interpolation and a pseudospectral parameterization, we can accurately estimate the ground truth linear velocity of the trajectory in an optimal fashion with best approximation error. We demonstrate how this approach performs on multiple robotic platforms where accurate state estimation is vital, and compare it to alternative approaches such as finite differences. The pseudospectral parameterization also provides a means of trajectory data compression as an additional benefit. Experimental results show our method provides a valid and accurate means of comparing state estimation systems, which is also easy to interpret and report.
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Despite their sophisticated capabilities, large language models (LLMs) encounter a major hurdle in effective assessment. This paper first revisits the prevalent evaluation method-multiple choice question answering (MCQA), which allows for straightforward accuracy measurement. Through a comprehensive evaluation of 24 models across 11 benchmarks, we highlight several potential drawbacks of MCQA, for instance, the inconsistency between the MCQA evaluation and the generation of open-ended responses in practical scenarios. In response, we introduce an RWQ-Elo rating system, engaging 24 LLMs such as GPT-4, GPT-3.5, Google-Gemini-Pro and LLaMA-1/-2, in a two-player competitive format, with GPT-4 serving as the judge. Each LLM receives an Elo rating thereafter. This system is designed to mirror real-world usage, and for this purpose, we have compiled a new benchmark called ``Real-world questions'' (RWQ), comprising 20,772 authentic user inquiries. Additionally, we thoroughly analyze the characteristics of our system and compare it with prior leaderboards like AlpacaEval and MT-Bench. Our analysis reveals the stability of our RWQ-Elo system, the feasibility of registering new models, and its potential to reshape LLM leaderboards.
Conformalized Quantile Regression (CQR) is a recently proposed method for constructing prediction intervals for a response $Y$ given covariates $X$, without making distributional assumptions. However, existing constructions of CQR can be ineffective for problems where the quantile regressors perform better in certain parts of the feature space than others. The reason is that the prediction intervals of CQR do not distinguish between two forms of uncertainty: first, the variability of the conditional distribution of $Y$ given $X$ (i.e., aleatoric uncertainty), and second, our uncertainty in estimating this conditional distribution (i.e., epistemic uncertainty). This can lead to intervals that are overly narrow in regions where epistemic uncertainty is high. To address this, we propose a new variant of the CQR methodology, Uncertainty-Aware CQR (UACQR), that explicitly separates these two sources of uncertainty to adjust quantile regressors differentially across the feature space. Compared to CQR, our methods enjoy the same distribution-free theoretical coverage guarantees, while demonstrating in our experiments stronger conditional coverage properties in simulated settings and real-world data sets alike.
Semantic scene completion (SSC) aims to predict complete 3D voxel occupancy and semantics from a single-view RGB-D image, and recent SSC methods commonly adopt multi-modal inputs. However, our investigation reveals two limitations: ineffective feature learning from single modalities and overfitting to limited datasets. To address these issues, this paper proposes a novel SSC framework - Adversarial Modality Modulation Network (AMMNet) - with a fresh perspective of optimizing gradient updates. The proposed AMMNet introduces two core modules: a cross-modal modulation enabling the interdependence of gradient flows between modalities, and a customized adversarial training scheme leveraging dynamic gradient competition. Specifically, the cross-modal modulation adaptively re-calibrates the features to better excite representation potentials from each single modality. The adversarial training employs a minimax game of evolving gradients, with customized guidance to strengthen the generator's perception of visual fidelity from both geometric completeness and semantic correctness. Extensive experimental results demonstrate that AMMNet outperforms state-of-the-art SSC methods by a large margin, providing a promising direction for improving the effectiveness and generalization of SSC methods.
Research on generative models to produce human-aligned / human-preferred outputs has seen significant recent contributions. Between text and image-generative models, we narrowed our focus to text-based generative models, particularly to produce captions for images that align with human preferences. In this research, we explored a potential method to amplify the performance of the Deep Neural Network Model to generate captions that are preferred by humans. This was achieved by integrating Supervised Learning and Reinforcement Learning with Human Feedback (RLHF) using the Flickr8k dataset. Also, a novel loss function that is capable of optimizing the model based on human feedback is introduced. In this paper, we provide a concise sketch of our approach and results, hoping to contribute to the ongoing advances in the field of human-aligned generative AI models.
In the past few years, there has been an explosive surge in the use of machine learning (ML) techniques to address combinatorial optimization (CO) problems, especially mixed-integer linear programs (MILPs). Despite the achievements, the limited availability of real-world instances often leads to sub-optimal decisions and biased solver assessments, which motivates a suite of synthetic MILP instance generation techniques. However, existing methods either rely heavily on expert-designed formulations or struggle to capture the rich features of real-world instances. To tackle this problem, we propose G2MILP, the first deep generative framework for MILP instances. Specifically, G2MILP represents MILP instances as bipartite graphs, and applies a masked variational autoencoder to iteratively corrupt and replace parts of the original graphs to generate new ones. The appealing feature of G2MILP is that it can learn to generate novel and realistic MILP instances without prior expert-designed formulations, while preserving the structures and computational hardness of real-world datasets, simultaneously. Thus the generated instances can facilitate downstream tasks for enhancing MILP solvers under limited data availability. We design a suite of benchmarks to evaluate the quality of the generated MILP instances. Experiments demonstrate that our method can produce instances that closely resemble real-world datasets in terms of both structures and computational hardness. The deliverables are released at //miralab-ustc.github.io/L2O-G2MILP.
We present the general forms of piece-wise functions on partitioned domains satisfying an intrinsic $C^0$ or $C^1$ continuity across the sub-domain boundaries. These general forms are constructed based on a strategy stemming from the theory of functional connections, and we refer to partitioned domains endowed with these general forms as functionally connected elements (FCE). We further present a method, incorporating functionally connected elements and a least squares collocation approach, for solving boundary and initial value problems. This method exhibits a spectral-like accuracy, with the free functions involved in the FCE form represented by polynomial bases or by non-polynomial bases of quasi-random sinusoidal functions. The FCE method offers a unique advantage over traditional element-based methods for boundary value problems involving relative boundary conditions. A number of linear and nonlinear numerical examples in one and two dimensions are presented to demonstrate the performance of the FCE method developed herein.
We propose a new method for cloth digitalization. Deviating from existing methods which learn from data captured under relatively casual settings, we propose to learn from data captured in strictly tested measuring protocols, and find plausible physical parameters of the cloths. However, such data is currently absent, so we first propose a new dataset with accurate cloth measurements. Further, the data size is considerably smaller than the ones in current deep learning, due to the nature of the data capture process. To learn from small data, we propose a new Bayesian differentiable cloth model to estimate the complex material heterogeneity of real cloths. It can provide highly accurate digitalization from very limited data samples. Through exhaustive evaluation and comparison, we show our method is accurate in cloth digitalization, efficient in learning from limited data samples, and general in capturing material variations. Code and data are available //github.com/realcrane/Bayesian-Differentiable-Physics-for-Cloth-Digitalization
Recent advances in machine learning have significantly impacted the field of information extraction, with Large Language Models (LLMs) playing a pivotal role in extracting structured information from unstructured text. This paper explores the challenges and limitations of current methodologies in structured entity extraction and introduces a novel approach to address these issues. We contribute to the field by first introducing and formalizing the task of Structured Entity Extraction (SEE), followed by proposing Approximate Entity Set OverlaP (AESOP) Metric designed to appropriately assess model performance on this task. Later, we propose a new model that harnesses the power of LLMs for enhanced effectiveness and efficiency through decomposing the entire extraction task into multiple stages. Quantitative evaluation and human side-by-side evaluation confirm that our model outperforms baselines, offering promising directions for future advancements in structured entity extraction.
We consider the differentially private (DP) facility location problem in the so called super-set output setting proposed by Gupta et al. [SODA 2010]. The current best known expected approximation ratio for an $\epsilon$-DP algorithm is $O\left(\frac{\log n}{\sqrt{\epsilon}}\right)$ due to Cohen-Addad et al. [AISTATS 2022] where $n$ denote the size of the metric space, meanwhile the best known lower bound is $\Omega(1/\sqrt{\epsilon})$ [NeurIPS 2019]. In this short note, we give a lower bound of $\tilde{\Omega}\left(\min\left\{\log n, \sqrt{\frac{\log n}{\epsilon}}\right\}\right)$ on the expected approximation ratio of any $\epsilon$-DP algorithm, which is the first evidence that the approximation ratio has to grow with the size of the metric space.
Graph Neural Networks (GNN) is an emerging field for learning on non-Euclidean data. Recently, there has been increased interest in designing GNN that scales to large graphs. Most existing methods use "graph sampling" or "layer-wise sampling" techniques to reduce training time. However, these methods still suffer from degrading performance and scalability problems when applying to graphs with billions of edges. This paper presents GBP, a scalable GNN that utilizes a localized bidirectional propagation process from both the feature vectors and the training/testing nodes. Theoretical analysis shows that GBP is the first method that achieves sub-linear time complexity for both the precomputation and the training phases. An extensive empirical study demonstrates that GBP achieves state-of-the-art performance with significantly less training/testing time. Most notably, GBP can deliver superior performance on a graph with over 60 million nodes and 1.8 billion edges in less than half an hour on a single machine.
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