We propose to minimize a generic differentiable objective with $L_1$ constraint using a simple reparametrization and straightforward stochastic gradient descent. Our proposal is the direct generalization of previous ideas that the $L_1$ penalty may be equivalent to a differentiable reparametrization with weight decay. We prove that the proposed method, \textit{spred}, is an exact differentiable solver of $L_1$ and that the reparametrization trick is completely ``benign" for a generic nonconvex function. Practically, we demonstrate the usefulness of the method in (1) training sparse neural networks to perform gene selection tasks, which involves finding relevant features in a very high dimensional space, and (2) neural network compression task, to which previous attempts at applying the $L_1$-penalty have been unsuccessful. Conceptually, our result bridges the gap between the sparsity in deep learning and conventional statistical learning.
相關內容
Model-based offline reinforcement learning (RL), which builds a supervised transition model with logging dataset to avoid costly interactions with the online environment, has been a promising approach for offline policy optimization. As the discrepancy between the logging data and online environment may result in a distributional shift problem, many prior works have studied how to build robust transition models conservatively and estimate the model uncertainty accurately. However, the over-conservatism can limit the exploration of the agent, and the uncertainty estimates may be unreliable. In this work, we propose a novel Model-based Offline policy optimization framework with Adversarial Network (MOAN). The key idea is to use adversarial learning to build a transition model with better generalization, where an adversary is introduced to distinguish between in-distribution and out-of-distribution samples. Moreover, the adversary can naturally provide a quantification of the model's uncertainty with theoretical guarantees. Extensive experiments showed that our approach outperforms existing state-of-the-art baselines on widely studied offline RL benchmarks. It can also generate diverse in-distribution samples, and quantify the uncertainty more accurately.
A pair of linear codes whose intersection is of dimension $\ell$, where $\ell$ is a non-negetive integer, is called an $\ell$-intersection pair of codes. This paper focuses on studying $\ell$-intersection pairs of $\lambda_i$-constacyclic, $i=1,2,$ and conjucyclic codes. We first characterize an $\ell$-intersection pair of $\lambda_i$-constacyclic codes. A formula for $\ell$ has been established in terms of the degrees of the generator polynomials of $\lambda_i$-constacyclic codes. This allows obtaining a condition for $\ell$-linear complementary pairs (LPC) of constacyclic codes. Later, we introduce and characterize the $\ell$-intersection pair of conjucyclic codes over $\mathbb{F}_{q^2}$. The first observation in the process is that there are no non-trivial linear conjucyclic codes over finite fields. So focus on the characterization of additive conjucyclic (ACC) codes. We show that the largest $\mathbb{F}_q$-subcode of an ACC code over $\mathbb{F}_{q^2}$ is cyclic and obtain its generating polynomial. This enables us to find the size of an ACC code. Furthermore, we discuss the trace code of an ACC code and show that it is cyclic. Finally, we determine $\ell$-intersection pairs of trace codes of ACC codes over $\mathbb{F}_4$.
Two new qubit stabilizer codes with parameters $[77, 0, 19]_2$ and $[90, 0, 22]_2$ are constructed for the first time by employing additive symplectic self-dual $\F_4$ codes from multidimensional circulant (MDC) graphs. We completely classify MDC graph codes for lengths $4\le n \le 40$ and show that many optimal $\dsb{\ell, 0, d}$ qubit codes can be obtained from the MDC construction. Moreover, we prove that adjacency matrices of MDC graphs have nested block circulant structure and determine isomorphism properties of MDC graphs.
Binary responses arise in a multitude of statistical problems, including binary classification, bioassay, current status data problems and sensitivity estimation. There has been an interest in such problems in the Bayesian nonparametrics community since the early 1970s, but inference given binary data is intractable for a wide range of modern simulation-based models, even when employing MCMC methods. Recently, Christensen (2023) introduced a novel simulation technique based on counting permutations, which can estimate both posterior distributions and marginal likelihoods for any model from which a random sample can be generated. However, the accompanying implementation of this technique struggles when the sample size is too large (n > 250). Here we present perms, a new implementation of said technique which is substantially faster and able to handle larger data problems than the original implementation. It is available both as an R package and a Python library. The basic usage of perms is illustrated via two simple examples: a tractable toy problem and a bioassay problem. A more complex example involving changepoint analysis is also considered. We also cover the details of the implementation and illustrate the computational speed gain of perms via a simple simulation study.
We consider a class of non-smooth strongly convex-strongly concave saddle point problems in a decentralized setting without a central server. To solve a consensus formulation of problems in this class, we develop an inexact primal dual hybrid gradient (inexact PDHG) procedure that allows generic gradient computation oracles to update the primal and dual variables. We first investigate the performance of inexact PDHG with stochastic variance reduction gradient (SVRG) oracle. Our numerical study uncovers a significant phenomenon of initial conservative progress of iterates of IPDHG with SVRG oracle. To tackle this, we develop a simple and effective switching idea, where a generalized stochastic gradient (GSG) computation oracle is employed to hasten the iterates' progress to a saddle point solution during the initial phase of updates, followed by a switch to the SVRG oracle at an appropriate juncture. The proposed algorithm is named Decentralized Proximal Switching Stochastic Gradient method with Compression (C-DPSSG), and is proven to converge to an $\epsilon$-accurate saddle point solution with linear rate. Apart from delivering highly accurate solutions, our study reveals that utilizing the best convergence phases of GSG and SVRG oracles makes C-DPSSG well suited for obtaining solutions of low/medium accuracy faster, useful for certain applications. Numerical experiments on two benchmark machine learning applications show C-DPSSG's competitive performance which validate our theoretical findings.
Recently, transformer-based methods have shown exceptional performance in monocular 3D object detection, which can predict 3D attributes from a single 2D image. These methods typically use visual and depth representations to generate query points on objects, whose quality plays a decisive role in the detection accuracy. However, current unsupervised attention mechanisms without any geometry appearance awareness in transformers are susceptible to producing noisy features for query points, which severely limits the network performance and also makes the model have a poor ability to detect multi-category objects in a single training process. To tackle this problem, this paper proposes a novel "Supervised Shape&Scale-perceptive Deformable Attention" (S$^3$-DA) module for monocular 3D object detection. Concretely, S$^3$-DA utilizes visual and depth features to generate diverse local features with various shapes and scales and predict the corresponding matching distribution simultaneously to impose valuable shape&scale perception for each query. Benefiting from this, S$^3$-DA effectively estimates receptive fields for query points belonging to any category, enabling them to generate robust query features. Besides, we propose a Multi-classification-based Shape$\&$Scale Matching (MSM) loss to supervise the above process. Extensive experiments on KITTI and Waymo Open datasets demonstrate that S$^3$-DA significantly improves the detection accuracy, yielding state-of-the-art performance of single-category and multi-category 3D object detection in a single training process compared to the existing approaches. The source code will be made publicly available at //github.com/mikasa3lili/S3-MonoDETR.
Polyp segmentation has recently garnered significant attention, and multiple methods have been formulated to achieve commendable outcomes. However, these techniques often confront difficulty when working with the complex polyp foreground and their surrounding regions because of the nature of convolution operation. Besides, most existing methods forget to exploit the potential information from multiple decoder stages. To address this challenge, we suggest combining MetaFormer, introduced as a baseline for integrating CNN and Transformer, with UNet framework and incorporating our Multi-scale Upsampling block (MU). This simple module makes it possible to combine multi-level information by exploring multiple receptive field paths of the shallow decoder stage and then adding with the higher stage to aggregate better feature representation, which is essential in medical image segmentation. Taken all together, we propose MetaFormer Multi-scale Upsampling Network (M$^2$UNet) for the polyp segmentation task. Extensive experiments on five benchmark datasets demonstrate that our method achieved competitive performance compared with several previous methods.
We present Viewset Diffusion, a diffusion-based generator that outputs 3D objects while only using multi-view 2D data for supervision. We note that there exists a one-to-one mapping between viewsets, i.e., collections of several 2D views of an object, and 3D models. Hence, we train a diffusion model to generate viewsets, but design the neural network generator to reconstruct internally corresponding 3D models, thus generating those too. We fit a diffusion model to a large number of viewsets for a given category of objects. The resulting generator can be conditioned on zero, one or more input views. Conditioned on a single view, it performs 3D reconstruction accounting for the ambiguity of the task and allowing to sample multiple solutions compatible with the input. The model performs reconstruction efficiently, in a feed-forward manner, and is trained using only rendering losses using as few as three views per viewset. Project page: szymanowiczs.github.io/viewset-diffusion.
Zero-shot referring image segmentation is a challenging task because it aims to find an instance segmentation mask based on the given referring descriptions, without training on this type of paired data. Current zero-shot methods mainly focus on using pre-trained discriminative models (e.g., CLIP). However, we have observed that generative models (e.g., Stable Diffusion) have potentially understood the relationships between various visual elements and text descriptions, which are rarely investigated in this task. In this work, we introduce a novel Referring Diffusional segmentor (Ref-Diff) for this task, which leverages the fine-grained multi-modal information from generative models. We demonstrate that without a proposal generator, a generative model alone can achieve comparable performance to existing SOTA weakly-supervised models. When we combine both generative and discriminative models, our Ref-Diff outperforms these competing methods by a significant margin. This indicates that generative models are also beneficial for this task and can complement discriminative models for better referring segmentation. Our code is publicly available at //github.com/kodenii/Ref-Diff.
Extreme multi-label text classification (XMC) aims to tag each input text with the most relevant labels from an extremely large label set, such as those that arise in product categorization and e-commerce recommendation. Recently, pretrained language representation models such as BERT achieve remarkable state-of-the-art performance across a wide range of NLP tasks including sentence classification among small label sets (typically fewer than thousands). Indeed, there are several challenges in applying BERT to the XMC problem. The main challenges are: (i) the difficulty of capturing dependencies and correlations among labels, whose features may come from heterogeneous sources, and (ii) the tractability to scale to the extreme label setting as the model size can be very large and scale linearly with the size of the output space. To overcome these challenges, we propose X-BERT, the first feasible attempt to finetune BERT models for a scalable solution to the XMC problem. Specifically, X-BERT leverages both the label and document text to build label representations, which induces semantic label clusters in order to better model label dependencies. At the heart of X-BERT is finetuning BERT models to capture the contextual relations between input text and the induced label clusters. Finally, an ensemble of the different BERT models trained on heterogeneous label clusters leads to our best final model. Empirically, on a Wiki dataset with around 0.5 million labels, X-BERT achieves new state-of-the-art results where the precision@1 reaches 67:80%, a substantial improvement over 32.58%/60.91% of deep learning baseline fastText and competing XMC approach Parabel, respectively. This amounts to a 11.31% relative improvement over Parabel, which is indeed significant since the recent approach SLICE only has 5.53% relative improvement.
小貼士
登錄享
注冊地址： 北京市海淀區羊坊店路18號2幢3層301-191