Connected decision boundaries are useful in several tasks like image segmentation, clustering, alpha-shape or defining a region in nD-space. However, the machine learning literature lacks methods for generating connected decision boundaries using neural networks. Thresholding an invex function, a generalization of a convex function, generates such decision boundaries. This paper presents two methods for constructing invex functions using neural networks. The first approach is based on constraining a neural network with Gradient Clipped-Gradient Penality (GCGP), where we clip and penalise the gradients. In contrast, the second one is based on the relationship of the invex function to the composition of invertible and convex functions. We employ connectedness as a basic interpretation method and create connected region-based classifiers. We show that multiple connected set based classifiers can approximate any classification function. In the experiments section, we use our methods for classification tasks using an ensemble of 1-vs-all models as well as using a single multiclass model on small-scale datasets. The experiments show that connected set-based classifiers do not pose any disadvantage over ordinary neural network classifiers, but rather, enhance their interpretability. We also did an extensive study on the properties of invex function and connected sets for interpretability and network morphism with experiments on toy and real-world data sets. Our study suggests that invex function is fundamental to understanding and applying locality and connectedness of input space which is useful for various downstream tasks.
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Physicists routinely need probabilistic models for a number of tasks such as parameter inference or the generation of new realizations of a field. Establishing such models for highly non-Gaussian fields is a challenge, especially when the number of samples is limited. In this paper, we introduce scattering spectra models for stationary fields and we show that they provide accurate and robust statistical descriptions of a wide range of fields encountered in physics. These models are based on covariances of scattering coefficients, i.e. wavelet decomposition of a field coupled with a point-wise modulus. After introducing useful dimension reductions taking advantage of the regularity of a field under rotation and scaling, we validate these models on various multi-scale physical fields and demonstrate that they reproduce standard statistics, including spatial moments up to 4th order. These scattering spectra provide us with a low-dimensional structured representation that captures key properties encountered in a wide range of physical fields. These generic models can be used for data exploration, classification, parameter inference, symmetry detection, and component separation.
Heterogeneous functional data are commonly seen in time series and longitudinal data analysis. To capture the statistical structures of such data, we propose the framework of Functional Singular Value Decomposition (FSVD), a unified framework with structure-adaptive interpretability for the analysis of heterogeneous functional data. We establish the mathematical foundation of FSVD by proving its existence and providing its fundamental properties using operator theory. We then develop an implementation approach for noisy and irregularly observed functional data based on a novel joint kernel ridge regression scheme and provide theoretical guarantees for its convergence and estimation accuracy. The framework of FSVD also introduces the concepts of intrinsic basis functions and intrinsic basis vectors, which represent two fundamental statistical structures for random functions and connect FSVD to various tasks including functional principal component analysis, factor models, functional clustering, and functional completion. We compare the performance of FSVD with existing methods in several tasks through extensive simulation studies. To demonstrate the value of FSVD in real-world datasets, we apply it to extract temporal patterns from a COVID-19 case count dataset and perform data completion on an electronic health record dataset.
Diffusion Transformer (DiT), an emerging diffusion model for image generation, has demonstrated superior performance but suffers from substantial computational costs. Our investigations reveal that these costs stem from the static inference paradigm, which inevitably introduces redundant computation in certain diffusion timesteps and spatial regions. To address this inefficiency, we propose Dynamic Diffusion Transformer (DyDiT), an architecture that dynamically adjusts its computation along both timestep and spatial dimensions during generation. Specifically, we introduce a Timestep-wise Dynamic Width (TDW) approach that adapts model width conditioned on the generation timesteps. In addition, we design a Spatial-wise Dynamic Token (SDT) strategy to avoid redundant computation at unnecessary spatial locations. Extensive experiments on various datasets and different-sized models verify the superiority of DyDiT. Notably, with <3% additional fine-tuning iterations, our method reduces the FLOPs of DiT-XL by 51%, accelerates generation by 1.73, and achieves a competitive FID score of 2.07 on ImageNet. The code is publicly available at //github.com/NUS-HPC-AI-Lab/ Dynamic-Diffusion-Transformer.
The development of video large multimodal models (LMMs) has been hindered by the difficulty of curating large amounts of high-quality raw data from the web. To address this, we propose an alternative approach by creating a high-quality synthetic dataset specifically for video instruction-following, namely LLaVA-Video-178K. This dataset includes key tasks such as detailed captioning, open-ended question-answering (QA), and multiple-choice QA. By training on this dataset, in combination with existing visual instruction tuning data, we introduce LLaVA-Video, a new video LMM. Our experiments demonstrate that LLaVA-Video achieves strong performance across various video benchmarks, highlighting the effectiveness of our dataset. We plan to release the dataset, its generation pipeline, and the model checkpoints.
The total variation (TV) method is an image denoising technique that aims to reduce noise by minimizing the total variation of the image, which measures the variation in pixel intensities. The TV method has been widely applied in image processing and computer vision for its ability to preserve edges and enhance image quality. In this paper, we propose an improved TV model for image denoising and the associated numerical algorithm to carry out the procedure, which is particularly effective in removing several types of noises and their combinations. Our improved model admits a unique solution and the associated numerical algorithm guarantees the convergence. Numerical experiments are demonstrated to show improved effectiveness and denoising quality compared to other TV models. Such encouraging results further enhance the utility of the TV method in image processing.
Neural Processes (NPs) are deep probabilistic models that represent stochastic processes by conditioning their prior distributions on a set of context points. Despite their obvious advantages in uncertainty estimation for complex distributions, NPs enforce parameterization coupling between the conditional prior model and the posterior model, thereby risking introducing a misspecified prior distribution. We hereby revisit the NP objectives and propose R\'enyi Neural Processes (RNP) to ameliorate the impacts of prior misspecification by optimizing an alternative posterior that achieves better marginal likelihood. More specifically, by replacing the standard KL divergence with the R\'enyi divergence between the model posterior and the true posterior, we scale the density ratio $\frac{p}{q}$ by the power of (1-$\alpha$) in the divergence gradients with respect to the posterior. This hyper parameter $\alpha$ allows us to dampen the effects of the misspecified prior for the posterior update, which has been shown to effectively avoid oversmoothed predictions and improve the expressiveness of the posterior model. Our extensive experiments show consistent log-likelihood improvements over state-of-the-art NP family models which adopt both the variational inference or maximum likelihood estimation objectives. We validate the effectiveness of our approach across multiple benchmarks including regression and image inpainting tasks, and show significant performance improvements of RNPs in real-world regression problems where the underlying prior model is misspecifed.
We develop variational search distributions (VSD), a method for finding discrete, combinatorial designs of a rare desired class in a batch sequential manner with a fixed experimental budget. We formalize the requirements and desiderata for this problem and formulate a solution via variational inference. In particular, VSD uses off-the-shelf gradient based optimization routines, can learn powerful generative models for designs, and can take advantage of scalable predictive models. We derive asymptotic convergence rates for learning the true conditional generative distribution of designs with certain configurations of our method. After illustrating the generative model on images, we empirically demonstrate that VSD can outperform existing baseline methods on a set of real sequence-design problems in various biological systems.
Minimizing cross-entropy over the softmax scores of a linear map composed with a high-capacity encoder is arguably the most popular choice for training neural networks on supervised learning tasks. However, recent works show that one can directly optimize the encoder instead, to obtain equally (or even more) discriminative representations via a supervised variant of a contrastive objective. In this work, we address the question whether there are fundamental differences in the sought-for representation geometry in the output space of the encoder at minimal loss. Specifically, we prove, under mild assumptions, that both losses attain their minimum once the representations of each class collapse to the vertices of a regular simplex, inscribed in a hypersphere. We provide empirical evidence that this configuration is attained in practice and that reaching a close-to-optimal state typically indicates good generalization performance. Yet, the two losses show remarkably different optimization behavior. The number of iterations required to perfectly fit to data scales superlinearly with the amount of randomly flipped labels for the supervised contrastive loss. This is in contrast to the approximately linear scaling previously reported for networks trained with cross-entropy.
Knowledge graph (KG) embedding encodes the entities and relations from a KG into low-dimensional vector spaces to support various applications such as KG completion, question answering, and recommender systems. In real world, knowledge graphs (KGs) are dynamic and evolve over time with addition or deletion of triples. However, most existing models focus on embedding static KGs while neglecting dynamics. To adapt to the changes in a KG, these models need to be re-trained on the whole KG with a high time cost. In this paper, to tackle the aforementioned problem, we propose a new context-aware Dynamic Knowledge Graph Embedding (DKGE) method which supports the embedding learning in an online fashion. DKGE introduces two different representations (i.e., knowledge embedding and contextual element embedding) for each entity and each relation, in the joint modeling of entities and relations as well as their contexts, by employing two attentive graph convolutional networks, a gate strategy, and translation operations. This effectively helps limit the impacts of a KG update in certain regions, not in the entire graph, so that DKGE can rapidly acquire the updated KG embedding by a proposed online learning algorithm. Furthermore, DKGE can also learn KG embedding from scratch. Experiments on the tasks of link prediction and question answering in a dynamic environment demonstrate the effectiveness and efficiency of DKGE.
The dominant sequence transduction models are based on complex recurrent or convolutional neural networks in an encoder-decoder configuration. The best performing models also connect the encoder and decoder through an attention mechanism. We propose a new simple network architecture, the Transformer, based solely on attention mechanisms, dispensing with recurrence and convolutions entirely. Experiments on two machine translation tasks show these models to be superior in quality while being more parallelizable and requiring significantly less time to train. Our model achieves 28.4 BLEU on the WMT 2014 English-to-German translation task, improving over the existing best results, including ensembles by over 2 BLEU. On the WMT 2014 English-to-French translation task, our model establishes a new single-model state-of-the-art BLEU score of 41.8 after training for 3.5 days on eight GPUs, a small fraction of the training costs of the best models from the literature. We show that the Transformer generalizes well to other tasks by applying it successfully to English constituency parsing both with large and limited training data.
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