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Recent works in dimensionality reduction for regression tasks have introduced the notion of sensitivity, an estimate of the importance of a specific datapoint in a dataset, offering provable guarantees on the quality of the approximation after removing low-sensitivity datapoints via subsampling. However, fast algorithms for approximating $\ell_p$ sensitivities, which we show is equivalent to approximate $\ell_p$ regression, are known for only the $\ell_2$ setting, in which they are termed leverage scores. In this work, we provide efficient algorithms for approximating $\ell_p$ sensitivities and related summary statistics of a given matrix. In particular, for a given $n \times d$ matrix, we compute $\alpha$-approximation to its $\ell_1$ sensitivities at the cost of $O(n/\alpha)$ sensitivity computations. For estimating the total $\ell_p$ sensitivity (i.e. the sum of $\ell_p$ sensitivities), we provide an algorithm based on importance sampling of $\ell_p$ Lewis weights, which computes a constant factor approximation to the total sensitivity at the cost of roughly $O(\sqrt{d})$ sensitivity computations. Furthermore, we estimate the maximum $\ell_1$ sensitivity, up to a $\sqrt{d}$ factor, using $O(d)$ sensitivity computations. We generalize all these results to $\ell_p$ norms for $p > 1$. Lastly, we experimentally show that for a wide class of matrices in real-world datasets, the total sensitivity can be quickly approximated and is significantly smaller than the theoretical prediction, demonstrating that real-world datasets have low intrinsic effective dimensionality.

The potential of Martian lava tubes for resource extraction and habitat sheltering highlights the need for robots capable to undertake the grueling task of their exploration. Driven by this motivation, in this work we introduce a legged robot system optimized for jumping in the low gravity of Mars, designed with leg configurations adaptable to both bipedal and quadrupedal systems. This design utilizes torque-controlled actuators coupled with springs for high-power jumping, robust locomotion, and an energy-efficient resting pose. Key design features include a 5-bar mechanism as leg concept, combined with springs connected by a high-strength cord. The selected 5-bar link lengths and spring stiffness were optimized for maximizing the jump height in Martian gravity and realized as a robot leg. Two such legs combined with a compact body allowed jump testing of a bipedal prototype. The robot is 0.472 m tall and weighs 7.9 kg. Jump testing with significant safety margins resulted in a measured jump height of 1.141 m in Earth's gravity, while a total of 4 jumping experiments are presented. Simulations utilizing the full motor torque and kinematic limits of the design resulted in a maximum possible jump height of 1.52 m in Earth's gravity and 3.63 m in Mars' gravity, highlighting the versatility of jumping as a form of locomotion and overcoming obstacles in lower gravity.

With the increasing computing power, using data-driven approaches to co-design a robot's morphology and controller has become a promising way. However, most existing data-driven methods require training the controller for each morphology to calculate fitness, which is time-consuming. In contrast, the dual-network framework utilizes data collected by individual networks under a specific morphology to train a population network that provides a surrogate function for morphology optimization. This approach replaces the traditional evaluation of a diverse set of candidates, thereby speeding up the training. Despite considerable results, the online training of both networks impedes their performance. To address this issue, we propose a concurrent network framework that combines online and offline reinforcement learning (RL) methods. By leveraging the behavior cloning term in a flexible manner, we achieve an effective combination of both networks. We conducted multiple sets of comparative experiments in the simulator and found that the proposed method effectively addresses issues present in the dual-network framework, leading to overall algorithmic performance improvement. Furthermore, we validated the algorithm on a real robot, demonstrating its feasibility in a practical application.

The utilization of performance monitoring probes is a valuable tool for programmers to gather performance data. However, the manual insertion of these probes can result in an increase in code size, code obfuscation, and an added burden of learning different APIs associated with performance monitoring tools. To mitigate these issues, EDPM, an embedded domain-specific language, was developed to provide a higher level of abstraction for annotating regions of code that require instrumentation in C and C++ programs. This paper presents the design and implementation of EDPM and compares it to the well-known tool PAPI, in terms of required lines of code, flexibility in configuring regions, and performance overhead. The results of this study demonstrate that EDPM is a low-resolution profiling tool that offers a reduction in required lines of code and enables programmers to express various configurations of regions. Furthermore, the design of EDPM is such that its pragmas are ignored by the standard compiler, allowing for seamless integration into existing software processes without disrupting build systems or increasing the size of the executable. Additionally, the design of the EDPM pre-compiler allows for the extension of available performance counters while maintaining a high level of abstraction for programmers. Therefore, EDPM offers a promising solution to simplify and optimize performance monitoring in C and C++ programs.

We propose EB-TC$\varepsilon$, a novel sampling rule for $\varepsilon$-best arm identification in stochastic bandits. It is the first instance of Top Two algorithm analyzed for approximate best arm identification. EB-TC$\varepsilon$ is an *anytime* sampling rule that can therefore be employed without modification for fixed confidence or fixed budget identification (without prior knowledge of the budget). We provide three types of theoretical guarantees for EB-TC$\varepsilon$. First, we prove bounds on its expected sample complexity in the fixed confidence setting, notably showing its asymptotic optimality in combination with an adaptive tuning of its exploration parameter. We complement these findings with upper bounds on its probability of error at any time and for any error parameter, which further yield upper bounds on its simple regret at any time. Finally, we show through numerical simulations that EB-TC$\varepsilon$ performs favorably compared to existing algorithms, in different settings.

We develop a flexible online version of the permutation test. This allows us to test exchangeability as the data is arriving, where we can choose to stop or continue without invalidating the size of the test. Our methods generalize beyond exchangeability to other forms of invariance under a compact group. Our approach relies on constructing an $e$-process that is the running product of multiple conditional $e$-values. To construct $e$-values, we first develop an essentially complete class of admissible $e$-values in which one can flexibly `plug in' almost any desired test statistic. To make the $e$-values conditional, we explore the intersection between the concepts of conditional invariance and sequential invariance, and find that the appropriate conditional distribution can be captured by a compact subgroup. To find powerful $e$-values for given alternatives, we develop the theory of likelihood ratios for testing group invariance yielding new optimality results for group invariance tests. These statistics turn out to exist in three different flavors, depending on the space on which we specify our alternative. We apply these statistics to test against a Gaussian location shift, which yields connections to the $t$-test when testing sphericity, connections to the softmax function and its temperature when testing exchangeability, and yields an improved version of a known $e$-value for testing sign-symmetry. Moreover, we introduce an impatience parameter that allows users to obtain more power now in exchange for less power in the long run.

While current NL2SQL tasks constructed using Foundation Models have achieved commendable results, their direct application to Natural Language to Graph Query Language (NL2GQL) tasks poses challenges due to the significant differences between GQL and SQL expressions, as well as the numerous types of GQL. Our extensive experiments reveal that in NL2GQL tasks, larger Foundation Models demonstrate superior cross-schema generalization abilities, while smaller Foundation Models struggle to improve their GQL generation capabilities through fine-tuning. However, after fine-tuning, smaller models exhibit better intent comprehension and higher grammatical accuracy. Diverging from rule-based and slot-filling techniques, we introduce R3-NL2GQL, which employs both smaller and larger Foundation Models as reranker, rewriter and refiner. The approach harnesses the comprehension ability of smaller models for information reranker and rewriter, and the exceptional generalization and generation capabilities of larger models to transform input natural language queries and code structure schema into any form of GQLs. Recognizing the lack of established datasets in this nascent domain, we have created a bilingual dataset derived from graph database documentation and some open-source Knowledge Graphs (KGs). We tested our approach on this dataset and the experimental results showed that delivers promising performance and robustness.Our code and dataset is available at //github.com/zhiqix/NL2GQL

Foundation models pretrained on diverse data at scale have demonstrated extraordinary capabilities in a wide range of vision and language tasks. When such models are deployed in real world environments, they inevitably interface with other entities and agents. For example, language models are often used to interact with human beings through dialogue, and visual perception models are used to autonomously navigate neighborhood streets. In response to these developments, new paradigms are emerging for training foundation models to interact with other agents and perform long-term reasoning. These paradigms leverage the existence of ever-larger datasets curated for multimodal, multitask, and generalist interaction. Research at the intersection of foundation models and decision making holds tremendous promise for creating powerful new systems that can interact effectively across a diverse range of applications such as dialogue, autonomous driving, healthcare, education, and robotics. In this manuscript, we examine the scope of foundation models for decision making, and provide conceptual tools and technical background for understanding the problem space and exploring new research directions. We review recent approaches that ground foundation models in practical decision making applications through a variety of methods such as prompting, conditional generative modeling, planning, optimal control, and reinforcement learning, and discuss common challenges and open problems in the field.

Click-through rate (CTR) prediction plays a critical role in recommender systems and online advertising. The data used in these applications are multi-field categorical data, where each feature belongs to one field. Field information is proved to be important and there are several works considering fields in their models. In this paper, we proposed a novel approach to model the field information effectively and efficiently. The proposed approach is a direct improvement of FwFM, and is named as Field-matrixed Factorization Machines (FmFM, or $FM^2$). We also proposed a new explanation of FM and FwFM within the FmFM framework, and compared it with the FFM. Besides pruning the cross terms, our model supports field-specific variable dimensions of embedding vectors, which acts as soft pruning. We also proposed an efficient way to minimize the dimension while keeping the model performance. The FmFM model can also be optimized further by caching the intermediate vectors, and it only takes thousands of floating-point operations (FLOPs) to make a prediction. Our experiment results show that it can out-perform the FFM, which is more complex. The FmFM model's performance is also comparable to DNN models which require much more FLOPs in runtime.

Image segmentation is considered to be one of the critical tasks in hyperspectral remote sensing image processing. Recently, convolutional neural network (CNN) has established itself as a powerful model in segmentation and classification by demonstrating excellent performances. The use of a graphical model such as a conditional random field (CRF) contributes further in capturing contextual information and thus improving the segmentation performance. In this paper, we propose a method to segment hyperspectral images by considering both spectral and spatial information via a combined framework consisting of CNN and CRF. We use multiple spectral cubes to learn deep features using CNN, and then formulate deep CRF with CNN-based unary and pairwise potential functions to effectively extract the semantic correlations between patches consisting of three-dimensional data cubes. Effective piecewise training is applied in order to avoid the computationally expensive iterative CRF inference. Furthermore, we introduce a deep deconvolution network that improves the segmentation masks. We also introduce a new dataset and experimented our proposed method on it along with several widely adopted benchmark datasets to evaluate the effectiveness of our method. By comparing our results with those from several state-of-the-art models, we show the promising potential of our method.