Stochastic resonance (SR), a phenomenon originally introduced in climate modeling, enhances signal detection by leveraging optimal noise levels within non-linear systems. Traditional SR techniques, mainly based on single-threshold detectors, are limited to signals whose behavior does not depend on time. Often large amounts of noise are needed to detect weak signals, which can distort complex signal characteristics. To address these limitations, this study explores multi-threshold systems and the application of SR in multiscale applications using wavelet transforms. In the multiscale domain signals can be analyzed at different levels of resolution to better understand the underlying dynamics. We propose a double-threshold detection system that integrates two single-threshold detectors to enhance weak signal detection. We evaluate it both in the original data domain and in the multiscale domain using simulated and real-world signals and compare its performance with existing methods. Experimental results demonstrate that, in the original data domain, the proposed double-threshold detector significantly improves weak signal detection compared to conventional single-threshold approaches. Its performance is further improved in the frequency domain, requiring lower noise levels while outperforming existing detection systems. This study advances SR-based detection methodologies by introducing a robust approach to weak signal identification, with potential applications in various disciplines.

Self-driving laboratories (SDLs) have shown promise to accelerate materials discovery by integrating machine learning with automated experimental platforms. However, errors in the capture of input parameters may corrupt the features used to model system performance, compromising current and future campaigns. This study develops an automated workflow to systematically detect noisy features, determine sample-feature pairings that can be corrected, and finally recover the correct feature values. A systematic study is then performed to examine how dataset size, noise intensity, and feature value distribution affect both the detectability and recoverability of noisy features. In general, high-intensity noise and large training datasets are conducive to the detection and correction of noisy features. Low-intensity noise reduces detection and recovery but can be compensated for by larger clean training data sets. Detection and correction results vary between features with continuous and dispersed feature distributions showing greater recoverability compared to features with discrete or narrow distributions. This systematic study not only demonstrates a model agnostic framework for rational data recovery in the presence of noise, limited data, and differing feature distributions but also provides a tangible benchmark of kNN imputation in materials data sets. Ultimately, it aims to enhance data quality and experimental precision in automated materials discovery.

Model pruning is an effective approach for compressing large language models. However, this process often leads to significant degradation of model capabilities. While post-training techniques such as instruction tuning are commonly employed to recover model performance, existing methods often overlook the uneven deterioration of model capabilities and incur high computational costs. Moreover, some instruction data irrelevant to model capability recovery may introduce negative effects. To address these challenges, we propose the \textbf{P}ost-training d\textbf{A}ta \textbf{S}election method for \textbf{E}fficient pruned large language model \textbf{R}ecovery (\textbf{PASER}). PASER aims to identify instructions where model capabilities are most severely compromised within a certain recovery data budget. Our approach first applies manifold learning and spectral clustering to group recovery data in the semantic space, revealing capability-specific instruction sets. We then adaptively allocate the data budget to different clusters based on the degrees of model capability degradation. In each cluster, we prioritize data samples where model performance has declined dramatically. To mitigate potential negative transfer, we also detect and filter out conflicting or irrelevant recovery data. Extensive experiments demonstrate that PASER significantly outperforms conventional baselines, effectively recovering the general capabilities of pruned LLMs while utilizing merely 4\%-20\% of the original post-training data.

The dynamical sampling problem is centered around reconstructing signals that evolve over time according to a dynamical process, from spatial-temporal samples that may be noisy. This topic has been thoroughly explored for one-dimensional signals. Multidimensional signal recovery has also been studied, but primarily in scenarios where the driving operator is a convolution operator. In this work, we shift our focus to the dynamical sampling problem in the context of three-dimensional signal recovery, where the evolution system can be characterized by tensor products. Specifically, we provide a necessary condition for the sampling set that ensures successful recovery of the three-dimensional signal. Furthermore, we reformulate the reconstruction problem as an optimization task, which can be solved efficiently. To demonstrate the effectiveness of our approach, we include some straightforward numerical simulations that showcase the reconstruction performance.

Unrolled networks have become prevalent in various computer vision and imaging tasks. Although they have demonstrated remarkable efficacy in solving specific computer vision and computational imaging tasks, their adaptation to other applications presents considerable challenges. This is primarily due to the multitude of design decisions that practitioners working on new applications must navigate, each potentially affecting the network's overall performance. These decisions include selecting the optimization algorithm, defining the loss function, and determining the number of convolutional layers, among others. Compounding the issue, evaluating each design choice requires time-consuming simulations to train, fine-tune the neural network, and optimize for its performance. As a result, the process of exploring multiple options and identifying the optimal configuration becomes time-consuming and computationally demanding. The main objectives of this paper are (1) to unify some ideas and methodologies used in unrolled networks to reduce the number of design choices a user has to make, and (2) to report a comprehensive ablation study to discuss the impact of each of the choices involved in designing unrolled networks and present practical recommendations based on our findings. We anticipate that this study will help scientists and engineers design unrolled networks for their applications and diagnose problems within their networks efficiently.

Prompt recovery in large language models (LLMs) is crucial for understanding how LLMs work and addressing concerns regarding privacy, copyright, etc. The trend towards inference-only APIs complicates this task by restricting access to essential outputs for recovery. To tackle this challenge, we extract prompt-related information from limited outputs and identify a strong(negative) correlation between output probability-based uncertainty and the success of prompt recovery. This finding led to the development of Deliberative PrOmpt RecoverY (DORY), our novel approach that leverages uncertainty to recover prompts accurately. DORY involves reconstructing drafts from outputs, refining these with hints, and filtering out noise based on uncertainty. Our evaluation across diverse LLMs and prompt benchmarks shows that DORY outperforms existing baselines, improving performance by approximately 10.82% and establishing a new state-of-the-art record in prompt recovery tasks. Significantly, DORY operates using a single LLM without any external resources or model, offering a cost-effective, user-friendly prompt recovery solution.

The HTP-style methods have been shown to have strong approximation guarantee and impressive numerical performance in high dimensional statistical learning applications. However, the current theoretical treatment of these methods has traditionally been restricted to the analysis of parameter estimation consistency. It remains an open problem to analyze the support recovery performance (a.k.a., sparsistency) of this type of methods for recovering the global minimizer of the original NP-hard problem. In this paper, we bridge this gap by showing, for the first time, that exact recovery of the global sparse minimizer is possible for HTP-style methods under restricted strong condition number bounding conditions. We further show that HTP-style methods are able to recover the support of certain relaxed sparse solutions without assuming bounded restricted strong condition number. Numerical results on simulated data confirms our theoretical predictions.

To alleviate the bias generated by the l1-norm in the low-rank tensor completion problem, nonconvex surrogates/regularizers have been suggested to replace the tensor nuclear norm, although both can achieve sparsity. However, the thresholding functions of these nonconvex regularizers may not have closed-form expressions and thus iterations are needed, which increases the computational loads. To solve this issue, we devise a framework to generate sparsity-inducing regularizers with closed-form thresholding functions. These regularizers are applied to low-tubal-rank tensor completion, and efficient algorithms based on the alternating direction method of multipliers are developed. Furthermore, convergence of our methods is analyzed and it is proved that the generated sequences are bounded and any limit point is a stationary point. Experimental results using synthetic and real-world datasets show that the proposed algorithms outperform the state-of-the-art methods in terms of restoration performance.

Despite the recent development in machine learning, most learning systems are still under the concept of "black box", where the performance cannot be understood and derived. With the rise of safety and privacy concerns in public, designing an explainable learning system has become a new trend in machine learning. In general, many machine learning problems are formulated as minimizing (or maximizing) some loss function. Since real data are most likely generated from non-linear models, the loss function is non-convex in general. Unlike the convex optimization problem, gradient descent algorithms will be trapped in spurious local minima in solving non-convex optimization. Therefore, it is challenging to provide explainable algorithms when studying non-convex optimization problems. In this thesis, two popular non-convex problems are studied: (1) low-rank matrix completion and (2) neural network learning.

In this work, we focus on the challenging problem of Label Enhancement (LE), which aims to exactly recover label distributions from logical labels, and present a novel Label Information Bottleneck (LIB) method for LE. For the recovery process of label distributions, the label irrelevant information contained in the dataset may lead to unsatisfactory recovery performance. To address this limitation, we make efforts to excavate the essential label relevant information to improve the recovery performance. Our method formulates the LE problem as the following two joint processes: 1) learning the representation with the essential label relevant information, 2) recovering label distributions based on the learned representation. The label relevant information can be excavated based on the "bottleneck" formed by the learned representation. Significantly, both the label relevant information about the label assignments and the label relevant information about the label gaps can be explored in our method. Evaluation experiments conducted on several benchmark label distribution learning datasets verify the effectiveness and competitiveness of LIB. Our source codes are available https://github.com/qinghai-zheng/LIBLE