Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models. Gaussian processes (GPs) are particularly suited to this task as they can model complex, nonlinear phenomena whilst incorporating prior knowledge and quantifying uncertainty. Current approaches have found some success but are limited as they either achieve poor computational scalings or focus only on the temporal setting. This work addresses these issues by introducing a variational spatio-temporal state-space GP that handles linear and non-linear physical constraints while achieving efficient linear-in-time computation costs. We demonstrate our methods in a range of synthetic and real-world settings and outperform the current state-of-the-art in both predictive and computational performance.

Fairness-aware learning involves designing algorithms that do not discriminate with respect to some sensitive feature (e.g., race or gender). Existing work on the problem operates under the assumption that the sensitive feature available in one's training sample is perfectly reliable. This assumption may be violated in many real-world cases: for example, respondents to a survey may choose to conceal or obfuscate their group identity out of fear of potential discrimination. This poses the question of whether one can still learn fair classifiers given noisy sensitive features. In this paper, we answer the question in the affirmative: we show that if one measures fairness using the mean-difference score, and sensitive features are subject to noise from the mutually contaminated learning model, then owing to a simple identity we only need to change the desired fairness-tolerance. The requisite tolerance can be estimated by leveraging existing noise-rate estimators from the label noise literature. We finally show that our procedure is empirically effective on two case-studies involving sensitive feature censoring.

There has been exciting progress in generating images from natural language or layout conditions. However, these methods struggle to faithfully reproduce complex scenes due to the insufficient modeling of multiple objects and their relationships. To address this issue, we leverage the scene graph, a powerful structured representation, for complex image generation. Different from the previous works that directly use scene graphs for generation, we employ the generative capabilities of variational autoencoders and diffusion models in a generalizable manner, compositing diverse disentangled visual clues from scene graphs. Specifically, we first propose a Semantics-Layout Variational AutoEncoder (SL-VAE) to jointly derive (layouts, semantics) from the input scene graph, which allows a more diverse and reasonable generation in a one-to-many mapping. We then develop a Compositional Masked Attention (CMA) integrated with a diffusion model, incorporating (layouts, semantics) with fine-grained attributes as generation guidance. To further achieve graph manipulation while keeping the visual content consistent, we introduce a Multi-Layered Sampler (MLS) for an "isolated" image editing effect. Extensive experiments demonstrate that our method outperforms recent competitors based on text, layout, or scene graph, in terms of generation rationality and controllability.

Learning the intents of an agent, defined by its goals or motion style, is often extremely challenging from just a few examples. We refer to this problem as task concept learning and present our approach, Few-Shot Task Learning through Inverse Generative Modeling (FTL-IGM), which learns new task concepts by leveraging invertible neural generative models. The core idea is to pretrain a generative model on a set of basic concepts and their demonstrations. Then, given a few demonstrations of a new concept (such as a new goal or a new action), our method learns the underlying concepts through backpropagation without updating the model weights, thanks to the invertibility of the generative model. We evaluate our method in five domains - object rearrangement, goal-oriented navigation, motion caption of human actions, autonomous driving, and real-world table-top manipulation. Our experimental results demonstrate that via the pretrained generative model, we successfully learn novel concepts and generate agent plans or motion corresponding to these concepts in (1) unseen environments and (2) in composition with training concepts.

Understanding the principles of causal inference in the visual system has a long history at least since the seminal studies by Albert Michotte. Many cognitive and machine learning scientists believe that intelligent behavior requires agents to possess causal models of the world. Recent ML algorithms exploit the dependence structure of additive noise terms for inferring causal structures from observational data, e.g. to detect the direction of time series; the arrow of time. This raises the question whether the subtle asymmetries between the time directions can also be perceived by humans. Here we show that human observers can indeed discriminate forward and backward autoregressive motion with non-Gaussian additive independent noise, i.e. they appear sensitive to subtle asymmetries between the time directions. We employ a so-called frozen noise paradigm enabling us to compare human performance with four different algorithms on a trial-by-trial basis: A causal inference algorithm exploiting the dependence structure of additive noise terms, a neurally inspired network, a Bayesian ideal observer model as well as a simple heuristic. Our results suggest that all human observers use similar cues or strategies to solve the arrow of time motion discrimination task, but the human algorithm is significantly different from the three machine algorithms we compared it to. In fact, our simple heuristic appears most similar to our human observers.

Vision-language foundation models (such as CLIP) have recently shown their power in transfer learning, owing to large-scale image-text pre-training. However, target domain data in the downstream tasks can be highly different from the pre-training phase, which makes it hard for such a single model to generalize well. Alternatively, there exists a wide range of expert models that contain diversified vision and/or language knowledge pre-trained on different modalities, tasks, networks, and datasets. Unfortunately, these models are "isolated agents" with heterogeneous structures, and how to integrate their knowledge for generalizing CLIP-like models has not been fully explored. To bridge this gap, we propose a general and concise TransAgent framework, which transports the knowledge of the isolated agents in a unified manner, and effectively guides CLIP to generalize with multi-source knowledge distillation. With such a distinct framework, we flexibly collaborate with 11 heterogeneous agents to empower vision-language foundation models, without further cost in the inference phase. Finally, our TransAgent achieves stateof-the-art performance on 11 visual recognition datasets. Under the same low-shot setting, it outperforms the popular CoOp with around 10% on average, and 20% on EuroSAT which contains large domain shifts.

Pure exploration (aka active testing) is the fundamental task of sequentially gathering information to answer a query about a stochastic environment. Good algorithms make few mistakes and take few samples. Lower bounds (for multi-armed bandit models with arms in an exponential family) reveal that the sample complexity is determined by the solution to an optimisation problem. The existing state of the art algorithms achieve asymptotic optimality by solving a plug-in estimate of that optimisation problem at each step. We interpret the optimisation problem as an unknown game, and propose sampling rules based on iterative strategies to estimate and converge to its saddle point. We apply no-regret learners to obtain the first finite confidence guarantees that are adapted to the exponential family and which apply to any pure exploration query and bandit structure. Moreover, our algorithms only use a best response oracle instead of fully solving the optimisation problem.

"...Provide some evidence that the parameterizations relate to structural properties of failure graphs arising from real There are many application scenarios where our parameterizations are reasonable. "Analyze the complexity of these problems in the more common scenarios 1, 2, and 3. Do the problems remain NP-hard We will add a specific remark about the above into the final version. "the paper said that it would use a spade to mark statements with omitted proofs, but they were not actually marked with We apologize for this confusion. We will fix this in the final version. "It might be helpful to add a chart to the introduction, indicating the map from parameter to tractable/intractable" Thank you for this suggestion.

Diffusion Probabilistic Models (DPMs) have been recently utilized to deal with various blind image restoration (IR) tasks, where they have demonstrated outstanding performance in terms of perceptual quality. However, the task-specific nature of existing solutions and the excessive computational costs related to their training, make such models impractical and challenging to use for different IR tasks than those that were initially trained for. This hinders their wider adoption, especially by those who lack access to powerful computational resources and vast amount of training data. In this work we aim to address the above issues and enable the successful adoption of DPMs in practical IR-related applications. Towards this goal, we propose a modular diffusion probabilistic IR framework (DP-IR), which allows us to combine the performance benefits of existing pre-trained stateof-the-art IR networks and generative DPMs, while it requires only the additional training of a relatively small module (0.7M params) related to the particular IR task of interest. Moreover, the architecture of the proposed framework allows for a sampling strategy that leads to at least four times reduction of neural function evaluations without suffering any performance loss, while it can also be combined with existing acceleration techniques such as DDIM. We evaluate our model on four benchmarks for the tasks of burst JDD-SR, dynamic scene deblurring, and superresolution. Our method outperforms existing approaches in terms of perceptual quality while it retains a competitive performance with respect to fidelity metrics.

Recent advancements in Automatic Prompt Optimization (APO) for text-to-image generation have streamlined user input while ensuring high-quality image output. However, most APO methods are trained assuming a fixed text-to-image model, which is impractical given the emergence of new models. To address this, we propose a novel task, model-generalized automatic prompt optimization (MGAPO), which trains APO methods on a set of known models to enable generalization to unseen models during testing.