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Stochastic partial differential equations have been used in a variety of contexts to model the evolution of uncertain dynamical systems. In recent years, their applications to geophysical fluid dynamics has increased massively. For a judicious usage in modelling fluid evolution, one needs to calibrate the amplitude of the noise to data. In this paper we address this requirement for the stochastic rotating shallow water (SRSW) model. This work is a continuation of [LvLCP23], where a data assimilation methodology has been introduced for the SRSW model. The noise used in [LvLCP23] was introduced as an arbitrary random phase shift in the Fourier space. This is not necessarily consistent with the uncertainty induced by a model reduction procedure. In this paper, we introduce a new method of noise calibration of the SRSW model which is compatible with the model reduction technique. The method is generic and can be applied to arbitrary stochastic parametrizations. It is also agnostic as to the source of data (real or synthetic). It is based on a principal component analysis technique to generate the eigenvectors and the eigenvalues of the covariance matrix of the stochastic parametrization. For SRSW model covered in this paper, we calibrate the noise by using the elevation variable of the model, as this is an observable easily obtainable in practical application, and use synthetic data as input for the calibration procedure.

Adversarial contrastive learning (ACL) does not require expensive data annotations but outputs a robust representation that withstands adversarial attacks and also generalizes to a wide range of downstream tasks. However, ACL needs tremendous running time to generate the adversarial variants of all training data, which limits its scalability to large datasets. To speed up ACL, this paper proposes a robustness-aware coreset selection (RCS) method. RCS does not require label information and searches for an informative subset that minimizes a representational divergence, which is the distance of the representation between natural data and their virtual adversarial variants. The vanilla solution of RCS via traversing all possible subsets is computationally prohibitive. Therefore, we theoretically transform RCS into a surrogate problem of submodular maximization, of which the greedy search is an efficient solution with an optimality guarantee for the original problem. Empirically, our comprehensive results corroborate that RCS can speed up ACL by a large margin without significantly hurting the robustness transferability. Notably, to the best of our knowledge, we are the first to conduct ACL efficiently on the large-scale ImageNet-1K dataset to obtain an effective robust representation via RCS.

Large language models (LLMs) have demonstrated remarkable zero-shot generalization abilities: state-of-the-art chatbots can provide plausible answers to many common questions that arise in daily life. However, so far, LLMs cannot reliably solve long-horizon planning problems. By contrast, classical planners, once a problem is given in a formatted way, can use efficient search algorithms to quickly identify correct, or even optimal, plans. In an effort to get the best of both worlds, this paper introduces LLM+P, the first framework that incorporates the strengths of classical planners into LLMs. LLM+P takes in a natural language description of a planning problem, then returns a correct (or optimal) plan for solving that problem in natural language. LLM+P does so by first converting the language description into a file written in the planning domain definition language (PDDL), then leveraging classical planners to quickly find a solution, and then translating the found solution back into natural language. Along with LLM+P, we define a diverse set of different benchmark problems taken from common planning scenarios. Via a comprehensive set of experiments on these benchmark problems, we find that LLM+P is able to provide optimal solutions for most problems, while LLMs fail to provide even feasible plans for most problems.\footnote{The code and results are publicly available at //github.com/Cranial-XIX/llm-pddl.git.

We present a neural network-based simulation super-resolution framework that can efficiently and realistically enhance a facial performance produced by a low-cost, realtime physics-based simulation to a level of detail that closely approximates that of a reference-quality off-line simulator with much higher resolution (26x element count in our examples) and accurate physical modeling. Our approach is rooted in our ability to construct - via simulation - a training set of paired frames, from the low- and high-resolution simulators respectively, that are in semantic correspondence with each other. We use face animation as an exemplar of such a simulation domain, where creating this semantic congruence is achieved by simply dialing in the same muscle actuation controls and skeletal pose in the two simulators. Our proposed neural network super-resolution framework generalizes from this training set to unseen expressions, compensates for modeling discrepancies between the two simulations due to limited resolution or cost-cutting approximations in the real-time variant, and does not require any semantic descriptors or parameters to be provided as input, other than the result of the real-time simulation. We evaluate the efficacy of our pipeline on a variety of expressive performances and provide comparisons and ablation experiments for plausible variations and alternatives to our proposed scheme.

Typical deep visual recognition models are capable of performing the one task they were trained on. In this paper, we tackle the extremely difficult problem of combining completely distinct models with different initializations, each solving a separate task, into one multi-task model without any additional training. Prior work in model merging permutes one model to the space of the other then adds them together. While this works for models trained on the same task, we find that this fails to account for the differences in models trained on disjoint tasks. Thus, we introduce "ZipIt!", a general method for merging two arbitrary models of the same architecture that incorporates two simple strategies. First, in order to account for features that aren't shared between models, we expand the model merging problem to additionally allow for merging features within each model by defining a general "zip" operation. Second, we add support for partially zipping the models up until a specified layer, naturally creating a multi-head model. We find that these two changes combined account for a staggering 20-60% improvement over prior work, making the merging of models trained on disjoint tasks feasible.

Agile quadrotor flight relies on rapidly planning and accurately tracking time-optimal trajectories, a technology critical to their application in the wild. However, the computational burden of computing time-optimal trajectories based on the full quadrotor dynamics (typically on the order of minutes or even hours) can hinder its ability to respond quickly to changing scenarios. Additionally, modeling errors and external disturbances can lead to deviations from the desired trajectory during tracking in real time. This letter proposes a novel approach to computing time-optimal trajectories, by fixing the nodes with waypoint constraints and adopting separate sampling intervals for trajectories between waypoints, which significantly accelerates trajectory planning. Furthermore, the planned paths are tracked via a time-adaptive model predictive control scheme whose allocated tracking time can be adaptively adjusted on-the-fly, therefore enhancing the tracking accuracy and robustness. We evaluate our approach through simulations and experimentally validate its performance in dynamic waypoint scenarios for time-optimal trajectory replanning and trajectory tracking.

In many board games and other abstract games, patterns have been used as features that can guide automated game-playing agents. Such patterns or features often represent particular configurations of pieces, empty positions, etc., which may be relevant for a game's strategies. Their use has been particularly prevalent in the game of Go, but also many other games used as benchmarks for AI research. In this paper, we formulate a design and efficient implementation of spatial state-action features for general games. These are patterns that can be trained to incentivise or disincentivise actions based on whether or not they match variables of the state in a local area around action variables. We provide extensive details on several design and implementation choices, with a primary focus on achieving a high degree of generality to support a wide variety of different games using different board geometries or other graphs. Secondly, we propose an efficient approach for evaluating active features for any given set of features. In this approach, we take inspiration from heuristics used in problems such as SAT to optimise the order in which parts of patterns are matched and prune unnecessary evaluations. This approach is defined for a highly general and abstract description of the problem -- phrased as optimising the order in which propositions of formulas in disjunctive normal form are evaluated -- and may therefore also be of interest to other types of problems than board games. An empirical evaluation on 33 distinct games in the Ludii general game system demonstrates the efficiency of this approach in comparison to a naive baseline, as well as a baseline based on prefix trees, and demonstrates that the additional efficiency significantly improves the playing strength of agents using the features to guide search.

The question of whether $Y$ can be predicted based on $X$ often arises and while a well adjusted model may perform well on observed data, the risk of overfitting always exists, leading to poor generalization error on unseen data. This paper proposes a rigorous permutation test to assess the credibility of high $R^2$ values in regression models, which can also be applied to any measure of goodness of fit, without the need for sample splitting, by generating new pairings of $(X_i, Y_j)$ and providing an overall interpretation of the model's accuracy. It introduces a new formulation of the null hypothesis and justification for the test, which distinguishes it from previous literature. The theoretical findings are applied to both simulated data and sensor data of tennis serves in an experimental context. The simulation study underscores how the available information affects the test, showing that the less informative the predictors, the lower the probability of rejecting the null hypothesis, and emphasizing that detecting weaker dependence between variables requires a sufficient sample size.

Image retrieval plays an important role in the Internet world. Usually, the core parts of mainstream visual retrieval systems include an online service of the embedding model and a large-scale vector database. For traditional model upgrades, the old model will not be replaced by the new one until the embeddings of all the images in the database are re-computed by the new model, which takes days or weeks for a large amount of data. Recently, backward-compatible training (BCT) enables the new model to be immediately deployed online by making the new embeddings directly comparable to the old ones. For BCT, improving the compatibility of two models with less negative impact on retrieval performance is the key challenge. In this paper, we introduce AdvBCT, an Adversarial Backward-Compatible Training method with an elastic boundary constraint that takes both compatibility and discrimination into consideration. We first employ adversarial learning to minimize the distribution disparity between embeddings of the new model and the old model. Meanwhile, we add an elastic boundary constraint during training to improve compatibility and discrimination efficiently. Extensive experiments on GLDv2, Revisited Oxford (ROxford), and Revisited Paris (RParis) demonstrate that our method outperforms other BCT methods on both compatibility and discrimination. The implementation of AdvBCT will be publicly available at //github.com/Ashespt/AdvBCT.

Data in many real-world applications are often accumulated over time, like a stream. In contrast to conventional machine learning studies that focus on learning from a given training data set, learning from data streams cannot ignore the fact that the incoming data stream can be potentially endless with overwhelming size and unknown changes, and it is impractical to assume to have sufficient computational/storage resource such that all received data can be handled in time. Thus, the generalization performance of learning from data streams depends not only on how many data have been received, but also on how many data can be well exploited timely, with resource and rapidity concerns, in addition to the ability of learning algorithm and complexity of the problem. For this purpose, in this article we introduce the notion of machine learning throughput, define Stream Efficient Learning and present a preliminary theoretical framework.