Label smoothing loss is a widely adopted technique to mitigate overfitting in deep neural networks. This paper studies label smoothing from the perspective of Neural Collapse (NC), a powerful empirical and theoretical framework which characterizes model behavior during the terminal phase of training. We first show empirically that models trained with label smoothing converge faster to neural collapse solutions and attain a stronger level of neural collapse. Additionally, we show that at the same level of NC1, models under label smoothing loss exhibit intensified NC2. These findings provide valuable insights into the performance benefits and enhanced model calibration under label smoothing loss. We then leverage the unconstrained feature model to derive closed-form solutions for the global minimizers for both loss functions and further demonstrate that models under label smoothing have a lower conditioning number and, therefore, theoretically converge faster. Our study, combining empirical evidence and theoretical results, not only provides nuanced insights into the differences between label smoothing and cross-entropy losses, but also serves as an example of how the powerful neural collapse framework can be used to improve our understanding of DNNs.

Many real-world datasets can be naturally represented as graphs, spanning a wide range of domains. However, the increasing complexity and size of graph datasets present significant challenges for analysis and computation. In response, graph reduction techniques have gained prominence for simplifying large graphs while preserving essential properties. In this survey, we aim to provide a comprehensive understanding of graph reduction methods, including graph sparsification, graph coarsening, and graph condensation. Specifically, we establish a unified definition for these methods and introduce a hierarchical taxonomy to categorize the challenges they address. Our survey then systematically reviews the technical details of these methods and emphasizes their practical applications across diverse scenarios. Furthermore, we outline critical research directions to ensure the continued effectiveness of graph reduction techniques, as well as provide a comprehensive paper list at https://github.com/ChandlerBang/awesome-graph-reduction. We hope this survey will bridge literature gaps and propel the advancement of this promising field.

Recent Meta-learning for Black-Box Optimization (MetaBBO) methods harness neural networks to meta-learn configurations of traditional black-box optimizers. Despite their success, they are inevitably restricted by the limitations of predefined hand-crafted optimizers. In this paper, we present \textsc{Symbol}, a novel framework that promotes the automated discovery of black-box optimizers through symbolic equation learning. Specifically, we propose a Symbolic Equation Generator (SEG) that allows closed-form optimization rules to be dynamically generated for specific tasks and optimization steps. Within \textsc{Symbol}, we then develop three distinct strategies based on reinforcement learning, so as to meta-learn the SEG efficiently. Extensive experiments reveal that the optimizers generated by \textsc{Symbol} not only surpass the state-of-the-art BBO and MetaBBO baselines, but also exhibit exceptional zero-shot generalization abilities across entirely unseen tasks with different problem dimensions, population sizes, and optimization horizons. Furthermore, we conduct in-depth analyses of our \textsc{Symbol} framework and the optimization rules that it generates, underscoring its desirable flexibility and interpretability.

In this paper, we propose the Continuous Time Fractional Topic Model (cFTM), a new method for dynamic topic modeling. This approach incorporates fractional Brownian motion~(fBm) to effectively identify positive or negative correlations in topic and word distribution over time, revealing long-term dependency or roughness. Our theoretical analysis shows that the cFTM can capture these long-term dependency or roughness in both topic and word distributions, mirroring the main characteristics of fBm. Moreover, we prove that the parameter estimation process for the cFTM is on par with that of LDA, traditional topic models. To demonstrate the cFTM's property, we conduct empirical study using economic news articles. The results from these tests support the model's ability to identify and track long-term dependency or roughness in topics over time.

Diffusion models have emerged as a powerful tool rivaling GANs in generating high-quality samples with improved fidelity, flexibility, and robustness. A key component of these models is to learn the score function through score matching. Despite empirical success on various tasks, it remains unclear whether gradient-based algorithms can learn the score function with a provable accuracy. As a first step toward answering this question, this paper establishes a mathematical framework for analyzing score estimation using neural networks trained by gradient descent. Our analysis covers both the optimization and the generalization aspects of the learning procedure. In particular, we propose a parametric form to formulate the denoising score-matching problem as a regression with noisy labels. Compared to the standard supervised learning setup, the score-matching problem introduces distinct challenges, including unbounded input, vector-valued output, and an additional time variable, preventing existing techniques from being applied directly. In this paper, we show that with a properly designed neural network architecture, the score function can be accurately approximated by a reproducing kernel Hilbert space induced by neural tangent kernels. Furthermore, by applying an early-stopping rule for gradient descent and leveraging certain coupling arguments between neural network training and kernel regression, we establish the first generalization error (sample complexity) bounds for learning the score function despite the presence of noise in the observations. Our analysis is grounded in a novel parametric form of the neural network and an innovative connection between score matching and regression analysis, facilitating the application of advanced statistical and optimization techniques.

Anomaly detection in multivariate time series (MTS) has been widely studied in one-class classification (OCC) setting. The training samples in OCC are assumed to be normal, which is difficult to guarantee in practical situations. Such a case may degrade the performance of OCC-based anomaly detection methods which fit the training distribution as the normal distribution. In this paper, we propose MTGFlow, an unsupervised anomaly detection approach for MTS anomaly detection via dynamic Graph and entity-aware normalizing Flow. MTGFlow first estimates the density of the entire training samples and then identifies anomalous instances based on the density of the test samples within the fitted distribution. This relies on a widely accepted assumption that anomalous instances exhibit more sparse densities than normal ones, with no reliance on the clean training dataset. However, it is intractable to directly estimate the density due to complex dependencies among entities and their diverse inherent characteristics. To mitigate this, we utilize the graph structure learning model to learn interdependent and evolving relations among entities, which effectively captures complex and accurate distribution patterns of MTS. In addition, our approach incorporates the unique characteristics of individual entities by employing an entity-aware normalizing flow. This enables us to represent each entity as a parameterized normal distribution. Furthermore, considering that some entities present similar characteristics, we propose a cluster strategy that capitalizes on the commonalities of entities with similar characteristics, resulting in more precise and detailed density estimation. We refer to this cluster-aware extension as MTGFlow_cluster. Extensive experiments are conducted on six widely used benchmark datasets, in which MTGFlow and MTGFlow cluster demonstrate their superior detection performance.

Variational dimensionality reduction methods are known for their high accuracy, generative abilities, and robustness. We introduce a framework to unify many existing variational methods and design new ones. The framework is based on an interpretation of the multivariate information bottleneck, in which an encoder graph, specifying what information to compress, is traded-off against a decoder graph, specifying a generative model. Using this framework, we rederive existing dimensionality reduction methods including the deep variational information bottleneck and variational auto-encoders. The framework naturally introduces a trade-off parameter extending the deep variational CCA (DVCCA) family of algorithms to beta-DVCCA. We derive a new method, the deep variational symmetric informational bottleneck (DVSIB), which simultaneously compresses two variables to preserve information between their compressed representations. We implement these algorithms and evaluate their ability to produce shared low dimensional latent spaces on Noisy MNIST dataset. We show that algorithms that are better matched to the structure of the data (in our case, beta-DVCCA and DVSIB) produce better latent spaces as measured by classification accuracy, dimensionality of the latent variables, and sample efficiency. We believe that this framework can be used to unify other multi-view representation learning algorithms and to derive and implement novel problem-specific loss functions.

The flexibility of Simultaneous Localization and Mapping (SLAM) algorithms in various environments has consistently been a significant challenge. To address the issue of LiDAR odometry drift in high-noise settings, integrating clustering methods to filter out unstable features has become an effective module of SLAM frameworks. However, reducing the amount of point cloud data can lead to potential loss of information and possible degeneration. As a result, this research proposes a LiDAR odometry that can dynamically assess the point cloud's reliability. The algorithm aims to improve adaptability in diverse settings by selecting important feature points with sensitivity to the level of environmental degeneration. Firstly, a fast adaptive Euclidean clustering algorithm based on range image is proposed, which, combined with depth clustering, extracts the primary structural points of the environment defined as ambient skeleton points. Then, the environmental degeneration level is computed through the dense normal features of the skeleton points, and the point cloud cleaning is dynamically adjusted accordingly. The algorithm is validated on the KITTI benchmark and real environments, demonstrating higher accuracy and robustness in different environments.

State-space models (SSMs), such as Mamba Gu & Dao (2034), have been proposed as alternatives to Transformer networks in language modeling, by incorporating gating, convolutions, and input-dependent token selection to mitigate the quadratic cost of multi-head attention. Although SSMs exhibit competitive performance, their in-context learning (ICL) capabilities, a remarkable emergent property of modern language models that enables task execution without parameter optimization, remain underexplored compared to Transformers. In this study, we evaluate the ICL performance of SSMs, focusing on Mamba, against Transformer models across various tasks. Our results show that SSMs perform comparably to Transformers in standard regression ICL tasks, while outperforming them in tasks like sparse parity learning. However, SSMs fall short in tasks involving non-standard retrieval functionality. To address these limitations, we introduce a hybrid model, \variant, that combines Mamba with attention blocks, surpassing individual models in tasks where they struggle independently. Our findings suggest that hybrid architectures offer promising avenues for enhancing ICL in language models.

Shapley values have emerged as a foundational tool in machine learning (ML) for elucidating model decision-making processes. Despite their widespread adoption and unique ability to satisfy essential explainability axioms, computational challenges persist in their estimation when ($i$) evaluating a model over all possible subset of input feature combinations, ($ii$) estimating model marginals, and ($iii$) addressing variability in explanations. We introduce a novel, self-explaining method that simplifies the computation of Shapley values significantly, requiring only a single forward pass. Recognizing the deterministic treatment of Shapley values as a limitation, we explore incorporating a probabilistic framework to capture the inherent uncertainty in explanations. Unlike alternatives, our technique does not rely directly on the observed data space to estimate marginals; instead, it uses adaptable baseline values derived from a latent, feature-specific embedding space, generated by a novel masked neural network architecture. Evaluations on simulated and real datasets underscore our technique's robust predictive and explanatory performance.