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Large language models, particularly those akin to the rapidly progressing GPT series, are gaining traction for their expansive influence. While there is keen interest in their applicability within medical domains such as psychology, tangible explorations on real-world data remain scant. Concurrently, users on social media platforms are increasingly vocalizing personal sentiments; under specific thematic umbrellas, these sentiments often manifest as negative emotions, sometimes escalating to suicidal inclinations. Timely discernment of such cognitive distortions and suicidal risks is crucial to effectively intervene and potentially avert dire circumstances. Our study ventured into this realm by experimenting on two pivotal tasks: suicidal risk and cognitive distortion identification on Chinese social media platforms. Using supervised learning as a baseline, we examined and contrasted the efficacy of large language models via three distinct strategies: zero-shot, few-shot, and fine-tuning. Our findings revealed a discernible performance gap between the large language models and traditional supervised learning approaches, primarily attributed to the models' inability to fully grasp subtle categories. Notably, while GPT-4 outperforms its counterparts in multiple scenarios, GPT-3.5 shows significant enhancement in suicide risk classification after fine-tuning. To our knowledge, this investigation stands as the maiden attempt at gauging large language models on Chinese social media tasks. This study underscores the forward-looking and transformative implications of using large language models in the field of psychology. It lays the groundwork for future applications in psychological research and practice.

We study stochastic Cubic Newton methods for solving general possibly non-convex minimization problems. We propose a new framework, which we call the helper framework, that provides a unified view of the stochastic and variance-reduced second-order algorithms equipped with global complexity guarantees. It can also be applied to learning with auxiliary information. Our helper framework offers the algorithm designer high flexibility for constructing and analyzing the stochastic Cubic Newton methods, allowing arbitrary size batches, and the use of noisy and possibly biased estimates of the gradients and Hessians, incorporating both the variance reduction and the lazy Hessian updates. We recover the best-known complexities for the stochastic and variance-reduced Cubic Newton, under weak assumptions on the noise. A direct consequence of our theory is the new lazy stochastic second-order method, which significantly improves the arithmetic complexity for large dimension problems. We also establish complexity bounds for the classes of gradient-dominated objectives, that include convex and strongly convex problems. For Auxiliary Learning, we show that using a helper (auxiliary function) can outperform training alone if a given similarity measure is small.

We consider outlier-robust and sparse estimation of linear regression coefficients, when the covariates and the noises are contaminated by adversarial outliers and noises are sampled from a heavy-tailed distribution. Our results present sharper error bounds under weaker assumptions than prior studies that share similar interests with this study. Our analysis relies on some sharp concentration inequalities resulting from generic chaining.

There have been recent advances in the analysis and visualization of 3D symmetric tensor fields, with a focus on the robust extraction of tensor field topology. However, topological features such as degenerate curves and neutral surfaces do not live in isolation. Instead, they intriguingly interact with each other. In this paper, we introduce the notion of {\em topological graph} for 3D symmetric tensor fields to facilitate global topological analysis of such fields. The nodes of the graph include degenerate curves and regions bounded by neutral surfaces in the domain. The edges in the graph denote the adjacency information between the regions and degenerate curves. In addition, we observe that a degenerate curve can be a loop and even a knot and that two degenerate curves (whether in the same region or not) can form a link. We provide a definition and theoretical analysis of individual degenerate curves in order to help understand why knots and links may occur. Moreover, we differentiate between wedges and trisectors, thus making the analysis more detailed about degenerate curves. We incorporate this information into the topological graph. Such a graph can not only reveal the global structure in a 3D symmetric tensor field but also allow two symmetric tensor fields to be compared. We demonstrate our approach by applying it to solid mechanics and material science data sets.

Mathematical notation makes up a large portion of STEM literature, yet finding semantic representations for formulae remains a challenging problem. Because mathematical notation is precise, and its meaning changes significantly with small character shifts, the methods that work for natural text do not necessarily work well for mathematical expressions. This work describes an approach for representing mathematical expressions in a continuous vector space. We use the encoder of a sequence-to-sequence architecture, trained on visually different but mathematically equivalent expressions, to generate vector representations (or embeddings). We compare this approach with a structural approach that considers visual layout to embed an expression and show that our proposed approach is better at capturing mathematical semantics. Finally, to expedite future research, we publish a corpus of equivalent transcendental and algebraic expression pairs.

The introduction and advancements in Local Differential Privacy (LDP) variants have become a cornerstone in addressing the privacy concerns associated with the vast data produced by smart devices, which forms the foundation for data-driven decision-making in crowdsensing. While harnessing the power of these immense data sets can offer valuable insights, it simultaneously poses significant privacy risks for the users involved. LDP, a distinguished privacy model with a decentralized architecture, stands out for its capability to offer robust privacy assurances for individual users during data collection and analysis. The essence of LDP is its method of locally perturbing each user's data on the client-side before transmission to the server-side, safeguarding against potential privacy breaches at both ends. This article offers an in-depth exploration of LDP, emphasizing its models, its myriad variants, and the foundational structure of LDP algorithms.

We show how to construct in an elementary way the invariant of the KHK discretisation of a cubic Hamiltonian system in two dimensions. That is, we show that this invariant is expressible as the product of the ratios of affine polynomials defining the prolongation of the three parallel sides of a hexagon. On the vertices of such a hexagon lie the indeterminacy points of the KHK map. This result is obtained analysing the structure of the singular fibres of the known invariant. We apply this construction to several examples, and we prove that a similar result holds true for a case outside the hypotheses of the main theorem, leading us to conjecture that further extensions are possible.

Pre-trained Language Models (PLMs) which are trained on large text corpus via self-supervised learning method, have yielded promising performance on various tasks in Natural Language Processing (NLP). However, though PLMs with huge parameters can effectively possess rich knowledge learned from massive training text and benefit downstream tasks at the fine-tuning stage, they still have some limitations such as poor reasoning ability due to the lack of external knowledge. Research has been dedicated to incorporating knowledge into PLMs to tackle these issues. In this paper, we present a comprehensive review of Knowledge-Enhanced Pre-trained Language Models (KE-PLMs) to provide a clear insight into this thriving field. We introduce appropriate taxonomies respectively for Natural Language Understanding (NLU) and Natural Language Generation (NLG) to highlight these two main tasks of NLP. For NLU, we divide the types of knowledge into four categories: linguistic knowledge, text knowledge, knowledge graph (KG), and rule knowledge. The KE-PLMs for NLG are categorized into KG-based and retrieval-based methods. Finally, we point out some promising future directions of KE-PLMs.

In contrast to batch learning where all training data is available at once, continual learning represents a family of methods that accumulate knowledge and learn continuously with data available in sequential order. Similar to the human learning process with the ability of learning, fusing, and accumulating new knowledge coming at different time steps, continual learning is considered to have high practical significance. Hence, continual learning has been studied in various artificial intelligence tasks. In this paper, we present a comprehensive review of the recent progress of continual learning in computer vision. In particular, the works are grouped by their representative techniques, including regularization, knowledge distillation, memory, generative replay, parameter isolation, and a combination of the above techniques. For each category of these techniques, both its characteristics and applications in computer vision are presented. At the end of this overview, several subareas, where continuous knowledge accumulation is potentially helpful while continual learning has not been well studied, are discussed.

Over the past few years, we have seen fundamental breakthroughs in core problems in machine learning, largely driven by advances in deep neural networks. At the same time, the amount of data collected in a wide array of scientific domains is dramatically increasing in both size and complexity. Taken together, this suggests many exciting opportunities for deep learning applications in scientific settings. But a significant challenge to this is simply knowing where to start. The sheer breadth and diversity of different deep learning techniques makes it difficult to determine what scientific problems might be most amenable to these methods, or which specific combination of methods might offer the most promising first approach. In this survey, we focus on addressing this central issue, providing an overview of many widely used deep learning models, spanning visual, sequential and graph structured data, associated tasks and different training methods, along with techniques to use deep learning with less data and better interpret these complex models --- two central considerations for many scientific use cases. We also include overviews of the full design process, implementation tips, and links to a plethora of tutorials, research summaries and open-sourced deep learning pipelines and pretrained models, developed by the community. We hope that this survey will help accelerate the use of deep learning across different scientific domains.