Recent diffusion probabilistic models (DPM) in the field of pansharpening have been gradually gaining attention and have achieved state-of-the-art (SOTA) performance. In this paper, we identify shortcomings in directly applying DPMs to the task of pansharpening as an inverse problem: 1) initiating sampling directly from Gaussian noise neglects the low-resolution multispectral image (LRMS) as a prior; 2) low sampling efficiency often necessitates a higher number of sampling steps. We first reformulate pansharpening into the stochastic differential equation (SDE) form of an inverse problem. Building upon this, we propose a Schr\"odinger bridge matching method that addresses both issues. We design an efficient deep neural network architecture tailored for the proposed SB matching. In comparison to the well-established DL-regressive-based framework and the recent DPM framework, our method demonstrates SOTA performance with fewer sampling steps. Moreover, we discuss the relationship between SB matching and other methods based on SDEs and ordinary differential equations (ODEs), as well as its connection with optimal transport. Code will be available.
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Estimators of doubly robust functionals typically rely on estimating two complex nuisance functions, such as the propensity score and conditional outcome mean for the average treatment effect functional. We consider the problem of how to estimate nuisance functions to obtain optimal rates of convergence for a doubly robust nonparametric functional that has witnessed applications across the causal inference and conditional independence testing literature. For several plug-in type estimators and a one-step type estimator, we illustrate the interplay between different tuning parameter choices for the nuisance function estimators and sample splitting strategies on the optimal rate of estimating the functional of interest. For each of these estimators and each sample splitting strategy, we show the necessity to undersmooth the nuisance function estimators under low regularity conditions to obtain optimal rates of convergence for the functional of interest. By performing suitable nuisance function tuning and sample splitting strategies, we show that some of these estimators can achieve minimax rates of convergence in all H\"older smoothness classes of the nuisance functions.
High dimensional expanders (HDXs) are a hypergraph generalization of expander graphs. They are extensively studied in the math and TCS communities due to their many applications. Like expander graphs, HDXs are especially interesting for applications when they are bounded degree, namely, if the number of edges adjacent to every vertex is bounded. However, only a handful of constructions are known to have this property, all of which rely on non-trivial algebraic techniques. In particular, no random or combinatorial construction of bounded degree HDXs is known. As a result, our understanding of these objects is limited. The degree of an $i$-face in an HDX is the number of $(i+1)$-faces containing it. In this work we construct HDXs whose higher dimensional faces have bounded degree. This is done by giving an elementary and deterministic algorithm that takes as input a regular $k$-dimensional HDX $X$ and outputs another $k$-dimensional HDX $\widehat{X}$ with twice as many vertices. While the degree of vertices in $\widehat{X}$ grows, the degree of the $(k-1)$-faces in $\widehat{X}$ stays the same. As a result, we obtain a new `algebra-free' construction of HDXs whose $(k-1)$-face degree is bounded. Our algorithm is based on a simple and natural generalization of the construction by Bilu and Linial (Combinatorica, 2006), which build expanders using lifts coming from edge signings. Our construction is based on local lifts of HDXs, where a local lift is a complex whose top-level links are lifts of links in the original complex. We demonstrate that a local lift of an HDX is an HDX in many cases. In addition, combining local lifts with existing bounded degree constructions creates new families of bounded degree HDXs with significantly different links than before. We use this technique to construct bounded degree high dimensional expanders with links that have arbitrarily large diameters.
Utilitarian algorithm configuration is a general-purpose technique for automatically searching the parameter space of a given algorithm to optimize its performance, as measured by a given utility function, on a given set of inputs. Recently introduced utilitarian configuration procedures offer optimality guarantees about the returned parameterization while provably adapting to the hardness of the underlying problem. However, the applicability of these approaches is severely limited by the fact that they only search a finite, relatively small set of parameters. They cannot effectively search the configuration space of algorithms with continuous or uncountable parameters. In this paper we introduce a new procedure, which we dub COUP (Continuous, Optimistic Utilitarian Procrastination). COUP is designed to search infinite parameter spaces efficiently to find good configurations quickly. Furthermore, COUP maintains the theoretical benefits of previous utilitarian configuration procedures when applied to finite parameter spaces but is significantly faster, both provably and experimentally.
Dataset condensation can be used to reduce the computational cost of training multiple models on a large dataset by condensing the training dataset into a small synthetic set. State-of-the-art approaches rely on matching the model gradients between the real and synthetic data. However, there is no theoretical guarantee of the generalizability of the condensed data: data condensation often generalizes poorly across hyperparameters/architectures in practice. This paper considers a different condensation objective specifically geared toward hyperparameter search. We aim to generate a synthetic validation dataset so that the validation-performance rankings of the models, with different hyperparameters, on the condensed and original datasets are comparable. We propose a novel hyperparameter-calibrated dataset condensation (HCDC) algorithm, which obtains the synthetic validation dataset by matching the hyperparameter gradients computed via implicit differentiation and efficient inverse Hessian approximation. Experiments demonstrate that the proposed framework effectively maintains the validation-performance rankings of models and speeds up hyperparameter/architecture search for tasks on both images and graphs.
Humans perceive the world by concurrently processing and fusing high-dimensional inputs from multiple modalities such as vision and audio. Machine perception models, in stark contrast, are typically modality-specific and optimised for unimodal benchmarks, and hence late-stage fusion of final representations or predictions from each modality (`late-fusion') is still a dominant paradigm for multimodal video classification. Instead, we introduce a novel transformer based architecture that uses `fusion bottlenecks' for modality fusion at multiple layers. Compared to traditional pairwise self-attention, our model forces information between different modalities to pass through a small number of bottleneck latents, requiring the model to collate and condense the most relevant information in each modality and only share what is necessary. We find that such a strategy improves fusion performance, at the same time reducing computational cost. We conduct thorough ablation studies, and achieve state-of-the-art results on multiple audio-visual classification benchmarks including Audioset, Epic-Kitchens and VGGSound. All code and models will be released.
Behaviors of the synthetic characters in current military simulations are limited since they are generally generated by rule-based and reactive computational models with minimal intelligence. Such computational models cannot adapt to reflect the experience of the characters, resulting in brittle intelligence for even the most effective behavior models devised via costly and labor-intensive processes. Observation-based behavior model adaptation that leverages machine learning and the experience of synthetic entities in combination with appropriate prior knowledge can address the issues in the existing computational behavior models to create a better training experience in military training simulations. In this paper, we introduce a framework that aims to create autonomous synthetic characters that can perform coherent sequences of believable behavior while being aware of human trainees and their needs within a training simulation. This framework brings together three mutually complementary components. The first component is a Unity-based simulation environment - Rapid Integration and Development Environment (RIDE) - supporting One World Terrain (OWT) models and capable of running and supporting machine learning experiments. The second is Shiva, a novel multi-agent reinforcement and imitation learning framework that can interface with a variety of simulation environments, and that can additionally utilize a variety of learning algorithms. The final component is the Sigma Cognitive Architecture that will augment the behavior models with symbolic and probabilistic reasoning capabilities. We have successfully created proof-of-concept behavior models leveraging this framework on realistic terrain as an essential step towards bringing machine learning into military simulations.
Embedding entities and relations into a continuous multi-dimensional vector space have become the dominant method for knowledge graph embedding in representation learning. However, most existing models ignore to represent hierarchical knowledge, such as the similarities and dissimilarities of entities in one domain. We proposed to learn a Domain Representations over existing knowledge graph embedding models, such that entities that have similar attributes are organized into the same domain. Such hierarchical knowledge of domains can give further evidence in link prediction. Experimental results show that domain embeddings give a significant improvement over the most recent state-of-art baseline knowledge graph embedding models.
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.
Embedding models for deterministic Knowledge Graphs (KG) have been extensively studied, with the purpose of capturing latent semantic relations between entities and incorporating the structured knowledge into machine learning. However, there are many KGs that model uncertain knowledge, which typically model the inherent uncertainty of relations facts with a confidence score, and embedding such uncertain knowledge represents an unresolved challenge. The capturing of uncertain knowledge will benefit many knowledge-driven applications such as question answering and semantic search by providing more natural characterization of the knowledge. In this paper, we propose a novel uncertain KG embedding model UKGE, which aims to preserve both structural and uncertainty information of relation facts in the embedding space. Unlike previous models that characterize relation facts with binary classification techniques, UKGE learns embeddings according to the confidence scores of uncertain relation facts. To further enhance the precision of UKGE, we also introduce probabilistic soft logic to infer confidence scores for unseen relation facts during training. We propose and evaluate two variants of UKGE based on different learning objectives. Experiments are conducted on three real-world uncertain KGs via three tasks, i.e. confidence prediction, relation fact ranking, and relation fact classification. UKGE shows effectiveness in capturing uncertain knowledge by achieving promising results on these tasks, and consistently outperforms baselines on these tasks.
We advocate the use of implicit fields for learning generative models of shapes and introduce an implicit field decoder for shape generation, aimed at improving the visual quality of the generated shapes. An implicit field assigns a value to each point in 3D space, so that a shape can be extracted as an iso-surface. Our implicit field decoder is trained to perform this assignment by means of a binary classifier. Specifically, it takes a point coordinate, along with a feature vector encoding a shape, and outputs a value which indicates whether the point is outside the shape or not. By replacing conventional decoders by our decoder for representation learning and generative modeling of shapes, we demonstrate superior results for tasks such as shape autoencoding, generation, interpolation, and single-view 3D reconstruction, particularly in terms of visual quality.
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