Deep learning models have been shown to outperform methods that rely on summary statistics, like the power spectrum, in extracting information from complex cosmological data sets. However, due to differences in the subgrid physics implementation and numerical approximations across different simulation suites, models trained on data from one cosmological simulation show a drop in performance when tested on another. Similarly, models trained on any of the simulations would also likely experience a drop in performance when applied to observational data. Training on data from two different suites of the CAMELS hydrodynamic cosmological simulations, we examine the generalization capabilities of Domain Adaptive Graph Neural Networks (DA-GNNs). By utilizing GNNs, we capitalize on their capacity to capture structured scale-free cosmological information from galaxy distributions. Moreover, by including unsupervised domain adaptation via Maximum Mean Discrepancy (MMD), we enable our models to extract domain-invariant features. We demonstrate that DA-GNN achieves higher accuracy and robustness on cross-dataset tasks (up to $28\%$ better relative error and up to almost an order of magnitude better $\chi^2$). Using data visualizations, we show the effects of domain adaptation on proper latent space data alignment. This shows that DA-GNNs are a promising method for extracting domain-independent cosmological information, a vital step toward robust deep learning for real cosmic survey data.
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The computation of correspondences between shapes is a principal task in shape analysis. To this end, methods based on partial differential equations (PDEs) have been established, encompassing e.g. the classic heat kernel signature as well as numerical solution schemes for geometric PDEs. In this work we focus on the latter approach. We consider here several time stepping schemes. The goal of this investigation is to assess, if one may identify a useful property of methods for time integration for the shape analysis context. Thereby we investigate the dependence on time step size, since the class of implicit schemes that are useful candidates in this context should ideally yield an invariant behaviour with respect to this parameter. To this end we study integration of heat and wave equation on a manifold. In order to facilitate this study, we propose an efficient, unified model order reduction framework for these models. We show that specific $l_0$ stable schemes are favourable for numerical shape analysis. We give an experimental evaluation of the methods at hand of classical TOSCA data sets.
Recent progress in self-supervised representation learning has resulted in models that are capable of extracting image features that are not only effective at encoding image level, but also pixel-level, semantics. These features have been shown to be effective for dense visual semantic correspondence estimation, even outperforming fully-supervised methods. Nevertheless, current self-supervised approaches still fail in the presence of challenging image characteristics such as symmetries and repeated parts. To address these limitations, we propose a new approach for semantic correspondence estimation that supplements discriminative self-supervised features with 3D understanding via a weak geometric spherical prior. Compared to more involved 3D pipelines, our model only requires weak viewpoint information, and the simplicity of our spherical representation enables us to inject informative geometric priors into the model during training. We propose a new evaluation metric that better accounts for repeated part and symmetry-induced mistakes. We present results on the challenging SPair-71k dataset, where we show that our approach demonstrates is capable of distinguishing between symmetric views and repeated parts across many object categories, and also demonstrate that we can generalize to unseen classes on the AwA dataset.
Achieving efficient and robust multi-channel data learning is a challenging task in data science. By exploiting low-rankness in the transformed domain, i.e., transformed low-rankness, tensor Singular Value Decomposition (t-SVD) has achieved extensive success in multi-channel data representation and has recently been extended to function representation such as Neural Networks with t-product layers (t-NNs). However, it still remains unclear how t-SVD theoretically affects the learning behavior of t-NNs. This paper is the first to answer this question by deriving the upper bounds of the generalization error of both standard and adversarially trained t-NNs. It reveals that the t-NNs compressed by exact transformed low-rank parameterization can achieve a sharper adversarial generalization bound. In practice, although t-NNs rarely have exactly transformed low-rank weights, our analysis further shows that by adversarial training with gradient flow (GF), the over-parameterized t-NNs with ReLU activations are trained with implicit regularization towards transformed low-rank parameterization under certain conditions. We also establish adversarial generalization bounds for t-NNs with approximately transformed low-rank weights. Our analysis indicates that the transformed low-rank parameterization can promisingly enhance robust generalization for t-NNs.
Graph federated learning (FL) has emerged as a pivotal paradigm enabling multiple agents to collaboratively train a graph model while preserving local data privacy. Yet, current efforts overlook a key issue: agents are self-interested and would hesitant to share data without fair and satisfactory incentives. This paper is the first endeavor to address this issue by studying the incentive mechanism for graph federated learning. We identify a unique phenomenon in graph federated learning: the presence of agents posing potential harm to the federation and agents contributing with delays. This stands in contrast to previous FL incentive mechanisms that assume all agents contribute positively and in a timely manner. In view of this, this paper presents a novel incentive mechanism tailored for fair graph federated learning, integrating incentives derived from both model gradient and payoff. To achieve this, we first introduce an agent valuation function aimed at quantifying agent contributions through the introduction of two criteria: gradient alignment and graph diversity. Moreover, due to the high heterogeneity in graph federated learning, striking a balance between accuracy and fairness becomes particularly crucial. We introduce motif prototypes to enhance accuracy, communicated between the server and agents, enhancing global model aggregation and aiding agents in local model optimization. Extensive experiments show that our model achieves the best trade-off between accuracy and the fairness of model gradient, as well as superior payoff fairness.
One potential drawback of using aggregated performance measurement in machine learning is that models may learn to accept higher errors on some training cases as compromises for lower errors on others, with the lower errors actually being instances of overfitting. This can lead to both stagnation at local optima and poor generalization. Lexicase selection is an uncompromising method developed in evolutionary computation, which selects models on the basis of sequences of individual training case errors instead of using aggregated metrics such as loss and accuracy. In this paper, we investigate how lexicase selection, in its general form, can be integrated into the context of deep learning to enhance generalization. We propose Gradient Lexicase Selection, an optimization framework that combines gradient descent and lexicase selection in an evolutionary fashion. Our experimental results demonstrate that the proposed method improves the generalization performance of various widely-used deep neural network architectures across three image classification benchmarks. Additionally, qualitative analysis suggests that our method assists networks in learning more diverse representations. Our source code is available on GitHub: //github.com/ld-ing/gradient-lexicase.
Recently, many mesh-based graph neural network (GNN) models have been proposed for modeling complex high-dimensional physical systems. Remarkable achievements have been made in significantly reducing the solving time compared to traditional numerical solvers. These methods are typically designed to i) reduce the computational cost in solving physical dynamics and/or ii) propose techniques to enhance the solution accuracy in fluid and rigid body dynamics. However, it remains under-explored whether they are effective in addressing the challenges of flexible body dynamics, where instantaneous collisions occur within a very short timeframe. In this paper, we present Hierarchical Contact Mesh Transformer (HCMT), which uses hierarchical mesh structures and can learn long-range dependencies (occurred by collisions) among spatially distant positions of a body -- two close positions in a higher-level mesh corresponds to two distant positions in a lower-level mesh. HCMT enables long-range interactions, and the hierarchical mesh structure quickly propagates collision effects to faraway positions. To this end, it consists of a contact mesh Transformer and a hierarchical mesh Transformer (CMT and HMT, respectively). Lastly, we propose a flexible body dynamics dataset, consisting of trajectories that reflect experimental settings frequently used in the display industry for product designs. We also compare the performance of several baselines using well-known benchmark datasets. Our results show that HCMT provides significant performance improvements over existing methods.
Contrastive learning models have achieved great success in unsupervised visual representation learning, which maximize the similarities between feature representations of different views of the same image, while minimize the similarities between feature representations of views of different images. In text summarization, the output summary is a shorter form of the input document and they have similar meanings. In this paper, we propose a contrastive learning model for supervised abstractive text summarization, where we view a document, its gold summary and its model generated summaries as different views of the same mean representation and maximize the similarities between them during training. We improve over a strong sequence-to-sequence text generation model (i.e., BART) on three different summarization datasets. Human evaluation also shows that our model achieves better faithfulness ratings compared to its counterpart without contrastive objectives.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
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.
Deep learning has yielded state-of-the-art performance on many natural language processing tasks including named entity recognition (NER). However, this typically requires large amounts of labeled data. In this work, we demonstrate that the amount of labeled training data can be drastically reduced when deep learning is combined with active learning. While active learning is sample-efficient, it can be computationally expensive since it requires iterative retraining. To speed this up, we introduce a lightweight architecture for NER, viz., the CNN-CNN-LSTM model consisting of convolutional character and word encoders and a long short term memory (LSTM) tag decoder. The model achieves nearly state-of-the-art performance on standard datasets for the task while being computationally much more efficient than best performing models. We carry out incremental active learning, during the training process, and are able to nearly match state-of-the-art performance with just 25\% of the original training data.
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