In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex multimodal and correlated posteriors in high-dimensional spaces. Our approach introduces novel bounds for approximate inference using implicit distributions by locally linearising the neural sampler. This is distinct from existing methods that rely on additional discriminator networks and unstable adversarial objectives. Furthermore, we present a new sampler architecture that, for the first time, enables implicit distributions over tens of millions of latent variables, addressing computational concerns by using differentiable numerical approximations. We empirically show that our method is capable of recovering correlations across layers in large Bayesian neural networks, a property that is crucial for a network's performance but notoriously challenging to achieve. To the best of our knowledge, no other method has been shown to accomplish this task for such large models. Through experiments in downstream tasks, we demonstrate that our expressive posteriors outperform state-of-the-art uncertainty quantification methods, validating the effectiveness of our training algorithm and the quality of the learned implicit approximation.
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This manuscript enriches the framework of continuous normalizing flows (CNFs) within causal inference, primarily to augment the geometric properties of parametric submodels used in targeted maximum likelihood estimation (TMLE). By introducing an innovative application of CNFs, we construct a refined series of parametric submodels that enable a directed interpolation between the prior distribution $p_0$ and the empirical distribution $p_1$. This proposed methodology serves to optimize the semiparametric efficiency bound in causal inference by orchestrating CNFs to align with Wasserstein gradient flows. Our approach not only endeavors to minimize the mean squared error in the estimation but also imbues the estimators with geometric sophistication, thereby enhancing robustness against misspecification. This robustness is crucial, as it alleviates the dependence on the standard $n^{\frac{1}{4}}$ rate for a doubly-robust perturbation direction in TMLE. By incorporating robust optimization principles and differential geometry into the estimators, the developed geometry-aware CNFs represent a significant advancement in the pursuit of doubly robust causal inference.
Recently, 3D generative models have made impressive progress, enabling the generation of almost arbitrary 3D assets from text or image inputs. However, these approaches generate objects in isolation without any consideration for the scene where they will eventually be placed. In this paper, we propose a framework that allows for the stylization of an existing 3D asset to fit into a given 2D scene, and additionally produce a photorealistic composition as if the asset was placed within the environment. This not only opens up a new level of control for object stylization, for example, the same assets can be stylized to reflect changes in the environment, such as summer to winter or fantasy versus futuristic settings-but also makes the object-scene composition more controllable. We achieve this by combining modeling and optimizing the object's texture and environmental lighting through differentiable ray tracing with image priors from pre-trained text-to-image diffusion models. We demonstrate that our method is applicable to a wide variety of indoor and outdoor scenes and arbitrary objects.
Model counting, a fundamental task in computer science, involves determining the number of satisfying assignments to a Boolean formula, typically represented in conjunctive normal form (CNF). While model counting for CNF formulas has received extensive attention with a broad range of applications, the study of model counting for Pseudo-Boolean (PB) formulas has been relatively overlooked. Pseudo-Boolean formulas, being more succinct than propositional Boolean formulas, offer greater flexibility in representing real-world problems. Consequently, there is a crucial need to investigate efficient techniques for model counting for PB formulas. In this work, we propose the first exact Pseudo-Boolean model counter, PBCount, that relies on knowledge compilation approach via algebraic decision diagrams. Our extensive empirical evaluation shows that PBCount can compute counts for 1513 instances while the current state-of-the-art approach could only handle 1013 instances. Our work opens up several avenues for future work in the context of model counting for PB formulas, such as the development of preprocessing techniques and exploration of approaches other than knowledge compilation.
Image captioning requires numerous annotated image-text pairs, resulting in substantial annotation costs. Recently, large models (e.g. diffusion models and large language models) have excelled in producing high-quality images and text. This potential can be harnessed to create synthetic image-text pairs for training captioning models. Synthetic data can improve cost and time efficiency in data collection, allow for customization to specific domains, bootstrap generalization capability for zero-shot performance, and circumvent privacy concerns associated with real-world data. However, existing methods struggle to attain satisfactory performance solely through synthetic data. We identify the issue as generated images from simple descriptions mostly capture a solitary perspective with limited context, failing to align with the intricate scenes prevalent in real-world imagery. To tackle this, we present an innovative pipeline that introduces multi-context data generation. Beginning with an initial text corpus, our approach employs a large language model to extract multiple sentences portraying the same scene from diverse viewpoints. These sentences are then condensed into a single sentence with multiple contexts. Subsequently, we generate intricate images using the condensed captions through diffusion models. Our model is exclusively trained on synthetic image-text pairs crafted through this process. The effectiveness of our pipeline is validated through experimental results in both the in-domain and cross-domain settings, where it achieves state-of-the-art performance on well-known datasets such as MSCOCO, Flickr30k, and NoCaps.
In turbulence modeling, we are concerned with finding closure models that represent the effect of the subgrid scales on the resolved scales. Recent approaches gravitate towards machine learning techniques to construct such models. However, the stability of machine-learned closure models and their abidance by physical structure (e.g. symmetries, conservation laws) are still open problems. To tackle both issues, we take the `discretize first, filter next' approach. In this approach we apply a spatial averaging filter to existing fine-grid discretizations. The main novelty is that we introduce an additional set of equations which dynamically model the energy of the subgrid scales. Having an estimate of the energy of the subgrid scales, we can use the concept of energy conservation to derive stability. The subgrid energy containing variables are determined via a data-driven technique. The closure model is used to model the interaction between the filtered quantities and the subgrid energy. Therefore the total energy should be conserved. Abiding by this conservation law yields guaranteed stability of the system. In this work, we propose a novel skew-symmetric convolutional neural network architecture that satisfies this law. The result is that stability is guaranteed, independent of the weights and biases of the network. Importantly, as our framework allows for energy exchange between resolved and subgrid scales it can model backscatter. To model dissipative systems (e.g. viscous flows), the framework is extended with a diffusive component. The introduced neural network architecture is constructed such that it also satisfies momentum conservation. We apply the new methodology to both the viscous Burgers' equation and the Korteweg-De Vries equation in 1D. The novel architecture displays superior stability properties when compared to a vanilla convolutional neural network.
With the wide application of machine translation, the testing of Machine Translation Systems (MTSs) has attracted much attention. Recent works apply Metamorphic Testing (MT) to address the oracle problem in MTS testing. Existing MT methods for MTS generally follow the workflow of input transformation and output relation comparison, which generates a follow-up input sentence by mutating the source input and compares the source and follow-up output translations to detect translation errors, respectively. These methods use various input transformations to generate test case pairs and have successfully triggered numerous translation errors. However, they have limitations in performing fine-grained and rigorous output relation comparison and thus may report false alarms and miss true errors. In this paper, we propose a word closure-based output comparison method to address the limitations of the existing MTS MT methods. Specifically, we first build a new comparison unit called word closure, where each closure includes a group of correlated input and output words in the test case pair. Word closures suggest the linkages between the appropriate fragment in the source output translation and its counterpart in the follow-up output for comparison. Next, we compare the semantics on the level of word closure to identify the translation errors. In this way, we perform a fine-grained and rigorous semantic comparison for the outputs and thus realize more effective violation identification. We evaluate our method with the test cases generated by five existing input transformations and translation outputs from three popular MTSs. Results show that our method significantly outperforms the existing works in violation identification by improving the precision and recall and achieving an average increase of 29.8% in F1 score. It also helps to increase the F1 score of translation error localization by 35.9%.
High-dimensional datasets often contain multiple meaningful clusterings in different subspaces. For example, objects can be clustered either by color, weight, or size, revealing different interpretations of the given dataset. A variety of approaches are able to identify such non-redundant clusterings. However, most of these methods require the user to specify the expected number of subspaces and clusters for each subspace. Stating these values is a non-trivial problem and usually requires detailed knowledge of the input dataset. In this paper, we propose a framework that utilizes the Minimum Description Length Principle (MDL) to detect the number of subspaces and clusters per subspace automatically. We describe an efficient procedure that greedily searches the parameter space by splitting and merging subspaces and clusters within subspaces. Additionally, an encoding strategy is introduced that allows us to detect outliers in each subspace. Extensive experiments show that our approach is highly competitive to state-of-the-art methods.
We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several extensions to derive practical training objectives. These include infinite-dimensional versions of Girsanov theorem, in order to be able to compute an ELBO, and of the sampling theorem, in order to guarantee that functional evaluations in a countable set of points are equivalent to infinite-dimensional functions. We use FDPs to build a new breed of generative models in function spaces, which do not require specialized network architectures, and that can work with any kind of continuous data. Our results on real data show that FDPs achieve high-quality image generation, using a simple MLP architecture with orders of magnitude fewer parameters than existing diffusion models.
The most successful multi-domain text classification (MDTC) approaches employ the shared-private paradigm to facilitate the enhancement of domain-invariant features through domain-specific attributes. Additionally, they employ adversarial training to align marginal feature distributions. Nevertheless, these methodologies encounter two primary challenges: (1) Neglecting class-aware information during adversarial alignment poses a risk of misalignment; (2) The limited availability of labeled data across multiple domains fails to ensure adequate discriminative capacity for the model. To tackle these issues, we propose a method called Regularized Conditional Alignment (RCA) to align the joint distributions of domains and classes, thus matching features within the same category and amplifying the discriminative qualities of acquired features. Moreover, we employ entropy minimization and virtual adversarial training to constrain the uncertainty of predictions pertaining to unlabeled data and enhance the model's robustness. Empirical results on two benchmark datasets demonstrate that our RCA approach outperforms state-of-the-art MDTC techniques.
Stochastic programs where the uncertainty distribution must be inferred from noisy data samples are considered. The stochastic programs are approximated with distributionally-robust optimizations that minimize the worst-case expected cost over ambiguity sets, i.e., sets of distributions that are sufficiently compatible with the observed data. In this paper, the ambiguity sets capture the set of probability distributions whose convolution with the noise distribution remains within a ball centered at the empirical noisy distribution of data samples parameterized by the total variation distance. Using the prescribed ambiguity set, the solutions of the distributionally-robust optimizations converge to the solutions of the original stochastic programs when the numbers of the data samples grow to infinity. Therefore, the proposed distributionally-robust optimization problems are asymptotically consistent. This is proved under the assumption that the distribution of the noise is uniformly diagonally dominant. More importantly, the distributionally-robust optimization problems can be cast as tractable convex optimization problems and are therefore amenable to large-scale stochastic problems.
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