OpenRaiser/Intern-Atlas huggingface dataset:
The SO(3) and SE(3) Lie Algebras of Rigid Body Rotations and Motions and their Application to Discrete Integration, Gradient Descent Optimization, and State Estimation
Venue: arXiv cs.RO 2023
Year: 2023

Classical mathematical techniques such as discrete integration, gradient descent optimization, and state estimation (exemplified by the Runge-Kutta method, Gauss-Newton minimization, and extended Kalman filter or EKF, respectively), rely on linear algebra and hence are only applicable to state vectors belonging to Euclidean spaces when implemented as described in the literature. This document discusses how to modify these methods so they can be applied to non-Euclidean state vectors, such as those containing rotations and full motions of rigid bodies. To do so, this document provides an in-depth review of the concept of manifolds or Lie groups, together with their tangent spaces or Lie algebras, their exponential and logarithmic maps, the analysis of perturbations, the treatment of uncertainty and covariance, and in particular the definitions of the Jacobians required to employ the previously mentioned calculus methods. These concepts are particularized to the specific cases of the SO(3) and SE(3) Lie groups, known as the special orthogonal and special Euclidean groups of R3, which represent the rigid body rotations and motions, describing their various possible parameterizations as well as their advantages and disadvantages.
On-Demand Redundancy Grouping: Selectable Soft-Error Tolerance for a Multicore Cluster
Venue: arXiv cs.DC 2023
Year: 2023

With the shrinking of technology nodes and the use of parallel processor clusters in hostile and critical environments, such as space, run-time faults caused by radiation are a serious cross-cutting concern, also impacting architectural design. This paper introduces an architectural approach to run-time configurable soft-error tolerance at the core level, augmenting a six-core open-source RISC-V cluster with a novel On-Demand Redundancy Grouping (ODRG) scheme. ODRG allows the cluster to operate either as two fault-tolerant cores, or six individual cores for high-performance, with limited overhead to switch between these modes during run-time. The ODRG unit adds less than 11% of a core's area for a three-core group, or a total of 1% of the cluster area, and shows negligible timing increase, which compares favorably to a commercial state-of-the-art implementation, and is 2.5$\times$ faster in fault recovery re-synchronization. Furthermore, when redundancy is not necessary, the ODRG approach allows the redundant cores to be used for independent computation, allowing up to 2.96$\times$ increase in performance for selected applications.
Rethinking Fano's Inequality in Ensemble Learning
Venue: arXiv cs.LG 2023
Year: 2023

We propose a fundamental theory on ensemble learning that answers the central question: what factors make an ensemble system good or bad? Previous studies used a variant of Fano's inequality of information theory and derived a lower bound of the classification error rate on the basis of the $\textit{accuracy}$ and $\textit{diversity}$ of models. We revisit the original Fano's inequality and argue that the studies did not take into account the information lost when multiple model predictions are combined into a final prediction. To address this issue, we generalize the previous theory to incorporate the information loss, which we name $\textit{combination loss}$. Further, we empirically validate and demonstrate the proposed theory through extensive experiments on actual systems. The theory reveals the strengths and weaknesses of systems on each metric, which will push the theoretical understanding of ensemble learning and give us insights into designing systems.
All about unambiguous polynomial closure
Venue: arXiv cs.FL 2023
Year: 2023

We study a standard operator on classes of languages: unambiguous polynomial closure. We prove that for every class C of regular languages satisfying mild properties, the membership problem for its unambiguous polynomial closure UPol(C) reduces to the same problem for C. We also show that unambiguous polynomial closure coincides with alternating left and right deterministic closure. Moreover, we prove that if additionally C is finite, the separation and covering problems are decidable for UPol(C). Finally, we present an overview of the generic logical characterizations of the classes built using unambiguous polynomial closure.
Surround-view Fisheye Camera Perception for Automated Driving: Overview, Survey and Challenges
Venue: arXiv cs.CV 2023
Year: 2023

Surround-view fisheye cameras are commonly used for near-field sensing in automated driving. Four fisheye cameras on four sides of the vehicle are sufficient to cover 360° around the vehicle capturing the entire near-field region. Some primary use cases are automated parking, traffic jam assist, and urban driving. There are limited datasets and very little work on near-field perception tasks as the focus in automotive perception is on far-field perception. In contrast to far-field, surround-view perception poses additional challenges due to high precision object detection requirements of 10cm and partial visibility of objects. Due to the large radial distortion of fisheye cameras, standard algorithms cannot be extended easily to the surround-view use case. Thus, we are motivated to provide a self-contained reference for automotive fisheye camera perception for researchers and practitioners. Firstly, we provide a unified and taxonomic treatment of commonly used fisheye camera models. Secondly, we discuss various perception tasks and existing literature. Finally, we discuss the challenges and future direction.
Efficient Approximation of Gromov-Wasserstein Distance Using Importance Sparsification
Venue: arXiv cs.LG 2023
Year: 2023

As a valid metric of metric-measure spaces, Gromov-Wasserstein (GW) distance has shown the potential for matching problems of structured data like point clouds and graphs. However, its application in practice is limited due to the high computational complexity. To overcome this challenge, we propose a novel importance sparsification method, called \textsc{Spar-GW}, to approximate GW distance efficiently. In particular, instead of considering a dense coupling matrix, our method leverages a simple but effective sampling strategy to construct a sparse coupling matrix and update it with few computations. The proposed \textsc{Spar-GW} method is applicable to the GW distance with arbitrary ground cost, and it reduces the complexity from $O(n^4)$ to $O(n^{2+δ})$ for an arbitrary small $δ>0$. Theoretically, the convergence and consistency of the proposed estimation for GW distance are established under mild regularity conditions. In addition, this method can be extended to approximate the variants of GW distance, including the entropic GW distance, the fused GW distance, and the unbalanced GW distance. Experiments show the superiority of our \textsc{Spar-GW} to state-of-the-art methods in both synthetic and real-world tasks.
Transformer for Partial Differential Equations' Operator Learning
Venue: arXiv cs.LG 2023
Year: 2023

Data-driven learning of partial differential equations' solution operators has recently emerged as a promising paradigm for approximating the underlying solutions. The solution operators are usually parameterized by deep learning models that are built upon problem-specific inductive biases. An example is a convolutional or a graph neural network that exploits the local grid structure where functions' values are sampled. The attention mechanism, on the other hand, provides a flexible way to implicitly exploit the patterns within inputs, and furthermore, relationship between arbitrary query locations and inputs. In this work, we present an attention-based framework for data-driven operator learning, which we term Operator Transformer (OFormer). Our framework is built upon self-attention, cross-attention, and a set of point-wise multilayer perceptrons (MLPs), and thus it makes few assumptions on the sampling pattern of the input function or query locations. We show that the proposed framework is competitive on standard benchmark problems and can flexibly be adapted to randomly sampled input.
FedFormer: Contextual Federation with Attention in Reinforcement Learning
Venue: arXiv cs.LG 2023
Year: 2023

A core issue in multi-agent federated reinforcement learning is defining how to aggregate insights from multiple agents. This is commonly done by taking the average of each participating agent's model weights into one common model (FedAvg). We instead propose FedFormer, a novel federation strategy that utilizes Transformer Attention to contextually aggregate embeddings from models originating from different learner agents. In so doing, we attentively weigh the contributions of other agents with respect to the current agent's environment and learned relationships, thus providing a more effective and efficient federation. We evaluate our methods on the Meta-World environment and find that our approach yields significant improvements over FedAvg and non-federated Soft Actor-Critic single-agent methods. Our results compared to Soft Actor-Critic show that FedFormer achieves higher episodic return while still abiding by the privacy constraints of federated learning. Finally, we also demonstrate improvements in effectiveness with increased agent pools across all methods in certain tasks. This is contrasted by FedAvg, which fails to make noticeable improvements when scaled.
Deep Deconfounded Content-based Tag Recommendation for UGC with Causal Intervention
Venue: arXiv cs.IR 2023
Year: 2023

Traditional content-based tag recommender systems directly learn the association between user-generated content (UGC) and tags based on collected UGC-tag pairs. However, since a UGC uploader simultaneously creates the UGC and selects the corresponding tags, her personal preference inevitably biases the tag selections, which prevents these recommenders from learning the causal influence of UGCs' content features on tags. In this paper, we propose a deep deconfounded content-based tag recommender system, namely, DecTag, to address the above issues. We first establish a causal graph to represent the relations among uploader, UGC, and tag, where the uploaders are identified as confounders that spuriously correlate UGC and tag selections. Specifically, to eliminate the confounding bias, causal intervention is conducted on the UGC node in the graph via backdoor adjustment, where uploaders' influence on tags leaked through backdoor paths can be eliminated for causal effect estimation. Observing that adjusting the causal graph with do-calculus requires integrating the entire uploader space, which is infeasible, we design a novel Monte Carlo (MC)-based estimator with bootstrap, which can achieve asymptotic unbiasedness provided that uploaders for the collected UGCs are i.i.d. samples from the population. In addition, the MC estimator has the intuition of substituting the biased uploaders with a hypothetical random uploader from the population in the training phase, where deconfounding can be achieved in an interpretable manner. Finally, we establish a YT-8M-Causal dataset based on the widely used YouTube-8M dataset with causal intervention and propose an evaluation strategy accordingly to unbiasedly evaluate causal tag recommenders. Extensive experiments show that DecTag is more robust to confounding bias than state-of-the-art causal recommenders.
Stochastic Gradient Methods with Compressed Communication for Decentralized Saddle Point Problems
Venue: arXiv cs.LG 2023
Year: 2023

We develop two compression based stochastic gradient algorithms to solve a class of non-smooth strongly convex-strongly concave saddle-point problems in a decentralized setting (without a central server). Our first algorithm is a Restart-based Decentralized Proximal Stochastic Gradient method with Compression (C-RDPSG) for general stochastic settings. We provide rigorous theoretical guarantees of C-RDPSG with gradient computation complexity and communication complexity of order $\mathcal{O}( (1+δ)^4 \frac{1}{L^2}{κ_f^2}κ_g^2 \frac{1}ε )$, to achieve an $ε$-accurate saddle-point solution, where $δ$ denotes the compression factor, $κ_f$ and $κ_g$ denote respectively the condition numbers of objective function and communication graph, and $L$ denotes the smoothness parameter of the smooth part of the objective function. Next, we present a Decentralized Proximal Stochastic Variance Reduced Gradient algorithm with Compression (C-DPSVRG) for finite sum setting which exhibits gradient computation complexity and communication complexity of order $\mathcal{O} \left((1+δ) \max \{κ_f^2, \sqrtδκ^2_fκ_g,κ_g \} \log\left(\frac{1}ε\right) \right)$. Extensive numerical experiments show competitive performance of the proposed algorithms and provide support to the theoretical results obtained.
Task-Agnostic Continual Reinforcement Learning: Gaining Insights and Overcoming Challenges
Venue: arXiv cs.LG 2023
Year: 2023

Continual learning (CL) enables the development of models and agents that learn from a sequence of tasks while addressing the limitations of standard deep learning approaches, such as catastrophic forgetting. In this work, we investigate the factors that contribute to the performance differences between task-agnostic CL and multi-task (MTL) agents. We pose two hypotheses: (1) task-agnostic methods might provide advantages in settings with limited data, computation, or high dimensionality, and (2) faster adaptation may be particularly beneficial in continual learning settings, helping to mitigate the effects of catastrophic forgetting. To investigate these hypotheses, we introduce a replay-based recurrent reinforcement learning (3RL) methodology for task-agnostic CL agents. We assess 3RL on a synthetic task and the Meta-World benchmark, which includes 50 unique manipulation tasks. Our results demonstrate that 3RL outperforms baseline methods and can even surpass its multi-task equivalent in challenging settings with high dimensionality. We also show that the recurrent task-agnostic agent consistently outperforms or matches the performance of its transformer-based counterpart. These findings provide insights into the advantages of task-agnostic CL over task-aware MTL approaches and highlight the potential of task-agnostic methods in resource-constrained, high-dimensional, and multi-task environments.
An unsupervised, open-source workflow for 2D and 3D building mapping from airborne LiDAR data
Venue: arXiv cs.CV 2023
Year: 2023

Despite the substantial demand for high-quality, large-area building maps, no established open-source workflow for generating 2D and 3D maps currently exists. This study introduces an automated, open-source workflow for large-scale 2D and 3D building mapping utilizing airborne LiDAR data. Uniquely, our workflow operates entirely unsupervised, eliminating the need for any training procedures. We have integrated a specifically tailored DTM generation algorithm into our workflow to prevent errors in complex urban landscapes, especially around highways and overpasses. Through fine rasterization of LiDAR point clouds, we've enhanced building-tree differentiation, reduced errors near water bodies, and augmented computational efficiency by introducing a new planarity calculation. Our workflow offers a practical and scalable solution for the mass production of rasterized 2D and 3D building maps from raw airborne LiDAR data. Also, we elaborate on the influence of parameters and potential error sources to provide users with practical guidance. Our method's robustness has been rigorously optimized and tested using an extensive dataset (> 550 km$^2$), and further validated through comparison with deep learning-based and hand-digitized products. Notably, through these unparalleled, large-scale comparisons, we offer a valuable analysis of large-scale building maps generated via different methodologies, providing insightful evaluations of the effectiveness of each approach. We anticipate that our highly scalable building mapping workflow will facilitate the production of reliable 2D and 3D building maps, fostering advances in large-scale urban analysis. The code will be released upon publication.
Decoupling Knowledge from Memorization: Retrieval-augmented Prompt Learning
Venue: arXiv cs.CL 2023
Year: 2023

Prompt learning approaches have made waves in natural language processing by inducing better few-shot performance while they still follow a parametric-based learning paradigm; the oblivion and rote memorization problems in learning may encounter unstable generalization issues. Specifically, vanilla prompt learning may struggle to utilize atypical instances by rote during fully-supervised training or overfit shallow patterns with low-shot data. To alleviate such limitations, we develop RetroPrompt with the motivation of decoupling knowledge from memorization to help the model strike a balance between generalization and memorization. In contrast with vanilla prompt learning, RetroPrompt constructs an open-book knowledge-store from training instances and implements a retrieval mechanism during the process of input, training and inference, thus equipping the model with the ability to retrieve related contexts from the training corpus as cues for enhancement. Extensive experiments demonstrate that RetroPrompt can obtain better performance in both few-shot and zero-shot settings. Besides, we further illustrate that our proposed RetroPrompt can yield better generalization abilities with new datasets. Detailed analysis of memorization indeed reveals RetroPrompt can reduce the reliance of language models on memorization; thus, improving generalization for downstream tasks. Code is available in https://github.com/zjunlp/PromptKG/tree/main/research/RetroPrompt.
Stochastic Zeroth Order Gradient and Hessian Estimators: Variance Reduction and Refined Bias Bounds
Venue: arXiv cs.LG 2023
Year: 2023

We study stochastic zeroth order gradient and Hessian estimators for real-valued functions in $\mathbb{R}^n$. We show that, via taking finite difference along random orthogonal directions, the variance of the stochastic finite difference estimators can be significantly reduced. In particular, we design estimators for smooth functions such that, if one uses $ Θ\left( k \right) $ random directions sampled from the Stiefel's manifold $ \text{St} (n,k) $ and finite-difference granularity $δ$, the variance of the gradient estimator is bounded by $ \mathcal{O} \left( \left( \frac{n}{k} - 1 \right) + \left( \frac{n^2}{k} - n \right) δ^2 + \frac{ n^2 δ^4 }{ k } \right) $, and the variance of the Hessian estimator is bounded by $\mathcal{O} \left( \left( \frac{n^2}{k^2} - 1 \right) + \left( \frac{n^4}{k^2} - n^2 \right) δ^2 + \frac{n^4 δ^4 }{k^2} \right) $. When $k = n$, the variances become negligibly small. In addition, we provide improved bias bounds for the estimators. The bias of both gradient and Hessian estimators for smooth function $f$ is of order $\mathcal{O} \left( δ^2 Γ\right)$, where $δ$ is the finite-difference granularity, and $ Γ$ depends on high order derivatives of $f$. Our results are evidenced by empirical observations.
TaSIL: Taylor Series Imitation Learning
Venue: arXiv cs.LG 2023
Year: 2023

We propose Taylor Series Imitation Learning (TaSIL), a simple augmentation to standard behavior cloning losses in the context of continuous control. TaSIL penalizes deviations in the higher-order Taylor series terms between the learned and expert policies. We show that experts satisfying a notion of $\textit{incremental input-to-state stability}$ are easy to learn, in the sense that a small TaSIL-augmented imitation loss over expert trajectories guarantees a small imitation loss over trajectories generated by the learned policy. We provide sample-complexity bounds for TaSIL that scale as $\tilde{\mathcal{O}}(1/n)$ in the realizable setting, for $n$ the number of expert demonstrations. Finally, we demonstrate experimentally the relationship between the robustness of the expert policy and the order of Taylor expansion required in TaSIL, and compare standard Behavior Cloning, DART, and DAgger with TaSIL-loss-augmented variants. In all cases, we show significant improvement over baselines across a variety of MuJoCo tasks.
AdaProp: Learning Adaptive Propagation for Graph Neural Network based Knowledge Graph Reasoning
Venue: arXiv cs.LG 2023
Year: 2023

Due to the popularity of Graph Neural Networks (GNNs), various GNN-based methods have been designed to reason on knowledge graphs (KGs). An important design component of GNN-based KG reasoning methods is called the propagation path, which contains a set of involved entities in each propagation step. Existing methods use hand-designed propagation paths, ignoring the correlation between the entities and the query relation. In addition, the number of involved entities will explosively grow at larger propagation steps. In this work, we are motivated to learn an adaptive propagation path in order to filter out irrelevant entities while preserving promising targets. First, we design an incremental sampling mechanism where the nearby targets and layer-wise connections can be preserved with linear complexity. Second, we design a learning-based sampling distribution to identify the semantically related entities. Extensive experiments show that our method is powerful, efficient, and semantic-aware. The code is available at https://github.com/LARS-research/AdaProp.
coVariance Neural Networks
Venue: arXiv cs.LG 2023
Year: 2023

Graph neural networks (GNN) are an effective framework that exploit inter-relationships within graph-structured data for learning. Principal component analysis (PCA) involves the projection of data on the eigenspace of the covariance matrix and draws similarities with the graph convolutional filters in GNNs. Motivated by this observation, we study a GNN architecture, called coVariance neural network (VNN), that operates on sample covariance matrices as graphs. We theoretically establish the stability of VNNs to perturbations in the covariance matrix, thus, implying an advantage over standard PCA-based data analysis approaches that are prone to instability due to principal components associated with close eigenvalues. Our experiments on real-world datasets validate our theoretical results and show that VNN performance is indeed more stable than PCA-based statistical approaches. Moreover, our experiments on multi-resolution datasets also demonstrate that VNNs are amenable to transferability of performance over covariance matrices of different dimensions; a feature that is infeasible for PCA-based approaches.
Evaluating Robustness to Dataset Shift via Parametric Robustness Sets
Venue: arXiv cs.LG 2023
Year: 2023

We give a method for proactively identifying small, plausible shifts in distribution which lead to large differences in model performance. These shifts are defined via parametric changes in the causal mechanisms of observed variables, where constraints on parameters yield a "robustness set" of plausible distributions and a corresponding worst-case loss over the set. While the loss under an individual parametric shift can be estimated via reweighting techniques such as importance sampling, the resulting worst-case optimization problem is non-convex, and the estimate may suffer from large variance. For small shifts, however, we can construct a local second-order approximation to the loss under shift and cast the problem of finding a worst-case shift as a particular non-convex quadratic optimization problem, for which efficient algorithms are available. We demonstrate that this second-order approximation can be estimated directly for shifts in conditional exponential family models, and we bound the approximation error. We apply our approach to a computer vision task (classifying gender from images), revealing sensitivity to shifts in non-causal attributes.