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We consider the problem of estimating the parameters of a Markov Random Field with hard-constraints using a single sample. As our main running examples, we use the $k$-SAT and the proper coloring models, as well as general $H$-coloring models; for all of these we obtain both positive and negative results. In contrast to the soft-constrained case, we show in particular that single-sample estimation is not always possible, and that the existence of an estimator is related to the existence of non-satisfiable instances. Our algorithms are based on the pseudo-likelihood estimator. We show variance bounds for this estimator using coupling techniques inspired, in the case of $k$-SAT, by Moitra's sampling algorithm (JACM, 2019); our positive results for colorings build on this new coupling approach. For $q$-colorings on graphs with maximum degree $d$, we give a linear-time estimator when $q>d+1$, whereas the problem is non-identifiable when $q\leq d+1$. For general $H$-colorings, we show that standard conditions that guarantee sampling, such as Dobrushin's condition, are insufficient for one-sample learning; on the positive side, we provide a general condition that is sufficient to guarantee linear-time learning and obtain applications for proper colorings and permissive models. For the $k$-SAT model on formulas with maximum degree $d$, we provide a linear-time estimator when $k\gtrsim 6.45\log d$, whereas the problem becomes non-identifiable when $k\lesssim \log d$.

The notion of 'resource' plays an important role in the overall efficiency and performance of most cross-docks. The processing time can often be described in terms of the resources allocated to different trucks. Conversely, for a given processing time, different combinations of resources can be prescribed. We study the problem of truck scheduling and dock assignment in the presence of resource constraints. In the absence of a closed-form (or well-defined) linear formulation describing the processing times as a function of resources, expert' knowledge has been mobilised to enable modelling of the problem as an integer linear model. Two cases are taken into account: In the first one, the expert believes in his/her estimation of the processing time for every truck and only proposes a different combination of resources for his/her estimation, while in the second one the expert proposes a limited number of resource deployment scenarios for serving trucks, each of which has a different combination of resources and different processing times. We propose a novel compact integer programming formulation for the problem, which is particularly designed with an embedded structure that can be exploited in dual decomposition techniques with a remarkably computationally efficient column generation approach in this case. The case in which a scenario with invariant processing time is considered and modelled as a special case of the proposed model. Since a direct application of commercial solvers such as CPLEX to solve instances of this problem is not realistic, we propose a branch-and-price framework and, moreover, several classes of valid inequalities. Our extensive computational experiments confirm that the proposed exact solution framework is very efficient and viable in solving real-size instances of the practice and in a reasonable amount of time.

Successfully training Physics Informed Neural Networks (PINNs) for highly nonlinear PDEs on complex 3D domains remains a challenging task. In this paper, PINNs are employed to solve the 3D incompressible Navier-Stokes (NS) equations at moderate to high Reynolds numbers for complex geometries. The presented method utilizes very sparsely distributed solution data in the domain. A detailed investigation on the effect of the amount of supplied data and the PDE-based regularizers is presented. Additionally, a hybrid data-PINNs approach is used to generate a surrogate model of a realistic flow-thermal electronics design problem. This surrogate model provides near real-time sampling and was found to outperform standard data-driven neural networks when tested on unseen query points. The findings of the paper show how PINNs can be effective when used in conjunction with sparse data for solving 3D nonlinear PDEs or for surrogate modeling of design spaces governed by them.

We consider the lossless compression bound of any single data sequence. If we fit the data by a parametric model, the entropy quantity $nH({\hat \theta}_n)$ obtained by plugging in the maximum likelihood estimate is an underestimate of the bound, where $n$ is the number of words. Shtarkov showed that the normalized maximum likelihood (NML) distribution or code length is optimal in a minimax sense for any parametric family. We show by the local asymptotic normality that the NML code length for the exponential families is $nH(\hat \theta_n) +\frac{d}{2}\log \, \frac{n}{2\pi} +\log \int_{\Theta} |I(\theta)|^{1/2}\, d\theta+o(1)$, where $d$ is the model dimension or dictionary size, and $|I(\theta)|$ is the determinant of the Fisher information matrix. We also demonstrate that sequentially predicting the optimal code length for the next word via a Bayesian mechanism leads to the mixture code, whose pathwise length is given by $nH({\hat \theta}_n) +\frac{d}{2}\log \, \frac{n}{2\pi} +\log \frac{|\, I({\hat \theta}_n)|^{1/2}}{w({\hat \theta}_n)}+o(1) $, where $w(\theta)$ is a prior. The asymptotics apply to not only discrete symbols but also continuous data if the code length for the former is replaced by the description length of the latter. The analytical result is exemplified by calculating compression bounds of protein-encoding DNA sequences under different parsing models. Typically, the highest compression is achieved when the parsing is in phase of the amino acid codons. On the other hand, the compression rates of pseudo-random sequences are larger than 1 regardless parsing models. These model-based results are in consistency with that random sequences are incompressible as asserted by the Kolmogorov complexity theory. The empirical lossless compression bound is particularly more accurate when dictionary size is relatively large.

Adopting a two-stage paradigm of pretraining followed by fine-tuning, Pretrained Language Models (PLMs) have achieved substantial advancements in the field of natural language processing. However, in real-world scenarios, data labels are often noisy due to the complex annotation process, making it essential to develop strategies for fine-tuning PLMs with such noisy labels. To this end, we introduce an innovative approach for fine-tuning PLMs using noisy labels, which incorporates the guidance of Large Language Models (LLMs) like ChatGPT. This guidance assists in accurately distinguishing between clean and noisy samples and provides supplementary information beyond the noisy labels, thereby boosting the learning process during fine-tuning PLMs. Extensive experiments on synthetic and real-world noisy datasets further demonstrate the superior advantages of our framework over the state-of-the-art baselines.

Pre-trained Vision-Language Models (VLMs), such as CLIP, have shown enhanced performance across a range of tasks that involve the integration of visual and linguistic modalities. When CLIP is used for depth estimation tasks, the patches, divided from the input images, can be combined with a series of semantic descriptions of the depth information to obtain similarity results. The coarse estimation of depth is then achieved by weighting and summing the depth values, called depth bins, corresponding to the predefined semantic descriptions. The zero-shot approach circumvents the computational and time-intensive nature of traditional fully-supervised depth estimation methods. However, this method, utilizing fixed depth bins, may not effectively generalize as images from different scenes may exhibit distinct depth distributions. To address this challenge, we propose a few-shot-based method which learns to adapt the VLMs for monocular depth estimation to balance training costs and generalization capabilities. Specifically, it assigns different depth bins for different scenes, which can be selected by the model during inference. Additionally, we incorporate learnable prompts to preprocess the input text to convert the easily human-understood text into easily model-understood vectors and further enhance the performance. With only one image per scene for training, our extensive experiment results on the NYU V2 and KITTI dataset demonstrate that our method outperforms the previous state-of-the-art method by up to 10.6\% in terms of MARE.

An in-depth understanding of uncertainty is the first step to making effective decisions under uncertainty. Deep/machine learning (ML/DL) has been hugely leveraged to solve complex problems involved with processing high-dimensional data. However, reasoning and quantifying different types of uncertainties to achieve effective decision-making have been much less explored in ML/DL than in other Artificial Intelligence (AI) domains. In particular, belief/evidence theories have been studied in KRR since the 1960s to reason and measure uncertainties to enhance decision-making effectiveness. We found that only a few studies have leveraged the mature uncertainty research in belief/evidence theories in ML/DL to tackle complex problems under different types of uncertainty. In this survey paper, we discuss several popular belief theories and their core ideas dealing with uncertainty causes and types and quantifying them, along with the discussions of their applicability in ML/DL. In addition, we discuss three main approaches that leverage belief theories in Deep Neural Networks (DNNs), including Evidential DNNs, Fuzzy DNNs, and Rough DNNs, in terms of their uncertainty causes, types, and quantification methods along with their applicability in diverse problem domains. Based on our in-depth survey, we discuss insights, lessons learned, limitations of the current state-of-the-art bridging belief theories and ML/DL, and finally, future research directions.

Pre-trained Language Models (PLMs) have achieved great success in various Natural Language Processing (NLP) tasks under the pre-training and fine-tuning paradigm. With large quantities of parameters, PLMs are computation-intensive and resource-hungry. Hence, model pruning has been introduced to compress large-scale PLMs. However, most prior approaches only consider task-specific knowledge towards downstream tasks, but ignore the essential task-agnostic knowledge during pruning, which may cause catastrophic forgetting problem and lead to poor generalization ability. To maintain both task-agnostic and task-specific knowledge in our pruned model, we propose ContrAstive Pruning (CAP) under the paradigm of pre-training and fine-tuning. It is designed as a general framework, compatible with both structured and unstructured pruning. Unified in contrastive learning, CAP enables the pruned model to learn from the pre-trained model for task-agnostic knowledge, and fine-tuned model for task-specific knowledge. Besides, to better retain the performance of the pruned model, the snapshots (i.e., the intermediate models at each pruning iteration) also serve as effective supervisions for pruning. Our extensive experiments show that adopting CAP consistently yields significant improvements, especially in extremely high sparsity scenarios. With only 3% model parameters reserved (i.e., 97% sparsity), CAP successfully achieves 99.2% and 96.3% of the original BERT performance in QQP and MNLI tasks. In addition, our probing experiments demonstrate that the model pruned by CAP tends to achieve better generalization ability.

This work addresses a novel and challenging problem of estimating the full 3D hand shape and pose from a single RGB image. Most current methods in 3D hand analysis from monocular RGB images only focus on estimating the 3D locations of hand keypoints, which cannot fully express the 3D shape of hand. In contrast, we propose a Graph Convolutional Neural Network (Graph CNN) based method to reconstruct a full 3D mesh of hand surface that contains richer information of both 3D hand shape and pose. To train networks with full supervision, we create a large-scale synthetic dataset containing both ground truth 3D meshes and 3D poses. When fine-tuning the networks on real-world datasets without 3D ground truth, we propose a weakly-supervised approach by leveraging the depth map as a weak supervision in training. Through extensive evaluations on our proposed new datasets and two public datasets, we show that our proposed method can produce accurate and reasonable 3D hand mesh, and can achieve superior 3D hand pose estimation accuracy when compared with state-of-the-art methods.

Deep Convolutional Neural Networks (CNNs) are a special type of Neural Networks, which have shown state-of-the-art results on various competitive benchmarks. The powerful learning ability of deep CNN is largely achieved with the use of multiple non-linear feature extraction stages that can automatically learn hierarchical representation from the data. Availability of a large amount of data and improvements in the hardware processing units have accelerated the research in CNNs and recently very interesting deep CNN architectures are reported. The recent race in deep CNN architectures for achieving high performance on the challenging benchmarks has shown that the innovative architectural ideas, as well as parameter optimization, can improve the CNN performance on various vision-related tasks. In this regard, different ideas in the CNN design have been explored such as use of different activation and loss functions, parameter optimization, regularization, and restructuring of processing units. However, the major improvement in representational capacity is achieved by the restructuring of the processing units. Especially, the idea of using a block as a structural unit instead of a layer is gaining substantial appreciation. This survey thus focuses on the intrinsic taxonomy present in the recently reported CNN architectures and consequently, classifies the recent innovations in CNN architectures into seven different categories. These seven categories are based on spatial exploitation, depth, multi-path, width, feature map exploitation, channel boosting and attention. Additionally, it covers the elementary understanding of the CNN components and sheds light on the current challenges and applications of CNNs.