The problems of Lasso regression and optimal design of experiments share a critical property: their optimal solutions are typically \emph{sparse}, i.e., only a small fraction of the optimal variables are non-zero. Therefore, the identification of the support of an optimal solution reduces the dimensionality of the problem and can yield a substantial simplification of the calculations. It has recently been shown that linear regression with a \emph{squared} $\ell_1$-norm sparsity-inducing penalty is equivalent to an optimal experimental design problem. In this work, we use this equivalence to derive safe screening rules that can be used to discard inessential samples. Compared to previously existing rules, the new tests are much faster to compute, especially for problems involving a parameter space of high dimension, and can be used dynamically within any iterative solver, with negligible computational overhead. Moreover, we show how an existing homotopy algorithm to compute the regularization path of the lasso method can be reparametrized with respect to the squared $\ell_1$-penalty. This allows the computation of a Bayes $c$-optimal design in a finite number of steps and can be several orders of magnitude faster than standard first-order algorithms. The efficiency of the new screening rules and of the homotopy algorithm are demonstrated on different examples based on real data.
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Previously, non-autoregressive models were widely perceived as being superior in generation efficiency but inferior in generation quality due to the difficulties of modeling multiple target modalities. To enhance the multi-modality modeling ability, we propose the diffusion glancing transformer, which employs a modality diffusion process and residual glancing sampling. The modality diffusion process is a discrete process that interpolates the multi-modal distribution along the decoding steps, and the residual glancing sampling approach guides the model to continuously learn the remaining modalities across the layers. Experimental results on various machine translation and text generation benchmarks demonstrate that DIFFGLAT achieves better generation accuracy while maintaining fast decoding speed compared with both autoregressive and non-autoregressive models.
We prove an inverse approximation theorem for the approximation of nonlinear sequence-to-sequence relationships using recurrent neural networks (RNNs). This is a so-called Bernstein-type result in approximation theory, which deduces properties of a target function under the assumption that it can be effectively approximated by a hypothesis space. In particular, we show that nonlinear sequence relationships that can be stably approximated by nonlinear RNNs must have an exponential decaying memory structure - a notion that can be made precise. This extends the previously identified curse of memory in linear RNNs into the general nonlinear setting, and quantifies the essential limitations of the RNN architecture for learning sequential relationships with long-term memory. Based on the analysis, we propose a principled reparameterization method to overcome the limitations. Our theoretical results are confirmed by numerical experiments. The code has been released in //github.com/radarFudan/Curse-of-memory
Snapshot compressive spectral imaging reconstruction aims to reconstruct three-dimensional spatial-spectral images from a single-shot two-dimensional compressed measurement. Existing state-of-the-art methods are mostly based on deep unfolding structures but have intrinsic performance bottlenecks: $i$) the ill-posed problem of dealing with heavily degraded measurement, and $ii$) the regression loss-based reconstruction models being prone to recover images with few details. In this paper, we introduce a generative model, namely the latent diffusion model (LDM), to generate degradation-free prior to enhance the regression-based deep unfolding method. Furthermore, to overcome the large computational cost challenge in LDM, we propose a lightweight model to generate knowledge priors in deep unfolding denoiser, and integrate these priors to guide the reconstruction process for compensating high-quality spectral signal details. Numeric and visual comparisons on synthetic and real-world datasets illustrate the superiority of our proposed method in both reconstruction quality and computational efficiency. Code will be released.
The integration of experimental data into mathematical and computational models is crucial for enhancing their predictive power in real-world scenarios. However, the performance of data assimilation algorithms can be significantly degraded when measurements are corrupted by biased noise, altering the signal magnitude, or when the system dynamics lack smoothness, such as in the presence of fast oscillations or discontinuities. This paper focuses on variational state estimation using the so-called Parameterized Background Data Weak method, which relies on a parameterized background by a set of constraints, enabling state estimation by solving a minimization problem on a reduced-order background model, subject to constraints imposed by the input measurements. To address biased noise in observations, a modified formulation is proposed, incorporating a correction mechanism to handle rapid oscillations by treating them as slow-decaying modes based on a two-scale splitting of the classical reconstruction algorithm. The effectiveness of the proposed algorithms is demonstrated through various examples, including discontinuous signals and simulated Doppler ultrasound data.
In scenarios with limited available or high-quality data, training the function-to-function neural PDE solver in an unsupervised manner is essential. However, the efficiency and accuracy of existing methods are constrained by the properties of numerical algorithms, such as finite difference and pseudo-spectral methods, integrated during the training stage. These methods necessitate careful spatiotemporal discretization to achieve reasonable accuracy, leading to significant computational challenges and inaccurate simulations, particularly in cases with substantial spatiotemporal variations. To address these limitations, we propose the Monte Carlo Neural PDE Solver (MCNP Solver) for training unsupervised neural solvers via the PDEs' probabilistic representation, which regards macroscopic phenomena as ensembles of random particles. Compared to other unsupervised methods, MCNP Solver naturally inherits the advantages of the Monte Carlo method, which is robust against spatiotemporal variations and can tolerate coarse step size. In simulating the random walk of particles, we employ Heun's method for the convection process and calculate the expectation via the probability density function of neighbouring grid points during the diffusion process. These techniques enhance accuracy and circumvent the computational memory and time issues associated with Monte Carlo sampling, offering an improvement over traditional Monte Carlo methods. Our numerical experiments on convection-diffusion, Allen-Cahn, and Navier-Stokes equations demonstrate significant improvements in accuracy and efficiency compared to other unsupervised baselines. The source code will be publicly available at: //github.com/optray/MCNP.
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.
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.
High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.
Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.
Detecting carried objects is one of the requirements for developing systems to reason about activities involving people and objects. We present an approach to detect carried objects from a single video frame with a novel method that incorporates features from multiple scales. Initially, a foreground mask in a video frame is segmented into multi-scale superpixels. Then the human-like regions in the segmented area are identified by matching a set of extracted features from superpixels against learned features in a codebook. A carried object probability map is generated using the complement of the matching probabilities of superpixels to human-like regions and background information. A group of superpixels with high carried object probability and strong edge support is then merged to obtain the shape of the carried object. We applied our method to two challenging datasets, and results show that our method is competitive with or better than the state-of-the-art.
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