Traditionally, robots are regarded as universal motion generation machines. They are designed mainly by kinematics considerations while the desired dynamics is imposed by strong actuators and high-rate control loops. As an alternative, one can first consider the robot's intrinsic dynamics and optimize it in accordance with the desired tasks. Therefore, one needs to better understand intrinsic, uncontrolled dynamics of robotic systems. In this paper we focus on periodic orbits, as fundamental dynamic properties with many practical applications. Algebraic topology and differential geometry provide some fundamental statements about existence of periodic orbits. As an example, we present periodic orbits of the simplest multi-body system: the double-pendulum in gravity. This simple system already displays a rich variety of periodic orbits. We classify these into three classes: toroidal orbits, disk orbits and nonlinear normal modes. Some of these we found by geometrical insights and some by numerical simulation and sampling.
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The multimedia community has shown a significant interest in perceiving and representing the physical world with multimodal pretrained neural network models, and among them, the visual-language pertaining (VLP) is, currently, the most captivating topic. However, there have been few endeavors dedicated to the exploration of 1) whether essential linguistic knowledge (e.g., semantics and syntax) can be extracted during VLP, and 2) how such linguistic knowledge impact or enhance the multimodal alignment. In response, here we aim to elucidate the impact of comprehensive linguistic knowledge, including semantic expression and syntactic structure, on multimodal alignment. Specifically, we design and release the SNARE, the first large-scale multimodal alignment probing benchmark, to detect the vital linguistic components, e.g., lexical, semantic, and syntax knowledge, containing four tasks: Semantic structure, Negation logic, Attribute ownership, and Relationship composition. Based on our proposed probing benchmarks, our holistic analyses of five advanced VLP models illustrate that the VLP model: i) shows insensitivity towards complex syntax structures and relies on content words for sentence comprehension; ii) demonstrates limited comprehension of combinations between sentences and negations; iii) faces challenges in determining the presence of actions or spatial relationships within visual information and struggles with verifying the correctness of triple combinations. We make our benchmark and code available at \url{//github.com/WangFei-2019/SNARE/}.
Although the open source model bears many advantages in software development, open source projects are always hard to sustain. Previous research on open source sustainability mainly focuses on projects that have already reached a certain level of maturity (e.g., with communities, releases, and downstream projects). However, limited attention is paid to the development of (sustainable) open source projects in their infancy, and we believe an understanding of early sustainability determinants is crucial for project initiators, incubators, newcomers, and users. In this paper, we aim to explore the relationship between early participation factors and long-term project sustainability. We leverage a novel methodology that measures the early participation of 290,255 GitHub projects during the first three months with reference to the Blumberg model, trains an XGBoost model to predict project's two-year sustained activity, and interprets the trained model using LIME. We quantitatively show that early participants have a positive effect on project's future sustained activity if they have prior experience in OSS project incubation and demonstrate concentrated focus and steady commitment. Participation from non-code contributors and detailed contribution documentation also promote project's sustained activity. Compared with individual projects, building a community that consists of more experienced core developers and more active peripheral developers is important for organizational projects. This study provides unique insights into the incubation and recognition of sustainable open source projects, and our interpretable prediction approach can also offer guidance to open source project initiators and newcomers.
Out-of-distribution (OOD) detection plays a vital role in enhancing the reliability of machine learning (ML) models. The emergence of large language models (LLMs) has catalyzed a paradigm shift within the ML community, showcasing their exceptional capabilities across diverse natural language processing tasks. While existing research has probed OOD detection with relative small-scale Transformers like BERT, RoBERTa and GPT-2, the stark differences in scales, pre-training objectives, and inference paradigms call into question the applicability of these findings to LLMs. This paper embarks on a pioneering empirical investigation of OOD detection in the domain of LLMs, focusing on LLaMA series ranging from 7B to 65B in size. We thoroughly evaluate commonly-used OOD detectors, scrutinizing their performance in both zero-grad and fine-tuning scenarios. Notably, we alter previous discriminative in-distribution fine-tuning into generative fine-tuning, aligning the pre-training objective of LLMs with downstream tasks. Our findings unveil that a simple cosine distance OOD detector demonstrates superior efficacy, outperforming other OOD detectors. We provide an intriguing explanation for this phenomenon by highlighting the isotropic nature of the embedding spaces of LLMs, which distinctly contrasts with the anisotropic property observed in smaller BERT family models. The new insight enhances our understanding of how LLMs detect OOD data, thereby enhancing their adaptability and reliability in dynamic environments.
Large language models (LLMs) and generative AI have played a transformative role in computer research and applications. Controversy has arisen as to whether these models output copyrighted data, which can occur if the data the models are trained on is copyrighted. LLMs are built on the transformer neural network architecture, which in turn relies on a mathematical computation called Attention that uses the softmax function. In this paper, we show that large language model training and optimization can be seen as a softmax regression problem. We then establish a method of efficiently performing softmax regression, in a way that prevents the regression function from generating copyright data. This establishes a theoretical method of training large language models in a way that avoids generating copyright data.
Soft robotics is an emergent and swiftly evolving field. Pneumatic actuators are suitable for driving soft robots because of their superior performance. However, their control is not easy due to their hysteresis characteristics. In response to these challenges, we propose an adaptive control method to compensate hysteresis of a soft actuator. Employing a novel dual pneumatic artificial muscle (PAM) bending actuator, the innovative control strategy abates hysteresis effects by dynamically modulating gains within a traditional PID controller corresponding with the predicted motion of the reference trajectory. Through comparative experimental evaluation, we found that the new control method outperforms its conventional counterparts regarding tracking accuracy and response speed. Our work reveals a new direction for advancing control in soft actuators.
Graph generation poses a significant challenge as it involves predicting a complete graph with multiple nodes and edges based on simply a given label. This task also carries fundamental importance to numerous real-world applications, including de-novo drug and molecular design. In recent years, several successful methods have emerged in the field of graph generation. However, these approaches suffer from two significant shortcomings: (1) the underlying Graph Neural Network (GNN) architectures used in these methods are often underexplored; and (2) these methods are often evaluated on only a limited number of metrics. To fill this gap, we investigate the expressiveness of GNNs under the context of the molecular graph generation task, by replacing the underlying GNNs of graph generative models with more expressive GNNs. Specifically, we analyse the performance of six GNNs in two different generative frameworks (GCPN and GraphAF), on six different molecular generative objectives on the ZINC-250k dataset. Through our extensive experiments, we demonstrate that advanced GNNs can indeed improve the performance of GCPN and GraphAF on molecular generation tasks, but GNN expressiveness is not a necessary condition for a good GNN-based generative model. Moreover, we show that GCPN and GraphAF with advanced GNNs can achieve state-of-the-art results across 17 other non-GNN-based graph generative approaches, such as variational autoencoders and Bayesian optimisation models, on the proposed molecular generative objectives (DRD2, Median1, Median2), which are important metrics for de-novo molecular design.
Focus on Large Language Model based agents should involve more than "human-centered" alignment or application. We argue that more attention should be paid to the agent itself and discuss the potential of social sciences for agents.
Graph Neural Networks (GNNs) have demonstrated superior performance on various graph learning tasks, including recommendation, where they leverage user-item collaborative filtering signals in graphs. However, theoretical formulations of their capability are scarce, despite their empirical effectiveness in state-of-the-art recommender models. Recently, research has explored the expressiveness of GNNs in general, demonstrating that message passing GNNs are at most as powerful as the Weisfeiler-Lehman test, and that GNNs combined with random node initialization are universal. Nevertheless, the concept of "expressiveness" for GNNs remains vaguely defined. Most existing works adopt the graph isomorphism test as the metric of expressiveness, but this graph-level task may not effectively assess a model's ability in recommendation, where the objective is to distinguish nodes of different closeness. In this paper, we provide a comprehensive theoretical analysis of the expressiveness of GNNs in recommendation, considering three levels of expressiveness metrics: graph isomorphism (graph-level), node automorphism (node-level), and topological closeness (link-level). We propose the topological closeness metric to evaluate GNNs' ability to capture the structural distance between nodes, which aligns closely with the objective of recommendation. To validate the effectiveness of this new metric in evaluating recommendation performance, we introduce a learning-less GNN algorithm that is optimal on the new metric and can be optimal on the node-level metric with suitable modification. We conduct extensive experiments comparing the proposed algorithm against various types of state-of-the-art GNN models to explore the explainability of the new metric in the recommendation task. For reproducibility, implementation codes are available at //github.com/HKUDS/GTE.
Non-convex optimization is ubiquitous in modern machine learning. Researchers devise non-convex objective functions and optimize them using off-the-shelf optimizers such as stochastic gradient descent and its variants, which leverage the local geometry and update iteratively. Even though solving non-convex functions is NP-hard in the worst case, the optimization quality in practice is often not an issue -- optimizers are largely believed to find approximate global minima. Researchers hypothesize a unified explanation for this intriguing phenomenon: most of the local minima of the practically-used objectives are approximately global minima. We rigorously formalize it for concrete instances of machine learning problems.
Compared with cheap addition operation, multiplication operation is of much higher computation complexity. The widely-used convolutions in deep neural networks are exactly cross-correlation to measure the similarity between input feature and convolution filters, which involves massive multiplications between float values. In this paper, we present adder networks (AdderNets) to trade these massive multiplications in deep neural networks, especially convolutional neural networks (CNNs), for much cheaper additions to reduce computation costs. In AdderNets, we take the $\ell_1$-norm distance between filters and input feature as the output response. The influence of this new similarity measure on the optimization of neural network have been thoroughly analyzed. To achieve a better performance, we develop a special back-propagation approach for AdderNets by investigating the full-precision gradient. We then propose an adaptive learning rate strategy to enhance the training procedure of AdderNets according to the magnitude of each neuron's gradient. As a result, the proposed AdderNets can achieve 74.9% Top-1 accuracy 91.7% Top-5 accuracy using ResNet-50 on the ImageNet dataset without any multiplication in convolution layer.
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